Chemical_Engineering_Design_Principles_Sinnott.pdf

Chemical Engineering Design Principles, Practice and Economics of Plant and Process Design Second Edition

Gavin Towler Ray Sinnott

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Butterworth-Heinemann is an imprint of Elsevier The Boulevard, Langford Lane, Kidlington, Oxford, OX5 1GB, UK 225 Wyman Street, Waltham, MA 02451, USA © 2013 Elsevier Ltd. All rights reserved No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the Publisher. Details on how to seek permission, further information about the Publisher’s permissions policies and our arrangements with organizations such as the Copyright Clearance Center and the Copyright Licensing Agency, can be found at our website: www.elsevier.com/permissions. This book and the individual contributions contained in it are protected under copyright by the Publisher (other than as may be noted herein). Notices Knowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary. Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein. In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility. To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas contained in the material herein. Library of Congress Cataloging-in-Publication Data Towler, Gavin P. Chemical engineering design : principles, practice, and economics of plant and process design / Gavin Towler, Ray Sinnott. – 2nd ed. p. cm. ISBN 978-0-08-096659-5 (hardback) 1. Chemical engineering. I. Sinnott, R. K. II. Title. TP155.T69 2012 660.068'5–dc23

2011044962

British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. For information on all Butterworth-Heinemann publications visit our website at www.elsevierdirect.com Typeset by: diacriTech, Chennai, India Printed in the United States of America 12 13 14 15 10 9 8 7 6 5 4 3 2 1

Preface to the Second Edition This book was originally written by Ray Sinnott as Volume 6 of the “Chemical Engineering” series edited by Coulson and Richardson. It was intended to be a standalone design textbook for undergraduate design projects that would supplement the other volumes in the Coulson and Richardson series. In 2008 we published the first edition of Chemical Engineering Design: Principles, Practice and Economics of Plant and Process Design as an adaptation of Coulson and Richardson Volume 6 for the North American market. Some older sections of the book were updated and references to laws, codes, and standards were changed to an American rather than British basis; however, the general layout and philosophy of the book remained unaltered. The first edition of this book was widely adopted and I received a great deal of valuable feedback from colleagues on both the strengths and weaknesses of the text in the context of a typical North American undergraduate curriculum. The experiences and frustrations of my students at Northwestern University and comments from coworkers at UOP also helped suggest areas where the book could be improved. The changes that have been made in this second edition are my attempt to make the book more valuable to students and industrial practitioners by incorporating new material to address obvious gaps, while eliminating some material that was dated or repetitive of foundation classes. The main change that I have made is to rearrange the order in which material is presented to fit better with a typical two-course senior design sequence. The book is now divided into two parts. Part I: Process Design covers the topics that are typically taught in a lecture class. The broad themes of Part I are flowsheet development, economic analysis, safety and environmental impact, and optimization. Part II: Plant Design contains chapters on equipment design and selection that can be used as supplements to a lecture course. These chapters contain step-by-step methods for designing most unit operations, together with many worked examples, and should become essential references for students when they begin working through their design projects or face design problems early in their industrial career. The coverage of process flowsheet development has been significantly increased in this edition. The introductory chapters on material and energy balances have been deleted and replaced with chapters on flowsheet development and energy recovery, which lead into the discussion of process simulation. The treatment of process economics has also been increased, with new chapters on capital cost estimating and operating costs, as well as a longer discussion of economic analysis and sensitivity analysis. The section on optimization is now presented as a separate chapter at the end of Part I, as most instructors felt that it was more logical to present this topic after introducing economic analysis and the constraints that come from safety and environmental considerations. Part II begins with an overview of common themes in equipment design. This is followed by the chapter on pressure vessel design, which underpins the design of most process vessels. The following chapters then proceed through reactors, separation processes, solids handling, heat exchange, and hydraulic equipment. My experience has been that students often struggle to make the connection from reaction engineering fundamentals to a realistic mechanical layout of a reactor, so a new chapter on reactor design has been added, with a focus on the practical aspects of reactor specification. The coverage of separation processes has been expanded to include adsorption, membrane

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Preface to the Second Edition

separations, chromatography, and ion exchange. The treatment of solids-handling processes has also been increased and solids-handling operations have been grouped together in a new chapter. Throughout the book I have attempted to increase the emphasis on batch processing, revamp designs, and design of biological processes, including fermentation and the separations commonly used in product recovery and purification from biochemical processes. Almost every chapter now contains examples of food, pharmaceutical, and biological processes and operations. Many graduating chemical engineers in the United States will find themselves working in established plants where they are more likely to work on revamp projects than new grassroots designs. A general discussion of revamp design is given in Part I and examples of rating calculations for revamps are presented throughout Part II. Chemical engineers work in a very diverse set of industries and many of these industries have their own design conventions and specialized equipment. I have attempted to include examples and problems from a broad range of process industries, but where space or my lack of expertise in the subject has limited coverage of a particular topic, references to specialized texts are provided. This book draws on Ray Sinnott’s and my experience of the industrial practice of process design, as well as our experience teaching design at the University of Wales Swansea, University of Manchester, and Northwestern University. Since the book is intended to be used in practice and not just as a textbook, our aim has been to describe the tools and methods that are most widely used in industrial process design. We have deliberately avoided describing idealized conceptual methods that have not yet gained wide currency in industry. The reader can find good descriptions of these methods in the research literature and in more academic textbooks. Standards and codes of practice are an essential part of engineering and the relevant North American standards are cited. The codes and practices covered by these standards will be applicable to other countries. They will be covered by equivalent national standards in most developed countries, and in some cases the relevant British, European, or international standards have also been cited. Brief summaries of important U.S. and Canadian safety and environmental legislation have been given in the relevant chapters. The design engineer should always refer to the original source references of laws, standards, and codes of practice, as they are updated frequently. Most industrial process design is carried out using commercial design software. Extensive reference has been made to commercial process and equipment design software throughout the book. Many of the commercial software vendors provide licenses of their software for educational purposes at nominal fees. I strongly believe that students should be introduced to commercial software at as early a stage in their education as possible. The use of academic design and costing software should be discouraged. Academic programs usually lack the quality control and support required by industry, and the student is unlikely to use such software after graduation. All computer-aided design tools must be used with some discretion and engineering judgment on the part of the designer. This judgment mainly comes with experience, but I have tried to provide helpful tips on how to best use computer tools. Ray wrote in the preface to the first edition of his book: “The art and practice of design cannot be learned from books. The intuition and judgment necessary to apply theory to practice will come only from practical experience.” In modifying the book to this new edition I hope that I have made it easier for readers to begin acquiring that experience. Gavin Towler

How to Use This Book This book has been written primarily for students on undergraduate courses in chemical engineering and has particular relevance to their senior design projects. It should also be of interest to new graduates working in industry who find they need to broaden their knowledge of unit operations and design. Some of the earlier chapters of the book can also be used in introductory chemical engineering classes and by other disciplines in the chemical and process industries.

PART I: PROCESS DESIGN Part I has been conceived as an introductory course in process design. The material can be covered in 20 to 30 lecture hours and presentation slides are available to qualified instructors in the supplementary material available at booksite.elsevier.com/towler. Chapter 1 is a general overview of process design and contains an introductory section on product design. Chapters 2 to 6 address the development of a process flowsheet from initial concept to the point where the designer is ready to begin estimating capital costs. Chapter 2 covers the selection of major unit operations and also addresses design for revamps and modification of conventional flowsheets. Chapter 3 introduces utility systems and discusses process energy recovery and heat integration. Chapter 4 provides an introduction to process simulation and shows the reader how to complete process material and energy balances. Chapter 5 covers those elements of process control that must be understood to complete a process flow diagram and identify where pumps and compressors are needed in the flowsheet. The selection of materials of construction can have a significant effect on plant costs, and this topic is addressed in Chapter 6. The elements of process economic analysis are introduced in Chapters 7 to 9. Capital cost estimation is covered in Chapter 7. Operating costs, revenues, and price forecasting are treated in Chapter 8. Chapter 9 concludes the economics section of the book with a brief introduction to corporate finance, a description of economic analysis methods, and a discussion on project selection criteria used in industry. Chapter 10 examines the role of safety considerations in design and introduces the methods used for process hazard analysis. Chapter 11 addresses site design and environmental impact. Part I concludes with a discussion of optimization methods in Chapter 12.

PART II: PLANT DESIGN Part II contains a more detailed treatment of design methods for common unit operations. Chapter 13 provides an overview of equipment design and is also a guide to the following chapters. Chapter 14 discusses the design of pressure vessels, and provides the necessary background for the reader to be able to design reactors, separators, distillation columns, and other operations that must be designed under pressure vessel codes. Chapter 15 covers the design of mixers and reactors, with an emphasis on the practical mechanical layout of reactors. Chapters 16 and 17 address fluid phase separations. Multistage column separations (distillation, absorption, stripping, and extraction) are described in Chapter 17, while other separation processes, such as adsorption, membrane separation, decanting,

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crystallization, precipitation, ion exchange, and chromatography, are covered in Chapter 16. Chapter 18 examines the properties of granular materials and introduces the processes used for storing, conveying, mixing, separating, heating, drying, and altering the particle size distribution of solids. Chapter 19 covers all aspects of the design of heat-transfer equipment, including plate exchangers, air coolers, fired heaters, and direct heat transfer to vessels, as well as design of shell and tube heat exchangers, boilers, and condensers. Chapter 20 addresses the design of plant hydraulics and covers design and selection of pumps, compressors, piping systems, and control valves. The material in Part II can be used to provide supplementary lectures in a design class, or as a supplement to foundation courses in chemical engineering. The chapters have also been written to serve as a guide to selection and design, with extensive worked examples, so that students can dip into individual chapters as they face specific design problems when working on a senior year design project.

SUPPLEMENTARY MATERIAL Many of the calculations described in the book can be performed using spreadsheets. Templates of spreadsheet calculations and equipment specification sheets are available in Microsoft Excel format online and can be downloaded from booksite.elsevier.com/Towler. An extensive set of design problems are included in the Appendices, which are also available at booksite.elsevier.com/Towler. Additional supplementary material, including Microsoft PowerPoint presentations to support most of the chapters and a full solutions manual, are available only to instructors, by registering at the Instructor section on booksite.elsevier.com/Towler.

Acknowledgments As stated in the preface, after launching the first edition of this book I received a great deal of very valuable feedback from students and colleagues. I have tried to make good use of this feedback in the second edition. Particular thanks are due to John Baldwin, Elizabeth Carter, Dan Crowl, Mario Eden, Mahmoud El-Halwagi, Igor Kourkine, Harold Kung, Justin Notestein, Matthew Realff, Tony Rogers, Warren Seider, and Bill Wilcox, all of whose suggestions I have gratefully incorporated. Many further improvements were suggested during the review phase and I would like to thank Mark James, Barry Johnston, Ken Joung, Yoshiaki Kawajiri, Peg Stine, Ross Taylor, and Andy Zarchy for their thoughtful reviews and input. Rajeev Gautam and Ben Christolini allowed me to pursue this project and make use of UOP’s extensive technical resources. As always, many colleagues at UOP, AIChE, and CACHE and students and colleagues at Northwestern have shared their experience and given me new insights into chemical engineering design and education. Material from the ASME Boiler and Pressure Vessel Code is reproduced with permission of ASME International, Three Park Avenue, New York NY 10016. Material from the API Recommended Practices is reproduced with permission of the American Petroleum Institute, 1220 L Street, NW, Washington, DC 20005. Material from British Standards is reproduced by permission of the British Standards Institution, 389 Chiswick High Road, London, W4 4AL, United Kingdom. Complete copies of the codes and standards can be obtained from these organizations. I am grateful to Aspen Technology Inc. and Honeywell Inc. for permission to include the screenshots that were generated using their software to illustrate the process simulation and costing examples. The material safety data sheet in Appendix I is reproduced with permission of Fischer Scientific Inc. Aspen Plus®, Aspen Process Economic Analyzer, Aspen Kbase, Aspen ICARUS, and all other AspenTech product names or logos are trademarks or registered trademarks of Aspen Technology Inc. or its subsidiaries in the United States and/or in other countries. All rights reserved. The supplementary material contains images of processes and equipment from many sources. I would like to thank the following companies for permission to use these images: Alfa-Laval, ANSYS, Aspen Technology, Bete Nozzle, Bos-Hatten Inc., Chemineer, Dresser, Dresser-Rand, Enardo Inc., Honeywell, Komax Inc., Riggins Company, Tyco Flow Control Inc., United Valve Inc., UOP LLC, and The Valve Manufacturer’s Association. Joe Hayton and Michael Joyce led the Elsevier team in developing this book and provided much useful editorial guidance. I would also like to thank Lisa Lamenzo for her excellent work in managing all the stages of production and printing. The biggest debt that I must acknowledge is to my coauthor, Ray Sinnott. Although Ray was not involved in writing this edition, it is built on the foundation of his earlier work, and his words can be found in every chapter. I hope I have remained true to Ray’s philosophy of design and have preserved the strengths of his book. It was necessary for me to remove some older material to make space for new sections in the book and I hope that Ray will forgive these changes. Needless to say, I am entirely responsible for any deficiencies or errors that have been introduced.

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My regular job at UOP keeps me very busy and I worked on this book in the evenings and on the weekends, so it would not have been possible without the love and support of my wife, Caroline, and our children Miranda, Jimmy, and Johnathan. Gavin P. Towler Inverness, Illinois

CHAPTER

Introduction to Design

KEY LEARNING OBJECTIVES • How design projects are carried out and documented in industry, including the formats used for design reports • Why engineers in industry use codes and standards in design • Why it is necessary to build margins into a design • Methods used by product design engineers to translate customer needs into product specifications

1.1 INTRODUCTION This chapter is an introduction to the nature and methodology of the design process, and its application to the design of chemical products and manufacturing processes.

1.2 NATURE OF DESIGN This section is a general discussion of the design process. The subject of this book is chemical engineering design, but the methodology described in this section applies equally to other branches of engineering. Chemical engineering has consistently been one of the highest paid engineering professions. There is a demand for chemical engineers in many sectors of industry, including the traditional process industries: chemicals, polymers, fuels, foods, pharmaceuticals, and paper, as well as other sectors such as electronic materials and devices, consumer products, mining and metals extraction, biomedical implants, and power generation. The reason that companies in such a diverse range of industries value chemical engineers so highly is the following: Starting from a vaguely defined problem statement such as a customer need or a set of experimental results, chemical engineers can develop an understanding of the important underlying physical science relevant to the problem and use this understanding to create a plan of action and set of detailed specifications, which, if implemented, will lead to a predicted financial outcome.

The creation of plans and specifications and the prediction of the financial outcome if the plans were implemented is the activity of chemical engineering design. Design is a creative activity, and as such can be one of the most rewarding and satisfying activities undertaken by an engineer. The design does not exist at the start of the project. The designer Chemical Engineering Design, Second Edition. DOI: 10.1016/B978-0-08-096659-5.00001-8 © 2013 Elsevier Ltd. All rights reserved.

CHAPTER 1 Introduction to Design

begins with a specific objective or customer need in mind, and by developing and evaluating possible designs, arrives at the best way of achieving that objective; be it a better chair, a new bridge, or for the chemical engineer, a new chemical product or production process. When considering possible ways of achieving the objective the designer will be constrained by many factors, which will narrow down the number of possible designs. There will rarely be just one possible solution to the problem, just one design. Several alternative ways of meeting the objective will normally be possible, even several best designs, depending on the nature of the constraints. These constraints on the possible solutions to a problem in design arise in many ways. Some constraints will be fixed and invariable, such as those that arise from physical laws, government regulations, and engineering standards. Others will be less rigid, and can be relaxed by the designer as part of the general strategy for seeking the best design. The constraints that are outside the designer’s influence can be termed the external constraints. These set the outer boundary of possible designs, as shown in Figure 1.1. Within this boundary there will be a number of plausible designs bounded by the other constraints, the internal constraints, over which the designer has some control; such as choice of process, choice of process conditions, materials, and equipment. Economic considerations are obviously a major constraint on any engineering design: plants must make a profit. Process costing and economics are discussed in Chapters 7, 8, and 9. Time will also be a constraint. The time available for completion of a design will usually limit the number of alternative designs that can be considered. The stages in the development of a design, from the initial identification of the objective to the final design, are shown diagrammatically in Figure 1.2. Each stage is discussed in the following sections.

Region of all designs

Resourc

da rd

nel

ds e

Tim

Possible designs ols

Government contr

FIGURE 1.1 Design constraints.

“Internal” constraints

“External” constraints

Eco

sa nd

son

Metho

Sta n

Per

aints

Plausible designs

co omic

s law

Materials

nstr

Pro con cess diti ons

ical

la f gu ice o o s ty Ch ces fe pro Sa re

s Phy

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1.2 Nature of Design

Determine customer needs

Set design specifications Build performance models Generate design concepts

R&D if needed Predict fitness for service

Customer approval

Evaluate economics, optimize & select design

Detailed design & equipment selection

Procurement & construction

Begin operation

FIGURE 1.2 The design process.

Figure 1.2 shows design as an iterative procedure. As the design develops, the designer will become aware of more possibilities and more constraints, and will be constantly seeking new data and evaluating possible design solutions.

1.2.1 The Design Objective (The Need) All design starts with a perceived need. In the design of a chemical product or process, the need is the public need for the product, creating a commercial opportunity, as foreseen by the sales and marketing organization. Within this overall objective the designer will recognize sub-objectives, the requirements of the various units that make up the overall process. Before starting work, the designer should obtain as complete, and as unambiguous, a statement of the requirements as possible. If the requirement (need) arises from outside the design group, from a customer or from another department, then the designer will have to elucidate the real requirements through discussion. It is important to distinguish between the needs that are “must haves” and those that are “should haves”. The “should haves” are those parts of the initial specification that may be thought desirable, but that can be relaxed if necessary as the design develops. For example, a particular product specification may be considered desirable by the sales department, but may be difficult and costly to obtain, and some relaxation of the specification may be possible, producing a saleable but cheaper product. Whenever possible, the designer should always question the design requirements (the project and equipment specifications) and keep them under review as the design progresses. It is important for the design engineer to work closely with the sales or marketing department or with the customer directly, to have as clear as possible an understanding of the customer’s needs.

CHAPTER 1 Introduction to Design

When writing specifications for others, such as for the mechanical design or purchase of a piece of equipment, the design engineer should be aware of the restrictions (constraints) that are being placed on other designers. A well-thought-out, comprehensive specification of the requirements for a piece of equipment defines the external constraints within which the other designers must work.

1.2.2 Setting the Design Basis The most important step in starting a process design is translating the customer need into a design basis. The design basis is a more precise statement of the problem that is to be solved. It will normally include the production rate and purity specifications of the main product, together with information on constraints that will influence the design such as: 1. 2. 3. 4.

The system of units to be used. The national, local, or company design codes that must be followed. Details of raw materials that are available. Information on potential sites where the plant might be located, including climate data, seismic conditions, and infrastructure availability. Site design is discussed in detail in Chapter 11. 5. Information on the conditions, availability, and price of utility services such as fuel gas, steam, cooling water, process air, process water, and electricity that will be needed to run the process. The design basis must be clearly defined before design can begin. If the design is carried out for a client, then the design basis should be reviewed with the client at the start of the project. Most companies use standard forms or questionnaires to capture design basis information. An example template is given in Appendix G and can be downloaded in MS Excel format from the online material at booksite.Elsevier.com/Towler.

1.2.3 Generation of Possible Design Concepts The creative part of the design process is the generation of possible solutions to the problem for analysis, evaluation, and selection. In this activity most designers largely rely on previous experience, their own and that of others. It is doubtful if any design is entirely novel. The antecedence of most designs can usually be easily traced. The first motor cars were clearly horse-drawn carriages without the horse; and the development of the design of the modern car can be traced step by step from these early prototypes. In the chemical industry, modern distillation processes have developed from the ancient stills used for rectification of spirits; and the packed columns used for gas absorption have developed from primitive, brushwood-packed towers. So, it is not often that a process designer is faced with the task of producing a design for a completely novel process or piece of equipment. Experienced engineers usually prefer the tried and tested methods, rather than possibly more exciting but untried novel designs. The work that is required to develop new processes, and the cost, are usually underestimated. Commercialization of new technology is difficult and expensive and few companies are willing to make multimillion dollar investments in technology that is not well proven (a phenomenon known in industry as “me third” syndrome). Progress is made more surely in small steps; however, when innovation is wanted, previous experience, through prejudice, can inhibit the generation and acceptance of new ideas (known as “not invented here” syndrome).

1.2 Nature of Design

The amount of work, and the way it is tackled, will depend on the degree of novelty in a design project. Development of new processes inevitably requires much more interaction with researchers and collection of data from laboratories and pilot plants. Chemical engineering projects can be divided into three types, depending on the novelty involved: 1. Modifications, and additions, to existing plant; usually carried out by the plant design group. Projects of this type represent about half of all the design activity in industry. 2. New production capacity to meet growing sales demand, and the sale of established processes by contractors. Repetition of existing designs, with only minor design changes, including designs of vendor’s or competitor’s processes carried out to understand whether they have a compellingly better cost of production. Projects of this type account for about 45% of industrial design activity. 3. New processes, developed from laboratory research, through pilot plant, to a commercial process. Even here, most of the unit operations and process equipment will use established designs. This type of project accounts for less than 5% of design activity in industry. The majority of process designs are based on designs that previously existed. The design engineer very rarely sits down with a blank sheet of paper to create a new design from scratch, an activity sometimes referred to as “process synthesis.” Even in industries such as pharmaceuticals, where research and new product development are critically important, the types of process used are often based on previous designs for similar products, so as to make use of well-understood equipment and smooth the process of obtaining regulatory approval for the new plant. The first step in devising a new process design will be to sketch out a rough block diagram showing the main stages in the process and to list the primary function (objective) and the major constraints for each stage. Experience should then indicate what types of unit operations and equipment should be considered. The steps involved in determining the sequence of unit operations that constitutes a process flowsheet are described in Chapter 2. The generation of ideas for possible solutions to a design problem cannot be separated from the selection stage of the design process; some ideas will be rejected as impractical as soon as they are conceived.

1.2.4 Fitness Testing When design alternatives are suggested, they must be tested for fitness for purpose. In other words, the design engineer must determine how well each design concept meets the identified need. In the design of chemical plants it is usually prohibitively expensive to build several designs to find out which one works best. Instead, the design engineer builds a mathematical model of the process, usually in the form of computer simulations of the process, reactors, and other key equipment. In some cases, the performance model may include a pilot plant or other facility for predicting plant performance and collecting the necessary design data. In other cases, the design data can be collected from an existing full-scale facility or can be found in the chemical engineering literature. The design engineer must assemble all of the information needed to model the process so as to predict its performance against the identified objectives. For process design this will include information on possible processes, equipment performance, and physical property data. Sources of process information are reviewed in Chapter 2.

CHAPTER 1 Introduction to Design

Many design organizations will prepare a basic data manual, containing all the process “know-how” on which the design is to be based. Most organizations will have design manuals covering preferred methods and data for the more frequently-used design procedures. The national standards are also sources of design methods and data. They are also design constraints, as new plants must be designed in accordance with national standards and regulations. If the necessary design data or models do not exist then research and development work is needed to collect the data and build new models. Once the data has been collected and a working model of the process has been established, the design engineer can begin to determine equipment sizes and costs. At this stage it will become obvious that some designs are uneconomical and they can be rejected without further analysis. It is important to make sure that all of the designs that are considered are fit for the service, i.e., meet the customer’s “must have” requirements. In most chemical engineering design problems this comes down to producing products that meet the required specifications. A design that does not meet the customer’s objective can usually be modified until it does so, but this always adds extra costs.

1.2.5 Economic Evaluation, Optimization, and Selection Once the designer has identified a few candidate designs that meet the customer objective, the process of design selection can begin. The primary criterion for design selection is usually economic performance, although factors such as safety and environmental impact may also play a strong role. The economic evaluation usually entails analyzing the capital and operating costs of the process to determine the return on investment, as described in Chapters 7, 8, and 9. The economic analysis of the product or process can also be used to optimize the design. Every design will have several possible variants that make economic sense under certain conditions. For example, the extent of process heat recovery is a trade-off between the cost of energy and the cost of heat exchangers (usually expressed as a cost of heat exchange area). In regions where energy costs are high, designs that use a lot of heat exchange surface to maximize recovery of waste heat for reuse in the process will be attractive. In regions where energy costs are low, it may be more economical to burn more fuel and reduce the capital cost of the plant. Techniques for energy recovery are described in Chapter 3. The mathematical techniques that have been developed to assist in the optimization of plant design and operation are discussed briefly in Chapter 12. When all of the candidate designs have been optimized, the best design can be selected. Very often, the design engineer will find that several designs have very close economic performance, in which case the safest design or that which has the best commercial track record will be chosen. At the selection stage an experienced engineer will also look carefully at the candidate designs to make sure that they are safe, operable, and reliable, and to ensure that no significant costs have been overlooked.

1.2.6 Detailed Design and Equipment Selection After the process or product concept has been selected, the project moves on to detailed design. Here the detailed specifications of equipment such as vessels, exchangers, pumps, and instruments are determined. The design engineer may work with other engineering disciplines, such as civil engineers for site preparation, mechanical engineers for design of vessels and structures, and electrical engineers for instrumentation and control.

1.3 The Organization of a Chemical Engineering Project

Many companies engage specialist Engineering, Procurement, and Construction (EPC) companies, commonly known as contractors, at the detailed design stage. The EPC companies maintain large design staffs that can quickly and competently execute projects at relatively low cost. During the detailed design stage there may still be some changes to the design and there will certainly be ongoing optimization as a better idea of the project cost structure is developed. The detailed design decisions tend to focus mainly on equipment selection though, rather than on changes to the flowsheet. For example, the design engineer may need to decide whether to use a U-tube or a floating-head exchanger, as discussed in Chapter 19, or whether to use trays or packing for a distillation column, as described in Chapter 17.

1.2.7 Procurement, Construction, and Operation When the details of the design have been finalized, the equipment can be purchased and the plant can be built. Procurement and construction are usually carried out by an EPC firm unless the project is very small. Because they work on many different projects each year, the EPC firms are able to place bulk orders for items such as piping, wire, valves, etc., and can use their purchasing power to get discounts on most equipment. The EPC companies also have a great deal of experience in field construction, inspection, testing, and equipment installation. They can therefore normally contract to build a plant for a client cheaper (and usually also quicker) than the client could build it on their own. Finally, once the plant is built and readied for start-up, it can begin operation. The design engineer will often then be called upon to help resolve any start-up issues and teething problems with the new plant.

1.3 THE ORGANIZATION OF A CHEMICAL ENGINEERING PROJECT The design work required in the engineering of a chemical manufacturing process can be divided into two broad phases. Phase 1: Process design, which covers the steps from the initial selection of the process to be used, through to the issuing of the process flowsheets; and includes the selection, specification, and chemical engineering design of equipment. In a typical organization, this phase is the responsibility of the process design group, and the work is mainly done by chemical engineers. The process design group may also be responsible for the preparation of the piping and instrumentation diagrams. Phase 2: Plant design, including the detailed mechanical design of equipment, the structural, civil, and electrical design, and the specification and design of the ancillary services. These activities will be the responsibility of specialist design groups, having expertise in the whole range of engineering disciplines. Other specialist groups will be responsible for cost estimation, and the purchase and procurement of equipment and materials. The sequence of steps in the design, construction, and start-up of a typical chemical process plant is shown diagrammatically in Figure 1.3, and the organization of a typical project group is shown in Figure 1.4. Each step in the design process will not be as neatly separated from the others

CHAPTER 1 Introduction to Design

Project specification

Initial evaluation. Process selection. Preliminary flow diagrams.

Material and energy balances. Preliminary equipment selection and design. Process flowsheeting.

Preliminary cost estimation. Authorisation of funds.

Detailed process design. Flowsheets. Chemical engineering equipment design and specifications. Reactors, unit operations, heat exchangers, miscellaneous equipment. Materials selection. Process manuals.

Piping and instrument design

Instrument selection and specification

Electrical, motors, switch gear, substations, etc.

Pumps and compressors. Selection and specification.

Piping design

Vessel design

Structural design

Heat exchanger design

Plant layout

Utilities and other services. Design and specification.

General civil work. Foundations, drains, roads, etc.

Buildings. Offices, laboratories, control rooms, etc.

Project cost estimation. Capital authorisation.

Purchasing/procurement

Raw material specification. (contracts).

Construction

Start-up

Operation

Sales

FIGURE 1.3 The structure of a chemical engineering project.

Operating manuals

1.3 The Organization of a Chemical Engineering Project

Process section Process evaluation Flowsheeting Equipment specifications

Construction section Construction Start-up

Procurement section Estimating Inspection Scheduling

Project manager

Specialist design sections Vessels Layout Control and instruments Compressors and turbines pumps

Civil work structures buildings

Piping valves

Heat exchangers fired heaters

Electrical

Utilities

FIGURE 1.4 Project organization.

as is indicated in Figure 1.3, nor will the sequence of events be as clearly defined. There will be a constant interchange of information between the various design sections as the design develops, but it is clear that some steps in a design must be largely completed before others can be started. A project manager, often a chemical engineer by training, is usually responsible for the coordination of the project, as shown in Figure 1.4. As was stated in Section 1.2.1, the project design should start with a clear specification defining the product, capacity, raw materials, process, and site location. If the project is based on an established process and product, a full specification can be drawn up at the start of the project. For a new product, the specification will be developed from an economic evaluation of possible processes, based on laboratory research, pilot plant tests, and product market research. Techniques for new product design are discussed in Section 1.8. Some of the larger chemical manufacturing companies have their own project design organizations and carry out the whole project design and engineering, and possibly construction, within their own organization. More usually, the design and construction, and possibly assistance with start-up, are subcontracted to one of the international Engineering, Procurement and Construction (EPC) firms. The technical “know-how” for the process could come from the operating company or could be licensed from the contractor or a technology vendor. The operating company, technology provider, and contractor will work closely together throughout all stages of the project.

CHAPTER 1 Introduction to Design

On many modern projects, the operating company may well be a joint venture between several companies. The project may be carried out between companies based in different parts of the world. Good teamwork, communications, and project management are therefore critically important in ensuring that the project is executed successfully.

1.4 PROJECT DOCUMENTATION As shown in Figure 1.4 and described in Section 1.3, the design and engineering of a chemical process requires the cooperation of many specialist groups. Effective cooperation depends on effective communications, and all design organizations have formal procedures for handling project information and documentation. The project documentation will include: 1. General correspondence within the design group and with government departments equipment vendors site personnel the client 2. Calculation sheets design calculations cost estimates material and energy balances 3. Drawings flowsheets piping and instrumentation diagrams layout diagrams plot/site plans equipment details piping diagrams (isometrics) architectural drawings design sketches 4. Specification sheets the design basis feed and product specifications an equipment list sheets for equipment, such as: heat exchangers, pumps, heaters, etc. 5. Health, safety, and environmental information materials safety data sheets (MSDS forms) HAZOP or HAZAN documentation (see Chapter 10) emissions assessments and permits 6. Purchase orders quotations invoices All documents are assigned a code number for easy cross-referencing, filing, and retrieval.

1.4 Project Documentation

1.4.1 Design Documents Calculation Sheets The design engineer should develop the habit of setting out calculations so that they can be easily understood and checked by others. It is good practice to include on calculation sheets the basis of the calculations, and any assumptions and approximations made, in sufficient detail for the methods, as well as the arithmetic, to be checked. Design calculations are normally set out on standard sheets. The heading at the top of each sheet should include the project title and identification number, the revision number and date and, most importantly, the signature (or initials) of the person who checked the calculation. A template calculation sheet is given in Appendix G and can be downloaded in MS Excel format from the online material at booksite.elsevier.com/Towler.

Drawings All project drawings are normally drawn on specially printed sheets, with the company name, project title and number, drawing title and identification number, and drafter’s name and person checking the drawing clearly set out in a box in the bottom right-hand corner. Provision should also be made for noting on the drawing all modifications to the initial issue. Drawings should conform to accepted drawing conventions, preferably those laid down by the national standards. The symbols used for flowsheets and piping and instrument diagrams are discussed in Chapters 2 and 5. Computer Aided Design (CAD) methods are used to produce the drawings required for all the aspects of a project: flowsheets, piping and instrumentation, mechanical and civil work. While the released versions of drawings are usually drafted by a professional, the design engineer will often need to mark up changes to drawings or make minor modifications to flowsheets, so it is useful to have some proficiency with the drafting software.

Specification Sheets Standard specification sheets are normally used to transmit the information required for the detailed design, or purchase, of equipment items, such as heat exchangers, pumps, columns, pressure vessels, etc. As well as ensuring that the information is clearly and unambiguously presented, standard specification sheets serve as checklists to ensure that all the information required is included. Examples of equipment specification sheets are given in MS Excel format in the online material at booksite.elsevier.com/Towler. These specification sheets are referenced and used in examples throughout the book. Standard worksheets are also often used for calculations that are commonly repeated in design.

Process Manuals Process manuals are usually prepared by the process design group to describe the process and the basis of the design. Together with the flowsheets, they provide a complete technical description of the process.

Operating Manuals Operating manuals give the detailed, step-by-step, instructions for operation of the process and equipment. They would normally be prepared by the operating company personnel, but may also be issued by a contractor or technology licensor as part of the technology transfer package for a less experienced client. The operating manuals are used for operator instruction and training, and for the preparation of the formal plant operating instructions.

CHAPTER 1 Introduction to Design

1.4.2 Design Reports Design reports are used as a means of organizing, recording, and communicating the information developed during a design project. The format of the report depends on the function of the design project. A techno-economic analysis of a new product or process might require a strong focus on marketing and commercial aspects of the project and less technical detail, whereas a basic engineering design package that is to be used to generate a ± 10% cost estimate will require substantial information on equipment designs but needs no financial analysis whatsoever. When writing a design report, the design engineer should begin by thinking about the needs of the audience that will be using the report. Information is usually conveyed in the form of tables and charts as much as possible, with brief descriptions in the text when necessary. Most design reports are compiled from flow diagrams, specification sheets, and standard templates for economic analysis, so that the technical information that users require is easily accessible. The written portion of the report is usually very brief and is limited to an explanation of the key design features, assumptions, decisions, and recommendations. The following examples illustrate some of the different report formats that are commonly used in industry, while the final example discusses a suitable format for university design projects. Example 1.1: Techno-Economic Analysis This type of report is used to summarize a preliminary technical and economic analysis of a proposed new product or process technology. Such a report might be written by an engineer working in product or process development, or by a consulting company that has been asked to assess a new product or manufacturing route. This type of report is also often written as an assessment of a competitor’s technology, or in an effort to understand a supplier’s cost structure. The purpose of the report is to provide sufficient technical and economic analysis of the process to determine whether it is economically attractive and to understand the costs of production, often in comparison to a conventional alternative. In addition to describing the technology and determining the cost of production, the report should also review the attractiveness of the market and assess the risks inherent in practicing the technology. A sample contents list with guidance on each section is given in Table 1.1.

Table 1.1 Techno-Economic Analysis 1. Executive summary (1–2 page summary of overall findings and recommendations including highlights of financial analysis) 2. Technology description 2.1. Process chemistry (describe the feeds, reaction mechanism, catalyst, reaction conditions, how important byproducts are formed) 2.2. Process specification (brief description of the process including block flow diagram) 3. Commercial analysis 3.1. Product applications (major end use markets, competing products, legislative issues) 3.2. Competitor assessment (market shares, competitor strengths, weaknesses, regional/geographic factors) 3.3. Existing and planned capacity (how much and where, include plants that make feed or consume product if these have an impact on project viability—usually presented as a table)

(Continued )

1.4 Project Documentation

Table 1.1 Techno-Economic Analysis—cont’d 3.4. Market forecast (estimate growth rate, future price trends, regional variations in market) 3.5. Project location criteria (discuss the criteria for locating a new plant, market issues, legislative factors, etc. [see Chapter 11]) 4. Economic analysis 4.1. Pricing basis (forecasting method, price, and/or margin assumptions) 4.2. Investment analysis (explain the basis for the capital cost estimate, e.g., factorial estimate based on equipment design, curve cost estimate, etc. [see Chapter 7]) 4.3. Cost of production analysis (breakdown of the cost of production of product, usually presented as a table showing variable and fixed cost components [see Chapter 8]) 4.4. Financial analysis (evaluation of project profitability, usually presented as standard tables [see Chapter 9]) 4.5. Sensitivity analysis (discuss the financial impact of varying key assumptions such as prices, plant capacity, investment cost, construction schedule [see Chapter 9]) 5. Risk analysis 5.1. Process hazard analysis summary (summary of critical safety issues in the design, issues raised during process hazard analysis) 5.2. Environmental impact assessment summary (summary of critical environmental issues) 5.3. Commercial risk assessment (discuss business risks inherent in the investment) 6. Appendices 6.1. Process flow diagram 6.2. Equipment list and capital cost summary

Example 1.2: Technical Proposal A technical proposal document is intended to convey the information needed to make a technology selection. When a company has decided to build a new plant they will often invite several engineering or licensing firms to submit proposals for the plant design. Although the proposal does not contain a complete design, there must be sufficient technical information for the customer to be able to select between the proposed design and the competitor’s proposals. Often, the customer will specify the contents and section headings of the proposal to ensure that all proposals follow the same format. Since the customer has already completed their own market analysis, this information is not required. Similarly, the plant capacity and location have usually already been specified. Instead, the focus of the report is on conveying the unique features of the design, the basis for selecting these features, and the proof that these features have worked in actual practice. A sample contents list is given in Table 1.2.

Table 1.2 Technical Proposal 1. Executive summary 1.1. Proposed technology (brief description of the process including block flow diagram) 1.2. Benefits and advantages (summarize key advantages relative to competing technologies)

(Continued )

CHAPTER 1 Introduction to Design

Table 1.2 Technical Proposal—cont’d 2. Proposal basis 2.1. Processing objectives (restate the design problem) 2.2. Feedstocks (describe available feedstocks, grades, quality issues) 2.3. Product grades (give product specifications, usually as tables or reference to ASTM specifications) 2.4. Processing options (describe technical alternatives evaluated) 3. Proposed technology 3.1. Process description (more detailed process description) 3.2. Reactor selection (what reactor type is recommended, why it was selected, and how it was designed) 3.3. Catalyst selection recommendations (what catalysts are recommended and why) 3.4. Key equipment recommendations (describe any critical unit operations and explain what was selected and how it was designed, key specifications, etc.) 3.5. Pilot plant and commercial experience (describe any work that proves that the proposed design will operate as described) 4. Technical and economic assessment 4.1. Estimated raw materials consumption (usually a table) 4.2. Estimated utility consumption (usually a table giving breakdowns for each utility [see Chapter 3]) 4.3. Estimated manpower requirements (how many operators are needed per shift) 4.4. Estimated cost of production (breakdown of the cost of production of product, usually presented as a table showing variable and fixed cost components [see Chapter 8]) 4.5. Estimated installed capital cost (breakdown by plant section of the plant capital cost estimate) 5. Process flow diagrams 6. Preliminary equipment specification sheets 7. Typical plot plan

Example 1.3: Basic Engineering Design A basic engineering design report (BEDR) is often used at the end of the process design phase to collect and review information before beginning the plant design phase and detailed design of equipment, piping, plot layout, etc. The purpose of the BEDR is to ensure that all the information necessary for detailed design has been assembled, reviewed, and approved, so as to minimize errors and rework during detailed design. The BEDR also serves as a reference document for the detailed design groups and provides them with stream flows, temperatures, pressures, and physical property information. One of the most important functions of a basic engineering design report is to document the decisions and assumptions made during the design and the comments and suggestions made during design review meetings. These are often documented as separate sections of the report so that other engineers who later join the project can understand the reasons why the design evolved to its current form. A sample contents list for a basic engineering design report is given in Table 1.3.

1.4 Project Documentation

Table 1.3 Basic Engineering Design 1. Process description and basis 1.1. Project definition (customer, location, key feeds, and products) 1.2. Process description (brief description of process flowsheet and chemistry, including block flow diagrams) 1.3. Basis and scope of design (plant capacity, project scope, design basis table) 2. Process flow diagrams 3. Mass and energy balances 3.1. Base case stream data (stream temperature and pressure, mass flow and molar flow of each component in all streams, stream mass and molar composition, and total stream mass and molar flow, usually given as tables) 3.2. Modified cases stream data (same data for each variant design case, for example winter/summer cases, start of run/end of run, different product grades, etc.) 3.3. Base case physical property data (physical properties required by detailed design groups, such as stream density, viscosity, thermal conductivity, etc.) 4. Process simulation (description of how the process was simulated and any differences between the simulation model and process flow diagram that detailed design groups need to understand) 5. Equipment list 6. Equipment specifications 6.1. Pressure vessels 6.2. Heaters 6.3. Heat exchangers 6.3.1. Tubular 6.3.2. Air cooled 6.4. Fluid handling equipment 6.4.1. Pumps 6.4.2. Compressors 6.5. Solid handling equipment 6.6. Drivers 6.6.1. Motors 6.6.2. Turbines 6.7. Unconventional or proprietary equipment 6.8. Instrumentation 6.9. Electrical specifications 6.10. Piping 6.11. Miscellaneous 7. Materials of construction (what materials are to be used in each section of the plant and why they were selected, often presented as a table or as a marked up version of the process flow diagram) 8. Preliminary hydraulics (pump-and-line calculations of pressure drop used as a basis for sizing pumps and compressors [see Chapter 20]) 9. Preliminary operating procedures (describe the procedures for plant start-up, shutdown, and emergency shutdown) 10. Preliminary hazard analysis (description of major materials and process hazards of the design [see Chapter 10])

(Continued )

CHAPTER 1 Introduction to Design

Table 1.3 Basic Engineering Design—cont’d 11. Capital cost estimate (breakdown of capital cost, usually for each piece of equipment plus bulks and installation, usually given as a table or list) 12. Heat integration and utilities estimate (overview of any pinch analysis or other energy optimization analysis, composite curves, table giving breakdown of utility consumption and costs [see Chapter 3]) 13. Design decisions and assumptions (description of the most significant assumptions and selection decisions made by the designers, including references to calculation sheets for alternatives that were evaluated and rejected) 14. Design review documentation 14.1. Meeting notes (notes taken during the design review meeting) 14.2. Actions taken to resolve design review issues (description of what was done to follow up on issues raised during the design review) 15. Appendices 15.1. Calculation sheets (calculations to support equipment selection and sizing, numbered and referenced elsewhere in the report) 15.2. Project correspondence (communications between the design team, marketing, vendors, external customers, regulatory agencies and any other parties whose input influenced the design)

Example 1.4: Undergraduate Design Project Senior year design projects have a range of objectives, but these always include demonstrating proficiency in engineering design and economic evaluation. More technical information is needed than Example 1.1, while more commercial and marketing analysis is needed than Examples 1.2 and 1.3, so none of the report formats used in industry is ideal. A reasonable approach is to use the format of Example 1.1 and include the material listed in Example 1.3 as appendices. For shorter classes, or when there is insufficient time to develop all the information listed in Example 1.3, some of the sections of Table 1.3 can be omitted.

1.5 CODES AND STANDARDS The need for standardization arose early in the evolution of the modern engineering industry; Whitworth introduced the first standard screw thread to give a measure of interchangeability between different manufacturers in 1841. Modern engineering standards cover a much wider function than the interchange of parts. In engineering practice they cover: 1. 2. 3. 4. 5.

Materials, properties, and compositions. Testing procedures for performance, compositions, and quality. Preferred sizes; for example, tubes, plates, sections, etc. Methods for design, inspection, and fabrication. Codes of practice for plant operation and safety.

1.5 Codes and Standards

The terms standard and code are used interchangeably, though code should really be reserved for a code of practice covering for example, a recommended design or operating procedure, and standard for preferred sizes, compositions, etc. All of the developed countries, and many of the developing countries, have national standards organizations, responsible for the issue and maintenance of standards for the manufacturing industries, and for the protection of consumers. In the United States, the government organization responsible for coordinating information on standards is the National Institute of Standards and Technology (NIST); standards are issued by federal, state, and various commercial organizations. The principal ones of interest to chemical engineers are those issued by the American National Standards Institute (ANSI), the American Petroleum Institute (API), the American Society for Testing Materials (ASTM), the American Society of Mechanical Engineers (ASME) (pressure vessels and pipes), the National Fire Protection Association (NFPA) (safety), the Tubular Exchanger Manufacturers Association (TEMA) (heat exchangers), and the International Society of Automation (ISA)(process control). Most Canadian provinces apply the same standards used in the United States. The preparation of the standards is largely the responsibility of committees of persons from the appropriate industry, the professional engineering institutions, and other interested organizations. The International Organization for Standardization (ISO) coordinates the publication of international standards. The European countries used to each maintain their own national standards, but these are now being superseded by common European standards. Lists of codes and standards and copies of the most current versions can be obtained from the national standards agencies or by subscription from commercial web sites such as IHS (www .ihs.com). As well as the various national standards and codes, the larger design organizations will have their own (in-house) standards. Much of the detail in engineering design work is routine and repetitive, and it saves time and money, and ensures conformity between projects, if standard designs are used whenever practicable. Equipment manufacturers also work to standards to produce standardized designs and size ranges for commonly used items, such as electric motors, pumps, heat exchangers, pipes, and pipe fittings. They will conform to national standards, where they exist, or to those issued by trade associations. It is clearly more economical to produce a limited range of standard sizes than to have to treat each order as a special job. For the designer, the use of a standardized component size allows for the easy integration of a piece of equipment into the rest of the plant. For example, if a standard range of centrifugal pumps is specified the pump dimensions will be known, and this facilitates the design of the foundation plates and pipe connections and the selection of the drive motors: standard electric motors would be used. For an operating company, the standardization of equipment designs and sizes increases interchangeability and reduces the stock of spares that must be held in maintenance stores. Though there are clearly considerable advantages to be gained from the use of standards in design, there are also some disadvantages. Standards impose constraints on the designer. The nearest standard size will normally be selected on completing a design calculation (rounding-up) but this will not necessarily be the optimum size; though as the standard size will be cheaper than a special size, it will usually be the best choice from the point of view of initial capital cost.

CHAPTER 1 Introduction to Design

The design methods given in the codes and standards are, by their nature, historical, and do not necessarily incorporate the latest techniques. The use of standards in design is illustrated in the discussion of pressure vessel design in Chapter 14 and the description of heat exchanger design in Chapter 19. Relevant design codes and standards are cited throughout the book.

1.6 DESIGN FACTORS (DESIGN MARGINS) Design is an inexact art; errors and uncertainties arise from uncertainties in the design data available and in the approximations necessary in design calculations. Experienced designers include a degree of overdesign known as a design factor, design margin, or safety factor, to ensure that the design that is built meets product specifications and operates safely. In mechanical and structural design, the design factors that are used to allow for uncertainties in material properties, design methods, fabrication, and operating loads are well established. For example, a factor of around 4 on the tensile strength, or about 2.5 on the 0.1% proof stress, is normally used in general structural design. The recommended design factors are set out in the codes and standards. The selection of design factors in mechanical engineering design is illustrated in the discussion of pressure vessel design in Chapter 14. Design factors are also applied in process design to give some tolerance in the design. For example, the process stream average flows calculated from material balances are usually increased by a factor, typically 10%, to give some flexibility in process operation. This factor will set the maximum flows for equipment, instrumentation, and piping design. Where design factors are introduced to give some contingency in a process design, they should be agreed within the project organization, and clearly stated in the project documents (drawings, calculation sheets, and manuals). If this is not done, there is a danger that each of the specialist design groups will add its own “factor of safety,” resulting in gross and unnecessary overdesign. Companies often specify design factors in their design manuals. When selecting the design factor, a balance has to be made between the desire to make sure the design is adequate and the need to design to tight margins to remain competitive. Greater uncertainty in the design methods and data requires the use of bigger design factors.

1.7 SYSTEMS OF UNITS Most of the examples and equations in this book use SI units; however, in practice the design methods, data, and standards that the designer will use are often only available in the traditional scientific and engineering units. Chemical engineering has always used a diversity of units, embracing the scientific CGS and MKS systems, and both the American and British engineering systems. Those engineers in older industries will also have had to deal with some bizarre traditional units, such as degrees Twaddle or degrees API for density and barrels for quantity. Although almost all of the engineering societies have stated support for the adoption of SI units, this is unlikely to happen worldwide for many years. Furthermore, much useful historic data will always be in the traditional units and the design engineer must know how to understand and convert this information. In a

1.7 Systems of Units

globalized economy, engineers are expected to use different systems of units even within the same company, particularly in the contracting sector where the choice of units is at the client’s discretion. Design engineers must therefore have a familiarity with SI, metric, and customary units, and a few of the examples and many of the exercises are presented in customary units. It is usually the best practice to work through design calculations in the units in which the result is to be presented; but, if working in SI units is preferred, data can be converted to SI units, the calculation made, and the result converted to whatever units are required. Conversion factors to the SI system from most of the scientific and engineering units used in chemical engineering design are given in Appendix D, which is at the end of this book as well as in the online material at booksite .elsevier.com/Towler. Some license has been taken in the use of the SI system in this volume. Temperatures are given in degrees Celsius (°C); degrees Kelvin are only used when absolute temperature is required in the calculation. Pressures are often given in bar (or atmospheres) rather than in Pascals (N/m2), as this gives a better feel for the magnitude of the pressures. In design calculations the bar can usually be taken as equivalent to an atmosphere, whatever definition is used for atmosphere. The abbreviations bara and barg are often used to denote bar absolute and bar gauge, analogous to psia and psig when the pressure is expressed in pound force per square inch. When bar is used on its own, without qualification, it is normally taken as absolute. For stress, N/mm2 have been used, as these units are now generally accepted by engineers, and the use of a small unit of area helps to indicate that stress is the intensity of force at a point (as is also pressure). The corresponding traditional unit for stress is the ksi or thousand pounds force per square inch. For quantity, kmol are generally used in preference to mol, and for flow, kmol/h instead of mol/s, as this gives more sensibly sized figures, which are also closer to the more familiar lb/h. For volume and volumetric flow, m3 and m3/h are used in preference to m3/s, which gives ridiculously small values in engineering calculations. Liters per second are used for small flow rates, as this is the preferred unit for pump specifications. Plant capacities are usually stated on an annual mass flow basis in metric tons per year. Unfortunately, the literature contains a variety of abbreviations for metric tons per year, including tonnes/y, metric tons/y, MT/y (also kMTA = thousand metric tons per year), mtpy, and the correct term, t/y. The nonstandard abbreviations have occasionally been used, as it is important for design engineers to be familiar with all of these terms. The unit t denotes a metric ton of 1000 kg. In this book the unit ton is generally used to describe a short ton or US ton of 2000 lb (907 kg) rather than a long ton or UK ton of 2240 lb (1016 kg), although some examples use long tons. The long ton is closer to the metric ton. A thousand metric tons is usually denoted as a kiloton (kt); the correct SI unit gigagram (Gg) is very rarely used. In the United States, the prefixes M and MM are often used to denote thousand and million, which can be confusing to anyone familiar with the SI use of M as an abbreviation for mega (×106). This practice has generally been avoided, except in the widely used units MMBtu (million British thermal units) and the common way of abbreviating $1 million as $1 MM. Most prices have been given in U.S. dollars, denoted US$ or $, reflecting the fact that the data originated in the United States. Where, for convenience, other than SI units have been used on figures or diagrams, the scales are also given in SI units, or the appropriate conversion factors are given in the text. Where equations are presented in customary units a metric equivalent is generally given.

CHAPTER 1 Introduction to Design

Table 1.4 Approximate Conversions between Customary Units and SI Units Quantity Energy Specific enthalpy Specific heat capacity Heat transfer coeff. Viscosity Surface tension Pressure

Density Volume Flow rate

Customary Unit 1 1 1 1 1 1 1 1 1

Btu Btu/lb Btu/lb°F Btu/ft2h°F centipoise lbf/ft h dyne/cm lbf/in2 (psi) atm

1 1 1 1

lb/ft3 g/cm3 US gal US gal/min

SI Unit Approx. 1 kJ 2 kJ/kg 4 kJ/kg°C 6 W/m2 °C 1 mNs/m2 0.4 mNs/m2 1 mN/m 7 kN/m2 1 bar 105 N/m2 16 kg/m3 1 kg/m3 3.8 × 10−3 m3 0.23 m3/h

Exact 1.05506 2.326 4.1868 5.678 1.000 0.4134 1.000 6.894 1.01325 16.0185 3.7854 × 10−3 0.227

Note: 1 US gallon = 0.84 imperial gallons (UK) 1 barrel (oil) = 42 US gallons ≈ 0.16 m3 (exact 0.1590) 1 kWh = 3.6 MJ

Some approximate conversion factors to SI units are given in Table 1.4. These are worth committing to memory, to give some feel for the units for those more familiar with the traditional engineering units. The exact conversion factors are also shown in the table. A more comprehensive table of conversion factors is given in Appendix D.

1.8 PRODUCT DESIGN The design of new chemical products goes through the same stages described in Section 1.2 and illustrated in Figure 1.2. The successful introduction of a new product usually requires not only the design of the product itself, but also the design of the plant that will make the product. In the process industries the conception and development of new chemical products are often led by chemists, biologists, pharmacists, food scientists, or electrical or biomedical engineers; however, chemical engineers can be involved from the earliest stages and will certainly be engaged in designing the manufacturing process and developing the first estimates of the cost of production and capital investment required. The launch of a new product always has high commercial risk. The new product must meet a customer need and outperform the existing alternatives. Customers may have multiple requirements of the product, and these requirements might not be stated in a way that is easy to relate to technical

1.8 Product Design

specifications. The company that introduces the product needs to build market share and command a high enough price to ensure that the investment in research, development, and new plant can be justified. Most of the engineering work that is done in launching a new product goes into the design of the manufacturing process, but considerable care must be taken to ensure that the commercial risks have also been properly addressed. Consequently, in new product design much more attention is paid to the steps of understanding customer preferences, translating these needs into product specifications, and market testing to ensure fitness for service. This section introduces some of the methods that are used for product development in the process industries, and that may be useful to chemical engineers engaged in new product design. Vast quantities of books on innovation and new product design have been published in the general engineering and business literature. Among the best are those by Cooper (2001), Ulrich and Eppinger (2008), and Cooper and Edgett (2009). Product design books aimed specifically at chemical engineers have been written by Cussler and Moggridge (2001) and Seider, Seader, Lewin, and Widagdo (2009).

1.8.1 New Chemical Products Chemical engineers work in many industries and may be engaged in designing all kinds of products, but for the purposes of this chapter the discussion will be limited to new products that are based on the application of novel chemistry, biology, or materials science. These can be broadly categorized as new molecules, new formulations, new materials, and new equipment and devices.

New Molecules The process industries produce and consume a surprisingly large number of distinct chemical species. Under the Toxic Substances Control Act of 1976 (TSCA) (15 U.S.C. 2601 et seq.), the U.S. Environmental Protection Agency (EPA) regulates the manufacture, import, and export of 83,000 chemicals. The European Chemicals Agency (ECHA) was established in 2006 under the European Regulation, Evaluation, Authorisation and Restriction of Chemicals (REACH) regulation, with the goal of registering all chemicals in use in Europe. At the time of writing, 143,000 chemicals have been submitted to ECHA for preregistration. The infinite possibilities of organic chemistry ensure that we will never run out of new molecular species to test for any given application. New molecules are often commercialized in high-value applications such as specialty chemicals, additives, and active pharmaceutical ingredients (APIs). New molecules may also be needed when use of an existing chemical is restricted for safety or environmental reasons. For example, chlorinated hydrocarbons were phased out as refrigerants and propellants under the Montreal protocol after concern that they caused ozone depletion. The fluorocarbon compounds that initially replaced them are in turn likely to be replaced due to concerns about their high global-warming potential as greenhouse gases. Various methods are used to identify new molecules for an application. Optimization of computer models based on molecular simulation or group contribution methods may provide insights into molecular structures that give desired properties. More often, chemists will look at variants on known molecules; for example, by addition, removal, or substitution of methyl-, ethyl-, phenyl- or other substituent groups. The chemists will also use their knowledge of synthesis routes to propose

CHAPTER 1 Introduction to Design

compounds that are easier to prepare in high yield using known chemical pathways and starting from available feeds. The same is true for biologically-derived compounds, where the biochemist or genetic engineer will attempt to isolate enzymes or strains that maximize the yield of the target molecule.

New Formulations Almost all process industry products sold to the general public are formulations made from multiple chemicals. Examples range from pharmaceuticals, cosmetics, healthcare products, fragrances, foods, and beverages to paints, adhesives, fuels, and cleaning products. Every household contains a multitude of mixtures of products. The prevalence of formulated products arises directly from the need to meet multiple customer requirements. You can wash your hands quite effectively using linear alkylbenzene sulfonate (a surfactant), but you probably prefer it to be blended into a gel that smells nice, has an attractive color, and provides some antibacterial action. The same surfactant would also be quite suitable for washing your car, clothes, dishes, carpets, hair, and toilet, but in each case specific user requirements lead to a different formulated product. Formulated products are usually produced in blending plants. In some simple cases the feed compounds are just mixed together and sent to a packaging line. More commonly, the mixing and blending operations must be carefully designed to ensure (or prevent) emulsification and guarantee uniform product properties. Formulation plants are also often designed to produce a range of different products tailored to different market segments, in which case the plant must be designed to switch between products with minimal downtime and product wastage. The blend composition of a formulated product is designed to meet the customer needs in a cost-effective manner that provides an adequate profit margin for the manufacturer. Where possible, manufacturers seek to substitute expensive components with cheaper materials that have the same effect; however, marketing and brand management can sometimes be used to justify using more expensive materials. For example, “natural” compounds derived from agricultural products can often be effectively marketed to replace cheaper synthetic alternatives. Consumer products are highly regulated and carry high potential liability risks because of the large number of end users. These factors place additional constraints on the product designers. Extensive product safety testing must be carried out when new chemicals are introduced into consumer product formulations.

New Materials Chemical engineers play a leading role in the manufacture of polymers, synthetic fibers, composite materials, papers, films, electronic materials, catalysts, and ceramics. The properties of these materials are often determined as much by the manufacturing process as by the chemical composition. For example, multiple grades of polyethylene can be produced, with very different properties, depending on the production route and distribution of molecular weight in the polymer. New product development in the manufacturing industries is often based on materials substitution. Injection-molded or film-blown polymers are usually a cheaper substitute for metal, wood, or glass components that require more labor-intensive casting or machining. Many chemical engineers work on tailoring the properties of engineering materials such as polymers, resins, and composites to optimize the material to particular end applications.

1.8 Product Design

The development of new materials applications requires close collaboration with the end user of the material. Most of the product specifications will be based on physical properties such as strength, elasticity, hardness, etc. and flow properties that affect ease of manufacture, but resistance to chemicals, solvents, oxidation, and corrosion can also be important factors.

New Equipment and Devices Many sensors, medical devices, and power systems are based on chemical or biological processes. If a device requires sound understanding of kinetics and transport processes, chemical engineers will probably be involved in its design. Chemical engineers also play an important role in the design of new proprietary equipment for the processing industries, and are frequently involved in the design and customization of equipment such as dryers, crystallizers, membrane units, and other proprietary separation devices. Device manufacture usually involves the assembly of multiple subcomponents and the production line methods that are used are very different from the methods used in the process industries. Evaluating the production costs of manufactured devices requires familiarity with industrial engineering methods and is beyond the scope of this book.

1.8.2 Understanding Customer Needs The first step in new product development is to find out what customers want and are prepared to pay for. If the new product is not better than existing alternatives in some way, then it will be difficult to build market share and generate a return on the investment. If new features are added, they must be of value to the customer; otherwise the new product will not be differentiated from the existing alternatives. One of the roles of the marketing group in a company is to develop an understanding of customer requirements and willingness to spend, and use this understanding to guide new product development teams. The level of market research that is needed depends on the nature of the product and the homogeneity of the customer base. In some cases, the customers may all have very similar needs. For example, when UOP developed a renewable jet fuel based on hydrotreated vegetable oils, it was clear that the product must meet all the standard ASTM specifications for jet fuels. More often, however, the customers fall into different groups, known as market segments, each with different requirements. The product development team must consider the needs of each segment and determine whether a product can be designed to meet the needs of several segments or whether it is necessary to develop customized products for each segment. It is important to distinguish between proximate and ultimate customers when carrying out market research. Many chemical products are sold to other manufacturers (proximate customers) who then incorporate the chemical product into their own products to sell to end users (ultimate customers). Some product features may be very valuable to the proximate customer while having little value to the ultimate customer. Improving the processability, handling, storage, or safety properties of a product will make it easier and potentially cheaper to use, but may have little effect on its end use application. For example, a paint composition with a faster drying time may be very attractive to an automobile manufacturer, but will not be noticed by the customer who buys the car. Many methods have been developed for market research. Interviews and customer conferences can be used when the number of customers is small or when a representative sample group can be

CHAPTER 1 Introduction to Design

assembled. When the customer base is large and diverse, manufacturers use surveys and focus groups. The questions that are posed in market research studies must be carefully formulated so as to not only discover customer preferences, but also identify latent needs that are not met by the existing products. Ulrich and Eppinger (2008) suggest the following generic questions that can be used in interviews or focus groups: • • • • •

When and why do you use this product? What do you like about the existing products? What do you dislike about the existing products? What issues do you consider when purchasing the product? What improvements would you make to the product?

In addition to finding customer needs, good market research studies also determine the relative importance of different needs and the willingness of the customer to pay for certain features. As the new product undergoes development it may be necessary to repeat the market research to validate the product concept and test how well it meets customer expectations.

1.8.3 Developing Product Specifications The needs stated by customers in the marketing study are usually not expressed in terms of technical product specifications. The design team must translate these needs into measurable properties of the product and then set a target value or range for each property. Product specifications must reflect all of the following factors: • • • • • •

Product safety and regulatory requirements Potential liability concerns Fitness for purpose Customer needs and preferences Marketing advantages Maximization of profit margin

When setting specifications, it is important to remember that a specification should tell you what the product does, but not how it does it. For example, a customer need for a beverage such as a milk shake is to have the right “mouth feel.” One way to accomplish this might be by setting a specification on viscosity. The design team could then modify the recipe to meet the viscosity specification in many different ways. It would not be as effective to set a specification on xantham gum concentration, as this presupposes the use of a particular thickener and overconstrains the design of the product. Regulations and standards can be important sources of specifications. If a product is subject to regulation then all the regulated specifications must be met and new features can only be introduced if they do not require regulation or have obtained the necessary approval. Product safety, disposal, and environmental impact considerations can also lead to specifications that may not have been articulated by the customers. It is also important for the design team to consider potential product liability. The fact that a product is not currently regulated does not mean that it is safe, and if there are concerns about public health or safety then these should be raised and properly evaluated so that the company can assess the potential for future litigation.

1.8 Product Design

Quality Function Deployment A method that is widely used in translating customer needs into specifications is Quality Function Deployment or QFD (Hauser & Clausing, 1988). Several variations of the QFD method have been developed, but all are based on the concept of relating customer needs to product specifications and comparing the proposed product to the existing competitors. A QFD analysis is set out as a table or matrix, and is usually carried out using a spreadsheet. Examples of simple QFD tables are given in Figures 1.5 and 1.6. The first column lists the customer needs identified by the market research study. Each customer need is assigned a priority or importance, P, which is usually an integer on a 1 to 10 scale, based on the customer feedback. In some versions of the method a measure or metric is assigned to each customer need; however, this is not always necessary. The design team then lists all the product specifications that they envision and enters each specification as a column in the table. The team assigns a score, s, to how strongly each specification impacts each customer need. A typical scoring scale might be 3 = critical, 2 = strong, 1 = weak, and 0 = no impact. The scores are multiplied by the corresponding customer priority and summed to give an overall relative importance of each specification, which is entered at the bottom of each column: (1.1)

Relative importance of specification i = ∑ Pj sij

Specification 1

Specification 2

Specification 3

Specification 4

Specification 5

Specification 6

Competing product 1

Competing product 2

Competing product 3

Need 1

s11

s21

s31

s41

s51

s61

c11

c21

etc.

Need 2

s12

s22

s32

s42

s52

s62

c12

c22

Need 3

s13

s23

s33

s43

s53

s63

c13

c23

etc.

Relative importance

ΣPjSij

etc.

Pj = priority assigned to need j by customer sij = score for how well specification i meets need j cij = score for how well competing product i meets need j

FIGURE 1.5 QFD table.

Competing product 5

Customer needs

Priority

where Pj = customer priority assigned to need j sij = score for how well specification i meets need j

Competing product 4

Abrasive content

Fluoride content

Non-sugar sweetener

Flavor content

Viscosity modifier

Solid thickener

Antiseptic content

Bleach content

CHAPTER 1 Introduction to Design

Priority

Cleans teeth

Removes plaque

Whitens teeth

Tastes fresh

Freshens breath

Squeezes out right

Not gritty

Strengthens teeth

Prevents gingivitis

Customer needs

Relative Importance

FIGURE 1.6 Completed QFD for toothpaste.

In some cases, additional columns are added to the right of the table for the existing competing products, as shown in Figure 1.5. Each existing product can be assigned a score, c, for how well it meets each customer need, using the same scoring scale used for the specifications. These scores can also be multiplied by the corresponding customer priority and summed to give an indication of the relative strength of the existing products. The QFD exercise has several uses. It helps the design team identify which specifications correlate most strongly with each customer need, and hence focuses effort on the aspects of the product that customers value most. If none of the specifications has a high score against a particular need then it can highlight the need for new features or specifications. It can help identify strengths and weaknesses in competitor’s products and identify which specifications must be adjusted to give superior performance to the competition. Lastly, it can help identify specifications that have an impact on multiple customer needs and potentially lead to trade-offs between different customer desires. A simplified example of a QFD analysis is given in Example 1.5. More information on details of the method is given in the book by Ulrich and Eppinger (2008) and the article by Hauser and Clausing (1988). The QFD method has become very widely used as part of the Six Sigma methodology; see Pyzdek and Keller (2009) for more on Six Sigma.

1.8 Product Design

Example 1.5: QFD Analysis Complete a QFD analysis to determine the important specifications for a toothpaste product.

Solution

One possible solution is shown in Figure 1.6. A market survey (with a very limited set of customers) identified the following customer needs for toothpaste: cleans teeth, removes plaque, whitens teeth, tastes fresh, freshens breath, squeezes out right, not gritty, strengthens teeth, and prevents gingivitis. These are entered in the first column, with the relative priorities listed in the second column. Some possible product specifications are then listed as additional columns. These include: abrasive content, fluoride content, non-sugar sweetener, flavor content, viscosity modifier, solid thickener, antiseptic content, and bleach content. Note that these specifications do not specify the use of a particular bleach, sweetener, flavor, etc., so the designers might be able to meet several specifications using the same compound. The scores are then entered for each specification. For example, the abrasive content is critical for “cleans teeth” and “removes plaque” (score 3 in both cases), but has no effect on “whitens teeth,” “tastes fresh,” or “freshens breath” (score 0). The abrasive content can have a strong effect on how the paste squeezes (score 2) and can have a critical impact on “not gritty” (score 3). Note that in this last case, the impact is negative and the customer desire for a particular mouth feel in the product is somewhat at odds with improving product performance. The relative importance of the specification is then calculated as the priority weighted sum of the scores, using equation 1.1. Relative importance for abrasive content = 8ð3Þ + 9ð3Þ + 5ð2Þ + 6ð3Þ = 24 + 27 + 10 + 18 = 79 Scores are then assigned to how well every other specification meets each need until the table is completed. Reviewing the completed table, we can see that all of the specifications have a critical impact on at least one of the customer needs, and some have an impact on several needs. The abrasive content clearly has a strong impact on product performance and also on “not gritty,” so one conclusion of the QFD study might be to focus on examining different abrasive materials or different particle size distributions of abrasive so as to attempt to strike a better balance between these conflicting needs.

1.8.4 Fitness Testing As the design team develops potential product concepts they will need to test each concept to determine how well it meets the desired specifications. In the cases of new molecules and new materials, testing will usually consist of synthesizing the material and carrying out experiments to determine its properties. For new equipment and formulations, more extensive prototyping and customer validation of the benefits of the design may be needed.

Prototype Testing Engineers build prototypes to address several different aspects of new product development: •

If new features are introduced in the design then it may be necessary to build a prototype to test these features and make sure that they work properly and safely.

• • •

•

CHAPTER 1 Introduction to Design

When a product is assembled from many components, it may be necessary to build a prototype to ensure that all the components work together properly when integrated as a system. The assembly of a prototype helps the designers understand the manufacturing process for the final product and can highlight features of the design that will make manufacturing easy or difficult. Prototyping is thus an important step in design for manufacture. In the design of formulated products, the manufacturer will often want to evaluate whether a component can be substituted with a cheaper material that has similar properties. It may be necessary to prepare alternative versions of the formulation with each component so that they can be tested side-by-side for properties and customer acceptance. A prototype can be used as a communication device to demonstrate features of a design. It can therefore be used to validate design features with potential customers or with management and hence confirm the marketing advantages of the new design.

Prototypes can take many forms, depending on the product type and stage of development. In the early stages of product development conceptual or computer models are widely used. Working models of subcomponents are usually easier to test than full products; however, a full physical working model or exact recipe must usually be created for final product testing. Note that the activity of prototyping is not restricted to equipment and devices; testing different formulations of shampoo or cookie dough accomplishes the same goals. Before a prototype is built, the design team should have a clear idea of the purpose of the prototype and the testing or experiments for which it will be used. Engineers from the manufacturing plant should be engaged as part of the development team to ensure that manufacturability concerns are flushed out and addressed. Several iterations of prototyping may need to be planned before a final product design can be selected.

Safety and Efficacy Testing One of the most rigorous new product testing processes is the procedure used for obtaining approval from the U.S. Food and Drug Administration (FDA) for new medicines. The evaluation process is designed to ensure both the safety and efficacy of new drugs. If a company believes it has developed a new molecule with a therapeutic application then it must go through the following steps: • • • •

Preclinical trials: Initial testing on enzymes or cells in a laboratory, followed by animal tests usually on at least two species. Phase I Studies: Testing on a small number of healthy volunteers (often medical students!) Phase II Studies: Testing on patients who have the same disease or condition that is to be treated. Phase III Studies: Testing on a large number (hundreds or thousands) of patients who have randomly been assigned either the drug or a placebo.

The results of the clinical trials are reviewed by an independent FDA panel to determine if the benefits of treatment outweigh the risks posed by any observed side effects. The entire process typically takes over eight years and can cost more than $800 million (DiMasi, Hansen, & Grabowski, 2003; FDA, 2006). Even when the product is approved, the manufacturer must still submit to FDA inspections to ensure that quality control procedures are adequate and the production facility complies with FDA current good manufacturing practices (cGMP). Additional information on GMP requirements is given in the discussion of bioreactor quality control in Section 15.9.8.

Problems

References Cooper, R. G. (2001). Winning at new products: Accelerating the process from idea to launch (3rd ed.). Basic Books. Cooper, R. G., & Edgett, S. J. (2009). Lean, rapid and profitable new product development. BookSurge Publishing. Cussler, E. L., & Moggridge, G. D. (2001). Chemical product design. Cambridge University Press. DiMasi, J. A., Hansen, R. W., & Grabowski, H. G. (2003). The price of innovation: New estimates of drug development costs. J. Health Econ., 22(2), 151. FDA. (2006). From test tube to patient: Protecting America’s health through human drugs (4th ed.). FDA Publ. 06-1524G. Hauser, J. R., & Clausing, D. (1988). The house of quality. Harvard Bus. Rev., 66(3), 63. Pyzdek, T., & Keller, P. (2009). The six sigma handbook (3rd ed.). McGraw-Hill. Seider, W. D., Seader, J. D., Lewin, D. R., & Widagdo, S. (2009). Product and process design principles (3rd ed.). Wiley. Ulrich, K. T., & Eppinger, S. D. (2008). Product design and development (4th ed.). McGraw-Hill.

NOMENCLATURE Dimensions in $MLTθ cij Pj sij

Score for how well competing product i meets customer need j Priority assigned by customer to need j Score for how well specification i meets customer need j

— — —

PROBLEMS 1.1. Develop project plans for the design and construction of the following processes. Use Figure 1.2 as a guide to the activities that must occur. Estimate the overall time required from launching the project to the start of operation. a. A petrochemical process using established technology, to be built on an existing site. b. A process for full scale manufacture of a new drug, based on a process currently undergoing pilot plant trials. c. A novel process for converting cellulose waste to fuel products. d. A spent nuclear fuel reprocessing facility. e. A solvent recovery system for an electronics production facility. 1.2. You are the project manager of a team that has been asked to complete the design of a chemical plant up to the stage of design selection. You have three engineers available (plus yourself) and the work must be completed in ten weeks. Develop a project plan and schedule of

CHAPTER 1 Introduction to Design

tasks for each engineer. Be sure to allow sufficient time for equipment sizing, costing, and optimization. What intermediate deliverables would you specify to ensure that the project stays on track? 1.3. You are part of a product design team that has been asked to develop a low-calorie chocolate chip cookie dough. a. Poll your classmates to determine customer requirements. b. Carry out a QFD analysis to map the customer requirements into product specifications.

CHAPTER

Process Flowsheet Development

KEY LEARNING OBJECTIVES • How to read and draw a process flow diagram (PFD) • When to design a batch process or a continuous process • Factors to consider when adopting or improving commercially-proven technology • How to develop a flowsheet for a revamp design • How to synthesize a flowsheet for an entirely new process • How to review a flowsheet and check for completeness and errors

2.1 INTRODUCTION This chapter covers the preparation and presentation of the process flowsheet, also known as the process flow diagram (PFD). The flowsheet is the key document in process design. It shows the arrangement of the equipment selected to carry out the process; the stream connections; stream flow rates and compositions; and the operating conditions. It is a diagrammatic model of the process. Chemical engineers in industry are usually very proficient at reading process flow diagrams and use the PFD as the primary means of transmitting and recording process information. The flowsheet is used by specialist design groups as the basis for their designs. These include piping, instrumentation, and equipment design and plant layout. It is also used by operating personnel for the preparation of operating manuals and operator training. During plant start-up and subsequent operation, the flowsheet forms a basis for comparison of operating performance with design. If the plant is later revamped to new specifications, the PFD of the original plant is the starting point for the revamp design. Several types of process flow diagrams are used by chemical engineers, depending on the level of detail required. A simple block flow diagram can be used to give a rough idea of the overall process flow structure, and may be useful when giving a presentation. A full PFD should include all of the process vessels and equipment and show all the process and utility flow lines. A full heat and material balance of the process showing the composition, flow rate, and temperature of every stream is usually included in or with a PFD. The PFD also indicates the location of every control valve, as control valves play an important role in determining the pressure balance of the process and hence in sizing of pumps and compressors. A piping and instrumentation diagram (P&ID) is a more detailed version of the PFD that also includes information on ancillary instruments and valves, Chemical Engineering Design, Second Edition. DOI: 10.1016/B978-0-08-096659-5.00002-X © 2013 Elsevier Ltd. All rights reserved.

CHAPTER 2 Process Flowsheet Development

sampling and drain lines, start-up and shutdown systems, and pipe sizes and metallurgy. The P&ID is used in detailed design and safety analysis. This chapter presents an overview of how to read and draw flowsheets and discusses how the unit operations of a process are selected to form the basic process flow structure. Chapter 3 discusses energy flows within a process and describes heat and power recovery methods that are used to make processes more energy-efficient. Chapter 4 covers the use of commercial process simulation tools to generate the heat and material balances for the flowsheet, and Chapter 5 introduces the elements of process control that must be understood to fill in the control systems on the PFD.

2.2 FLOWSHEET PRESENTATION As the process flowsheet is the definitive document on the process, the presentation must be clear, comprehensive, accurate, and complete. This section describes how to read and draw process flow diagrams.

2.2.1 Block Diagrams A block diagram is the simplest form of flow diagram. Each block can represent a single piece of equipment or a complete stage in the process. Block diagrams are useful for showing simple processes. For complex processes, their use is limited to showing the overall process, broken down into its principal stages. Block diagrams are useful for representing a process in a simplified form in reports, textbooks and presentations, but have limited use as engineering documents. The stream flow rates and compositions can be shown on the diagram adjacent to the stream lines, when only a small amount of information is to be shown, or tabulated separately. Figure 2.1 shows a block flow diagram of a steam reforming process for making hydrogen from methane. The methane feed enters on the left and is mixed with steam and preheated in the

Furnace reactor

Cooler

Shift reactor

Cooler Compressor

CO2 removal

PSA unit PSA

Steam Methane

FIGURE 2.1 Block flow diagram of steam reforming process for hydrogen.

CO2

Hydrogen

2.2 Flowsheet Presentation

convective section of a fired heater. The steam-methane mixture then passes through the reactor tubes in the radiant section of the heater where the steam reforming reaction takes place: CH4 + H2 O ↔ CO + 3H2 The products from the steam reformer are sent to a shift reactor. The shift reactor increases the amount of hydrogen in the product by allowing the water-gas-shift reaction to re-equilibrate at a lower temperature: CO + H2 O ↔ CO2 + H2 The shift reactor products are then further cooled and scrubbed in an absorber to remove carbon dioxide, before being sent to a pressure-swing adsorption process that separates hydrogen from carbon dioxide, unconverted methane, and water vapor. Block diagrams are often drawn using simple graphics programs such as Microsoft Visio™ or PowerPoint™.

2.2.2 PFD Symbols On the detailed flowsheets used for design and operation, the equipment is normally drawn in a stylized pictorial form. For tender documents or company brochures, actual scale drawings of the equipment are sometimes used, but it is more usual to use a simplified representation. There are several international standards for PFD symbols, but most companies use their own standard symbols, as the cost of converting all of their existing drawings would be excessive. ISO 10628 is the international standard for PFD drawing symbols. Most European countries have adopted ISO 10628 as their standard, but very few North American companies apply this standard and there is currently no U.S. standard for PFD symbols. The symbols given in British Standard, BS 1553 (1977) “Specification for graphical symbols for general engineering. Part 1: Piping systems and plant” are more typical of those in common use. The professional edition of Microsoft Visio™ contains a library of PFD icons that includes the ISO 10628 symbols as well as symbols commonly used in the United States and Canada. Examples of standard symbols are given in Appendix A, which is available in the online material at booksite.Elsevier.com/Towler. Figure 2.2 shows symbols that are used for reactors, mixers, vessels, and tanks. Figure 2.3 shows symbols used for heat transfer equipment. Figure 2.4 provides symbols for fluid-handling equipment and Figure 2.5 gives symbols for solids-handling operations. Some general symbols that are used in combination with other symbols are shown in Figure 2.6. The symbols that are used for process instruments, valves, and controllers are given in the section on P&ID diagram symbols in Chapter 5. The operation and design of the different types of equipment illustrated in these figures are described in Part II of this book. Note that some types of equipment have generic symbols as well as symbols that describe a particular equipment type. If the wrong symbol is selected, this can cause confusion for other engineers who read the flowsheet. For example, Figure 2.2(i) shows an in-line mixer, which would be used downstream of a T-junction to ensure rapid mixing of two liquid streams. Figure 2.5(f ) shows a solids mixer or blender that would be used to mix solids into a liquid. Figure 2.6(c) is the symbol for a propeller agitator that might be used in a mixing tank. All of these symbols could be referred to as a “mixer”, but the designer’s intention is obviously different in each case.

CHAPTER 2 Process Flowsheet Development

(a) Drum or vertical vessel

(b) Horizontal vessel

(f) Tubular reactor

(g) Serpentine tubular reactor or coil

(k) Open tank

(l) Covered tank

(d) Trayed columns

(e) Autoclave, stirred tank reactor

(i) In-line mixer

(j) Sparger

(n) Fixed-roof tank

(o) Liquefied gas storage sphere

(h) Three phase decanter

(m) Floating-roof tank

FIGURE 2.2 PFD symbols for reactors, vessels, mixers, and tanks.

(a) Heat exchangers (basic symbols)

(b) Fired heater with process duty in radiant section

(f) Tube bundle or stab-in reboiler

(g) Kettle reboiler

(k) Plate heat exchanger

(l) Electric heater

(h) Finned tube exchanger

(d) Shell and tube exchangers

(e) Air coolers

(i) U-tube exchanger

(j) Heating or cooling coil

(m) Cooling tower

FIGURE 2.3 PFD symbols for heat transfer equipment.

2.2.3 Presentation of Stream Flow Rates The data on the flow rate of each individual component, on the total stream flow rate, and the percentage composition, can be shown on the flowsheet in various ways. The simplest method, suitable for simple processes with few pieces of equipment, is to tabulate the data in blocks alongside the

2.2 Flowsheet Presentation

(a) Centrifugal pumps

(b) Reciprocating pumps or compressors

(e) Axial or centrifugal compressor

(f) Turbine

(d) Gear pump

(g) Ejector

FIGURE 2.4 PFD symbols for fluid-handling equipment.

(a) Storage bin or hopper

(f) Solids mixer, slurrying tank

(b) Belt conveyor

(g) Kneader, extruder

(h) Ribbon blender

(d) Elevator

(e) Cyclone

(i) Crusher M

(k) Ball mill

(p) Prill tower or spray dryer

(l) Filter (basic symbol)

(q) Belt dryer (conveyor dryer)

(m) Drum filter

(r) Tray dryer

(n) Centrifuge

(s) Rotary dryer

(j) Hammer mill M

(o) Disc-bowl centrifuge

(t) Granulator or rotary agglomerator

FIGURE 2.5 PFD symbols for solids-handling equipment.

process stream lines, as shown in Figure 2.7. Only a limited amount of information can be shown this way, and it is difficult to make neat alterations or to add additional data. A better method for the presentation of data on flowsheets is shown in Figures 2.8 and 2.9. In this method each stream line is numbered and the data are tabulated at the bottom of the sheet. Alterations and additions can be easily made. This is the method generally used by professional

CHAPTER 2 Process Flowsheet Development

(a) Motor

(b) Fan

(e) Vent

(f) Drain

(d) Spray device

(g) Flanged joint

FIGURE 2.6 General PFD symbols used with other symbols. AN 500 Water 2500 Total 3000

H1 Water 5000 Total 5000

15°C

60°C

DM water Steam From storages

15°C

40°C

60°C

To dryer

CW 60°C R1

Cat. 5 Water 100 Total 105 From catalyst prep

AN Water Polymer Salts Total

50 2600 450 5 3105

Water AN Polymer Salts Total

7300 45 2 5 7352

AN Water Polymer Salts Total

5 300 448 trace 753

Equipment key R1 Polymer reactor H1 Water heater F1 Vacuum filter

FIGURE 2.7 Flowsheet: polymer production.

design offices. A typical commercial flowsheet is shown in Figure 2.10. Guide rules for the layout of this type of flowsheet presentation are given in Section 2.2.5.

2.2.4 Information to be Included The amount of information shown on a flowsheet will depend on the custom and practice of the particular design office. The list given below has therefore been divided into essential items and optional items. The essential items must always be shown; the optional items add to the usefulness of the flowsheet but are not always included.

Tail gas To sheet no 9317 1 10

Water 11

2 Air Filter

8 Absorber

Compressor 2A 1A 1 Ammonia 14 From sheet no 9315 Vaporiser

Steam 5

Cooler 9

6 4

Filter W. H. B.

Reactor (Oxidiser)

12 Mixer

7 Condenser

13 Product Flows kg/h pressures nominal 1 Ammonia feed

1A Ammonia vapor

NH3 O2 N2 NO NO2 HNO3 H2O

731.0

Total

731.0

8 15

8 20

Press bar Temp. °C

2 Filtered air

2A Oxidiser air

3 Oxidiser feed

4 Oxidiser outlet

3036.9 9990.8

2628.2 8644.7

731.0 2628.2 8644.7

Nil 935.7 (935.7)(1) 8668.8 8668.8 1238.4 (1238.4)(1) Trace (?)(1) Nil Nil 1161.0 1161.0

Trace

5 W.H.B. outlet

13,027.7 11,272.9 12,003.9 12,003.9 12,003.9 1 15

8 230

FIGURE 2.8 Flowsheet: simplified nitric acid process.

8 204

8 907

8 234

6 Condenser gas

7 Condenser acid

8 Secondary air

275.2 8668.8 202.5 967.2

Trace Trace

408.7 1346.1

683.9 371.5 10,014.7 10,014.7 202.5 21.9 967.2 (Trace)(1)

29.4

850.6 1010.1

10,143.1

1860.7

1754.8

8 40

1 40

8 40

9 Absorber feed

10 Tail(2) gas

11 12 13 Water Absorber Product feed acid acid

1376.9

Trace Trace Trace Trace 1704.0 1136.0

Trace Trace Trace Trace 2554.6 2146.0

11,897.7 10,434.4 1376.9

2840.0

4700.6

1 40

1 43

29.4

8 40

26.3

1 25

8 25

C & R Construction Inc

Nitric acid 60 percent 100,000 t/y Client BOP chemicals SLIGO Sheet no. 9316

Dwg by Date Checked 25/7/1980

2.2 Flowsheet Presentation

Line no. Stream component

CHAPTER 2 Process Flowsheet Development

FIGURE 2.9

Alternative presentation.

2.2 Flowsheet Presentation

FIGURE 2.10 A typical flowsheet.

CHAPTER 2 Process Flowsheet Development

Essential Information 1. Always show all process equipment, including feed and product storage and equipment used for transporting fluids and solids. 2. Always indicate the location of process control valves. 3. Stream composition, either i. tabulate the flow rate of each individual component, kg/h, which is preferred, or ii. give the stream composition as a weight fraction. 4. Total stream flow rate, kg/h. 5. Stream temperature, degrees Celsius preferred. 6. Nominal operating pressure (the required operating pressure). 7. Stream enthalpy, kJ/h.

Optional Information 1. Molar percentage composition and/or molar flow rates. 2. Physical property data, mean values for the stream, such as i. density, kg/m3, ii. viscosity, mN s/m2. 3. Stream name, a brief, one- or two-word description of the nature of the stream, for example “ACETONE COLUMN BOTTOMS,”

2.2.5 Layout The sequence of the main equipment items shown symbolically on the flowsheet follows that of the proposed plant layout. Some license must be exercised in the placing of ancillary items, such as heat exchangers and pumps, or the layout will be too congested. The aim should be to show the flow of material from stage to stage as it will occur, and to give a general impression of the layout of the actual process plant. The equipment should be drawn approximately to scale. Again, some license is allowed for the sake of clarity, but the principal equipment items such as reactors, vessels, and columns should be drawn roughly in the correct proportion. Ancillary items can be drawn out of proportion. For a complex process, with many process units, several sheets may be needed, and the continuation of the process streams from one sheet to another must be clearly shown. One method of indicating a line continuation is shown in Figure 2.8; those lines that are continued over to another drawing are indicated by a double concentric circle around the line number and the continuation sheet number is written below. An alternative method is to extend lines to the side of the page and then indicate the drawing sheet on which the line is continued. The equipment should be well spaced out so that streams can be labeled without the drawing becoming cluttered. It is better to use several continuation sheets than to try to fit everything on one page. The table of stream flows and other data can be placed above or below the equipment layout. Normal practice is to place it below. The components should be listed down the left-hand side of the table, as in Figures 2.8 and 2.9. For a long table, it is good practice to repeat the list at the right-hand side, so the components can be traced across from either side.

2.2 Flowsheet Presentation

The stream line numbers should follow consecutively from left to right of the layout, as far as is practicable, so that when reading the flowsheet it is easy to locate a particular line and the associated column containing the data. All the process stream lines shown on the flowsheet should be numbered and the data for the stream given. On a large flowsheet, the designers sometimes use different series of numbers for different plant sections; for example beginning the stream numbering at 100 for feed preparation, 200 for reaction, 300 for separation, and 400 for purification. This can be helpful in quickly tracing a stream to a section of the plant. There is always a temptation to leave out the data on a process stream if it is clearly just formed by the addition of two other streams, as at a junction, or if the composition is unchanged when flowing through a process unit, such as a heat exchanger; this temptation should be avoided. What may be clear to the process designer is not necessarily clear to the others who will use the flowsheet. Complete, unambiguous information on all streams should be given, even if this involves some repetition. The purpose of the flowsheet is to show the function of each process unit, even when the function has no discernible impact on the mass and energy balance.

2.2.6 Precision of Data The total stream and individual component flows do not normally need to be shown to a high precision on the process flowsheet; three or four significant figures are all that is usually justified by the accuracy of the flowsheet calculations, and will typically be sufficient. The flows should, however, balance to within the precision shown. If a stream or component flow is so small that it is less than the precision used for the larger flows, it can be shown to a greater number of places, if its accuracy justifies this and the information is required. If the composition of a component is very low, but is specified as a process constraint, as, say, for an effluent stream or product quality specification, it can be shown in parts per million, ppm. Imprecise small flows are best shown as “TRACE”. A trace quantity should not be shown as zero, or the space in the tabulation left blank, unless the process designer is sure that it has no significance. The process designer should be aware that if the space in the data table is left blank opposite a particular component, the quantity may be assumed to be zero by the specialist design groups who take their information from the flowsheet. Trace quantities can be important. Only a trace of an impurity is needed to poison a catalyst, and trace quantities can determine the selection of the materials of construction; see Chapter 6.

2.2.7 Basis of the Calculation It is good practice to show on the flowsheet the basis used for the flowsheet calculations. This includes the operating hours per year, the reaction and physical yields, and the datum temperature used for energy balances. It is also helpful to include a list of the principal assumptions used in the calculations. This alerts the user to any limitations that may have to be placed on the flowsheet information. If the amount of information that needs to be presented is excessive, it can be summarized in a separate document that is referenced on the flowsheet. In some cases, mass and energy balances are prepared for multiple scenarios. These might include winter and summer operating conditions, start of catalyst life and end of catalyst life, manufacture of different products or product grades, etc. Usually these different scenarios are shown as several tables on the same flowsheet, but occasionally different flowsheets are drawn for each case.

CHAPTER 2 Process Flowsheet Development

2.2.8 Batch Processes Flowsheets drawn up for batch processes normally show the quantities required to produce one batch. If a batch process forms part of an otherwise continuous process, it can be shown on the same flowsheet, providing a clear break is made when tabulating the data between the continuous and batch sections; i.e., the change from kg/h to kg/batch. A continuous process may include batch makeup of minor reagents, such as the catalyst for a polymerization process. Batch flows into a continuous process are usually labeled “Normally no flow” and show the flow rates that will be obtained when the stream is flowing. It is these instantaneous flow rates that govern the equipment design, rather than the much lower time-averaged flow rates.

2.2.9 Utilities To avoid cluttering up the flowsheet, it is not normal practice to show the utility (service) headers and lines on the process flowsheet. The utility connections required on each piece of equipment should be shown and labeled, for example, “CTW” for cooling tower water. The utility requirements for each piece of equipment should be tabulated on the flowsheet. Utility systems are described in more detail in Chapter 3.

2.2.10 Equipment Identification Each piece of equipment shown on the flowsheet must be identified with a code number and name. The identification number (usually a letter and some digits) is normally that assigned to a particular piece of equipment as part of the general project control procedures, and is used to identify it in all the project documents. If the flowsheet is not part of the documentation for a project, then a simple, but consistent, identification code should be devised. The easiest code is to use an initial letter to identify the type of equipment, followed by digits to identify the particular piece: for example, H—heat exchangers, C—columns, and R—reactors. Most companies have a standard convention that should be followed, but if there is no agreed standard then the key to the code should be shown on the flowsheet.

2.2.11 Flowsheet Drafting Programs Most design offices use drafting software for the preparation of flowsheets and other process drawings. With drafting software, standard symbols representing the process equipment, instruments, and control systems are held in files, and these symbols are called up as required when drawing flowsheets and piping and instrumentation diagrams. Final flowsheet drawings are usually produced by professional drafters, who are experienced with the drafting software and conventions, rather than by the design engineer. The design engineer has to provide the required numbers, sketch the flowsheet, and review the final result. Although most process simulation programs feature a graphical user interface (GUI) that creates a drawing that resembles a PFD, printouts of these drawings should not be used as actual process flow diagrams. The unit operations shown in the process simulation usually do not exactly match the unit operations of the process. The simulation may include dummy items that do not physically exist and may omit some equipment that is needed in the plant but is not part of the simulation.

2.3 The Anatomy of a Chemical Manufacturing Process

2.3 THE ANATOMY OF A CHEMICAL MANUFACTURING PROCESS This section describes the basic components of chemical processes and discusses how designers select between batch and continuous processes. The effects of reactor yield and selectivity on flowsheet structure are examined and used to illustrate how flowsheets become complex when there are multiple feeds and products.

2.3.1 Components of a Chemical Process The basic components of a typical chemical process are shown in Figure 2.11, in which each block represents a stage in the overall process for producing a product from the raw materials. Figure 2.11 represents a generalized process; not all the stages will be needed for any particular process and the complexity of each stage will depend on the nature of the process. Chemical engineering design is concerned with the selection and arrangement of the stages and the selection, specification, and design of the equipment required to perform the function of each stage.

Stage 1. Raw Material Storage Unless the raw materials (also called feed stocks or feeds) are supplied as intermediate products (intermediates) from a neighboring plant, some provision will have to be made to hold several days’, or weeks’, storage to smooth out fluctuations and interruptions in supply. Even when the materials come from an adjacent plant some provision is usually made to hold a few hours’, or even days’, inventory to decouple the processes. The storage required depends on the nature of the raw materials, the method of delivery, and what assurance can be placed on the continuity of supply. If materials are delivered by ship (tanker or bulk carrier) several weeks’ stocks may be necessary; whereas if they are received by road or rail, in smaller lots, less storage will be needed.

Stage 2. Feed Preparation Some purification and preparation of the raw materials will usually be necessary before they are sufficiently pure, or in the right form, to be fed to the reaction stage. For example, acetylene generated by the carbide process contains arsenic and sulfur compounds, and other impurities, which must be removed by scrubbing with concentrated sulfuric acid (or other processes) before it is sufficiently pure for reaction with hydrochloric acid to produce dichloroethane. Feed contaminants that can poison process catalysts, enzymes, or microorganisms must be removed. Liquid feeds need to Recycle of unreacted material

By-products Wastes

Raw material storage

Feed preparation

Reaction

Product separation

Product purification

Product storage

Stage 1

Stage 2

Stage 3

Stage 4

Stage 5

Stage 6

FIGURE 2.11 Anatomy of a chemical process.

Sales

CHAPTER 2 Process Flowsheet Development

be vaporized before being fed to gas-phase reactors and solids may need crushing, grinding, and screening. Solid feeds may also need to be weighed and mixed into slurries or solutions so that they can be brought to process pressure and easily mixed with other components. The feed preparation stage always includes means for getting the feeds out of storage and into the process. Liquids are usually pumped out of storage through control valves that regulate the feed flow rate. Gases and vapors may need compression if the storage is not pressurized. Solids are conveyed from storage using a variety of equipment, described in Chapter 18. Biological processes require very careful feed preparation. The growth media and any other fluids that are fed to the cell culture must be sterile to prevent unwanted organisms from entering the process. Sterilization is usually accomplished by heating the feed to a high temperature and keeping it hot for long enough to kill unwanted organisms, then cooling the feed to the desired temperature for the reactor. The preparation of biological reactor feeds is discussed in more detail in Section 15.9.

Stage 3. Reaction The reaction stage is the heart of a chemical manufacturing process. In the reactor the raw materials are brought together under conditions that promote the production of the desired product; almost invariably, some byproducts will also be formed, either through the reaction stoichiometry, by side-reactions, or from reactions of impurities present in the feed. Reactor design is discussed in Chapter 15.

Stage 4. Product Separation After the reactor(s) the products and byproducts are separated from any unreacted material. If in sufficient quantity, the unreacted material will be recycled to the reaction stage or to the feed purification and preparation stage. The byproducts may also be separated from the products at this stage, and may undergo further processing for recovery or sale. In most chemical processes there are multiple reaction steps, each followed by one or more separation steps.

Stage 5. Purification Before sale, the main product will often need purification to meet the product specifications. If produced in economic quantities, the byproducts may also be purified for sale. For byproducts, there will always be an economic trade-off between purifying the byproduct for sale or disposing of it as recycle or waste.

Stage 6. Product Storage Some inventory of finished product must be held to match production with sales. Provision for product packaging and transport is also needed, depending on the nature of the product. Liquids are normally dispatched in drums and in bulk tankers (road, rail, and sea), solids in sacks, cartons, or bales. The amount of stock that is held will depend on the nature of the product and the market.

Ancillary Processes In addition to the main process stages shown in Figure 2.11, provision must be made for the supply of the utilities needed, such as process water, cooling water, compressed air, and steam. The design of utility systems is discussed in Chapter 3.

2.3 The Anatomy of a Chemical Manufacturing Process

2.3.2 Continuous and Batch Processes Continuous processes are designed to operate 24 hours a day, 7 days a week, throughout the year. Some down time will be allowed for maintenance and, in some processes, for catalyst regeneration. The plant attainment or operating rate is the percentage of the available hours in a year that the plant operates, and is usually between 90 and 95%. Attainment % =

hours operated × 100 8760

(2.1)

A typical design basis would assume 8000 operating hours per year. Batch processes are designed to operate intermittently, with some, or all, of the process units being frequently shut down and started up. It is quite common for batch plants to use a combination of batch and continuous operations. For example, a batch reactor may be used to feed a continuous distillation column. Continuous processes will usually be more economical for large scale production. Batch processes are used when some flexibility is wanted in production rate or product specifications. The advantages of batch processing are: • • • • • •

Batch processing allows production of multiple different products or different product grades in the same equipment. In a batch plant, the integrity of a batch is preserved as it moves from operation to operation. This can be very useful for quality control purposes. The production rate of batch plants is very flexible, as there are no turndown issues when operating at low output. Batch plants are easier to clean and maintain in sterile operation. Batch processes are easier to scale up from chemist’s recipes. Batch plants have low capital for small production volumes. The same piece of equipment can often be used for several unit operations.

The drawbacks of batch processing are: • • • • • •

The scale of production is limited. It is difficult to achieve economies of scale by going to high production rates. Batch-to-batch quality can vary, leading to high production of waste products or off-spec product. Recycle and heat recovery are harder, making batch plants less energy efficient and more likely to produce waste byproducts. Asset utilization is lower for batch plants as the plant almost inevitably is idle part of the time. Batch plants are more labor-intensive and so the fixed costs of production are much higher for batch plants on a $/unit mass of product basis.

Choice of Continuous versus Batch Production Given the higher fixed costs and lower plant utilization of batch processes, batch processing usually only makes sense for products that have high value and are produced in small quantities. Batch plants are commonly used for: • •

Food products Pharmaceutical products such as drugs, vaccines, and hormones

• • •

CHAPTER 2 Process Flowsheet Development

Personal care products Blended products with multiple grades, such as paints, detergents, etc. Specialty chemicals

Even in these sectors, continuous production is favored if the process is well understood, the production volume is large, and the market is competitive.

2.3.3 Effect of Reactor Conversion and Yield on Flowsheet Structure It is important to distinguish between conversion and yield. Conversion is related to reactants; yield to products.

Conversion Conversion is a measure of the fraction of the reagent that reacts. To optimize reactor design and minimize byproduct formation, the conversion of a particular reagent is often less than 100%. If more than one reactant is used, the reagent on which the conversion is based must be specified. Conversion is defined by the following expression: amount of reagent consumed amount supplied ðamount in feed streamÞ − ðamount in product streamÞ = ðamount in feed streamÞ

Conversion =

(2.2)

This definition gives the total conversion of the particular reagent to all products. Example 2.1 In the manufacture of vinyl chloride (VC) by the pyrolysis of dichloroethane (DCE), the reactor conversion is limited to 55% to reduce carbon formation, which fouls the reactor tubes. Calculate the quantity of DCE fed to the reactor to produce 5000 kg/h VC.

Solution

Basis: 5000 kg/h VC (the required quantity). Reaction: C2 H4 Cl2 → C2 H3 Cl + HCl Molar weights: DCE 99, VC 62.5 kmol=h VC produced = 5000 = 80 62:5 From the stoichiometric equation, 1 kmol DCE produces 1 kmol VC. Let X be DCE feed in kmol/h: Percent conversion = 55 = 80 × 100 X X = 80 = 145:5 kmol=h 0:55 In this example, the small loss of DCE to carbon and other products has been neglected. All the DCE reacted has been assumed to be converted to VC.

2.3 The Anatomy of a Chemical Manufacturing Process

Selectivity Selectivity is a measure of the efficiency of the reactor in converting reagent to the desired product. It is the fraction of the reacted material that was converted into the desired product. If no byproducts are formed, then the selectivity is 100%. If side reactions occur and byproducts are formed, then the selectivity decreases. Selectivity is always expressed as the selectivity of feed A for product B, and is defined by the equation Selectivity =

moles of B formed moles of B that could have been formed if all A reacted to give B

moles of B formed = moles of A consumed × stoichiometric factor

(2.3)

Stoichiometric factor = moles of B produced per mole of A reacted in the reaction stoichiometric equation Selectivity is usually improved by operating the reactor at low conversion. At high conversion, the reactor has low concentrations of at least one reagent and high concentrations of products, so reactions that form byproducts are more likely to occur. Reagents that are not converted in the reactor can be recovered and recycled. Reagents that become converted to byproducts usually cannot be recovered and the byproducts must be purified for sale or else disposed as waste (see Section 8.2.3). The optimum reactor conditions thus usually favor low reactor conversion to give high selectivity for the desired products when all of these costs are taken into account.

Yield Yield is a measure of the performance of a reactor or plant. Several different definitions of yield are used, and it is important to state clearly the basis of any yield numbers. This is often not done when yields are quoted in the literature, and judgment must be used to decide what was intended. The yield of product B from feed A is defined by Yield =

moles of B formed moles of A supplied × stoichiometric factor

(2.4)

For a reactor, the yield is the product of conversion and selectivity: Reaction yield = Conversion × Selectivity =

moles A consumed moles B formed × moles A supplied moles A consumed × stoichiometric factor

(2.5)

With industrial reactors, it is necessary to distinguish between “reaction yield” (chemical yield), which includes only chemical losses to side products, and the overall “reactor yield”, which also includes physical losses, such as losses by evaporation into vent gas. If the conversion is near 100% it may not be worth separating and recycling the unreacted material; the overall process yield would then include the loss of unreacted material. If the unreacted material is separated and recycled, the overall process yield taken over the reactor and separation step would include any physical losses from the separation step.

CHAPTER 2 Process Flowsheet Development

Plant yield is a measure of the overall performance of the plant and includes all chemical and physical losses. Plant yield (applied to the complete plant or any stage) =

moles of product produced moles of reagent supplied to the process × stoichiometric factor

(2.6)

Where more than one reagent is used, or product produced, it is essential that the product and reagent to which the yield refers is clearly stated. The plant yield of B from A is the product of the reactor selectivity of feed A for product B and the separation efficiency (recovery) of each separation step that handles product B or reagent A. As a useful check, the plant yield should be greater than the reactor yield if a separation and feed recycle scheme has been implemented. If the feed recovery and recycle system were 100% efficient, the plant yield would approach the reactor selectivity. Example 2.2 In the production of ethanol by the hydrolysis of ethylene, diethyl ether is produced as a byproduct. A typical feed stream composition is 55% ethylene, 5% inerts, and 40% water. A typical product stream is 52.26% ethylene, 5.49% ethanol, 0.16% ether, 36.81% water, and 5.28% inerts. Calculate the selectivity of ethylene for ethanol and for ether.

Solution Reactions: C2 H4 + H2 O → C2 H5 OH 2C2 H5 OH → ðC2 H5 Þ2 O + H2 O Basis: 100 moles feed (easier calculation than using the product stream) Note: the flow of inerts will be constant as they do not react, and it can thus be used to calculate the other flows from the compositions. Feed stream ethylene

55 mol

inerts

5 mol

water

40 mol

Product stream ethylene = 52:26 × 5 = 49:49 mol 5:28 5:49 × 5 = 5:20 mol ethanol = 5:28 ether = 0:16 × 5 = 0:15 mol 5:28 Amount of ethylene reacted = 55:0 – 49:49 = 5:51 mol Selectivity of ethylene for ethanol =

5:20 × 100 = 94:4% 5:51 × 1:0

2.3 The Anatomy of a Chemical Manufacturing Process

As 1 mol of ethanol is produced per mol of ethylene the stoichiometric factor is 1. Selectivity of ethylene for ether =

0:15 × 100 = 5:44% 5:51 × 0:5

The stoichiometric factor is 0.5, as 2 mol of ethylene produce 1 mol of ether. Note that the conversion of ethylene, to all products, is given by Conversion = mols fed − mols out ¼ 55 − 49:49 × 100 mols fed 55 = 10 % The selectivity based on water could also be calculated but is of no real interest as water is relatively inexpensive compared with ethylene. Water is clearly fed to the reactor in considerable excess. The yield of ethanol based on ethylene is: Reaction yield =

5:20 × 100 = 9:45% 55 × 1:0

Example 2.3 In the chlorination of ethylene to produce dichloroethane (DCE), the conversion of ethylene is reported as 99.0%. If 94 mol of DCE are produced per 100 mol of ethylene reacted, calculate the selectivity and the overall yield based on ethylene. The unreacted ethylene is not recovered.

Solution Reaction: C2 H4 + Cl2 ! C2 H4 Cl2 The stoichiometric factor is 1. Selectivity =

moles DCE produced × 100 moles ethylene reacted × 1

= 94 × 100 = 94% 100 moles DCE produced × 100 Overall yield ðincluding physical lossesÞ = moles ethylene fed × 1 99 moles of ethylene are reacted for 100 moles fed, so Overall yield = 94 × 99 = 93:1% 100 100 Note that we get the same answer by multiplying the selectivity (0.94) and conversion (0.99). The principal byproduct of this process is trichloroethane.

CHAPTER 2 Process Flowsheet Development

Effect of Conversion, Selectivity, and Yield on Flowsheet Structure Very few processes produce the desired product in stoichiometric yield with no byproducts and no equilibrium limitations. If the desired reaction is limited by equilibrium between the feeds and products, the reaction will not proceed to 100% conversion in the reactor and it will be necessary to separate the product from unreacted feed components. It will usually be economically attractive to recover the unconverted feeds either to the reactor section or to the feed preparation section of the plant. In most chemical processes the designer must also address the formation of byproducts through unwanted reactions, in which case the selectivity of the feed for the desired product is less than 100%. The presence of nonselective reactions can have a number of undesirable effects on process economics. The most important impact of byproduct formation is that byproducts represent a loss of potential product. Since feedstock costs are usually the main component of the overall cost of production, low selectivity can have a strong negative impact on process economics. The byproducts must be separated from the desired product, causing additional complexity and cost in the separation section. If the byproducts have value, they can be purified and sold, but this adds additional equipment to the process. If the byproducts are not worth recovering then in some cases they can be recycled within the process and converted back to feed or products. These recycles also add cost and complexity to the process. If the byproducts cannot be sold or recycled, they must be disposed of as waste streams. Additional processing steps may be needed to bring the waste stream to a safe condition for discharge or disposal. Because of the high costs of dealing with byproducts, most processes are operated under conditions that maximize reactor selectivity. This often means operating at low conversion and accepting large recycles of feeds. Alternatively, a cheaper feed may be used in excess, so that a high conversion of the more expensive feed can be achieved at high selectivity, as discussed below.

Use of Excess Reagent In industrial reactions the components are seldom fed to the reactor in exact stoichiometric proportions. A reagent may be supplied in excess to promote the desired reaction; to maximize the use of an expensive reagent; or to ensure complete reaction of a reagent, as in combustion. The percentage excess reagent is defined by the following equation: Percent excess =

quantity supplied − stoichiometric × 100 stoichiometric quantity

(2.7)

It is necessary to state clearly to which reagent the excess refers. Example 2.4 To ensure complete combustion, 20% excess air is supplied to a furnace burning natural gas. The gas composition (by volume) is methane 95%, ethane 5%. Calculate the moles of air required per mole of fuel.

Solution

Basis: 100 mol gas, as the analysis is volume percentage. Reactions: CH4 + 2O2 → CO2 + 2H2 O C2 H6 + 3:5O2 → 2CO2 + 3H2 O

2.3 The Anatomy of a Chemical Manufacturing Process

Stoichiometric moles of O2 required = 95 × 2 + 5 × 3.5 = 207.5 With 20% excess, moles of O2 required = 207.5 × 1.2 = 249 Moles of air (21% O2) = 249 × 100/21 = 1185.7 Air per mole of fuel = 1185.7/100 = 11.86 mol

Sources of Conversion, Selectivity, and Yield Data If there is minimal byproduct formation, then the reactor costs (volume, catalyst, heating, etc.) can be traded off against the costs of separating and recycling unconverted reagents to determine the optimal reactor conversion. More frequently, the selectivity of the most expensive feeds for the desired product is less than 100%, and byproduct costs must also be taken into account. The reactor optimization then requires a relationship between reactor conversion and selectivity, not just for the main product, but for all the byproducts that are formed in sufficient quantity to have an impact on process costs. In simple cases, when the number of byproducts is small, it may be possible to develop a mechanistic model of the reaction kinetics that predicts the rate of formation of the main product and byproducts. If such a model is fitted to experimental data over a suitably wide range of process conditions, then it can be used for process optimization. The development of reaction kinetics models is discussed in Section 15.3 and is described in most reaction engineering textbooks. See, for example, Levenspiel (1998), Froment & Bischoff (1990), and Fogler (2005). In cases where the reaction quickly proceeds to equilibrium, the yields are easily estimated as the equilibrium yields. Under these circumstances, the only possibilities for process optimization are to change the temperature, pressure, or feed composition, so as to obtain a different equilibrium mixture. The calculation of reaction equilibrium is easily carried out using commercial process simulation programs, as described in Section 4.5.1. When the number of components, or reactions, is too large, or the mechanism is too complex to deduce with statistical certainty, then response surface models can be used instead. Methods for the statistical design of experiments can be applied, reducing the amount of experimental data that must be collected to form a statistically meaningful correlation of selectivity and yield to the main process parameters. See Montgomery (2001) for a good introduction to the statistical design of experiments. In the early stages of design, the design engineer will often have neither a response surface, nor a detailed mechanistic model of the reaction kinetics. Few companies are prepared to dedicate a laboratory or pilot plant and the necessary staff to collecting reaction kinetics data until management has been satisfied that the process under investigation is economically attractive. A design is thus needed before the necessary selectivity and yield data set has been collected. Under such circumstances, the design engineer must select the optimal reactor conditions from whatever data are available. This initial estimate of reactor yield may come from a few data points collected by a chemist or taken from a patent or research paper. The use of data from patents is discussed in Section 2.4.1. For the purposes of completing a design, only a single estimate of reactor yield is needed. Additional yield data taken over a broader range of process conditions gives the designer greater ability to properly optimize the design. In process synthesis projects, one purpose of the design may be to set yield targets for a research team, as described in Section 2.6.1.

CHAPTER 2 Process Flowsheet Development

2.3.4 Recycles and Purges Processes in which a flow stream is returned (recycled) to an earlier stage in the processing sequence are common. If the conversion of a valuable reagent in a reaction process is appreciably less than 100%, the unreacted material is usually separated and recycled. Separation processes can also be a source of recycles. The return of reflux to the top of a distillation column is an example of a recycle process in which there is no reaction. The presence of recycle streams makes the calculation of process material and energy balances more difficult. Without recycle, the material balances on a series of processing steps can be carried out sequentially, taking each unit in turn; the calculated flows out of one unit becoming the feeds to the next. If a recycle stream is present, then the point where the recycle is returned the flow will not be known as it will depend on downstream flows not yet calculated. Without knowing the recycle flow, the sequence of calculations cannot be continued to the point where the recycle flow can be determined. Two approaches to the solution of recycle problems are possible: 1. The cut and try (“tear”) method. The recycle stream flows can be estimated and the calculations continued to the point where the recycle is calculated. The estimated flows are then compared with those calculated, and a better estimate is made. The procedure is continued until the difference between the estimated and the calculated flows is within an acceptable tolerance. 2. The formal, algebraic, method. The presence of recycle implies that some of the mass balance equations must be solved simultaneously. The equations are set up with the recycle flows as unknowns and solved using standard methods for the solution of simultaneous equations. With simple problems that have only one or two recycle loops, the calculation can often be simplified by the careful selection of the basis of calculation and the system boundaries. This is illustrated in Example 2.5. The solution of more complex material balance problems involving several recycle loops is discussed in Chapter 4. Example 2.5 The block diagram in Figure 2.12 shows the main steps in the balanced process for the production of vinyl chloride from ethylene. Each block represents a reactor and several other processing units. The main reactions are: Block A, Chlorination

C2 H4 + Cl2 → C2 H4 Cl2 , yield on ethylene 98% Block B, Oxyhydrochlorination

C2 H4 + 2HCl + 0:5O2 → C2 H4 Cl2 + H2 O, yields: on ethylene 95%, on HCl 90% Block C, Pyrolysis

C2 H4 Cl2 → C2 H3 Cl + HCl, selectivity of DCE to VC 99%, selectivity to HCl 99:5%

2.3 The Anatomy of a Chemical Manufacturing Process

Cl2

A Chlorination

Recycle DCE C Pyrolysis

Ethylene

Oxygen

D Separation

B Oxyhydrochlorination Recycle HCl

FIGURE 2.12 Block flow diagram of balanced process for vinyl chloride.

The HCl from the pyrolysis step is recycled to the oxyhydrochlorination step. The flow of ethylene to the chlorination and oxyhydrochlorination reactors is adjusted so that the production of HCl is in balance with the requirement. The conversion in the pyrolysis reactor is limited to 55%, and the unreacted dichloroethane (DCE) is separated and recycled. Using the yields given, and neglecting any other losses, calculate the flow of ethylene to each reactor and the flow of DCE to the pyrolysis reactor, for a production rate of 12,500 kg/h vinyl chloride (VC).

Solution

Molecular weights: vinyl chloride 62.5, DCE 99.0, HCl 36.5. VC per hour =

12,500 = 200 kmol=h 62:5

Draw a system boundary around each block, enclosing the separation section (block D) and the DCE recycle within the boundary of step C, as shown in Figure 2.12. Let the flow of ethylene to block A be X and to block B be Y, and let the HCl recycle be Z. Then the total moles of DCE produced = 0.98X + 0.95Y, allowing for the yields, and the moles of HCl produced in block C = ð0:98X + 0:95YÞ0:995 = Z

(a)

Consider the flows to and from block B. The yield of DCE based on HCl is 90%, so the moles of DCE produced = 0:5 × 0:90Z Note: the stoichiometric factor is 0.5 (2 mol HCl per mol DCE). The yield of DCE based on ethylene is 95%, so 0:5 × 0:90Z = 0:95Y Z = 0:95 × 2Y/0:9

CHAPTER 2 Process Flowsheet Development

Substituting for Z into equation (a) gives Y = ð0:98X + 0:95YÞ0:995 ×

0:9 2 × 0:95

Y = 0:837X

(b)

Turning to block C, the total VC produced = 0.99 × total DCE, so 0:99ð0:98X + 0:95YÞ = 200 kmol=h Substituting for Y from equation ðbÞ gives X = 113:8 kmol=h and

Y = 0:837 × 113:8 = 95:3 kmol=h

HCl recycle from equation (a): Z = ð0:98 × 113:8 + 0:95 × 95:3Þ0:995 = 201:1 kmol=h 200 × 100 = 96 % ð113:8 + 95:3Þ The total flow of DCE from blocks A and B is 200 = 202 kmol=h, but this does not include the recycle. 0:99 Since the conversion is 55%, if the recycle flow is R, then 202/(202 + R) = 0.55, hence the total flow of DCE to the pyrolysis reactor is 202 + R = 202/0.55 = 367.3 kmol/h.

Note: overall yield on ethylene =

Purge It is usually necessary to bleed off a portion of a recycle stream to prevent the buildup of unwanted material. For example, if a reactor feed contains inert components or byproducts that are not separated from the recycle stream in the separation units, these inerts would accumulate in the recycle stream until the stream eventually consisted entirely of inerts. Some portion of the stream must be purged to keep the inert level within acceptable limits. A continuous purge would normally be used. Under steady-state conditions: Loss of inert in the purge = Rate of feed of inerts into the system The concentration of any component in the purge stream is the same as that in the recycle stream at the point where the purge is taken off. So the required purge rate can be determined from the following relationship: ½Feed stream flow rate × ½Feed stream inert concentration = ½Purge stream flow rate × ½Specified ðdesiredÞ recycle inert concentration

Example 2.6 In the production of ammonia from hydrogen and nitrogen the conversion, based on either raw material, is limited to 15%. The ammonia produced is condensed from the reactor (converter) product stream and the unreacted material is recycled. If the feed contains 0.2% argon (from the nitrogen separation process), calculate the purge rate required to hold the argon in the recycle stream below 5.0%. Percentages are by volume.

2.4 Selection, Modification, and Improvement

Solution

Basis: 100 moles feed (purge rate will be expressed as moles per 100 mol feed, as the production rate is not given). Process diagram: Recycle Feed 0.2% argon

Purge 5% argon

Reactor Condenser

Liquid NH3

Volume percentages are taken as equivalent to mol%. Argon entering system with feed = 100 × 0.2/100 = 0.2 mol. Let purge rate per 100 mol feed be F. Argon leaving system in purge = F × 5/100 = 0.05 F. At the steady state, argon leaving = argon entering 0:05 F = 0:2 0:2 F= =4 0:05 Purge required: 4 mol per 100 mol feed.

Bypass A flow stream may be divided and some part diverted (bypassed) around some units. This procedure is often used to control stream composition or temperature. Material balance calculations on processes with bypass streams are similar to those involving recycle, except that the stream is fed forward instead of backward. This usually makes the calculations easier than with recycle.

2.4 SELECTION, MODIFICATION, AND IMPROVEMENT OF COMMERCIALLY-PROVEN PROCESSES Engineers in industry do not usually design a new process from scratch if a commercially-proven alternative is available. Companies usually seek to avoid the extra costs and risks inherent in technology commercialization. New molecules are usually made using adaptations of processes that have been shown to work for similar compounds. Even when a brand new process is contemplated, the design team will usually also prepare a conventional design for comparison. The use of a proven basic flow scheme does not eliminate innovation from the design. Several alternative designs may already be in commercial practice, each optimized around different feeds, catalysts, or reactor concepts. The design team must evaluate the different designs and optimize each to the local design basis to select the best. The commercial processes may need modification to make the desired product or byproducts, or to process an unusual feed material. It may be possible to

CHAPTER 2 Process Flowsheet Development

improve the existing technology by substitution of one or more unit operations, by use of better catalysts or enzymes, by deploying improved separation or reactor technology, or by using different solvents to reduce environmental impact. The scale of production may also cause changes to the flowsheet; for example, if a large new plant requires reactors or separation columns to be constructed in parallel trains. This section discusses factors a design team should consider when developing a flowsheet based on a commercially-proven technology. The special case of developing a flowsheet for the revamp of an existing plant is treated in Section 2.5.

2.4.1 Sources of Information on Manufacturing Processes This section gives a brief overview of sources of information on commercial processes that can be found in the open literature. The chemical process industries are competitive, and the information that is published on commercial processes is restricted. The articles on particular processes published in the technical literature and in textbooks invariably give only a superficial account of the chemistry and unit operations used. They lack the detailed information on reaction kinetics, process conditions, equipment parameters, and physical properties that is needed for process design. The information that can be found in the general literature is, however, useful in the early stages of a project, when searching for possible process routes. It is often sufficient for a flowsheet of the process to be drawn up and a rough estimate of the capital and production costs made. The most comprehensive collection of information on manufacturing processes is probably the Encyclopedia of Chemical Technology edited by Kirk & Othmer (2001, 2003), which covers the whole range of chemical and associated products. An abridged version of the Kirk-Othmer encyclopedia was published in paperback (Grayson, 1989), and was an excellent bargain, but is now out of print. The latest version of the Kirk-Othmer encyclopedia is available through the Wiley online library at http://onlinelibrary.wiley.com. Another encyclopedia covering manufacturing processes is that edited by McKetta (2001). Several books have also been published that give brief summaries of the production processes used for commercial chemicals and chemical products. The best known of these is probably Shreve’s book on the chemical process industries, now updated by Austin and Basta (1998). Comyns (1993) lists named chemical manufacturing processes, with references. The extensive German reference work on industrial processes, Ullmann’s Encyclopedia of Industrial Technology, is now available in an English translation, Ullmann (2002). Specialized texts have been published on some of the more important bulk industrial chemicals, such as that by Miller (1969) on ethylene and its derivatives; these are too numerous to list but should be available in the larger reference libraries and can be found by reference to the library catalog. Meyers (2003) gives a good introduction to the processes used in oil refining. Kohl & Nielsen (1997) provide an excellent overview of the processes used for gas treating and sulfur recovery. Many of the references cited above are available in electronic format from Knovel. Most companies and universities have Knovel subscriptions. Access to Knovel is also available to members of professional societies such as the American Institute of Chemical Engineers (AIChE). Books quickly become outdated, and many of the processes described are obsolete, or at best obsolescent. More up-to-date descriptions of the processes in current use can be found in the technical

2.4 Selection, Modification, and Improvement

journals. The journal Hydrocarbon Processing publishes an annual review of petrochemical processes, which was entitled Petrochemical Developments and is now called Petrochemicals Notebook; this gives flow diagrams and brief process descriptions of new process developments.

Patents Patents can be a useful source of information, but some care is needed in extracting information from them. To obtain a patent, an inventor is legally obliged to disclose the best mode of practice of the invention; failure to do so could render the patent invalid if it were contested. Most patents therefore include one or more examples illustrating how the invention is practiced and differentiating it from the prior art. The examples given in a patent often give an indication of the process conditions used, though they are frequently examples of laboratory preparations, rather than of the full-scale manufacturing process. Many process patents also include examples based on computer simulations, in which case the data should be viewed with suspicion. When using data from patents, it is important to carefully read the section that describes the experimental procedure to be sure that the experiments were run under appropriate conditions. A patent gives its owner the right to sue anyone who practices the technology described in the patent claims without a license from the patent owner. Patent attorneys generally try to write patents to claim broad ranges of process conditions, so as to maximize the range of validity and make it hard for competitors to avoid the patent by making a slight change in temperature, pressure, or other process parameters. Very often, a patent will say something along the lines of “the reaction is carried out at a temperature in the range 50 to 500 ºC, more preferably in the range 100 to 300 ºC, and most preferably in the range 200 to 250 ºC.” It is usually possible to use engineering judgment to determine the optimal conditions from such ranges. The best conditions will usually be at or near the upper or lower end of the narrowest defined range. The examples in the patent will often indicate the best operating point. Patents can be downloaded for free from the web site of the U.S. patent office, www.uspto.gov. The USPTO web site also has limited search capability. The entire USPTO collection is also available at www.google.com/patents. Most large companies subscribe to more sophisticated patent search services such as Delphion (www.delphion.com), PatBase (www.patbase.com), or GetthePatent (www.getthepatent.com). Several guides have been written to help engineers understand the use of patents for the protection of inventions, and as sources of information, such as those by Auger (1992) and Gordon & Cookfair (2000).

Consultants Engineers in industry often hire specialist consulting firms to prepare analyses of commercial technology. Consultants can be used to provide an impartial assessment of a competitor’s or vendor’s process. Some consulting firms such as SRI and Nexant regularly publish assessments of the technology available for making different chemicals. These assessments are based on flowsheets and design models that the consultants have developed from information that they gathered from the literature and from direct contact with the technology suppliers. Some caution is needed when working with consultants. The client must carry out due diligence to ensure that the consultant is truly impartial and does not bias their analysis. The client should also cross check the information provided by the consultant against recent patents and publications to ensure that the consultant is working from the latest information.

CHAPTER 2 Process Flowsheet Development

Vendors Technology suppliers and contractors will sometimes make design information available to a client in the hope of securing a sale. If a project team requires information to make a technology selection, the technology vendors may be willing to supply edited PFDs (for example, with stream flows blanked out or with some information missing), reactor yields, or even designs from a similar plant at a smaller production scale. More detailed information is usually provided by vendors when bidding on a contract for a project that has a high likelihood of going forward.

2.4.2 Factors Considered in Process Selection Once the design team has assembled information on the alternative commercial processes, they will usually need to carry out substantial customization and optimization of the designs before a selection can be made. The information given in the open literature is usually restricted to block flow diagrams and (occasionally) reactor yields. The first step is usually to complete a full PFD and mass and energy balance of the process. These can be used for preliminary sizing and costing of the main process equipment to obtain an estimate of the required capital investment, as described in Chapter 7. The feed and product flow rates and energy consumption can be used to estimate the costs of production, as described in Chapter 8. The economic analysis methods introduced in Chapter 9 can then be applied to determine the overall project economics and choose which design gives the best overall economic performance according to the criteria established by the company. If one process flowsheet has a particular cost advantage, this will usually become clear in the economic analysis. Factors such as feedstock or fixed cost advantages that can be very important in selecting between projects are usually less important when selecting between flowsheets within a given project. The selection between flowsheets is usually influenced more by process yields, energy consumption, and capital requirements, and hence is sensitive to catalyst, organism, or enzyme performance and process design and optimization. In an industrial context, technology vendors or Engineering, Procurement, and Construction (EPC) contractors will often supply detailed PFDs and material and energy balances to a client when invited to bid on a project. Some diligence is always needed in checking the information in proposals and verifying performance claims against the actual performance of recent plants built by the vendor. Although an economic analysis is always carried out, it is usually not the sole criterion for technology selection. Some other important factors are described below.

Freedom to Practice Freedom to practice is a legal concept that arises from patent law. If a process, catalyst, enzyme, genetically modified organism, or chemical route is patented, it can only legally be used under license from the patent holder. If another company were to use the technology without a license, they would be infringing on the patent and the patent holder could sue to stop the use and demand damages. Determination of freedom to practice usually requires the expert advice of patent attorneys. In rapidly evolving new fields it can be difficult to assess, as patent applications typically are not published until one to two years after they are filed, so a decision may be made to proceed with

2.4 Selection, Modification, and Improvement

building a plant before the intellectual property space can be completely mapped. Another complication is that competing technology vendors may have overlapping patents or patents that appear to block features of each others’ designs. All patents are only valid for a fixed term; in the United States at the time of writing this is twenty years from the date the patent was filed. When a patent has expired, anyone is free to practice the technology. Care must still be taken to check that the original technology developer has not made more recent improvements that are still under patent protection. Many conventional processes are no longer protected by patents and can be bought from EPC companies without paying a royalty or license fee. When a customer licenses technology from a vendor, the vendor will usually indemnify the customer against patent infringement. This means the technology vendor asserts that they have ownership of the technology and freedom to practice and that they will help the customer fight any patent infringement suits brought by their competitors. Technology vendors sometimes minimize the potential for such lawsuits by forming cross-licensing agreements.

Safety and Environmental Performance All commercially-practiced technologies should meet or exceed the minimum legally acceptable safety standards, but some older processes may no longer have acceptable environmental performance. An economic analysis will usually not distinguish whether one process is safer or more environmentally acceptable than another. The methods described in Chapters 10 and 11 can be used to make an assessment of process safety and environmental impact. When assessing commercial technology, visits to existing sites and reviews of their safety and operational performance can also be helpful.

Government and International Restrictions Governments sometimes place restrictions on companies that can influence technology selection. It is fairly common for nationally owned companies in developing countries to be required to maximize use of indigenous technology, equipment, and parts, so as to stimulate the development of local engineering industries and reduce hard currency outflows. This may lead a company to develop its own version of an older technology rather than working with a technology vendor or major international company that can supply the latest technology. International sanctions can also play an important role in process flowsheet selection. Sanctions can disqualify some companies from offering to supply technology and reduce the set of options available. Sanctions can also restrict the availability of feedstocks. During the 1970s and 1980s, South African companies developed many processes for making chemicals from coal in response to the international sanctions aimed at ending apartheid that restricted their ability to purchase crude oil.

Experience and Reliability One of the critical factors in selecting a commercially-proven technology is the extent and diversity of operating experience that has been established. If a process has been widely adopted and proven in many locations by different operating companies then it is likely to be easy to apply in a new plant. A technology that has only been built once or twice may still experience “teething troubles” and be more difficult to implement.

CHAPTER 2 Process Flowsheet Development

As more operating experience is gained, the company also gains a better understanding of the reliability of the process. If a particular section of the flowsheet or piece of equipment is known to cause reliability problems, this may create a need to modify the equipment design or even make changes to the flowsheet.

2.4.3 Modification and Improvement of Established Processes All designs evolve over time. Engineers make modifications to improve process economics, safety, reliability, and environmental impact. Most changes will be minor, such as addition of instrumentation or substitution of equipment; however, significant changes in the flowsheet are sometimes needed. Modifications that are made to an existing commercial plant are known as revamp designs, and are addressed in Section 2.5. This section describes techniques for modifying an established process for use in a new plant.

Modifications to Improve Process Economics Improvements in process economics usually come from reduced capital investment or improved cost of production. Designers seeking improvements in process economics usually start by completing a PFD of the existing design and determining the current estimated capital investment and cost of production (see Chapters 7, 8 and 9). The following tactics can then be applied: •

• •

•

Improve reactor selectivity and process yield. Feedstock costs are usually more than 80% of the cost of production, so improving yields gives the biggest impact on process economics. Improved yields usually require the development of more selective catalysts, enzymes, or organisms, or a more effective reactor design, but sometimes a more efficient separation scheme or better purification of a feed or recycle will also improve yield. Improve process energy efficiency. Energy costs are usually next largest after feedstock costs for chemicals produced on a large scale. Energy costs can be reduced by improving process energy efficiency. Several different approaches to improving process energy use are described in Chapter 3. Improve process fixed costs. Fixed costs are usually second to feedstock costs in small-scale processes used for fine chemicals and pharmaceuticals manufacture. Fixed costs are described in Section 8.5. Fixed costs can be reduced by making the process more continuous and less laborintensive, and by increasing the plant attainment of batch processes. Reduce capital investment. Design engineers look for pieces of equipment that can be combined or eliminated to reduce capital cost. In batch plants, this is often done by carrying out several steps in the same piece of equipment. For example, the feed can be charged to a reactor, heated in the reactor, reacted, cooled down, and the product crystallized before pumping out the product as a slurry and repeating the process. Reduce working capital. Working capital is described in Section 9.2.3. Working capital can be reduced by decreasing inventories of raw materials, work in progress, and consumables. Making a process more continuous or using fewer different solvents in a process both lead to a reduction in working capital.

It can be seen that some of the above suggestions contradict each other; for example, “make batch plants more continuous” but “carry out more operations in the same piece of equipment”.

2.4 Selection, Modification, and Improvement

Lists of design guidelines (known as heuristic rules) often contain apparent contradictions. The designer must either choose which rule is most appropriate to the case under consideration using experience and judgment, or else carry out a full design and costing of both alternatives. Heuristic rules are discussed further in the context of process synthesis in Section 2.6.4.

Modifications to Improve Plant Safety Plants can be made more inherently safe by reducing inventories of hazardous materials by making vessels and other plant equipment smaller; substituting less hazardous materials for feeds, solvents, and intermediates; eliminating explosive mixtures and exothermic reactions; eliminating use of operations that are open to the atmosphere; minimizing worker exposure to chemicals; and other methods discussed in Chapter 10. Improvements in the safety of a design can be quantified using the methods for risk assessment described in Section 10.8.

Modifications to Improve Plant Reliability When a plant has been in operation for a few years the operators will have a good idea of which plant sections or pieces of equipment lead to the most operational problems, require the most maintenance, and cause the most unplanned shutdowns. Reliability problems are usually caused by equipment failures. The most common problems are usually experienced with solids-handling equipment, rotating equipment such as pumps and compressors, heat exchangers that are prone to fouling, and instruments and valves. Sometimes, specification of a more reliable piece of equipment can solve a process reliability problem. More often, a flowsheet change is needed, such as designing with two or more pieces of equipment in parallel so that the plant can continue to operate while one is taken offline for repair or cleaning. This approach is very commonly applied for pumps, which are relatively cheap and very prone to stalling in operation. Corrosion, erosion, and plugging caused by corrosion products can be major contributors to poor reliability. Methods to address corrosion in design are described in Chapter 6.

Modifications to Improve Environmental Impact Many conventional processes were first designed over forty years ago, when different environmental laws and standards applied. Existing plants may have been modified by the addition of end-of-pipe systems for reducing environmental impact; however, changes in the process flowsheet can sometimes achieve the same or better environmental performance at lower cost. Modifications that are typically used to improve environmental impact include: • • • •

Use of new catalysts, enzymes, or organisms that have better selectivity for the desired product and consequently lead to less waste formation. Optimization of reactor design to give better mixing or heat transfer and hence improve reactor selectivity and reduce byproduct formation. Elimination of solvents or other consumables that become degraded to waste products by the process. Elimination of materials that have high environmental impact, such as halogenated solvents, mercury, endocrine disruptors, and compounds that persist in the environment.

CHAPTER 2 Process Flowsheet Development

Cooler To vent or flare Heater

Air or inert gas

Process flow

Solvent

Process flow (a) Rotary dryer with oncethrough gas flow

Blower

Heater

(b) Rotary dryer with gas recirculation and solvent recovery

FIGURE 2.13 Dryer gas circulation designs.

•

Adoption of closed-loop recirculating gas systems instead of once-through gas flow, hence reducing volatile organic compound (VOC) emissions. For example, Figure 2.13(a) shows a once-through dryer, in which the drying gas is vented or sent to a flare, potentially leading to VOC emissions. Figure 2.13(b) shows an alternative design in which a blower is used to circulate the gas. The hot gas leaving the dryer is cooled to allow solvent to be condensed and recovered. There is much less potential for VOC emissions in the closed-loop design and the consumption of solvent is also reduced. Substitution of chemicals with materials that have reduced environmental impact. For example, the cheapest way to neutralize waste sulfuric acid is to react it with lime (CaO) to form gypsum (CaSO4), which is inert and can be sent to landfill. Instead, if ammonia is used to neutralize the acid the product will be ammonium sulfate, which can be used as a fertilizer.

Methods for analyzing and reducing the environmental impact of a process are described in Chapter 11.

2.5 REVAMPS OF EXISTING PLANTS Flowsheet development for plant revamps is a specialized subject in its own right. Revamp design is rarely taught in universities, as revamp studies require access to an operating plant and the data it produces. Revamps generally fall into two categories. Debottlenecking projects are carried out to increase the production rate of a plant while making the same product. Retrofit projects are carried out to change the design of a plant to handle different feeds; make different products; exploit better reactor, catalyst, or separation technology; or improve plant safety or environmental impact in response to new regulatory requirements.

2.5.1 Flowsheet Development in Revamp Projects Figure 2.14 gives an overall work process for developing a revamp design flowsheet. One of the critical requirements of a revamp project is always to minimize project cost by maximizing reuse of existing equipment. The revamped flowsheet therefore always requires compromises between desired objectives and what can be obtained with the equipment available.

2.5 Revamps of Existing Plants

Benchmark existing design

Confirm “as is” PFD

Complete “as is” flowsheet

Confirm equipment limits

List current operating scenarios

Determine revamp scope

Increase production rate by X%

Improve HS&E performance

Change feed

Change products

Other

Modify appropriate section of PFD to revamped case

Determine major equipment bottlenecks

Redesign plant heat integration

Perform rating calculations

Design new heat exchange network

Redesign plant hydraulics & solids handling

Create flowsheet for revamped process

Consider equipment enhancements

Determine scope for HX re-use

Re-rate pumps and control valves

Test revamped design vs. scenarios

Consider alternate use of equipment

Consider HX enhancement

Determine scope for re-use or modification

Cost new components

Consider adding parallel equipment

Consider where new heaters, exchangers and coolers are needed

Design new hydraulic components

Estimate off-site costs of revamp

Compare to cost of building new plant

FIGURE 2.14 Steps in revamp design.

Many features of a revamped flowsheet will be different from the flowsheet of a corresponding new plant. For example, in a revamp it may make sense to add a second distillation column in parallel to an existing column rather than tearing down the existing column and building a new larger one. The use of two small columns in parallel would not be contemplated in a new design. The development of a revamped flowsheet thus requires a lot of information on the performance of existing equipment so that the equipment can be re-rated or modified for a role in the new flowsheet. When the existing equipment cannot be upgraded, the designer must find the cheapest method to add new capacity or augment the existing capacity. Once the revamped flowsheet has been completed, the designers can assess the costs of the new components that must be added. The cost of revamping a plant should always be compared to the cost of building a new plant from scratch. The revamp will usually be a cheaper method for adding small increments of capacity, but for larger capacity increases a new unit will become more attractive. The steps in developing a revamped process flowsheet are described in the following sections. Although there is a great deal of retrofit and revamp activity in the chemical industry, particularly in regions such as the United States and Europe where the industry has been long-established, the

CHAPTER 2 Process Flowsheet Development

authors are not aware of any comprehensive reference works on the subject. The books by Briggs, Buck, & Smith (1997) and Douglas (1988) contain short sections on revamp design.

2.5.2 Major Equipment Debottlenecking In a revamp design, the capacity of existing equipment determines whether additional equipment must be added in series or parallel, and hence plays a major role in determining the revamped design flowsheet. Most major equipment is initially specified with a design factor or margin of 10% to 20%; see Section 1.6. This overdesign allows for errors in the design data and methods, but also creates some room for potential expansion of capacity. When a plant is considered for revamp, some of the equipment may still be operating below its full capacity. The general procedure for equipment debottlenecking follows the steps shown in Figure 2.14. Once a mass and energy balance has been established for the existing plant, a simulation model of the equipment can be built. The model can then be tested under the proposed new process conditions to determine if the equipment is fit for the new service. For equipment that is difficult to model (for example, centrifuges, fired heaters, and dryers) a specialist or the original equipment vendor may need to be consulted. After establishing the maximum capacity that the equipment can attain while maintaining specifications, modifications to improve capacity can be considered. If it is not possible to satisfy the desired process duty with modifications to the existing equipment, then the cheapest means of adding capacity must be established. This may include complete replacement of the original equipment with reuse of the original equipment elsewhere in the process. Some specific examples of techniques for equipment debottlenecking are given below. Revamp of heat transfer equipment is discussed in Section 2.5.3 and revamp of hydraulic and solids handling equipment is described in Section 2.5.4.

Reactor Debottlenecking Reactors are designed with a specified residence time that has been determined to give a desired conversion. For reactors that use a fixed bed of catalyst this is usually expressed instead as a space velocity: τ= SV =

V v

(2.8)

v Vcat

(2.9)

where τ = residence time, SV = space velocity, V = reactor volume, Vcat = fixed bed catalyst volume, and v = volumetric flow rate Space velocity is usually given on an hourly basis and defined on the basis of gas phase flow (GHSV = gas hourly space velocity), liquid phase flow (LHSV = liquid hourly space velocity) or total mass flow (WHSV = weight hourly space velocity = kg/h feed per kg of catalyst inventory). Any consistent set of units can be used for residence time and space velocity.

2.5 Revamps of Existing Plants

Equations 2.8 and 2.9 clearly show that an increase in flow rate must lead to a proportional change in volume, residence time, or space velocity. Adding volume usually requires building additional reactors, so unless the reactors are very inexpensive, the revamp design will focus on ways to reduce residence time or increase space velocity, while trying to maintain the same conversion if possible, so as to minimize the impact on the separation and recycle sections of the plant. An increase in space velocity or decrease in residence time can be obtained by increasing temperature, backing off on conversion, reducing the concentration of diluents, or using a more active catalyst, enzyme, or organism. Increasing temperature and reducing diluents or solvents (if any are present) will generally lead to worse selectivity and increased cost elsewhere in the process. Many fixed-bed catalytic processes are operated on a temperature cycle, where the reactor temperature is slowly increased over a one- to ten-year period to compensate for catalyst deactivation, and the catalyst is then replaced at the end of the cycle. In such cases, raising the temperature shortens the catalyst run length and requires more frequent plant shutdown. Reducing the reactor conversion also creates additional cost elsewhere in the process, as the amount of unreacted feed recycle is increased. Improving the catalyst performance is often the least expensive way to boost capacity, and the availability of new catalysts often sets the scope for revamp projects. An additional problem with revamping fixed-bed catalytic reactors is the effect of reactor pressure drop. The pressure drop across a packed bed is proportional to the flow rate squared, so pressure drop increases rapidly as flow rate is increased. Approaches that can be taken to reduce reactor pressure drop include rearranging series reactors into parallel flow, Figure 2.15, and converting downflow reactors to radial flow, Figure 2.16. (A more detailed drawing of a radial flow reactor is given in Chapter 15; see Figure 15.29). With packed beds that are in upflow, care must be taken to avoid fluidizing the catalyst in the revamped design. If the upflow velocity is close to the minimum fluidization velocity then the reactor should be converted to downflow or replaced with a larger reactor. Sizing of packed bed reactors is discussed in more detail in Section 15.7.3. When it is necessary to add reactor capacity, a technique that is widely used is to add a prereactor to the existing reactor sequence, as in Figure 2.17. Because a prereactor typically runs at low conversion, it can be operated under conditions that would not normally be good for selectivity; for example, at higher temperature or with less solvent or diluent. This makes the prereactor more volume-efficient than the existing reactor sequence, without compromising on overall selectivity. When a detailed model of the reaction kinetics, including side reactions, is available, more complex reactor networks can be designed that give improved selectivity and yield of desired products.

(a) Base case

FIGURE 2.15 Series to parallel reactor revamp.

(b) Revamped case

CHAPTER 2 Process Flowsheet Development

(a) Base case

(b) Revamped case

FIGURE 2.16 Downflow to radial-flow reactor revamp.

Feed B

Feed A

New pre-reactor

Existing reactors

FIGURE 2.17 Reactor revamp using a prereactor.

A revamp project can then add reactor capacity to bring the reactor section performance closer to that of the ideal reactor network. The design of reactors and reactor networks is discussed in more detail in Chapter 15.

Separation Column Debottlenecking The capacity of separation columns is usually limited by column hydraulics; see Section 17.13. If the feed flow rate increases, the vapor rate in the column increases proportionately, and at some point the column will flood and become inoperable. Two approaches can be taken to obtain more capacity: 1. Increase the open area for vapor flow to delay the onset of flooding. 2. Increase the number of stages in the column by using high-efficiency trays or trays that allow a closer tray spacing, so that the reflux ratio, and hence vapor rate, can be reduced. Both of these methods are used by separation tray and packing vendors, and there are many proprietary designs of high-efficiency, high-capacity trays and packing on the market. When revamping a column, the common practice is to contact the tray and packing vendors, who will then supply an estimate of how many trays must be replaced to achieve a desired capacity. It is often not necessary to re-tray the entire column. The detailed design of distillation columns is discussed in Chapter 17.

2.5 Revamps of Existing Plants

Distillate

Feed

Prefractionator column Bottoms Original column

FIGURE 2.18 Distillation column revamp using a prefractionator.

When it is necessary to add capacity to a distillation column and the use of high-capacity trays is not sufficient, a prefractionator scheme is sometimes used, as illustrated in Figure 2.18. The prefractionator makes a preliminary separation of the feed that reduces the reflux requirements of the main column. A revamped prefractionator is usually provided with its own reboiler and condenser to avoid increasing the load on the main column reboiler and condenser. Another common tactic in debottlenecking separation sections is to reuse the existing distillation columns in a different application. If a plant has three or more columns then a revamp can be carried out by building one new column to replace the largest of the existing columns, revamping the largest old column to replace the second largest, etc. In this context, largest refers to the largest diameter, which governs vapor rate and capacity. If the columns do not have sufficient height for the new application, they can be re-trayed with high efficiency internals or combined in series. In some cases, particularly for relatively short low-pressure columns, it may even make sense to add height to a column by welding on a new top section.

2.5.3 Revamp of Heat Exchange Networks The heat exchangers, heaters, and coolers of a plant will cause many of the bottlenecks to plant expansion. When a plant is revamped to a new purpose such as changed feed or products, the existing heat recovery system will no longer be optimal and may no longer make good sense. The common practice in major revamps is to complete the revamp design of the other major equipment first, then address the heaters, coolers, and exchangers subsequently, as shown in Figure 2.14. The design of heat recovery systems and heat-exchanger networks is covered in Chapter 3. Chapter 19 addresses the detailed design of heat exchangers, heaters, and coolers. Revamp of a

CHAPTER 2 Process Flowsheet Development

complex heat-exchange system should always be treated as a network problem rather than by revamping each item individually, as the lowest-cost solution will always be that obtained by optimizing the system as a whole. The revamp of heat-exchanger networks has been the subject of much research, and very effective techniques and software for heat exchange network revamp have been developed. The network pinch method developed by Asante and Zhu (1997) is now the most widely used method in industry. This method has been automated (Zhu & Asante, 1999) and is used by most of the companies that offer heat integration consulting services. Smith (2005) gives a concise overview of the network pinch approach. For simple processes, with only a few heaters and coolers, the tactics described in the following sections can be used.

Heat Exchangers For a heat exchanger: Q = UAΔTm

(2.10)

Q = mi Cp,i ΔTi

(2.11)

and

where Q U A ΔTm mi Cp,i ΔTi

= = = = = = =

heat transferred per unit time, W, the overall heat-transfer coefficient, W/m2K, heat-transfer area, m2, the mean temperature difference, the temperature driving force, °C the mass flow rate of stream i, kg/s the specific heat capacity of stream i, J/kgK the change in temperature of stream i for a stream that undergoes only sensible heat changes, °C.

Increasing the flow rate increases the required duty and therefore requires an increase in heat transfer coefficient, area, or effective temperature difference. The correlations that are used to predict heat transfer coefficients for sensible heat transfer are usually proportional to Re0.8, where Re is the Reynolds number, which is proportional to flow rate. Hence, the process-side transfer coefficient increases almost in ratio to the increase in flow unless the exchanger is boiling or condensing the process stream. For heaters and coolers it may therefore be possible to reuse the exchanger in the same service if an increase in utility-side heat transfer coefficient or a change in utility temperature can make up the rest of the required duty. This is explored in Example 2.7. One of the first and most important steps in revamping a heat exchange system is to benchmark the current system and estimate the heat transfer coefficients that are currently being obtained. If these are substantially lower than expected from the original design of the process, this may indicate fouling, plugging, or other problems that should be addressed during the revamp. There are several proprietary methods for enhancing the performance of tubular exchangers. Tube inserts such as hiTRAN®, TURBOTAL®, and Spirelf® can be used to increase turbulence and tube-side heat transfer coefficient. Low-fin tubes can be used to increase shell-side effective area

2.5 Revamps of Existing Plants

(Wolverine, 1984; see also Section 19.14). Reboiling and condensing coefficients can be increased by use of UOP High Flux™ or High Cond™ tubing. Plate exchangers usually do not require enhancement methods. Gasketed plate exchangers are very easy to revamp, as more plates can simply be added to the exchanger; see Section 19.12. Welded plate exchangers are not amenable to use of inserts or to expansion by adding plates.

Heaters and Coolers The techniques described for heat exchangers apply equally well to steam or oil heaters and water coolers. Decreasing cooling water return temperature (by increasing cooling water flow rate) or raising hot oil temperature are widely used methods in plant revamps. Fired heaters are usually difficult to revamp and require the involvement of heater and burner specialists. If there is space in the heater, additional tubes can be added. Similarly, if there is space in the convective section then it can be used for preheat to off-load some of the furnace duty. In some cases, the addition of improved burners will allow more uniform heating and higher average tube-wall heat flux. Fired heater design is discussed in more detail in Section 19.17. Air coolers (Section 19.16) are also difficult to revamp. The designer does not have the ability to specify a lower ambient temperature! Common air cooler revamps include: • •

Adding additional banks of tubes and installing more powerful fans. Adding water-spray systems to increase cooling capacity on the hottest days. Water-spray systems are effective, but can increase air-side fouling over time.

Example 2.7 Figure 2.19 shows a simple heat-exchange system. A feed stream is heated by heat exchange in a plate exchanger and then further heated in a steam heater before entering a fixed-bed reactor. The product from the reactor is cooled in the plate exchanger and then further cooled using cooling water. Exchanger specifications and current performance are given in the figure. Propose modifications to the system to allow a revamp to 50% higher capacity.

Solution

Start with the plate heat exchanger, E101. A 50% increase in flow through the exchanger would give a (1.5)2 = 2.25 factor increase in exchanger pressure drop. If this was acceptable, then assuming that the heat transfer coefficient is proportional to Re0.8: New heat transfer coefficient = 350 × ð1:5Þ0:8 = 484 W=m2 K Assuming the reactor operates at the same outlet temperature, we can make heat balances for the base case and revamp case. Base case: Q101 = 800 × 103 = mf Cp,f ð120 − 40Þ = mp Cp,p ð140 − 60Þ mf Cp,f = mp Cp,p = 104 where subscript f denotes feed and p denotes product.

CHAPTER 2 Process Flowsheet Development

E101

E102

R101

E103

ST T1

Feed T2

CW T3

Exchanger

E101

E102

E103

Type Duty (kW)

Plate 800

S&T 400

S&T 200

140 60 40 120 1

180 180 120 160 1

60 40 25 35 0.92

700 700 350

2000 500 400

700 700 350

114 20

27.5 36.4

31.7 19.6

Hot side T in (°C) Hot side T out (°C) Cold side T in (°C) Cold side T out (°C) Ft factor Hot side heat transfer coefficient (W/m2K) 2K)

Cold side heat transfer coefficient (W/m Overall heat transfer coefficient (W/m2K) Area (m2) ΔTlm

FIGURE 2.19 Heat exchange system for Example 2.7.

Revamp case: Q101 = 1:5 mf Cp,f ðT1 − 40Þ = 1:5 mp Cp,p ð140 − T2 Þ T1 = 180 − T2 and Q101 = U A ΔTm = 484 × 114 × ð140 − T1 Þ So 1:5 × 104 × ðT1 − 40Þ = 484 × 114 × ð140 − T1 Þ

2.5 Revamps of Existing Plants

hence T1 = 118:6 °C T2 = 61:4 °C So we only lose 1.4 degrees of heat exchange as long as the increase in pressure drop that results from the higher flow rate is acceptable. Now look at the steam heater, E102. In the revamp case: Q102 = 1:5 × 104 × ð160 − 118:6Þ = 621 kW The heat transfer coefficient is only increased on the process (cold) side: New cold-side coefficient = 500 × ð1:5Þ0:8 = 691:6 W/m2 K New overall heat transfer coefficient = ðð2000Þ−1 + ð691:6Þ−1 Þ−1 = 513 W/m2 K (overall heat transfer coefficient calculated using equation 19.2) So for the exchanger to be feasible, we would need to raise the steam temperature to Ts, where Q102 = U A ΔTm

BðTs − 160Þ − ðTs − 118:6ÞC C 621 × 103 = 513 × 27:5 × B A @ Ts − 160 ln Ts − 118:6 Ts = 186:5 °C So the heater remains viable if the steam temperature can be increased by 6.5 ºC. This might be accomplished by raising the local pressure of the medium pressure steam system; for example, by making adjustments in the steam pressure regulator valve set points. If that was not possible, and if the heater was rated for a sufficiently high pressure, then high pressure steam could be considered instead of medium pressure steam. Turning to the cooler, E103. In the revamp case: Q103 = 1:5 × 104 × ð61:4 − 40Þ = 321 kW To meet this extra duty we need to increase the cooling water flow rate by a factor Fcw, which changes the cooling water outlet temperature to Tw, where Q103 = 321 × 103 = Fcw × 20 × 103 × ðTw − 25Þ and 321 × 103 = U A F ΔTlm For the revamp case, the logarithmic mean temperature difference ΔTlm depends on Tw and the overall heat transfer coefficient will be 1 = 1 1 + U 700 × ð1:5Þ0:8 700 × ðFcw Þ0:8

CHAPTER 2 Process Flowsheet Development

These equations must be solved iteratively. This is easily done using a spreadsheet, giving Fcw = 1:89 Tw = 33:5 °C The exchanger would be feasible if we could accept this increase in cooling water flow rate; however, such a large increase would give a very large increase in pressure drop. The pressure drop is proportional to flow rate squared and so would increase by a factor (1.89)2 = 3.57, which would probably not be acceptable. An alternative approach for E103 is to see what the outlet temperature would be if cooling water flow was limited. Suppose the cooling water flow cannot be increased more than 20%, giving a 44% increase in pressure drop. If we allow the cold outlet temperature and hot outlet temperature to vary, the same spreadsheet model can be solved to give Tw = 36:4 °C T3 = 43:1 °C So in this case the designer would have to consider whether the product stream could be made 3.1 ºC hotter, which depends on the downstream processing. If this option was also unacceptable, the designer would have to consider adding an additional cooler. A simple approach would be to split the hot stream leaving E101 into two streams in ratio 2:1. The larger stream could still be sent to E103 and the smaller one could be sent to a parallel cooler of half the size of E103. This option would not push the operation of E103 much beyond the current operating mode. In summary, one option that would allow a 50% increase in throughput would be:

• • •

E101: No change, as long as a factor 2.25 increase in pressure drop is acceptable on hydraulic review. E102: Increase steam temperature to 186.5 °C, no capital modification needed. E103: Consider accepting a 3.1 °C warmer product. If this is unacceptable, add a new exchanger E104, half the size of E103, in parallel to E103 and split the hot stream leaving E101 in 2:1 ratio between E103 and E104.

Alternatively, if E101 is a gasketed plate heat exchanger (see Section 19.12.1), the designer could also consider adding more plates to increase the area available in E101. We can increase the plates in E101 until we achieve the same channel velocity and pressure drop as the base case, then solve the remaining problem for E102 and E103, or, alternatively, increase the plates in E101 until the existing E102 and E103 are able to satisfy all of the remaining heating and cooling load without modifications. This alternative solution is explored in Problem 2.11. The addition of plates to E101 would be more expensive than just altering a few temperatures, but would most likely be less costly than adding E104, and could even be cheaper than making the hydraulic modifications necessary to cope with a large increase in pressure drop.

2.5.4 Revamp of Plant Hydraulics Any revamp project that leads to increases in plant throughput will have a significant effect on the plant hydraulic equipment. Since pressure drop is proportional to velocity (and hence flow rate) squared, a 40% increase in flow is sufficient to double the pressure drop. The introduction of

2.5 Revamps of Existing Plants

parallel equipment in the flowsheet may also create a need for additional control valves to regulate flow in the desired ratios, which adds additional pressure drop to the plant. Adding equipment to modify the process also has an impact on the hydraulic design. Much of the design effort in revamp projects goes into evaluating and redesigning the plant hydraulics. All of the pump-and-line calculations and control valve sizing calculations must be repeated for the revamped design case. It is usually not cost effective to replace the piping with new pipe of more optimal diameter, so usually the designers will accept a higher pressure drop in the pipes and process equipment and then redesign the pumps and control valves accordingly. The design of pumps, compressors, piping systems, and control valves is discussed in more detail in Chapter 20. The sections below provide some specific guidelines relevant to revamp flowsheet development.

Compressors

Pressure

Compressors are the largest and most expensive items in the plant hydraulic equipment. Compressor design is covered in more detail in Section 20.6. Because compressors are expensive to replace, experienced designers usually try to reuse the existing compressors in the new flowsheet. The relationship between flow rate and pressure delivered depends on the type of compressor (see Figure 2.20), but the pressure delivered will usually decrease if the compressor operates at higher flow. The only exception to this rule is large reciprocating compressors, which are usually designed with a recycle from the product to the feed, known as a spill-back. If the spill-back flow is large enough, some increase in flow can be obtained by reducing the spill-back with no loss in delivered pressure. When two compressors are used in parallel, the total flow increases, but the delivered pressure cannot be greater than the lower pressure delivered by either compressor; see Figure 2.21. When two compressors are used in series, the pressure delivered increases, but the flow rate does not; see Figure 2.22.

Axial Centrifugal Reciprocating

Flow

FIGURE 2.20 Pressure—Flow rate curves for different compressor types.

CHAPTER 2 Process Flowsheet Development

Flow

Pressure

Flow

FIGURE 2.21 Compressors in parallel.

Flow

B =

Flow

Pressure

Flow

FIGURE 2.22 Compressors in series.

In a revamp flowsheet design, the designer seeks to increase the pressure delivered to overcome the increased plant pressure drop, as well as an increase in flow rate. From Figures 2.21 and 2.22 it can be seen that the only way to increase both the pressure delivered and the flow rate while adding only one compressor is somewhat paradoxically to reduce the flow rate in the existing compressor so that it delivers a higher pressure, and then add a second machine in parallel, as shown in Figure 2.23. The extent to which the flow rate can be reduced depends on the type of compressor and current operating conditions. In this scenario, the revamped flowsheet would need to show two compressors in parallel. A revamp from one machine operating at 100% flow rate to two similar machines in parallel each at 70% flow rate would give an overall 40% increase in flow.

2.5 Revamps of Existing Plants

(a) Base case

(b) Revamped case

A A

Pressure

Operating point

A+B

B +

Flow

FIGURE 2.23 Compressor revamp.

If it is not possible to meet the desired flow and pressure with the addition of only one new compressor, it will usually be preferable to replace the existing compressor rather than adding new compressors in series and parallel. If a compressor cannot be reused in its current location in the revamped flowsheet, it should be evaluated for other process uses. Air compressors and blowers should also always be re-evaluated, and can be used to assist heaters, boilers, dryers, or even site instrument air systems if there are no suitable process uses.

Pumps Pumps are relatively inexpensive compared to compressors, and will often be replaced entirely in a revamp. Pumps are discussed in more detail in Section 20.7. The most commonly used pumps are centrifugal pumps. Centrifugal pumps exhibit pressure-flow behavior similar to that shown for centrifugal compressors in Figure 2.20. A typical pump curve is given in Figure 20.15. The same pump can deliver a set of different performance curves depending on the impeller diameter and motor speed. The designer can therefore sometimes obtain the required performance just by selecting new impellers for the existing pumps.

Control Valves All control valves must always be rated to confirm that they are correctly sized for the revamped design case and will give the desired controllability, turndown, and ability to meet different operating scenarios. Control valve design and sizing are discussed in Section 20.11. When parallel equipment is introduced into the revamped flowsheet, the design engineers must determine how the flow is to be split between the existing and new equipment. A simple T-junction or branch will often not be effective, as the rate of fouling or pressure-drop accumulation of the

CHAPTER 2 Process Flowsheet Development

new and old equipment will not be the same, even if they have the same capacity and design, and flow would then preferentially go through one piece of equipment, leading to poor performance of both. The desired split ratio is rarely 1:1, and may need to be adjusted once the plant is put into operation. The most common approach is to put a new control valve on the branch that leads to the new equipment. The existing equipment is likely to be limited by pressure drop, so the new equipment can be designed with lower pressure drop to allow for the pressure drop associated with the control valve. A less costly, but less effective, alternative is to use a manual valve or even a restriction orifice in the bypass line, and make manual adjustments until the desired flow ratio is obtained. Control valves that act discontinuously and handle low flow rates will sometimes be suitable for reuse in the revamped plant as long as the new actuation rate is acceptable. Control valves on main plant flows will usually need to be replaced, as will control valves on gas or vapor streams. The revamped flowsheet does not need to indicate which existing valves are reused and which are replaced, but should show all new control valves that are added.

2.6 SYNTHESIS OF NOVEL FLOWSHEETS The terms process synthesis and conceptual process design are used for the invention of completely new process flowsheets. As stated previously, very few entirely new designs are developed commercially because of the high financial risks inherent in using unproven technology. The primary goals of process synthesis are therefore to reduce commercialization risk and to maximize economic attractiveness so as to generate sufficient financial reward to balance the risk. Process synthesis has been the subject of a great deal of academic and industrial research over the past forty years. Many problems that were previously solved using inspired guesswork can now be formally posed and optimized. The use of process simulation programs has also made it much easier to evaluate and optimize alternative flowsheets; see Chapter 4 for more on process simulation. Several prominent researchers in the field of process synthesis have written textbooks on process design that strongly emphasize process synthesis. These are listed in the bibliography at the end of this chapter. Several excellent books have been written on process synthesis in its own right (Rudd, Powers, & Siirola, 1973; Douglas, 1988; El-Halwagi, 2006), as well as on aspects of process synthesis such as distillation sequencing (Doherty & Malone, 2001), mass integration (El-Halwagi, 1997), and heat integration (Shenoy, 1995; Kemp, 2007). While it is beyond the scope of this book to cover all aspects of process synthesis, this section sets out an overall framework for flowsheet synthesis that addresses the key issues encountered in developing and commercializing new processes. The reader is encouraged to read the books listed above and in the bibliography for more insights into the subject.

2.6.1 Overall Procedure for Flowsheet Synthesis Most efforts to systematize process synthesis begin by setting out a sequence or hierarchy of steps for the designer to follow. Design hierarchies recognize that some steps need to come before others and should guide the designer to eliminate unattractive options and focus effort on designs that are most likely to be successful. The most intuitively obvious design hierarchy is the so-called onion diagram. Figure 2.24 shows a version of the onion diagram given by Smith (2005). The onion diagram represents a design starting with the reactors, adding separation and recycle systems, then proceeding to add heat recovery,

2.6 Synthesis of Novel Flowsheets

Reactor

Separation and recycle system Heat recovery system Heating and cooling utilities Water and effluent treatment

FIGURE 2.24 Onion diagram (Smith, 2005).

Table 2.1 Hierarchy of Process Synthesis Decisions (Douglas, 1988) 1. 2. 3. 4.

Batch vs. continuous Input-output structure of the flowsheet Recycle structure of the flowsheet General structure of the separation system a. Vapor recovery system b. Liquid recovery system 5. Heat exchanger network

utility systems, and environmental systems. Rudd et al. (1973) proposed a more theoretically abstract synthesis hierarchy that essentially follows the same steps, but included an additional step of integrating reaction, mixing, separation, or change of state tasks into unit processes or operations. Douglas (1988) set out a somewhat different approach, summarized in Table 2.1. Douglas emphasized early introduction of process economics to guide the elimination of weaker alternatives, with continuous refinement of the economic model as more detail is added to the flowsheet. This is a useful approach, as it can highlight deficiencies in the design at an early stage. The reality of process development in industry is usually a lot less systematic than the idealized picture painted by academic researchers. In industrial practice, process development is more interdisciplinary, more iterative, and much less linear than the simple synthesis models suggest. The flowsheet synthesis step is usually part of a larger effort that involves chemists, biologists, and other engineers and includes laboratory and pilot plant experiments to determine reactor

CHAPTER 2 Process Flowsheet Development

performance and establish yields and product recoveries. The engineers working on synthesis seldom have all the data that are needed to properly optimize the design, and often must guide the research members of the team to collect additional data under conditions that will be more favorable to process economics. Many industrial processes involve multiple reaction steps carried out in sequence with intermediate separation steps, and it may be difficult to assess the performance of later steps without good information on the nature and quantity of byproducts that are carried over from earlier steps in the sequence. The design team therefore needs to form a rough impression of the process flow diagram and economics using minimal information on process chemistry, so as to develop an understanding that can guide the efforts of the research team. Figure 2.25 sets out an approach to flowsheet synthesis that sets flowsheet development in the context of working with a research team to establish yields and reactor performance. The Douglas hierarchy and onion diagram form substeps in this procedure, as described below.

4. Refine process structure (Figure 2.27)

Start

1. Initial economics attractive?

STOP

5. Complete and review PFD

Continue research

6. Preliminary process hazard analysis (PHA)

Y 2. Set yield targets

N Yield targets met ?

Give up?

7. Revise economic assessment

Y 3. Preliminary economic assessment (Figure 2.26)

Preliminary cost of production

Cost of production attractive? N Revise yield targets

FIGURE 2.25 Procedure for process synthesis.

Review largest cost components

Updated cost of production

Cost of production attractive? Y Optimize and go to detailed design

2.6 Synthesis of Novel Flowsheets

Step 1. Initial Economics The very first step should be to collect prices for feeds and products and confirm that the cost of production will be attractive if a stoichiometric yield is obtained. If the cost of feed is more than the product value, then there is no hope of developing an economically attractive process and the work should be stopped unless the team has strong evidence that prices will change in the future. This step is particularly important when assessing nontraditional feeds; for example, when looking at processes for converting food-based renewable feeds into chemicals.

Step 2. Set Yield Targets The research team needs to be set realistic targets that will lead to an attractive process. The term yield targets includes targets for byproduct selectivity as well as main product selectivity and conversion. Methods for setting and revising yield targets are given in Section 2.6.3. The researchers will generally need to carry out process development experiments to optimize reactor conditions and catalyst, enzyme, or organism performance to meet the yield targets. On the first pass through the procedure, the designers may choose to just accept whatever yields and selectivities the research chemists or biologists have already established. When more information on process economics has been generated, the targets can be revised and improved. If the yield targets are not met, the company must make a strategic decision on whether to continue or abandon the research. Research discoveries are often serendipitous and can be hard to plan. Companies often choose to allow a low level of research activity to continue over a long period of time once clear success criteria have been established.

Step 3. Preliminary Economic Assessment The goal of a preliminary economic assessment is to arrive at a preliminary estimate of the cost of production once the yield targets have been met. The substeps in carrying out a preliminary economic assessment are illustrated in Figure 2.26. This procedure is similar to that of Douglas (1988), but it should be emphasized that less detail is put into the design and the goal is not to arrive at a PFD or even a detailed block flow diagram at this point. The components of cost of production and methods for calculating each component are discussed in detail in Chapter 8. For most processes, 80% or more of the cost of production will be feedstock cost less credits for any economically viable byproducts. The rest of the cost of production is chiefly made up of utility costs (mostly energy), fixed costs (mostly labor), and annualized payments to generate an expected return on the capital investment. The split between these depends on the type and scale of the process. Small-scale batch processes will have a higher proportion of fixed costs, while large-scale petrochemicals or solids-handling plants will have a higher proportion of utility costs. In a preliminary economic assessment, the designer seeks to make a quick estimate of these major components of cost, and hence determine whether the process will be able to make product at an attractive price. The first step is to look at the yields and identify any significant byproducts. Byproducts can be formed by the reaction stoichiometry, by side reactions, or from extraneous components in the feeds. Byproducts must be refined and sold, treated as waste streams, or recycled to extinction in the process. A quick examination of the yields and prices of the byproducts is usually sufficient to establish which are suitable for recovery. The economic assessment of byproduct recovery is discussed in more detail in Section 8.2.3.

CHAPTER 2 Process Flowsheet Development

Yield targets met? Y Determine byproducts

Byproduct values

Determine recycles

Preliminary reactionseparation-recycle structure

Preliminary simulation

Preliminary equipment sizing

Mass and energy balance

Preliminary capital cost estimate

Pinch analysis

Preliminary utilities

Preliminary cost of production

FIGURE 2.26 Preliminary economic assessment.

Once the designer has a notion of which byproducts are worth recovering and which byproducts must be recycled, a preliminary reaction-separation-recycle structure can be sketched. It is not important to have the best or optimal flowsheet at this point, and the design team may want to propose a few alternatives to see which is least costly. A process simulation model can then be built and used to generate a mass and energy balance and obtain rough sizing of the major process equipment. The preliminary simulation should include all recycles, reactors, and separation equipment and should capture all changes in temperature and pressure. It does not need to include a heat recovery design, and should use heaters and coolers instead of heat exchangers whenever there is a change in temperature. The use of commercial programs for process simulation is discussed in Chapter 4. The preliminary simulation model does not have to be built using a commercial simulation program, but it will usually be convenient to do so, so that the model can be extended as the flowsheet is subsequently refined.

2.6 Synthesis of Novel Flowsheets

The preliminary equipment sizes from the simulation model (or hand calculations) can be used to develop an initial estimate of the capital cost of building a plant. Estimation of capital costs is covered in Chapter 7. The capital cost is then annualized so that it can be added to the other costs of production. Annualization of capital costs is covered in Section 9.7. In a preliminary economic assessment the designers usually annualize capital costs by dividing by 3. The basis for this rule of thumb is set out in Section 9.7.2. The process energy consumption and utility costs are difficult to assess without completing a process simulation and energy balance. Most processes have significant opportunity to reduce energy costs by heat recovery, so simply adding up all the heating and cooling duties would be a gross overestimate. Instead, a first estimate of energy consumption can be made by carrying out the targeting step of pinch analysis to get hot and cold utility targets. Pinch analysis and other heat recovery methods are described in Chapter 3. At this point in the design it is not necessary to design the heat recovery system, as the targets are adequate for the preliminary economic assessment. The preliminary estimates of main product and byproduct production rates, feed and energy consumption, and capital cost can be used to make a preliminary estimate of the cost of production, as described in Chapter 8. If the cost of production appears attractive, the design team proceeds to the next step. If not, the economic assessment can be used to highlight the major components of cost that must be reduced to make the process economically interesting. Having identified the cost components that must be addressed, the design team can either look at alternative flowsheets that reduce these costs or else set more aggressive yield targets and go back to the research stage.

Step 4. Refine Process Structure If the preliminary economic assessment indicates that the process is potentially economically attractive, then it is important to develop a complete PFD and make sure that no costs have been overlooked. The steps in completing a more rigorous design are shown in Figure 2.27. It can be seen that these follow roughly the same sequence as the onion diagram of Figure 2.24. The first step is to optimize the reaction-separation-recycle structure of the flowsheet and confirm the yields under the optimal conditions. The preferred conditions can be estimated by optimization of the preliminary simulation model and economic model. Additional experimental data may be needed if the optimal conditions are different from the conditions originally proposed. The reactor designs must be tested and yields confirmed in the presence of recycle streams, which may require construction of a pilot plant that can operate in recycle mode. The design of reactors is described in Chapter 15. The design of the separation systems encompasses not only those separations associated with product recovery and recycles, but also feed purification, product purification, and byproduct recovery. The design of separation processes is covered in detail in Chapters 16, 17, and 18. In some cases, product purification or byproduct recovery will require additional reaction steps. For example, in the recovery of ethylene produced by steam cracking of light hydrocarbons, it is easier to hydrogenate byproduct acetylene than to separate it by distillation; see Figure 2.28. When the byproduct separation and recovery sections have been designed in more detail, the attractiveness of recovering the byproducts can be revisited. If the costs of producing the byproducts are excessive, the designer should revisit the reaction-separation-recycle structure or return to the preliminary economic analysis step.

CHAPTER 2 Process Flowsheet Development

Preliminary cost of production attractive? Y Optimize reactionseparation-recycle structure

Confirm yields under optimized reactor conditions

Design reactors

Design separations

Design by-product recovery sections

Including feed and product purification

Confirm by-product attractiveness

N By-products still attractive?

Y Design heat and power recovery

Design control systems

Design plant hydraulics

Update simulation

Prepare PFD

Proceed to step 5 of Figure 2.25

FIGURE 2.27 Refining the process flowsheet.

When designing the reaction and separation steps, as much use as possible should be made of proven process subsections. If a particular reaction, separation, recovery, or purification step is already practiced commercially, then the same method will probably be least costly and will most likely have the least technical risk for the new design. Borrowing proven concepts from established technology is one of the most effective strategies for reducing commercialization

Compression

Refrigeration

Demethanizer

De-ethanizer

Acetylene saturation

C2 splitter

Stabilizer Hydrogen

Ethylene

Hydrogen

Hydrogen methane

Acetylene saturation unit

Ethane Product from cracking furnace Refrigerant

Propane

Butenes Depropanizer

FIGURE 2.28

C3 splitter

2.6 Synthesis of Novel Flowsheets

Propylene

Ethylene recovery from steam cracking.

CHAPTER 2 Process Flowsheet Development

risk. Some caution is needed when applying this strategy if the new case is not identical to the commercially-proven design, and the designer should take particular care to ensure that slight differences do not lead to potential safety or operability issues. The designer must also ensure that there are no active patents on the features that are borrowed so that there is freedom to practice them. Once the major process equipment has been specified, the design team should have a good idea of the stream temperature and pressure requirements and the heat recovery system can be designed. Process heat recovery is described in Chapter 3 and heat transfer equipment is covered in Chapter 19. The design of the plant hydraulics and control system are interlinked, as control valves introduce additional pressure drop into the process and can create a requirement for additional pumps. Once the major equipment, including heat exchangers, has been specified, a preliminary PFD can be drafted, which can be developed into a full PFD by adding the location of control valves, pumps, and compressors. The design of plant control systems and location of control valves is discussed in Chapter 5. The design of hydraulic equipment is covered in Chapter 20, and solids handling systems are described in Chapter 18. When all the equipment has been added to the PFD, the process simulation can be updated to produce mass and energy balances to complete the flowsheet. The PFD is then ready for review.

Step 5. PFD Review Review of a process flow diagram is one of the most important steps in flowsheet development. A full PFD review is always carried out in design, regardless of whether the process is a revamp or new unit, or whether it uses novel or proven technology. This vital step is discussed in more detail in Section 2.7.

Step 6. Preliminary Process Hazard Analysis (PHA) When a completed PFD and mass and energy balance are available, a preliminary process hazard analysis (PHA) can be carried out. A process hazard analysis will identify major hazards inherent in the process, and may indicate a need to alter some process conditions, substitute different equipment, or completely redesign sections of the process. If the preliminary PHA identifies major modifications to the PFD, the design team should go back to the relevant stage of the procedure and generate a safer alternative design. The role of safety in design is discussed in detail in Chapter 10.

Step 7. Revise Economic Assessment The completed PFD and mass and energy balance allow the design team to make more accurate designs of the process equipment, and hence arrive at more accurate estimates of the capital cost and cost of production. If the process still appears to be attractive then it may be worth developing as an investment, and other methods of economic assessment will be used to determine a viable project for implementing the technology; see Chapter 9. The models that have been developed now have sufficient accuracy to enable more rigorous optimization and can be used as a starting point for detailed design of the plant and equipment. Optimization methods in process design are discussed in Chapter 12. If the updated cost of production is no longer attractive, the added detail can be used to further define the major cost components and identify areas for process improvement. This will often involve reducing byproduct and recycle handling, and hence translate into setting tougher yield targets.

2.6 Synthesis of Novel Flowsheets

2.6.2 Economic Analysis in Process Synthesis In process synthesis it is important to use economic analysis to inform decision making at every step. The procedure outlined in Figure 2.25 begins with a very rough economic analysis and then adds detail to this analysis as information is accumulated. Like an artist beginning with a rough pencil sketch and then filling in details and adding colors, the process design engineer needs to have an overall sense of the composition before getting into the details. The procedure set out in Figure 2.25 has three economic checkpoints at steps 1, 3, and 7, corresponding to the initial, preliminary, and updated estimates of the cost of production. At these checkpoints the estimated cost of production should be compared to the product sales price that the marketing organization has forecasted. Usually, the criterion for success will be that the cost of production must be low enough to ensure an acceptable return on the capital deployed. Forecasting of prices and calculation of cost of production are covered in Chapter 8, and methods of economic analysis are described in Chapter 9. Although these three steps in the procedure are formal checks, experienced designers do not wait until the checkpoint to calculate process costs. As soon as information is developed, its impact on the cost of production should be determined. In general, costs accumulate as detail is added to the design, so the design team wants to be aware of large costs as early as possible so that they can start considering alternative design features. Companies usually use other economic analysis methods such as net present value (NPV) and internal rate of return (IRR) instead of cost of production when assessing capital investment projects; however, very few companies launch a capital project without having already completed the process synthesis. At the synthesis stage, cost of production is the most useful economic measure, as it is very easily factored into components such as raw material costs, byproduct values, energy costs, etc. Understanding the components of cost of production can help the design team to focus on areas of high cost if the target cost of production is not achieved.

2.6.3 Use of Targets in Process Synthesis Design engineers use targets as a means of setting bounds on design performance that can quickly eliminate unattractive options. Targets also help designers and researchers to focus their efforts on areas that will most effectively improve economic performance. Several different types of targets are used in the synthesis procedure set out in Figures 2.25, 2.26, and 2.27: • • • •

The cost of production is compared to a price target set by the marketing organization at steps 1, 3, and 7. The design team sets yield and selectivity targets for the research team at step 2. Hot and cold utility targets calculated by pinch analysis are used for initial estimates of process energy consumption. The preliminary economic analysis sets targets for capital cost and the components of cost of production that the design team must confirm as they refine the process structure and fill in the PFD.

The basis for targets should always be clearly stated. Whenever possible, targets should be calculated from economic criteria, and the assumptions in the calculations should be made explicit. For example, a badly stated yield target would be “Find me a catalyst that doesn’t make byproduct X.”

CHAPTER 2 Process Flowsheet Development

A better way of stating this target might be “If reactor selectivity to byproduct X is < 0.5% of selectivity to main product we can eliminate a separation and purification section of the process, with expected 15% savings in capital cost and 20% savings in energy cost.” Targets must not be unrealistically tough, or they will never be achieved and will not be taken seriously. Lenient yield targets are usually not as problematic, as they tend to lead to failure at the preliminary economic assessment stage and are then revised to something more realistic. Lenient targets for cost of production are very dangerous, as they allow the design to go forward, and much time and effort can be wasted before harsh economic reality kills the project. Good price forecasting and market analysis are critically important in setting cost of production targets. These topics are discussed in Chapter 8.

It is important to understand whether a target should be treated as a hard constraint or a soft constraint. Companies sometimes address this question by providing must have targets that are hard constraints and should have targets that are soft constraints. The design team can then reject designs that do not meet the hard constraints, but keep concepts that come close to the soft targets. Soft and hard targets are explored in Example 2.8. Example 2.8 The marketing group is planning to launch a new product and has forecasted that the mean price for the product will be 5 $/kg, normally distributed with standard deviation 40 ¢/kg. The cost of the stoichiometric amount of feed required to make the product is 3 $/kg. Propose preliminary targets for cost of production and yields.

Solution

If the forecast is accurate and the mean product price is 5 $/kg, then there is a 50% probability the project will have economic success if the cost of production (including capital recovery) is 5 $/kg. Using the standard deviation given in the forecast, we can form the following table: Cost of Production (COP), $/kg 3.80 4.20 4.60 5.00 5.40

(= 5 − (3 × 0.4)) (= 5 − (2 × 0.4)) (= 5 − (1 × 0.4)) (= 5 + (1 × 0.4))

Probability of Success 99.9% 97.7% 84% 50% 16%

We can note immediately that this process would pass the initial economic assessment even if we chose a target cost of production with 99.9% chance of success. The probability of success that we require depends on how risk averse or aggressive the company is. A 98% chance of success might be too conservative and would give a high chance that the project would not meet the targets. A 50% chance of success would probably be too aggressive and would allow the project to go forward and spend money with low likelihood of financial success. As a compromise, management might set a must have target for COP of 4.60 $/kg, with a should have target of 4.40 $/kg. Note that we are not

2.6 Synthesis of Novel Flowsheets

constrained to using integral multiples of the standard deviation in setting the targets; for example, a price target of 4.34 $/kg (= 5 − (1.65 × 0.4)) corresponds to 95% probability of success and would be equally easy to justify as a must have or should have target. The COP target can now be translated into preliminary yield targets. In Section 2.6.1 it was stated that feed costs are typically at least 80% of COP. Using this rule of thumb, we can state Target feed cost = 0:8 × target COP The yield targets obviously depend on the number of feeds, the relative costs of individual feeds and the number of reaction and product recovery steps. From equations 2.4 and 2.6 we know product formed Yield = stoichiometric product formed so Target plant yield =

stoichiometric cost=kg target feed cost=kg

So if the target COP is 4.60 $/kg Target plant yield =

3 = 0:815 0:8 × 4:60

Note that this is the target yield over all the steps in the process. If we assume that we lose roughly 5% of the product during all the steps of product recovery and purification then Target plant yield from reactors = 0:815 = 0:858 0:95 If we have two reaction steps and one feed is more expensive than the others then we could further decompose the yield target into targets for each step: Target plant yield from reactors = Y1 Y2 where Y1 and Y2 are yields of reaction steps 1 and 2. We could set equal targets for each step: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Y1 = Y2 = ð0:858Þ = 0:926 or we could use our knowledge of the process chemistry or biology to define a suitable allocation between the steps. Note that the targets calculated are plant yields, not reactor yields. If costly unconverted feeds can be recycled, the plant yields translate into reactor selectivity targets, not reactor yield targets (see Section 2.3.3). Note also that even in this simplistic example, the apparently very favorable economics quickly translated into rather tough targets for reactor performance.

2.6.4 Use of Heuristic Rules in Process Synthesis Heuristic is an adjective, meaning “of, or pertaining to, or based on, experimentation, evaluation, or trial and error methods,” which pretty much sums up most engineering knowledge. The terms heuristic rules or design heuristics are commonly used to describe rules of thumb and design

CHAPTER 2 Process Flowsheet Development

guidelines that have been developed based on experience. Experience is good, but it is rarely acquired instantly or bought cheaply. Design guidelines based on generalizations are only useful if the designer has sufficient experience to understand when to apply the guideline and when to make an exception. There is often confusion about what constitutes a design heuristic. Consider the following statements, most of which have been made in this chapter: 1. 2. 3. 4. 5.

“The heat of condensation of steam is about 2000 kJ/kg.” “Pressure drop is usually proportional to velocity squared.” “Feedstock costs are typically at least 80% of the total cost of production.” “Capital costs can be annualized by dividing by 3.” “When designing reaction and separation steps, use proven process subsections as much as possible.”

Statement 1 is a convenient data approximation. It is accurate within ± 10% for saturated steam over a temperature range from 100 °C to 240 °C, which covers most temperatures at which steam is used for process heating. Remembering this fact may save an engineer some time when carrying out hand calculations, but it does not provide any guidance for design. Statement 2 is a convenient summary of several correlations for pressure drop. It may be very useful for making quick calculations in revamp designs, but again provides no guidance for design. Statement 3 is a generalization that can be useful as a rough check on cost of production calculations. As illustrated in Example 2.8, it can also be used as a basis for setting initial targets in process synthesis. It is, however, rather too general to provide guidance in design. Statement 4 is one way of annualizing capital costs. It would be equally valid to state “Capital costs can be annualized by dividing by 2” or “…by dividing by 5,” depending on the assumptions made. The basis for deriving these numbers is given in Section 9.7.2. Statement 5 is clearly a design guideline based on a general desire to minimize the number of unproven concepts in the flowsheet. Although all of these statements are useful as rules of thumb and can help make quick calculations to assess a design, only statement 5 actually provides guidance on how to design a process. It might be very useful for an engineer to recall approximate data and generalizations, and several compilations of such rules of thumb have been written (Chopey, 1984; Fisher, 1991; Branan, 2005), but these are only helpful in process design when making quick calculations in meetings. Some design texts provide extensive lists of rules of thumb and selection guidelines. That approach is not adopted here, as heuristics easily lose their meaning when taken out of context. For example, one design text gives the rule for vessel design: “optimal length to diameter ratio = 3,” This is questionable even for horizontal and vertical flash drums (see Section 16.3), but is clearly nonsense when wrongly applied to reactors and distillation columns. Inexperienced engineers often have difficulty determining when to apply such heuristic rules, so in this text all shortcut calculations, convenient approximations, and design guidelines will be presented and explained under the relevant design topic. The most important heuristic rule, which should always be followed, is “Never use a heuristic rule unless you understand where it came from and how it was derived.”

2.7 PFD Review

2.6.5 Role of Optimization in Process Synthesis Optimization methods are used in process synthesis to select the best flowsheet options, process conditions, and equipment sizes. The designer must be reasonably sure that design alternatives have been optimized before selecting between them. Optimization underpins all design decisions, and the subject is addressed in more detail in Chapter 12. The problem that is often encountered when applying optimization methods in process synthesis is that insufficient data are available to properly formulate an optimization problem. For example, it would be good to optimize reactor performance as soon as possible, but the research team may not yet have collected data in the presence of recycle streams or at conditions close to the optimal reactor conditions. Under the circumstances, the designer must optimize the design with the data available and then revisit the optimization later when more data have been collected and the reaction kinetics model has been updated. Most processes are too complex to formulate a single optimization problem that includes all possible structural flowsheet variations as well as all continuous process variables. Instead, different aspects of flowsheet synthesis are usually treated as separate optimization tasks. It is, however, important to have an overall optimization model that captures the major design trade-offs. The cost of production model developed in the preliminary economic assessment can serve as an initial model for optimization. The optimization of subproblems is discussed in Section 12.5.

2.7 PFD REVIEW The most important step in developing a process flowsheet is for the PFD to be rigorously reviewed. This is true regardless of whether the flowsheet is for an established design, a revamp, or a newly invented process. The purpose of a PFD review is to review the design decisions and assumptions and ensure that the flowsheet is complete and shows all the equipment needed to really operate the process. A PFD review is usually attended by the design team and a few outside experts. These may include: • • • • • • • • •

Senior managers Technical experts on process design Technical experts on process chemistry, catalysis, or biology Equipment or plant design experts Process safety experts Metallurgists Plant operations staff Plant mechanical engineers Process control engineers

Some companies have rules and procedures governing who must be present at a PFD review, but the review can be effective with only a few people as long as they engage actively with the team.

2.7.1 PFD Review Procedure A PFD review is usually carried out as a group exercise. A large printout of the PFD is typically taped or pinned to a wall so that the group can mark up corrections, notes, and other revisions as

CHAPTER 2 Process Flowsheet Development

the review proceeds. The PFD is usually drawn well spaced out to leave room for additions, and may run to several sheets of drawings. One member of the group takes notes and documents any actions that are agreed or concerns that are raised. If the heat and material balances and stream conditions are not shown on the PFD, printouts are usually provided for the reviewers. For complex processes, a PFD review may begin with a brief overview of the process chemistry and block flow diagram to establish the context for the reviewers. In some cases the design basis assumptions are also reviewed at the start. The main part of a PFD review is a “walkthrough” of the process by the process design engineer. Starting with one feed stream, the designer follows the stream from storage through all the process operations that it encounters. At each process operation, the designer explains the purpose of the operation, the design criteria, and the resulting condition of the stream at the exit. For example, the feed section shown in Figure 2.29 would be described as follows: Feed of 99% pure technical grade A leaves floating roof storage tank T101 through line 101 at ambient conditions. The governing ambient temperature for heater design is winter low temperature of −5 °C and for pump design is summer high temperature of 30 °C. Stream 101 is pumped by centrifugal pump 101 to a pressure of 10 bar gauge, forming stream 102. Pump 101 has a standby spare, shown. Flow of feed A is regulated by flow control valve FCV100, with design pressure drop 1.3 bar. Stream 103 exits FCV100 and is sent to steam heater E101. The purpose of heater E101 is to heat feed to the reaction temperature of 180 °C. High pressure steam at 240 °C is used as heat source. The steam rate is controlled by temperature controller TC101, which receives input from temperature indicator on the process stream leaving E101 in Stream 104. The steam has been placed tube side in E101 because the process stream is nonfouling and steam is at high pressure, so this is expected to lead to lowest cost design. A pressure drop allowance of 0.7 bar has been assigned to E101. Stream 104 leaves E101 at the desired reactor feed temperature of 180 °C and at reactor pressure 8 bar gauge, and enters reactor R1.

As the designer steps through the PFD, the review group asks questions to challenge the design assumptions and identify potential missing equipment. In the previous example, some relevant questions could have been: • • • • • • •

Is it necessary to pass the feed through a filter before FCV100 to remove any crud that accumulated in the tank or came in with the feed? Why use HP steam to heat all the way from ambient temperature? Couldn’t process heat recovery be used for at least part of the heating? Why not use LP steam to heat to 110 °C then HP steam to final temperature? Should FCV100 be a separate control loop? Shouldn’t it be in ratio to other reactor feeds? Did the team look at using a variable speed drive on the pump to regulate flow instead of a pump and control valve? This would give lower energy consumption. What was the basis for choosing 180 °C and 8 bar gauge as the reactor conditions? Does the feed need to enter the reactor at reactor conditions? Would a colder or hotter feed reduce the reactor cooling or heating duty?

Some additional typical PFD review questions are given in Table 2.2.

T101

P101

101

FCV100

102

E101

FIC

103

TIC

104

726

From sheet 2.29.7

201

HP ST

To sheet 2.29.2

FIGURE 2.29

2.7 PFD Review

Feed to a reactor.

CHAPTER 2 Process Flowsheet Development

Table 2.2 Sample Questions That Can Be Asked in a PFD Review Process Section

Questions

Feed preparation

How is (each) feed delivered? How is (each) feed stored? How much inventory of (each) feed is required? How is feed transferred from storage to the process? How is the rate of feed supply controlled? Is any feed pretreatment necessary before the feed is sent to the process? For solid feeds, is any feed size adjustment necessary? Is any heating or cooling needed before the feed is sent to the process? What are the reacting species? What side reactions occur? What are the reaction conditions and why were they chosen? How are the reaction conditions maintained or controlled? How are inventories of solids, liquid or vapor in the reactor controlled? What are the reactor design specifications (e.g. residence time, interfacial area)? What are the estimated reactor yield and selectivity? What reactor type was chosen and why was it selected? Is a catalyst used? If so, is the catalyst stable or does it require periodic regeneration? Is heat addition or removal necessary? Are there specific safety issues that should be considered? (Additional information on reactor design is given in Chapter 15, which may prompt more questions) What is the purpose of each separation? What are the process conditions (temperature, pressure, etc.)? What are the equipment specifications (recovery, purity, etc.)? Why was a particular separation selected? Is heat removal or addition necessary? Can heat addition or removal be accomplished by process-to-process heat transfer? How are inventories of vapor, liquid or solid controlled in each operation? How is the operation controlled to achieve the desired specifications? Are there specific safety issues that should be considered? What are the final product specifications? What are the specifications for any byproducts? What are the specifications for any effluents discharged to the environment? What are the specifications for any recycle streams returned to the process? What are the specifications for any waste streams sent to disposal? How are final purity specifications on any stream leaving the process achieved? How is the process controlled to ensure that purity specifications can be achieved?

Reaction

Product Recovery

Purification

2.8 Overall Procedure for Flowsheet Development

If the questions lead to modifications to the flowsheet that are immediately obvious and agreed by all the reviewers, then these are marked up as corrections. If further analysis is required before deciding on a modification, it is noted as a follow-up action for the team. The same procedure is followed for every stream in the PFD. Since it is often necessary to jump from one drawing or section of the flowsheet to another and back again, it is a good idea to mark streams with a highlighter when they have been completed so that the group does not overlook any streams. Sufficient time must be allowed to complete the PFD review to the satisfaction of all the reviewers. The amount of time needed depends on the complexity and novelty of the design and the familiarity of the reviewers with the technology. For complex designs, a full PFD review can take several days to complete.

2.7.2 PFD Review Documentation and Issue Resolution The notes taken at a PFD review usually include a long list of items that require follow-up by the design team. It is a good idea to include these notes and a description of how any issues and concerns were resolved in the design documentation. The notes should be circulated to meeting attendees immediately after the PFD review meeting to ensure that all issues were correctly captured. If a PFD review indicated a need for substantial modification of the flowsheet, the group should reconvene after the modifications have been made to review the modified PFD. In process synthesis projects, several rounds of PFD review may be necessary.

2.8 OVERALL PROCEDURE FOR FLOWSHEET DEVELOPMENT Figure 2.30 shows an overall strategy for flowsheet selection and development. The chart in Figure 2.30 will generally lead to the selection of a commercially-proven process or a modification of such a process when one exists. This reflects the commercial reality that very few business leaders are willing to risk a large sum of money (and their career and reputation) on unproven technology unless the financial return is very good and no good alternatives are available. Although process synthesis is very enjoyable as a creative activity, the industrial practice of process design is usually more concerned with delivering designs that will work reliably and quickly make money to generate a return on investment. Successful companies are usually good at focusing the creativity of their employees on critical areas where innovation can provide a competitive advantage, without turning every project into an open-ended research problem.

CHAPTER 2 Process Flowsheet Development

Start

Current plant exists? Y

Follow revamp design procedure: section 2.5 and figure 2.14

Commercial process exists? N

Commercial process exists for similar chemistry/biology?

Optimize and evaluate existing commercial alternatives

Y Improvement needed?

Follow process synthesis procedure: section 2.6 and figure 2.25

Modify existing design: section 2.4.3

Proceed with existing design: section 2.4

FIGURE 2.30 Overall procedure for flowsheet development.

References Asante, N. D. K., & Zhu, X. X. (1997). An automated and interactive approach for heat exchanger network retrofit. Chem. Eng. Res. Des., 75(A3), 349. Auger, C. P. (Eds.). (1992). Information sources in patents. Bower-Saur. Austin, G. T., & Basta, N. (1998). Shreve’s chemical process industries handbook. McGraw-Hill. Branan, C. R. (2005). Rules of thumb for chemical engineers. Gulf. Briggs, M., Buck, S., & Smith, M. (1997). Decommissioning, mothballing and revamping. ButterworthHeinemann. Chopey, N. P. (Eds.). (1984). Handbook of chemical engineering calculations. McGraw-Hill.

References

Comyns, A. E. (1993). Dictionary of named chemical processes. Oxford University Press. Doherty, M. F., & Malone, M. F. (2001). Conceptual design of distillation columns. McGraw-Hill. Douglas, J. M. (1988). Conceptual design of chemical processes. McGraw-Hill. El-Halwagi, M. M. (1997). Pollution prevention through process integration: Systematic design tools. Academic Press. El-Halwagi, M. M. (2006). Process integration. Academic Press. Fisher, D. J. (1991). Rules of thumb for engineers and scientists. Gulf. Fogler, H. S. (2005). Elements of chemical reaction engineering (3rd ed.). Prentice Hall. Froment, G. F., & Bischoff, K. B. (1990). Chemical reactor analysis and design (2nd ed.). Wiley. Gordon, T. T., & Cookfair, A. S. (2000). Patent fundamentals for scientists and engineers. CRC Press. Grayson, M. (Ed.). (1989). Kirk-othmer concise encyclopedia of chemical technology. Wiley. Kemp, I. C. (2007). Pinch analysis and process integration (2nd ed.). A User Guide on Process Integration for Efficient Use of Energy. Butterworth-Heinemann. Kirk, R. E., & Othmer, D. F. (Eds.). (2001). Encyclopedia of chemical technology (4th ed.). Wiley. Kirk, R. E., & Othmer, D. F. (Eds.). (2003). Encyclopedia of chemical technology: concise edition. Wiley. Kohl, A. L., & Nielsen, R. B. (1997). Gas purification (5th ed.). Gulf Publishing. Levenspiel, O. (1998). Chemical reaction engineering (3rd ed.). Wiley. McKetta, J. J. (Eds.). (2001). Encyclopedia of chemical processes and design. Marcel Dekker. Meyers, R. A. (2003). Handbook of petroleum refining processes (3rd ed.). McGraw-Hill. Miller, S. A. (1969). Ethylene and its industrial derivatives. Benn. Montgomery, D. C. (2001). Design and analysis of experiments (5th ed.). Wiley. Rudd, D. F., Powers, G. J., & Siirola, J. J. (1973). Process synthesis. Prentice-Hall. Shenoy, U. V. (1995). Heat exchanger network synthesis: Process optimization by energy and resource analysis. Gulf. Smith, R. (2005). Chemical process design and integration. Wiley. Ullmann. (2002). Ullmann’s encyclopaedia of industrial chemistry (5th ed.). Wiley VCH. Wolverine. (1984). Wolverine tube heat transfer data book—low fin tubes. Wolverine Inc. Zhu, X. X., & Asante, N. D. K. (1999). Diagnosis and optimization approach for heat exchanger network retrofit. AIChE J., 45(7), 1488.

International Standards BS 1553-1. (1977). Specification for graphical symbols for general engineering. part 1: piping systems and plant. British Standards Institute. ISO 10628. (1997). Flow diagrams for process plants – general rules (1st ed.). International Organization for Standardization.

Bibliography: General References on Process Synthesis Biegler, L. T., Grossman, I. E., & Westerberg, A. W. (1997). Systematic methods of chemical process design. Prentice Hall. Douglas, J. M. (1988). Conceptual design of chemical processes. McGraw-Hill. Rudd, D. F., & Watson, C. C. (1968). Strategy of process design. Wiley. Rudd, D. F., Powers, G. J., & Siirola, J. J. (1973). Process synthesis. Prentice-Hall. Seider, W. D., Seader, J. D., Lewin, D. R., & Widagdo, S. (2009). Product and process design principles (3rd ed.). Wiley. Smith, R. (2005). Chemical process design and integration. Wiley. Turton, R., Bailie, R. C., Whiting, W. B., & Shaeiwitz, J. A. (2003). Analysis, synthesis and design of chemical processes (2nd ed.). Prentice Hall.

CHAPTER 2 Process Flowsheet Development

NOMENCLATURE Dimensions in MLT A Cp,f Cp,i Cp,p F Fcw Ft mf mi mp Q SV T1 T2 T3 Ts Tw ΔTi ΔTlm ΔTm U V Vcat v X Y Z τ

Area for heat exchange Specific heat capacity of feed Specific heat capacity of stream i Specific heat capacity of product Unknown flow, Example 2.6 Flow rate of cooling water Log mean temperature difference correction factor (see Chapter 19) Mass flow rate of feed Mass flow rate of stream i Mass flow rate of product Rate of heat transfer Space velocity Unknown temperature, Example 2.7 Unknown temperature, Example 2.7 Unknown temperature, Example 2.7 Steam temperature Cooling water outlet temperature Change in temperature of stream i for a stream undergoing sensible heat changes Logarithmic mean temperature difference Mean temperature difference for heat transfer Overall heat transfer coefficient Reactor volume Catalyst fixed bed volume Volumetric flow rate Unknown flow, Examples 2.1, 2.5 Unknown flow, Example 2.5 Unknown flow, Example 2.5 Residence time

L2 L2T−2θ−1 L2T−2θ−1 L2T−2θ−1 MT−1 MT−1 — MT−1 MT−1 MT−1 ML2T−3 T−1 θ θ θ θ θ θ θ θ MT−3θ−1 L3 L3 L3T−1 MT−1 MT−1 MT−1 T

PROBLEMS 2.1. Cinnamic aldehyde (a fragrance compound) can be made by base-catalyzed aldol condensation reaction between benzaldehyde and acetaldehyde. The feeds are contacted with sodium hydroxide in a stirred tank reactor. The product is neutralized and washed with water to remove salts. The washed product is usually separated by batch distillation, in which unreacted feeds are recovered first, followed by product, and a polymeric waste is left as residue. The batch distillation product can be further purified by vacuum distillation. Sketch a block flow diagram of the process.

Problems

2.2. Cumene is made by alkylation of benzene with propylene over zeolitic catalyst. To maximize selectivity to desired products, several beds of catalyst are used inside the same reactor. A mixture of feed and recycle benzene enters the top of the reactor and the feed propylene is split so that a portion of the propylene is fed to each catalyst bed. A large excess of benzene is used, to minimize propylene oligomerization and ensure complete reaction of propylene. The reactor product is cooled and sent to a stabilizer column that removes any light hydrocarbons. The bottoms from this column is sent to a benzene column that recovers benzene overhead for recycle to the alkylation and transalkylation reactors. The bottoms from the benzene column is distilled to give cumene product and a heavy stream. The heavy stream is further distilled in a heavies column to give a mixture of dipropyl- and tripropyl-benzene overhead and a heavy waste stream as bottoms. The distillate from the heavies column is sent to a transalkylation reactor and reacted with excess benzene. The product from the transalkylation reactor is returned to the benzene column. Sketch a block flow diagram of the process. 2.3. Cyclosporin A is produced by fermentation using either Cylindrocarpon lucidum Booth or Tolypocladium inflatum Gams. The fermentation is carried out in batch reactors, which are filled with a feed medium, inoculated with the fungi, and aerated for a period of 13 days. The reactor product is milled and extracted with 90% methanol. The methanol is evaporated off to give an aqueous solution that is then extracted with ethylene chloride. The organic solution is evaporated to dryness and then the product is purified by chromatography in methanol over aluminum oxide or silica gel. Sketch a block flow diagram of the process. 2.4. The composition of a gas derived by the gasification of coal is, volume percentage: carbon dioxide 4, carbon monoxide 16, hydrogen 50, methane 15, ethane 3, benzene 2, balance nitrogen. If the gas is burnt in a furnace with 20% excess air, calculate a. the amount of air required per 100 kmol of gas, b. The amount of flue gas produced per 100 kmol of gas, c. the composition of the flue gases, on a dry basis. Assume complete combustion. 2.5. The off-gases from a gasoline stabilizer are fed to a steam reforming plant to produce hydrogen. The composition of the off-gas, molar%, is: CH4 77.5, C2H6 9.5, C3H8 8.5, C4H10 4.5. The gases entering the reformer are at a pressure of 2 bara and 35 °C and the feed rate is 2000 m3/h. The reactions in the reformer are 1: C2 H2n + 2 + nðH2 OÞ → nðCOÞ + ð2n + 1ÞH2 2: CO + H2 O → CO2 + H2 The molar conversion of C2H2n+2 in reaction (1) is 96% and of CO in reaction (2) is 92%. Calculate a. the average molecular mass of the off-gas, b. the mass of gas fed to the reformer, kg/h, c. the mass of hydrogen produced, kg/h.

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CHAPTER 2 Process Flowsheet Development

2.6. Allyl alcohol can be produced by the hydrolysis of allyl chloride. Together with the main product, allyl alcohol, diallyl ether is produced as a byproduct. The conversion of allyl chloride is typically 97% and the selectivity to alcohol is 90%, both on a molar basis. Assuming that there are no other significant side reactions, calculate masses of alcohol and ether produced, per 1000 kg of allyl chloride fed to the reactor. 2.7. Aniline is produced by the hydrogenation of nitrobenzene. A small amount of cyclo-hexylamine is produced as a byproduct. The reactions are: 1: C6 H5 NO2 + 3H2 → C6 H5 NH2 + 2H2 O 2: C6 H5 NO2 + 6H2 → C6 H11 NH2 + 2H2 O Nitrobenzene is fed to the reactor as a vapor, with three times the stoichiometric quantity of hydrogen. The conversion of the nitrobenzene, to all products, is 96%, and the selectivity for aniline is 95%. The unreacted hydrogen is separated from the reactor products and recycled to the reactor. A purge is taken from the recycle stream to maintain the inerts in the recycle stream below 5%. The fresh hydrogen feed is 99.5% pure, the remainder being inerts. All percentages are molar. For a feed rate of 100 kmol/h of nitrobenzene, calculate a. the fresh hydrogen feed, b. the purge rate required, c. the composition of the reactor outlet stream. 2.8. Guaifenesin (Guaiacol glyceryl ether, 3-(2-Methoxyphenoxy)-1,2-propanediol, C10H14O4) is an expectorant that is found in cough medicines such as Actifed™ and Robitussin™. U.S. 4,390,732 (to Degussa) describes a preparation of the active pharmaceutical ingredient (API) from guaiacol (2-methoxyphenol, C 7 H 8 O 2 ) and glycidol (3-hydroxy propylene oxide, C3H6O2). When the reaction is catalyzed by NaOH, the reaction yield is 93.8%. The product is purified in a thin-film evaporator giving an overall plant yield of 87%. a. Estimate the feed flow rates of glycidine and guaiacol that would be needed to produce 100 kg/day of the API. b. Estimate how much product is lost in the thin-film evaporator. c. How would you recover the product lost in the evaporator? 2.9. 11-[N-ethoxycarbonyl-4-piperidylidene]-8-chloro-6,11-dihydro-5H-benzo-[5,6]-cyclohepta[1,2-b]-pyridine (C22H23ClN2O2) is a nonsedative antihistamine, known as Loratadine and marketed as Claritin™. The preparation of the active pharmaceutical ingredient (API) is described in U.S. 4,282,233 (to Schering). The patent describes reacting 16.2g of 11-[N-methyl-4-piperidylidene]-8-chloro-6,11-dihydro-5H-benzo-[5,6]-cyclohepta-[1,2-b]-pyridine (C20H21ClN2) in 200ml of benzene with 10.9g of ethylchloroformate (C3H5ClO2) for 18 hours. The mixture is cooled, poured into ice water, and separated into aqueous and organic phases. The organic layer is washed with water and evaporated to dryness. The residue is triturated (ground to a fine powder) with petroleum ether and recrystallized from isopropyl ether.

Problems

101

a. What is the reaction byproduct? b. The reaction appears to be carried out under conditions that maximize both selectivity and conversion (long time at low temperature), as might be expected given the cost of the raw material. If the conversion is 99.9% and the selectivity for the desired ethoxycarbonyl substituted compound is 100%, how much excess ethylchloroformate remains at the end of the reaction? c. What fraction of the ethylchloroformate feed is lost to waste products? d. Assuming that the volumes of water and isopropyl ether used in the quenching, washing, and recrystallization steps are the same as the initial solvent volume, and that none of these materials are reused in the process, estimate the total mass of waste material produced per kg of the API. e. If the recovery (plant yield) of the API from the washing and recrystallization steps is 92%, estimate the feed flow rates of 11-[N-methyl-4-piperidylidene]-8-chloro-6, 11-dihydro-5H-benzo-[5,6]-cyclohepta-[1,2-b]-pyridine and ethylchloroformate required to produce a batch of 10 kg of the API. f. How much API could be produced per batch in a 3.8 m3 (1000 US gal) reactor? g. What would be the advantages and disadvantages of carrying out the other process steps in the same vessel? h. Sketch a block flow diagram of the process. 2.10. Describe the main commercial process used to make each of the following compounds. Include a block flow diagram. a. b. c. d. e.

Phosphoric acid Adipic acid Polyethylene terephthalate Insulin Sorbitol

2.11. Example 2.7 introduced a heat exchange system revamp problem. If the plate heat exchanger E101 in Figure 2.19 is the gasketed-plate type, then the exchanger area can be increased by adding plates to the exchanger. How much additional area must be added to E101 to allow the system to operate at 50% above base case flow rate with no changes in temperature of steam or cooling water feed temperatures and no modification to exchangers E102 and E103? 2.12. Styrene is made by dehydrogenation of ethylbenzene, which is formed by alkylation of benzene with ethylene. Propose target yields for the alkylation and dehydrogenation steps if the forecasted prices per metric ton are styrene $800, ethylene $800, and benzene $500. Note: Structures for the compounds in Problems 2.3, 2.8, and 2.9 can be found in the Merck Index, but are not required to solve the problems.

CHAPTER

Utilities and Energy Efficient Design

KEY LEARNING OBJECTIVES • How processes are heated and cooled • The systems used for delivering steam, cooling water, and other site utilities • Methods used for recovering process waste heat • How to use the pinch design method to optimize process heat recovery • How to design a heat-exchanger network • How energy is managed in batch processes

3.1 INTRODUCTION Very few chemical processes are carried out entirely at ambient temperature. Most require process streams to be heated or cooled to reach the desired operation temperature, to add or remove heats of reaction, mixing, adsorption, etc., to sterilize feed streams, or to cause vaporization or condensation. Gas and liquid streams are usually heated or cooled by indirect heat exchange with another fluid: either another process stream or a utility stream such as steam, hot oil, cooling water, or refrigerant. The design of heat exchange equipment for fluids is addressed in Chapter 19. Solids are usually heated and cooled by direct heat transfer, as described in Chapter 18. This chapter begins with a discussion of the different utilities that are used for heating, cooling, and supplying other needs such as power, water, and air to a process. The consumption of energy is a significant cost in many processes. Energy costs can be reduced by recovering waste heat from hot process streams and by making use of the fuel value of waste streams. Section 3.4 discusses how to evaluate waste stream combustion as a source of process heat. Section 3.3 introduces other heat recovery approaches. When it is economically attractive, heating and cooling are accomplished by heat recovery between process streams. The design of a network of heat exchangers for heat recovery can be a complex task if there are many hot and cold streams in a process. Pinch analysis, introduced in Section 3.5, is a systematic method for simplifying this problem. The efficient use of energy in batch and cyclic processes is made more complicated by the sequential nature of process operations. Some approaches to energy efficient design of batch and cyclic processes are discussed in Section 3.6.

103

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3.2 UTILITIES The word “utilities” is used for the ancillary services needed in the operation of any production process. These services are normally supplied from a central site facility, and include: 1. Electricity 2. Fuel for fired heaters 3. Fluids for process heating a. Steam b. Hot oil or specialized heat transfer fluids 4. Fluids for process cooling a. Cooling water b. Chilled water c. Refrigeration systems 5. Process water a. Water for general use b. Demineralized water 6. Compressed air 7. Inert-gas supplies (usually nitrogen) Most plants are located on sites where the utilities are provided by the site infrastructure. The price charged for a utility is mainly determined by the operating cost of generating and transmitting the utility stream. Some companies also include a capital recovery charge in the utility cost, but if this is done then the offsite (OSBL) capital cost of projects must be reduced to avoid double counting and biasing the project capital-energy trade-off, leading to poor use of capital. Some smaller plants purchase utilities “over the fence” from a supplier such as a larger site or a utility company, in which case the utility prices are set by contract and are typically pegged to the price of natural gas, fuel oil, or electricity. The utility consumption of a process cannot be estimated accurately without completing the material and energy balances and carrying out a pinch analysis, as described in Section 3.5.6. The pinch analysis gives targets for process heat recovery and hence for the minimum requirements of hot and cold utilities. More detailed optimization then translates these targets into expected demands for fired heat, steam, electricity, cooling water, and refrigeration. In addition to the utilities required for heating and cooling, the process may also need process water and air for applications such as washing, stripping, and instrument air supply. Good overviews of methods for design and optimization of utility systems are given by Smith (2005) and Kemp (2007).

3.2.1 Electricity The electricity demand of the process is mainly determined by the work required for pumping, compression, air coolers, and solids-handling operations, but also includes the power needed for instruments, lights, and other small users. The power required may be generated on site, but will more usually be purchased from the local supply company. Some plants generate their own electricity using a gas-turbine cogeneration plant with a heat recovery steam generator (waste-heat boiler) to raise steam (Figure 3.1). The overall thermal efficiency of such systems can be in the range 70% to 80%; compared with the 30% to 40% obtained from a conventional power station, where the

3.2 Utilities

105

Fuel Combustor Air

Turbine Dynamo Steam

Compressor

Flue gas to stack Supplementary fuel

Secondary combustor Boiler feed water

Waste heat boiler

FIGURE 3.1 Gas-turbine-based cogeneration plant.

heat in the exhaust steam is wasted in the condenser. The cogeneration plant can be sized to meet or exceed the plant electricity requirement, depending on whether the export of electricity is an attractive use of capital. This “make or buy” scenario gives chemical producers strong leverage when negotiating electric power contracts and they are usually able to purchase electricity at or close to wholesale prices. Wholesale electricity prices vary regionally (see www.eia.gov for details), but are typically about $0.06/kWh in North America at the time of writing. The voltage at which the supply is taken or generated will depend on the demand. In the United States, power is usually transmitted over long distances at 135, 220, 550, or 750 kV. Local substations step the power down to 35 to 69 kV for medium voltage transmission and then to 4 to 15 kV local distribution lines. Transformers at the plant are used to step down the power to the supply voltages used on site. Most motors and other process equipment run on 208 V three-phase power, while 120/240 V single-phase power is used for offices, labs, and control rooms. On any site it is always worth considering driving large compressors and pumps with steam turbines instead of electric motors and using the exhaust steam for local process heating. Electric power is rarely used for heating in large-scale chemical plants, although it is often used in smaller batch processes that handle nonflammable materials, such as biological processes. The main disadvantages of electrical heating for large-scale processes are: • • • •

Heat from electricity is typically two to three times more expensive than heat from fuels, because of the thermodynamic inefficiency of power generation. Electric heating requires very high power draws that would substantially increase the electrical infrastructure costs of the site. Electric heating apparatus is expensive, requires high maintenance, and must comply with stringent safety requirements when used in areas where flammable materials may be present. Electric heaters are intrinsically less safe than steam systems. The maximum temperature that a steam heater can reach is the temperature of the steam. The maximum temperature of an electric

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CHAPTER 3 Utilities and Energy Efficient Design

heater is determined by the temperature controller (which could fail) or by burn-out of the heating element. Electric heaters therefore have a higher probability of overheating. Electric heating is more likely to be attractive in small-scale batch or cyclic processes, particularly when the cost of heating is a small fraction of overall process costs and when the process calls for rapid on-off heating. A detailed account of the factors to be considered when designing electrical distribution systems for chemical process plants, and the equipment used (transformers, switch gear, and cables), is given by Silverman (1964). Requirements for electrical equipment used in hazardous (classified) locations are given in the National Electrical Code (NFPA 70), as described in Section 10.3.5.

3.2.2 Fired Heat Fired heaters are used for process heating duties above the highest temperatures that can be reached using high pressure steam, typically about 250 ºC (482 ºF). Process streams may be heated directly in the furnace tubes, or indirectly using a hot oil circuit or heat transfer fluid, as described in Section 3.2.4. The design of fired heaters is described in Section 19.17. The cost of fired heat can be calculated from the price of the fuel fired. Most fired process heaters use natural gas as fuel, as it is cleaner burning than fuel oil and therefore easier to fit NOx control systems and obtain permits. Natural gas also requires less maintenance of burners and fuel lines and natural gas burners can often co-fire process waste streams such as hydrogen, light organic compounds, or air saturated with organic compounds. Natural gas and heating oil are traded as commodities and prices can be found at any online trading site or business news site (e.g., www.cnn.money.com). Historic prices for forecasting can be found in the Oil and Gas Journal or from the U.S. Energy Information Adminstration (www.eia.gov). The fuel consumed in a fired heater can be estimated from the fired heater duty divided by the furnace efficiency. The furnace efficiency will typically be about 0.85 if both the radiant and convective sections are used (see Chapter 19) and about 0.6 if the process heating is in the radiant section only. Example 3.1 Estimate the annual cost of providing heat to a process from a fired heater using natural gas as fuel if the process duty is 4 MW and the price of natural gas is $3.20 /MMBtu (million Btu).

Solution

If we assume that the fired heater uses both the radiant and convective sections then we can start by assuming a heater efficiency of 0.85, so Fuel required = Heater duty/heater efficiency = 4/0:85 = 4:71 MW 1 Btu/h = 0:29307 W, so 4:71 MW = 4:71/0:29307 = 16:07 MMBtu/h Assuming 8000 operating hours per year, the total annual fuel consumption would be Annual fuel use = 16:07 × 8000 = 128:6 × 103 MMBtu Annual cost of fired heat = 128:6 × 103 × 3:20 = $411, 400

3.2 Utilities

107

Note that if we had decided to carry out all of the heating in the radiant section only, then the fuel required would have been 4/0.6 = 6.67 MW and the annual cost of heating would increase to $582,600 unless we could find some other process use for the heat available in the convective section of the heater.

3.2.3 Steam Steam is the most widely-used heat source in most chemical plants. Steam has a number of advantages as a hot utility: • • • •

The heat of condensation of steam is high, giving a high heat output per pound of utility at constant temperature (compared to other utilities such as hot oil and flue gas that release sensible heat over a broad temperature range). The temperature at which heat is released can be precisely controlled by controlling the pressure of the steam. This enables tight temperature control, which is important in many processes. Condensing steam has very high heat transfer coefficients, leading to cheaper heat exchangers. Steam is nontoxic, nonflammable, visible if it leaks externally, and inert to many (but not all) process fluids.

Most sites have a pipe network supplying steam at three or more pressure levels for different process uses. A typical steam system is illustrated in Figure 3.2. Boiler feed water at high pressure is preheated and fed to boilers where high pressure steam is raised and superheated above the dew point to allow for heat losses in the piping. Boiler feed water preheat can be accomplished using process waste heat or convective section heating in the boiler plant. High pressure (HP) steam is Boiler & superheat HP main Process heating

BFW preheat

MP main Process heating LP main

Vent

Process heating

Live steam Degassing Make-up

FIGURE 3.2 Steam system.

Process heating

Condensate return

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CHAPTER 3 Utilities and Energy Efficient Design

typically at about 40 bar, corresponding to a condensing temperature of 250 ºC, but every site is different. Some of the HP steam is used for process heating at high temperatures. The remainder of the HP steam is expanded either through let-down valves or steam turbines known as back-pressure turbines to form medium pressure (MP) steam. The pressure of the MP steam mains varies widely from site to site, but is typically about 20 bar, corresponding to a condensing temperature of 212 ºC. Medium pressure steam is used for intermediate temperature heating or expanded to form low pressure (LP) steam, typically at about 3 bar, condensing at 134 ºC. Some of the LP steam may be used for process heating if there are low-temperature heat requirements. Low pressure (or MP or HP) steam can also be expanded in condensing turbines to generate shaft work for process drives or electricity production. A small amount of LP steam is used to strip dissolved noncondensable gases such as air from the condensate and make-up water. Low pressure steam is also often used as “live steam” in the process, for example, as stripping vapor or for cleaning, purging, or sterilizing equipment. When steam is condensed without coming into contact with process fluids, the hot condensate can be collected and returned to the boiler feed water system. Condensate can also sometimes be used as a low-temperature heat source if the process requires low-temperature heat. The price of HP steam can be estimated from the cost of boiler feed water treatment, the price of fuel, and the boiler efficiency: PHPS = PF ×

dHb + PBFW ηB

(3.1)

where PHPS = price of high pressure steam ($/1000 lb, commonly written $/Mlb) PF = price of fuel ($/MMBtu) dHb = heating rate (MMBtu/Mlb steam) ηB = boiler efficiency PBFW = price or cost of boiler feed water ($/Mlb) Package boilers typically have efficiencies similar to fired heaters, in the range 0.8 to 0.9. The heating rate should include boiler feed water preheat, the latent heat of vaporization, and the superheat specified. The steam for process heating is usually generated in water-tube boilers, using the most economical fuel available. The cost of boiler feed water includes allowances for water make-up, chemical treatment, and degassing, and is typically about twice the cost of raw water; see Section 3.2.7. If no information on the price of water is available, then 0.50 $/1000 lb can be used as an initial estimate. If the steam is condensed and the condensate is returned to the boiler feed water (which will normally be the case), then the price of steam should include a credit for the condensate. The condensate credit will often be close enough to the boiler feed water cost that the two terms cancel each other out and can be neglected. The prices of medium and low pressure steam are usually discounted from the high pressure steam price, to allow for the shaft work credit that can be gained by expanding the steam through a turbine, and also to encourage process heat recovery by raising steam at intermediate levels and using low-grade heat when possible. Several methods of discounting are used. The most rational of these is to calculate the shaft work generated by expanding the steam between levels and price this

3.2 Utilities

109

as equivalent to electricity (which could be generated by attaching the turbine to a dynamo or else would be needed to run a motor to replace the turbine if it is used as a driver). The value of the shaft work then sets the discount between steam at different levels. This is illustrated in the following example.

Example 3.2 A site has steam levels at 40 bar, 20 bar, and 6 bar. The price of fuel is $6/MMBtu and electricity costs $0.05/kWh. If the boiler efficiency is 0.8 and the steam turbine efficiency is 0.85, suggest prices for HP, MP, and LP steam.

Solution

The first step is to look up the steam conditions, enthalpies, and entropies in steam tables: Steam level Pressure (bar) Saturation temperature (ºC)

HP 40 250

MP 20 212

LP 6 159

The steam will be superheated above the saturation temperature to allow for heat losses in the pipe network. The following superheat temperatures were set to give an adequate margin above the saturation temperature for HP steam and also to give (roughly) the same specific entropy for each steam level. The actual superheat temperatures of MP and LP steam will be higher, due to the nonisentropic nature of the expansion. Superheat temperature (ºC) Specific entropy, sg, (kJ/kg.K) Specific enthalpy, hg, (kJ/kg)

400 6.769 3214

300 6.768 3025

160 6.761 2757

We can then calculate the difference in enthalpy between levels for isentropic expansion: Isentropic delta enthalpy (kJ/kg)

189

268

Multiplying by the turbine efficiency gives the nonisentropic enthalpy of expansion: Actual delta enthalpy (kJ/kg)

161

228

This can be converted to give the shaft work in customary units: Shaft work (kWh/Mlb)

20.2

28.7

Multiplying by the price of electricity converts this into a shaft work credit: Shaft work credit ($/Mlb)

1.01

1.44

The price of high pressure steam can be found from Equation 3.1, assuming that the boiler feed water cost is cancelled out by a condensate credit. The other prices can then be estimated by subtracting the shaft work credits. Steam price ($/Mlb)

6.48

5.47

4.03

For quick estimates, this example can easily be coded into a spreadsheet and updated with the current prices of fuel and power. A sample steam costing spreadsheet is available in the online material at booksite.elsevier.com/ Towler.

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CHAPTER 3 Utilities and Energy Efficient Design

3.2.4 Hot Oil and Heat Transfer Fluids Circulating systems of hot oil or specialized heat transfer fluids are often used as heat sources in situations where fired heat or steam are not suitable. Heat transfer fluids and mineral oils can be used over a temperature range from 50 ºC to 400 ºC. The upper temperature limit on use of hot oils is usually set by thermal decomposition of the oil, fouling, or coking of heat-exchange tubes. Some heat transfer fluids are designed to be vaporized and condensed in a similar manner to the steam system, though at lower pressures; however, vaporization of mineral oils is usually avoided, as less volatile components in the oil could accumulate and decompose, causing accelerated fouling. The most common situation where a hot oil system is used is in plants that have many relatively small high-temperature heating requirements. Instead of building several small fired heaters, it can be more economical to supply heat to the process from circulating hot oil streams and build a single fired heater that heats the hot oil. Use of hot oil also reduces the risk of process streams being exposed to high tube-wall temperatures that might be experienced in a fired heater. Hot oil systems are often attractive when there is a high pressure differential between the process stream and HP steam and use of steam would entail using thicker tubes. Hot oil systems can sometimes be justified on safety grounds if the possibility of steam leakage into the process is very hazardous. The most commonly used heat transfer fluids are mineral oils and Dowtherm A. Mineral oil systems usually require large flow rates of circulating liquid oil. When the oil is taken from a process stream, as is common in oil refining processes, then it is sometimes called a pump-around system. Dowtherm A is a mixture of 26.5 wt% diphenyl in diphenyl oxide. Dowtherm A is very thermally stable and is usually operated in a vaporization-condensation cycle similar to the steam system, although condensed liquid Dowtherm is sometimes used for intermediate temperature heating requirements. The design of Dowtherm systems and other proprietary heat transfer fluids are discussed in detail in Singh (1985) and Green and Perry (2007). The cost of the initial charge of heat transfer fluid usually makes a negligible contribution to the overall cost of running a hot oil system. The main operating cost is the cost of providing heat to the hot oil in the fired heater or vaporizer. If a pumped liquid system is used then the pumping costs should also be evaluated. The costs of providing fired heat are discussed in Section 3.2.2. Hot oil heaters or vaporizers usually use both the radiant and convective sections of the heater and have heater efficiencies in the range 80% to 85%.

3.2.5 Cooling Water When a process stream requires cooling at high temperature, various heat recovery techniques should be considered. These include transferring heat to a cooler process stream, raising steam, preheating boiler feed water, etc., as discussed in Section 3.3. When heat must be rejected at lower temperatures, below about 120 ºC (248 ºF) (more strictly, below the pinch temperature), then a cold utility stream is needed. Cooling water is the most commonly used cold utility in the temperature range 120 ºC to 40 ºC, although air cooling is preferred in regions where water is expensive or the ambient humidity is too high for cooling water systems to operate effectively. The selection and design of air coolers are discussed in Section 19.16. If a process stream must be cooled to a temperature below 40 ºC, cooling water or air cooling would be

3.2 Utilities

111

used down to a temperature in the range 40 ºC to 50 ºC, followed by chilled water or refrigeration down to the target temperature. Natural and forced-draft cooling towers are generally used to provide the cooling water required on a site, unless water can be drawn from a convenient river or lake in sufficient quantity. Sea water, or brackish water, can be used at coastal sites and for offshore operations, but if used directly will require the use of more expensive materials of construction for heat exchangers (see Chapter 6). The minimum temperature that can be reached with cooling water depends on the local climate. Cooling towers work by evaporating part of the circulating water to ambient air, causing the remaining water to be chilled. If the ambient temperature and humidity are high, then a cooling water system will be less effective and air coolers or refrigeration would be used instead. A schematic of a cooling water system is shown in Figure 3.3. Cooling water is pumped from the cooling tower to provide coolant for the various process cooling duties. Each process cooler is served in parallel and cooling water almost never flows to two coolers in series. The warmed water is returned to the cooling tower and cooled by partial evaporation. A purge stream known as a blowdown is removed upstream of the cooling tower, to prevent the accumulation of dissolved solids as water evaporates from the system. A make-up stream is added to compensate for evaporative losses, blowdown losses, and any other losses from the system. Small amounts of chemical additives are also usually fed into the cooling water to act as biocides and corrosion and fouling inhibitors. The cooling tower consists of a means of providing high surface area for heat and mass transfer between the warm water and ambient air, and a means of causing air to flow countercurrent to the water. The surface area for contact is usually provided by flowing the water over wooden slats or high-voidage packing. The cooled water is then collected at the bottom of the tower. In most modern cooling towers the air flow is induced by fans that are placed above the packed section of the tower. For very large cooling loads natural-draft cooling towers are used, in which a large hyperbolic chimney is placed above the packed section to induce air flow. Some older plants use spray ponds instead of cooling towers. Process duties Losses

Make-up and additives Evaporation losses

Blowdown Circulation pumps

FIGURE 3.3 Schematic of cooling water system.

Cooling tower

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CHAPTER 3 Utilities and Energy Efficient Design

Cooling water systems can be designed using a psychrometric chart if the ambient conditions are known. A psychrometric chart is given in Figure 3.4. The cooling tower is usually designed so that it will operate effectively except under the hottest (or most humid) conditions that can be expected to occur no more than a few days each year. The ambient temperature and humidity can be plotted on the psychrometric chart, allowing the inlet air wet bulb temperature to be determined. This is the coldest temperature that the cooling water could theoretically reach; however, in practice most cooling towers operate with a temperature approach to the air wet bulb temperature of at least 2.8 ºC (5 ºF). Adding the approach temperature to the inlet air wet bulb temperature, we can then mark the outlet water condition on the saturation curve. For example, if the hottest ambient condition for design purposes is a dry bulb temperature of 35 ºC (95 ºF) with 80% humidity, then we can mark this point on the psychrometric chart (point A) and read the wet bulb temperature as roughly 32 ºC (89.6 ºF). Adding a 2.8 ºC temperature approach would give a cold water temperature of about 35 ºC (95 ºF), which can then be marked on the saturation line (point B). The inlet water condition, or cooling water return temperature, is found by optimizing the tradeoff between water circulation costs and cooling tower cost. The difference between the cooling water supply (coldest) and return (hottest) temperatures is known as the range or cooling range of

150

s, re tu nt te m

po i

0.030

20% 0.020

0.015

1000

et bu l

2000

3000

0.025

0.035

de w

4000

40%

110

0.040

5000

0.045

130

120 100

0.050

°C

6000

0.055 60%

140

Spe

7000

160

0.010

0°C

0.005

20 30 Dry-bulb temperature, TDB, °C

FIGURE 3.4 Psychrometric chart (adapted with permission from Balmer (2010)).

0.000

ω, kg water per kg dry air

Barometric pressure 101325 N/m2 h# = ha + ω hw ha datum 15.0 °C hw from steam tables

0.060

80%

Water vapor partial pressure, pw, N/m2

8000

cific kJ/( enthalp kg d ry a y h #, ir)

φ = 100%

170

3.2 Utilities

113

the cooling tower. As the cooling range is increased, the cost of the cooling tower is increased, but the water flow rate that must be circulated decreases, and hence the pumping cost decreases. Note that since most of the cooling is accomplished by evaporation of water rather than transfer of sensible heat to the air, the evaporative losses do not vary much with the cooling range. Most cooling towers are operated with a cooling range between 5 ºF and 20 ºF (2.8 ºC to 11.1 ºC). A typical initial design point would be to assume a cooling water return temperature about 10 ºF (5.5 ºC) hotter than the cold water temperature. In the example above, this would give a cooling water return temperature of 40.5 ºC (105 ºF), which can also be marked on the psychrometric chart (point C). The difference in air humidity across the cooling tower can now be read from the right-hand axis as the difference in moisture loadings between the inlet air (point A) and the outlet air (point C). The cooling tower design can then be completed by determining the cooling load of the water from an energy balance and hence determining the flow rate of air that is needed based on the change in air humidity between ambient air and the air exit condition. The exit air is assumed to have a dry bulb temperature equal to the cooling water return temperature, and the minimum air flow will be obtained when the air leaves saturated with moisture. Examples of the detailed design of cooling towers are given in Green and Perry (2007). When carrying out the detailed design of a cooling tower it is important to check that the cooling system has sufficient capacity to meet the site cooling needs over a range of ambient conditions. In practice, multiple cooling water pumps are usually used so that a wide range of cooling water flow rates can be achieved. When new capacity is added to an existing site, the limit on the cooling system is usually the capacity of the cooling tower. If the cooling tower fans cannot be upgraded to meet the increased cooling duty, additional cooling towers must be added. In such cases, it is often cheaper to install air coolers for the new process rather than upgrading the cooling water system. The cost of providing cooling water is mainly determined by the cost of electric power. Cooling water systems use power for pumping the cooling water through the system and for running fans (if installed) in the cooling towers. They also have costs for water make-up and chemical treatment. The power used in a typical recirculating cooling water system is usually between 1 and 2 kWh/ 1000 gal of circulating water. The costs of water make-up and chemical treatment usually add about $0.02/1000 gal.

3.2.6 Refrigeration Refrigeration is needed for processes that require temperatures below those that can be economically obtained with cooling water, i.e., below about 40 ºC. For temperatures down to around 10 °C, chilled water can be used. For lower temperatures, down to −30 °C, salt brines (NaCl and CaCl2) are sometimes used to distribute the “refrigeration” around the site from a central refrigeration machine. Large refrigeration duties are usually supplied by a standalone packaged refrigeration system. Vapor compression refrigeration machines are normally used, as illustrated in Figure 3.5. The working fluid (refrigerant) is compressed as a vapor, and then cooled and condensed at high pressure, allowing heat rejection at high temperature in an exchanger known as a condenser. Heat is usually rejected to a coolant such as cooling water or ambient air. The liquid refrigerant is then expanded across a valve to a lower pressure, where it is vaporized in an exchanger known as an evaporator, taking up heat at low temperature. The vapor is then returned to the compressor, completing the cycle.

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CHAPTER 3 Utilities and Energy Efficient Design

Coolant Condenser

Expansion valve

Compressor

Process fluid

Evaporator

FIGURE 3.5 Simple refrigeration cycle.

The working fluid for a refrigeration system must satisfy a broad range of requirements. It should have a boiling point that is colder than the temperature that must be reached in the process at a pressure that is above atmospheric pressure (to prevent leaks into the system). It should have a high latent heat of evaporation, to reduce refrigerant flow rate. The system should operate well below the critical temperature and pressure of the refrigerant, and the condenser pressure should not be too high or the cost will be excessive. The freezing temperature of the refrigerant must be well below the minimum operating temperature of the system. The refrigerant should also be nontoxic, nonflammable, and have minimal environmental impact. A wide range of materials have been developed for use as refrigerants, most of which are halogenated hydrocarbons. In some situations ammonia, nitrogen, and carbon dioxide are used. Cryogenic gas separation processes usually use the process fluids as working fluid; for example, ethylene and propylene refrigeration cycles are used in ethylene plants. Refrigeration systems use power to compress the refrigerant. The power can be estimated using the cooling duty and the refrigerator coefficient of performance (COP). COP =

Refrigeration produced ðBtu=hr or MWÞ Shaft work used ðBtu=hr or MWÞ

(3.2)

The COP is a strong function of the temperature range over which the refrigeration cycle operates. For an ideal refrigeration cycle (a reverse Carnot cycle), the COP is COP =

Te ðTc − Te Þ

(3.3)

where Te = evaporator absolute temperature (K) Tc = condenser absolute temperature (K) The COP of real refrigeration cycles is always less than the Carnot efficiency. It is usually about 0.6 times the Carnot efficiency for a simple refrigeration cycle, but can be as high as 0.9 times the Carnot efficiency if complex cycles are used. If the temperature range is too large then it may be more economical to use a cascaded refrigeration system, in which a low-temperature cycle rejects heat to a higher-temperature cycle that rejects heat to cooling water or ambient air. Good

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115

overviews of refrigeration cycle design are given by Dincer (2003), Stoecker (1998), and Trott and Welch (1999). The operating cost of a refrigeration system can be determined from the power consumption and the price of power. Refrigeration systems are usually purchased as packaged modular plants and the capital cost can be estimated using commercial cost estimating software as described in Section 7.10. An approximate correlation for the capital cost of packaged refrigeration systems is also given in Table 7.2.

Example 3.3 Estimate the annual operating cost of providing refrigeration to a condenser with duty 1.2 MW operating at −5 ºC. The refrigeration cycle rejects heat to cooling water that is available at 40 ºC, and has an efficiency of 80% of the Carnot cycle efficiency. The plant operates for 8000 hours per year and electricity costs $0.06/kWh.

Solution

The refrigeration cycle needs to operate with an evaporator temperature below −5 ºC, say at −10 ºC or 263 K. The condenser must operate above 40 ºC, say at 45 ºC (318 K). For this temperature range the Carnot cycle efficiency is COP =

Te 263 = = 4:78 ðTc − Te Þ 318 − 263

(3.3)

If the cycle is 80% efficient then the actual coefficient of performance = 4.78 × 0.8 = 3.83 The shaft work needed to supply 1.2 MW of cooling is given by Shaft work required =

Cooling duty = 1:2 = 0:313 MW 3:83 COP

The annual operating cost is then = 313 kW × 8000 h/y × 0.06 $/kWh = 150,000 $/y

3.2.7 Water The water required for general purposes on a site will usually be taken from the local mains supply, unless a cheaper source of suitable quality water is available from a river, lake, or well. Raw water is brought in to make up for losses in the steam and cooling water systems and is also treated to generate demineralized and deionized water for process use. Water is also used for process cleaning operations and to supply fire hydrants. The price of water varies strongly by location, depending on fresh water availability. Water prices are often set by local government bodies and often include a charge for waste water rejection. This charge is usually applied on the basis of the water consumed by the plant, regardless of whether that water is actually rejected as a liquid (as opposed to being lost as vapor or incorporated into a product by reaction). A very rough estimate of water costs can be made by assuming $2 per 1000 gal ($0.5 per metric ton).

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Demineralized Water Demineralized water, from which all the minerals have been removed by ion-exchange, is used where pure water is needed for process use, and as boiler feed water. Mixed and multiple-bed ionexchange units are used; one resin converting the cations to hydrogen and the other removing the anions. Water with less than 1 part per million of dissolved solids can be produced. The design of ion exchange units is discussed in Section 16.5.5. Demineralized water typically costs about double the price of raw water, but this obviously varies strongly with the mineral content of the water and the disposal cost of blowdown from the demineralization system. A correlation for the cost of a water ion exchange plant is given in Table 7.2.

3.2.8 Compressed Air Compressed air is needed for general use, for oxidation reactions, air strippers, aerobic fermentation processes, and for pneumatic control actuators that are used for plant control. Air is normally distributed at a mains pressure of 6 bar (100 psig), but large process air requirements are typically met with standalone air blowers or compressors. Rotary and reciprocating single-stage or two-stage compressors are used to supply utility and instrument air. Instrument air must be dry and clean (free from oil). Air is usually dried by passing it over a packed bed of molecular sieve adsorbent. For most applications, the adsorbent is periodically regenerated using a temperature-swing cycle. Temperature swing adsorption (TSA) is discussed in more detail in Section 16.2.1. Air at 1 atmosphere pressure is freely available in most chemical plants. Compressed air can be priced based on the power needed for compression (see Section 20.6). Drying the air, for example for instrument air, typically adds about $0.005 per standard m3 ($0.14/1000 scf).

Cooling Air Ambient air is used as a coolant in many process operations; for example, air cooled heat exchangers, cooling towers, solids coolers, and prilling towers. If the air flow is caused by natural draft then the cooling air is free, but the air velocity will generally be low, leading to high equipment cost. Fans or blowers are commonly used to ensure higher air velocities and reduce equipment costs. The cost of providing cooling air is then the cost of operating the fan, which can be determined from the fan power consumption. Cooling fans typically operate with very high flow rates and very low pressure drop, on the order of a few inches of water. The design of a cooling fan is illustrated in the discussion of air cooled heat exchangers in Section 19.16.

3.2.9 Nitrogen Where a large quantity of inert gas is required for the inert blanketing of tanks and for purging (see Chapter 10) this will usually be supplied from a central facility. Nitrogen is normally used, and can be manufactured on site in an air liquefaction plant, or purchased as liquid in tankers. Nitrogen and oxygen are usually purchased from one of the industrial gas companies via pipeline or a small dedicated “over-the-fence” plant. The price varies depending on local power costs, but is typically in the range $0.01 to $0.03 per lb for large facilities.

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117

3.3 ENERGY RECOVERY Process streams at high pressure or temperature contain energy that can be usefully recovered. Whether it is economical to recover the energy content of a particular stream depends on the value of the energy that can be usefully extracted and the cost of recovery. The value of the energy is related to the marginal cost of energy at the site. The cost of recovery will be the capital and operating cost of any additional equipment required. If the savings exceed the total annualized cost, including capital charges, then the energy recovery will usually be worthwhile. Maintenance costs should be included in the annualized cost (see Chapter 9). Some processes, such as air separation, depend on efficient energy recovery for economic operation, and in all processes the efficient use of energy will reduce product cost. When setting up process simulation models, the design engineer needs to pay careful attention to operations that have an impact on the energy balance and heat use within the process. Some common problems to watch out for include: 1. Avoid mixing streams at very different temperatures. This usually represents a loss of heat (or cooling) that could be better used in the process. 2. Avoid mixing streams at different pressures. The mixed stream will be at the lowest pressure of the feed streams. The higher pressure streams will undergo cooling as a result of adiabatic expansion. This may lead to increased heating or cooling requirements or lost potential to recover shaft work during the expansion. 3. Segment heat exchangers to avoid internal pinches. This is particularly necessary for exchangers where there is a phase change. When a liquid is heated, boiled, and superheated, the variation of stream temperature with enthalpy added looks like Figure 3.6. Liquid is heated to the boiling point (A–B), then the heat of vaporization is added (B–C) and the vapor is superheated (C–D). This is a different temperature-enthalpy profile than a straight line between the initial and final states (A–D). If the stream in Figure 3.6 were matched against a heat source that had a temperature profile like line E-F in Figure 3.7, then the exchanger would appear feasible based on the inlet and outlet temperatures, but would in fact be infeasible because of the cross-over of

F T

D B

B C

FIGURE 3.6

FIGURE 3.7

Temperature-enthalpy profile for a stream that is vaporized and superheated.

Heat transfer to a stream that is vaporized and superheated.

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the temperature profiles at B. A simple way to avoid this problem is to break up the preheat, boiling, and superheat into three exchangers in the simulation model, even if they will be carried out in a single piece of equipment in the final design. The same problem also occurs with condensers that incorporate desuperheat and subcooling. 4. Check for heat of mixing. This is important whenever acids or bases are mixed with water. If the heat of mixing is large, two or more stages of mixing with intercoolers may be needed. If a large heat of mixing is expected, but is not predicted by the model, then check that the thermodynamic model includes heat of mixing effects. 5. Remember to allow for process inefficiency and design margins. For example, when sizing a fired heater, if process heating is carried out in the radiant section only, the heating duty calculated in the simulation is only 60% of the total furnace duty (see Sections 3.2.2 and 19.17). The operating duty will then be the process duty divided by 0.6. The design duty must be increased further by a suitable design factor, say 10%. The design duty of the fired heater is then 1.1/0.6 = 1.83 times the process duty calculated in the simulation. Some of the techniques used for energy recovery in chemical process plants are described briefly in the following sections. The references cited give fuller details of each technique. Miller (1968) gives a comprehensive review of process energy systems, including heat exchange and power recovery from high-pressure fluid streams. Kenney (1984) reviews the application of thermodynamic principles to energy recovery in the process industries. Kemp (2007) gives a detailed description of pinch analysis and several other methods for heat recovery.

3.3.1 Heat Exchange The most common energy-recovery technique is to use the heat in a high-temperature process stream to heat a colder stream. This saves part or all of the cost of heating the cold stream, as well as part or all of the cost of cooling the hot stream. Conventional shell and tube exchangers are normally used. The cost of the heat exchange surface may be increased relative to using a hot utility as heat source, due to the reduced temperature driving forces, or decreased, due to needing fewer exchangers. The cost of recovery will be reduced if the streams are located conveniently close within the plant. The amount of energy that can be recovered depends on the temperature, flow, heat capacity, and temperature change possible, in each stream. A reasonable temperature driving force must be maintained to keep the exchanger area to a practical size. The most efficient exchanger will be the one in which the shell and tube flows are truly countercurrent. Multiple tube-pass exchangers are usually used for practical reasons. With multiple tube passes the flow is part countercurrent and part cocurrent and temperature crosses can occur, which reduce the efficiency of heat recovery (see Chapter 19). In cryogenic processes, where heat recovery is critical to process efficiency, brazed or welded plate exchangers are used to obtain true countercurrent performance and very low temperature approaches on the order of a few degrees Celsius are common. The hot process streams leaving a reactor or a distillation column are frequently used to preheat the feed streams (“feed-effluent” or “feed-bottoms” exchangers). In an industrial process there will be many hot and cold streams and there will be an optimum arrangement of the streams for energy recovery by heat exchange. The problem of synthesizing a

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119

network of heat exchangers has been the subject of much research and is covered in more detail in Section 3.5.

3.3.2 Waste-heat Boilers If the process streams are at a sufficiently high temperature and there are no attractive options for process-to-process heat transfer, then the heat recovered can be used to generate steam. Waste-heat boilers are often used to recover heat from furnace flue gases and the process gas streams from high-temperature reactors. The pressure, and superheat temperature, of the steam generated depend on the temperature of the hot stream and the approach temperature permissible at the boiler exit. As with any heat-transfer equipment, the area required increases as the mean temperature driving force (log mean ΔT) is reduced. The permissible exit temperature may also be limited by process considerations. If the gas stream contains water vapor and soluble corrosive gases, such as HCl or SO2, the exit gas temperature must be kept above the dew point. Hinchley (1975) discusses the design and operation of waste-heat boilers for chemical plants. Both fire-tube and water-tube boilers are used. A typical arrangement of a water-tube boiler on a reformer furnace is shown in Figure 3.8 and a fire-tube boiler in Figure 3.9. The application of a waste-heat boiler to recover energy from the reactor exit streams in a nitric acid plant is shown in Figure 3.10. The selection and operation of waste-heat boilers for industrial furnaces is discussed by Dryden (1975). Water in Gas outlet

Steam/water out

Metal shroud Refractory lining

Gas inlet

FIGURE 3.8 Reformed gas waste-heat boiler arrangement of vertical U-tube water-tube boiler. (Reprinted by permission of the Council of the Institution of Mechanical Engineers from the Proceedings of the Conference on Energy Recovery in the Process Industries, London, 1975.)

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Ferrule wrapped with insulating fiber Process gas outlet 550 °C

Steam/water riser pipes Alloy 800 ferrule

Concrete Alloy 800 production plate External insulation Water downcomer pipes Process gas 1200/1000 °C

Blowdown connection

Refractory/concrete

Insulating concrete

FIGURE 3.9 Reformed gas waste-heat boiler, principal features of typical natural circulation fire-tube boilers. (Reprinted by permission of the Council of the Institution of Mechanical Engineers from the Proceedings of the Conference on Energy Recovery in the Process Industries, London, 1975.)

Air

To stack

From absorption tower no. 5

1 Secondary air

Air from bleacher

4 3 Stream 6

7 13

9 5 Ammonia

.... ....

15 16

17 To oxidation tower

12 Water Water

1. Air entry 2. Ammonia vaporiser 3. Ammonia filter 4. Control valves 5. Air-scrubbing tower

6. Air preheater 7. Gas mixer 8. Gas filters 9. Converters

12 HNO3

10. Lamont boilers 11. Steam drum 12. Gas cooler No. 1 13. Exhaust turbine

(From nitric acid manufacture, Miles (1961), with permission)

FIGURE 3.10 Connections of a nitric acid plant, intermediate pressure type.

202 HNO3

To absorption

14. Compressor 15. Steam turbine 16. Heat exchanger 17. Gas cooler No. 2

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121

3.3.3 High-temperature Reactors If a reaction is highly exothermic, cooling will be needed. If the reactor temperature is high enough, the heat removed can be used to generate steam. The lowest steam pressure normally used in the process industries is about 2.7 bar (25 psig), so any reactor with a temperature above 150 °C is a potential steam generator. Steam is preferentially generated at as high a pressure as possible, as high pressure steam is more valuable than low pressure steam (see Section 3.2.3). If the steam production exceeds the site steam requirements, some steam can be fed to condensing turbines to produce electricity to meet site power needs. Three systems are used: 1. Figure 3.11(a). An arrangement similar to a conventional water-tube boiler. Steam is generated in cooling pipes within the reactor and separated in a steam drum. 2. Figure 3.11(b). Similar to the first arrangement but with the water kept at high pressure to prevent vaporization. The high-pressure water is flashed to steam at lower pressure in a flash drum. This system would give more responsive control of the reactor temperature. 3. Figure 3.11(c). In this system a heat-transfer fluid, such as Dowtherm A (see Section 3.2.4 and Singh (1985) for details of heat-transfer fluids), is used to avoid the need for high-pressure tubes. The steam is raised in an external boiler.

3.3.4 High-pressure Process Streams Where high-pressure gas or liquid process streams are throttled to lower pressures, energy can be recovered by carrying out the expansion in a suitable turbine.

Gas Streams The economic operation of processes that involve the compression and expansion of large quantities of gases, such as ammonia synthesis, nitric acid production, and air separation, depends on the efficient recovery of the energy of compression. The energy recovered by expansion is often used to drive the compressors directly, as shown in Figure 3.10. If the gas contains condensable components, it may be advisable to consider heating the gas by heat exchange with a higher temperature

Steam

Flash drum

Steam drum

Steam Boiler Feed water

Feed pump Reactor (a)

FIGURE 3.11 Steam generation.

Reactor (b)

Reactor (c)

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process stream before expansion. The gas can then be expanded to a lower pressure without condensation and the power generated increased. The process gases do not have to be at a particularly high pressure for expansion to be economical if the gas flow rate is high. For example, Luckenbach (1978) in U.S. patent 4,081,508 describes a process for recovering power from the off-gas from a fluid catalytic cracking process by expansion from about 2 to 3 bar (15 to 25 psig) down to just over atmospheric pressure (1.5 to 2 psig). The energy recoverable from the expansion of a gas can be estimated by assuming polytropic expansion; see Section 20.6.3 and Example 20.4. The design of turboexpanders for the process industries is discussed by Bloch et al. (1982).

Liquid Streams As liquids are essentially incompressible, less energy is stored in a compressed liquid than a gas; however, it is often worth considering power recovery from high-pressure liquid streams (>15 bar), as the equipment required is relatively simple and inexpensive. Centrifugal pumps are used as expanders and are often coupled directly to other pumps. The design, operation, and cost of energy recovery from high-pressure liquid streams is discussed by Jenett (1968), Chada (1984), and Buse (1981).

3.3.5 Heat Pumps A heat pump is a device for raising low-grade heat to a temperature at which the heat can be used. It pumps the heat from a low temperature source to the higher temperature sink, using a small amount of energy relative to the heat energy recovered. A heat pump is essentially the same as a refrigeration cycle (Section 3.2.6 and Figure 3.5), but the objective is to deliver heat to the process in the condensation step of the cycle, as well as (or instead of) removing heat in the evaporation step. Heat pumps are increasingly finding applications in the process industries. A typical application is the use of the low-grade heat from the condenser of a distillation column to provide heat for the reboiler; see Barnwell and Morris (1982) and Meili (1990). Heat pumps are also used with dryers; heat is abstracted from the exhaust air and used to preheat the incoming air. Details of the thermodynamic cycles used for heat pumps can be found in most textbooks on engineering thermodynamics, and in Reay and MacMichael (1988). In the process industries, heat pumps operating on the mechanical vapor compression cycle are normally used. A vapor compression heat pump applied to a distillation column is shown in Figure 3.12(a). The working fluid, usually a commercial refrigerant, is fed to the reboiler as a vapor at high pressure and condenses, giving up heat to vaporize the process fluid. The liquid refrigerant from the reboiler is then expanded over a throttle valve and the resulting wet vapor is fed to the column condenser. In the condenser the wet refrigerant is dried, taking heat from the condensing process vapor. The refrigerant vapor is then compressed and recycled to the reboiler, completing the working cycle. If the conditions are suitable, the process fluid can be used as the working fluid for the heat pump. This arrangement is shown in Figure 3.12(b). The hot process liquid at high pressure is expanded over the throttle valve and fed to the condenser, to provide cooling to condense the vapor from the column. The vapor from the condenser is compressed and returned to the base of the column. In an alternative arrangement, the process vapor is taken from the top of the column, compressed, and fed to the reboiler to provide heating.

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123

Feed

Vapor

Compressor

Expansion valve

Condenser

Low pressure

High pressure

Reboiler Liquid (a)

(b)

FIGURE 3.12 Distillation column with heat pump: (a) separate refrigerant circuit; (b) using column fluid as the refrigerant.

The “efficiency” of a heat pump is measured by the heat pump coefficient of performance, COPh: COPh =

energy delivered at higher temperature energy input to the compressor

(3.4)

The COPh depends principally on the working temperatures. Heat pumps are more efficient (higher COPh) when operated over a narrow temperature range. They are thus most often encountered on distillation columns that separate close-boiling compounds. Note that the COPh of a heat pump is not the same as the COP of a refrigeration cycle (Section 3.2.6). The economics of the application of heat pumps in the process industries is discussed by Holland and Devotta (1986). Details of the application of heat pumps in a wide range of industries are given by Moser and Schnitzer (1985).

3.4 WASTE STREAM COMBUSTION Process waste products that contain significant quantities of combustible material can be used as low-grade fuels, for raising steam or direct process heating. Their use will only be economic if the intrinsic value of the fuel justifies the cost of special burners and other equipment needed to burn the waste. If the combustible content of the waste is too low to support combustion, the waste must be supplemented with higher calorific value primary fuels.

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3.4.1 Reactor Off-gases Reactor off-gases (vent gas) and recycle stream purges are often of high enough calorific value to be used as fuels. Vent gases will typically be saturated with organic compounds such as solvents and high volatility feed compounds. The calorific value of a gas can be calculated from the heats of combustion of its constituents; the method is illustrated in Example 3.4. Other factors which, together with the calorific value, determine the economic value of an offgas as a fuel are the quantity available and the continuity of supply. Waste gases are best used for steam raising, rather than for direct process heating, as this decouples the source from the use and gives greater flexibility. Example 3.4: Calculation of Waste-Gas Calorific Value The typical vent-gas analysis from the recycle stream in an oxyhydrochlorination process for the production of dichloroethane (DCE) (British patent BP 1,524,449) is given below, percentages on volume basis. O2 7:96, CO2 + N2 87:6, CO 1:79, C2 H4 1:99, C2 H6 0:1, DCE 0:54 Estimate the vent-gas calorific value.

Solution

Component calorific values, from Perry and Chilton (1973): CO 67.6 kcal/mol = 283 kJ/mol C2H4 372.8 = 1560.9 C2H6 337.2 = 1411.9 The value for DCE can be estimated from the heats of formation. Combustion reaction: C2 H4 Cl2 ðgÞ + 21O2 ðgÞ → 2CO2 ðgÞ + H2 OðgÞ + 2HClðgÞ 2

The heats of formation ΔHf° are given in Appendix C, which is available in the online material at booksite .Elsevier.com/Towler. CO2 = H2O = HCl = DCE = ΔHc° = = =

−393.8 kJ/mol −242.0 −92.4 −130.0 ∑ΔHf° products − ∑ΔHf° reactants [2(−393.8) − 242.0 + 2(−92.4)] − [−130.0] −1084.4 kJ

Estimation of vent-gas calorific value, basis 100 mol. Component CO C2H4 C2H6 DCE

mol/100 mol 1.79 1.99 0.1 0.54

Calorific Value 283.0 1560.9 1411.9 1084.4

Total

Heating Value (kJ/mol) 506.6 3106.2 141.2 585.7 4339.7

3.4 Waste Stream Combustion

125

Formaldehyde off-gas Oxychlorination vent fume NaOH soln.

Steam VCM waste fume

Feed water

Liquid chlorinated H.C.

88 °C 85 °C

Mono-chem. fume H2O Nat. gas

1090 °C min.

316 °C Waste heat boiler

Fume incinerator Combustion air

Secondary scrubber

Primary scrubber HCL soln.

FIGURE 3.13 Typical incinerator-heat recovery-scrubber system for vinyl-chloride-monomer process waste. (Courtesy of John Thurley Ltd.)

4339:7 = 43:4 kJ/mol 100 43:4 = × 103 = 1938 kJ/m3 ð52 Btu/ft3 Þ at 1 bar, 0 °C 22:4

Calorific value of vent gas =

This calorific value is very low compared to 37 MJ/m3 (1000 Btu/ft3) for natural gas. The vent gas is barely worth recovery, but if the gas has to be burnt to avoid pollution it could be used in an incinerator such as that shown in Figure 3.13, giving a useful steam production to offset the cost of disposal.

3.4.2 Liquid and Solid Wastes Combustible liquid and solid waste can be disposed of by burning, which is usually preferred to dumping. Incorporating a steam boiler in the incinerator design will enable an otherwise unproductive, but necessary, operation to save energy. If the combustion products are corrosive, corrosionresistant materials will be needed, and the flue gases must be scrubbed to reduce air pollution. An incinerator designed to handle chlorinated and other liquid and solid wastes is shown in Figure 3.13. This incinerator incorporates a steam boiler and a flue-gas scrubber. The disposal of chlorinated wastes is discussed by Santoleri (1973).

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Dunn and Tomkins (1975) discuss the design and operation of incinerators for process wastes. They give particular attention to the need to comply with the current clean-air legislation, and the problem of corrosion and erosion of refractories and heat-exchange surfaces.

3.5 HEAT-EXCHANGER NETWORKS The design of a heat-exchanger network for a simple process with only one or two streams that need heating and cooling is usually straightforward. When there are multiple hot and cold streams, the design is more complex and there may be many possible heat exchange networks. The design engineer must determine the optimum extent of heat recovery, while ensuring that the design is flexible to changes in process conditions and can be started up and operated easily and safely. In the 1980s, there was a great deal of research into design methods for heat-exchanger networks; see Gundersen and Naess (1988). One of the most widely applied methods that emerged was a set of techniques termed pinch technology, which was developed by Bodo Linnhoff and his collaborators at ICI, Union Carbide, and the University of Manchester. The term derives from the fact that in a plot of the system temperatures versus the heat transferred, a pinch usually occurs between the hot stream and cold stream curves, see Figure 3.19. It has been shown that the pinch represents a distinct thermodynamic break in the system and that, for minimum energy requirements, heat should not be transferred across the pinch, Linnhoff et al. (1982). In this section the fundamental principles of the pinch technology method for energy integration will be outlined and illustrated with reference to a simple problem. The method and its applications are described fully in a guide published by the Institution of Chemical Engineers, Kemp (2007); see also Douglas (1988), Smith (2005), and El-Halwagi (2006).

3.5.1 Pinch Technology The development and application of the method can be illustrated by considering the problem of recovering heat between four process streams: two hot streams that require cooling, and two cold streams that must be heated. The process data for the streams is set out in Table 3.1. Each stream starts from a source temperature Ts, and is to be heated or cooled to a target temperature Tt. The heat capacity flow rate of each stream is shown as CP. For streams where the specific heat capacity can be taken as constant, and there is no phase change, CP will be given by (3.5)

CP = mCp where m = mass flow-rate, kg/s Cp = average specific heat capacity between Ts and Tt kJ kg−1°C−1 Table 3.1 Data for Heat Integration Problem Stream Number

Type

Heat Capacity Flow Rate CP, kW/°C

1 2 3 4

hot hot cold cold

3.0 1.0 2.0 4.5

Ts °C 180 150 20 80

Tt °C 60 30 135 140

Heat Load, kW 360 120 230 270

3.5 Heat-exchanger Networks

127

The heat load shown in the table is the total heat required to heat, or cool, the stream from the source to the target temperature. There is clearly scope for energy integration between these four streams. Two require heating and two cooling, and the stream temperatures are such that heat can be transferred from the hot to the cold streams. The task is to find the best arrangement of heat exchangers to achieve the target temperatures.

Simple Two-stream Problem Before investigating the energy integration of the four streams shown in Table 3.1, the use of a temperature-enthalpy diagram will be illustrated for a simple problem involving only two streams. The general problem of heating and cooling two streams from source to target temperatures is shown in Figure 3.14. Some heat is exchanged between the streams in the heat exchanger. Additional heat, to raise the cold stream to the target temperature, is provided by the hot utility (usually steam) in the heater; and additional cooling, to bring the hot stream to its target temperature, is provided by the cold utility (usually cooling water) in the cooler. In Figure 3.15(a) the stream temperatures are plotted on the y-axis and the enthalpy change of each stream on the x-axis. This is known as a temperature-enthalpy (T-H) diagram. For heat to be exchanged, a minimum temperature difference must be maintained between the two streams. This is shown as ΔTmin on the diagram. The practical minimum temperature difference in a heat exchanger will usually be between 5 °C and 30 °C; see Chapter 19. The slope of the lines in the T-H plot is proportional to 1/CP, since ΔH = CP × ΔT, so dT/dH = 1/CP. Streams with low heat capacity flow rate thus have steep slopes in the T-H plot and streams with high heat capacity flow rate have shallow slopes. The heat transferred between the streams is given by the range of enthalpy over which the two curves overlap each other, and is shown on the diagram as ΔHex. The heat transferred from the hot utility, ΔHhot, is given by the part of the cold stream that is not overlapped by the hot stream. The heat transferred to the cold utility, ΔHcold, is similarly given by the part of the hot stream that is not overlapped by the cold stream. The heats can also be calculated as ΔH = CP × ðtemperature changeÞ Since we are only concerned with changes in enthalpy, we can treat the enthalpy axis as a relative scale and slide either the hot stream or the cold stream horizontally. As we do so, we change Cold utility Tt

Hot stream

Tt Hot utility

FIGURE 3.14 Two-stream exchanger problem.

Exchanger

Cold stream

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CHAPTER 3 Utilities and Energy Efficient Design

Hot stream T

T Cold stream ∆Tmin

∆Tmin ∆Hcold

∆Hex

∆Hhot

∆Hcold

∆Hex

∆Hhot H

H (a)

(b)

FIGURE 3.15 Temperature-enthalpy (T-H ) diagram for two-stream example. Total cost Cost

Energy cost

Capital cost ΔToptimum

Minimum approach temperature

FIGURE 3.16 The capital-energy trade-off in process heat recovery.

the minimum temperature difference between the streams, ΔTmin, and also the amount of heat exchanged and the amounts of hot and cold utilities required. Figure 3.15(b) shows the same streams plotted with a lower value of ΔTmin. The amount of heat exchanged is increased and the utility requirements have been reduced. The temperature driving force for heat transfer has also been reduced, so the heat exchanger has both a larger duty and a smaller log-mean temperature difference. This leads to an increase in the heat transfer area required and in the capital cost of the exchanger. The capital cost increase is partially offset by capital cost savings in the heater and cooler, which both become smaller, as well as by savings in the costs of hot and cold utility. In general, there will be an optimum value of ΔTmin, as illustrated in Figure 3.16. This optimum is usually rather flat over the range 10 ºC to 30 ºC. The maximum feasible heat recovery is reached at the point where the hot and cold curves touch each other on the T-H plot, as illustrated in Figure 3.17. At this point, the temperature driving force at one end of the heat exchanger is zero and an infinite heat exchange surface is required, so the design is not practical. The exchanger is said to be pinched at the end where the hot and cold curves meet. In Figure 3.17, the heat exchanger is pinched at the cold end.

3.5 Heat-exchanger Networks

129

It is not possible for the hot and cold streams to cross each other, as this would be a violation of the second law of thermodynamics and would give an infeasible design.

Four-stream Problem In Figure 3.18(a) the hot streams given in Table 3.1 are shown plotted on a temperature-enthalpy diagram. As the diagram shows changes in the enthalpy of the streams, it does not matter where a particular curve is plotted on the enthalpy axis; as long as the curve runs between the correct temperatures. This means that where more than one stream appears in a temperature interval, the stream heat capacities can be added to form a composite curve, as shown in Figure 3.18(b).

∆Hcold

∆Hex

∆Hhot H

FIGURE 3.17 Maximum feasible heat recovery for two-stream example.

200 180

140

120

Stream 1 CP = 3.0

Streams 1 + 2 CP = 3.0 + 1.0 = 4.0

Stre

Temperature, °C

160

100 80 60

Stream 2 CP =1.0 kW/°C

40 20 0

100

200

300

400

Enthalpy, kW (a)

500

600

100

200

300

400

Enthalpy, kW (b)

FIGURE 3.18 Hot stream temperature v. enthalpy: (a) separate hot streams; (b) composite hot stream.

500

600

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CHAPTER 3 Utilities and Energy Efficient Design

Hot utility 50 kW

200 180 160

Temperature, °C

140

tr ts

120 100

d Col

stre

Pinch

∆Tmin = 10 °C

80 60 40 30 kW Cold utility

20 0

100

200

300

400

500

600

Enthalpy, kW

FIGURE 3.19 Hot and cold stream composite curves.

In Figure 3.19, the composite curve for the hot streams and the composite curve for the cold streams are drawn with a minimum temperature difference, the displacement between the curves, of 10 °C. This implies that in any of the exchangers to be used in the network the temperature difference between the streams will not be less than 10 °C. As for the two-stream problem, the overlap of the composite curves gives a target for heat recovery, and the displacements of the curves at the top and bottom of the diagram give the hot and cold utility requirements. These will be the minimum values needed to satisfy the target temperatures. This is valuable information. It gives the designer target values for the utilities to aim for when designing the exchanger network. Any design can be compared with the minimum utility requirements to check if further improvement is possible. In most exchanger networks the minimum temperature difference will occur at only one point. This is termed the pinch. In the problem being considered, the pinch occurs at between 90 °C on the hot stream curve and 80 °C on the cold stream curve. For multi-stream problems, the pinch will usually occur somewhere in the middle of the composite curves, as illustrated in Figure 3.19. The case when the pinch occurs at the end of one of the composite curves is termed a threshold problem and is discussed in Section 3.5.5.

Thermodynamic Significance of the Pinch The pinch divides the system into two distinct thermodynamic regions. The region above the pinch can be considered a heat sink, with heat flowing into it from the hot utility, but no heat flow out of it. Below the pinch the converse is true. Heat flows out of the region to the cold utility. No heat flows across the pinch, as shown in Figure 3.20(a).

3.5 Heat-exchanger Networks

∆Hhot

131

∆Hhot +∆Hxp

T ∆Hxp

∆Hcold

∆Hcold + ∆Hxp H (a)

H (b)

FIGURE 3.20 Pinch decomposition.

If a network is designed in which heat is transferred from any hot stream at a temperature above the pinch (including hot utilities) to any cold stream at a temperature below the pinch (including cold utilities), then heat is transferred across the pinch. If the amount of heat transferred across the pinch is ΔHxp, then in order to maintain energy balance the hot utility and cold utility must both be increased by ΔHxp, as shown in Figure 3.20(b). Cross-pinch heat transfer thus always leads to consumption of both hot and cold utilities that is greater than the minimum values that could be achieved. The pinch decomposition is very useful in heat-exchanger network design, as it decomposes the problem into two smaller problems. It also indicates the region where heat transfer matches are most constrained, at or near the pinch. When multiple hot or cold utilities are used there may be other pinches, termed utility pinches, that cause further problem decomposition. Problem decomposition can be exploited in algorithms for automatic heat-exchanger network synthesis.

3.5.2 The Problem Table Method The problem table is a numerical method for determining the pinch temperatures and the minimum utility requirements, introduced by Linnhoff and Flower (1978). It eliminates the sketching of composite curves, which can be useful if the problem is being solved manually. It is not widely used in industrial practice any more, due to the wide availability of computer tools for pinch analysis (see Section 3.5.7). The procedure is as follows: 1. Convert the actual stream temperatures Tact into interval temperatures Tint by subtracting half the minimum temperature difference from the hot stream temperatures, and by adding half to the cold stream temperatures: ΔTmin 2 ΔTmin cold streams Tint = Tact + 2 hot streams Tint = Tact −

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The use of the interval temperature rather than the actual temperatures allows the minimum temperature difference to be taken into account. ΔTmin = 10 °C for the problem being considered; see Table 3.2. 2. Note any duplicated interval temperatures. These are bracketed in Table 3.2. 3. Rank the interval temperatures in order of magnitude, showing the duplicated temperatures only once in the order; see Table 3.3. 4. Carry out a heat balance for the streams falling within each temperature interval. For the nth interval: ΔHn = ð∑CPc − ∑CPh Þ ðΔTn Þ where ΔHn = net heat required in the nth interval ΣCPc = sum of the heat capacities of all the cold streams in the interval ΣCPh = sum of the heat capacities of all the hot streams in the interval ΔTn = interval temperature difference = (Tn−1 − Tn) See Table 3.4. 5. “Cascade” the heat surplus from one interval to the next down the column of interval temperatures; see Figure 3.21(a). Cascading the heat from one interval to the next implies that the temperature difference is such that the heat can be transferred between the hot and cold streams. The presence of a negative value in the column indicates that the temperature gradient is in the wrong direction and that the exchange is not thermodynamically possible. This difficulty can be overcome if heat is introduced into the top of the cascade: Table 3.2 Interval Temperatures for ΔTmin = 10 °C Stream

Actual Temperature

1 2 3 4

180 150 20 80

Interval Temperature 60 30 135 140

175 145 (25) 85

55 25 140 (145)

Table 3.3 Ranked Order of Interval Temperatures Rank 175 145 140 85 55 25

Interval ΔTn °C 30 5 55 30 30

Streams in Interval −1 4 − (2 + 1) (3 + 4) − (1 + 2) 3 − (1 + 2) 3−2

Note: Duplicated temperatures are omitted. The interval ΔT and streams in the intervals are included as they are needed for Table 3.4.

3.5 Heat-exchanger Networks

133

Table 3.4 Problem Table Interval 1 2 3 4 5

Interval Temp. °C

ΣCPc − ΣCPh* kW/°C

ΔTn °C

175 145 140 85 55 25

30 5 55 30 30

−3.0 0.5 2.5 −2.0 1.0

ΔH kW −90 2.5 137.5 −60 30

Surplus or Deficit s d d s d

*Note: The streams in each interval are given in Table 3.3.

Interval temp. 0 kW

50 kW

175 °C −90 kW 145 °C

−90 kW 90 kW

2.5 kW 140 °C

140 kW 2.5 kW

87.5 kW 137.5 kW

85 °C

135.5 kW 137.5 kW

−50 kW

55 °C

0.0 kW −60 kW

−60 kW 10 kW 30 kW 25 °C

60 kW 30 kW

−20 kW (a)

30 kW (b)

From (b) pinch occurs at interval temperature 85°C.

FIGURE 3.21 Heat cascade.

6. Introduce just enough heat to the top of the cascade to eliminate all the negative values; see Figure 3.21(b). Comparing the composite curve, Figure 3.19, with Figure 3.21(b) shows that the heat introduced to the cascade is the minimum hot utility requirement and the heat removed at the bottom is the minimum cold utility required. The pinch occurs in Figure 3.21(b) where the heat flow in the cascade is zero. This is as would be expected from the rule that for minimum utility requirements no heat flows across the pinch. In Figure 3.21(b) the pinch is at an interval temperature

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of 85 ºC, corresponding to a cold stream temperature of 80 ºC and a hot stream temperature of 90 °C, as was found using the composite curves. It is not necessary to draw up a separate cascade diagram. This was done in Figure 3.21 to illustrate the principle. The cascaded values can be added to the problem table as two additional columns; see Example 3.5.

Summary For maximum heat recovery and minimum use of utilities: 1. Do not transfer heat across the pinch. 2. Do not use hot utilities below the pinch. 3. Do not use cold utilities above the pinch.

3.5.3 Heat-exchanger Network Design Grid Representation It is convenient to represent a heat-exchanger network as a grid; see Figure 3.22. The process streams are drawn as horizontal lines, with the stream numbers shown in square boxes. Hot streams are drawn at the top of the grid, and flow from left to right. The cold streams are drawn at the bottom, and flow from right to left. The stream heat capacities CP are shown in a column at the end of the stream lines. Heat exchangers are drawn as two circles connected by a vertical line. The circles connect the two streams between which heat is being exchanged; that is, the streams that would flow through the actual exchanger. Heaters and coolers can be drawn as a single circle, connected to the appropriate utility. If multiple utilities are used then these can also be shown as streams. Exchanger duties are usually marked under the exchanger and temperatures are also sometimes indicated on the grid diagram.

Network Design for Maximum Energy Recovery The analysis carried out in Figure 3.19 and Figure 3.21 has shown that the minimum utility requirements for the problem set out in Table 3.1 are 50 kW of the hot and 30 kW of the cold utility, and that the pinch occurs where the cold streams are at 80 ºC and the hot streams are at 90 °C. The grid representation of the streams is shown in Figure 3.23. The vertical dotted lines represent the pinch and separate the grid into the regions above and below the pinch. Note that the hot and cold streams are offset at the pinch, because of the difference in pinch temperature.

Cooler C

Hot stream n n

m Cold stream m

H Heater

FIGURE 3.22 Grid representation.

Exchanger

3.5 Heat-exchanger Networks

135

CP (kW/°C) 1

180 °C

90 °C

60 °C

3.0

150 °C

90 °C

30 °C

1.0

135 °C

80 °C

20 °C

140 °C

80 °C

2.0

4.5

FIGURE 3.23 Grid for four-stream problem.

For maximum energy recovery (minimum utility consumption) the best performance is obtained if no cooling is used above the pinch. This means that the hot streams above the pinch should be brought to the pinch temperature solely by exchange with the cold streams. The network design is therefore started at the pinch, finding feasible matches between streams to fulfill this aim. In making a match adjacent to the pinch the heat capacity CP of the hot stream must be equal to or less than that of the cold stream. This is to ensure that the minimum temperature difference between the curves is maintained. The slope of a line on the temperature-enthalpy diagram is equal to the reciprocal of the heat capacity. So, above the pinch the lines will converge if CPh exceeds CPc and as the streams start with a separation at the pinch equal to ΔTmin, the minimum temperature condition would be violated. Every hot stream must be matched with a cold stream immediately above the pinch, otherwise it will not be able to reach the pinch temperature. Below the pinch the procedure is the same; the aim being to bring the cold streams to the pinch temperature by exchange with the hot streams. For streams adjacent to the pinch the criterion for matching streams is that the heat capacity of the cold stream must be equal to or greater than the hot stream, to avoid breaking the minimum temperature difference condition. Every cold stream must be matched with a hot stream immediately below the pinch.

Network Design Above the Pinch CPh ≤ CPc 1. Applying this condition at the pinch, stream 1 can be matched with stream 4, but not with 3. Matching streams 1 and 4 and transferring the full amount of heat required to bring stream 1 to the pinch temperature gives ΔHex = CPðTs − Tpinch Þ ΔHex = 3:0ð180 − 90Þ = 270 kW

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CP (kW/°C)

1 2

180 °C

90 °C

60 °C

3.0

150 °C

90 °C

30 °C

1.0

80 °C

20 °C

135 °C 140 °C

H 50 kW

60 kW

80 °C

2.0

4.5

270 kW

FIGURE 3.24 Network design above the pinch.

This will also satisfy the heat load required to bring stream 4 to its target temperature: ΔHex = 4:5ð140 − 80Þ = 270 kW 2. Stream 2 can be matched with stream 3, while satisfying the heat capacity restriction. Transferring the full amount to bring stream 2 to the pinch temperature: ΔHex = 1:0ð150 − 90Þ = 60 kW 3. The heat required to bring stream 3 to its target temperature, from the pinch temperature, is ΔH = 2:0ð135 − 80Þ = 110 kW So a heater will have to be included to provide the remaining heat load: ΔHhot = 110 − 60 = 50 kW This checks with the value given by the problem table, Figure 3.21(b). The proposed network design above the pinch is shown in Figure 3.24.

Network Design Below the Pinch CPh ≥ CPc 4. Stream 4 begins at the pinch temperature, Ts = 80 °C, and so is not available for any matches below the pinch. 5. A match between streams 1 and 3 adjacent to the pinch will satisfy the heat capacity restriction but not one between streams 2 and 3. So 1 is matched with 3 transferring the full amount to bring stream 1 to its target temperature: ΔHex = 3:0ð90 − 60Þ = 90 kW

3.5 Heat-exchanger Networks

180 °C

90 °C 90 °C

150 °C

90 °C 90 °C

135 °C

80 °C 80 °C

H 50 kW 140 °C

60 kW

C 30 kW

137

CP (kW/ °C)

ΔH (kW)

60 °C

3.0

360

30 °C

1.0

120

2.0

230

4.5

270

20 °C

90 kW 30 kW

80 °C 270 kW

FIGURE 3.25 Proposed heat exchanger network for ΔTmin = 10 °C.

6. Stream 3 requires more heat to bring it to the pinch temperature; the amount needed is ΔH = 2:0ð80 − 20Þ − 90 = 30 kW This can be provided from stream 2, as the match is now away from the pinch. The rise in temperature of stream 3 will be given by ΔT = ΔH/CP So transferring 30 kW will raise the temperature from the source temperature to 20 + 30/2:0 = 35 °C and this gives a stream temperature difference on the outlet side of the exchanger of 90 − 35 = 55 °C So the minimum temperature difference condition, 10 °C, will not be violated by this match. 7. Stream 2 needs further cooling to bring it to its target temperature, so a cooler must be included; the cooling required is ΔHcold = 1:0ð90 − 30Þ − 30 = 30 kW which is the amount of the cold utility predicted by the problem table. The proposed network for maximum energy recovery is shown in Figure 3.25.

Stream Splitting If the heat capacities of streams are such that it is not possible to make a match at the pinch without violating the minimum temperature difference condition, then the heat capacity can be altered by splitting a stream. Dividing the stream will reduce the mass flow rates in each leg and hence the heat capacities. This is illustrated in Example 3.5.

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Similarly, if there are not enough streams available to make all of the required matches at the pinch then streams with large CP can be split to increase the number of streams. Guide rules for stream matching and splitting are given in the Institution of Chemical Engineers Guide, Kemp (2007) and by Smith (2005).

Summary The guide rules for devising a network for maximum heat recovery are given below: 1. Divide the problem at the pinch. 2. Design away from the pinch. 3. Above the pinch match streams adjacent to the pinch, meeting the restriction CPh ≤ CPc 4. Below the pinch match streams adjacent to the pinch, meeting the restriction CPh ≥ CPc 5. If the stream matching criteria cannot be satisfied, split a stream. 6. Maximize the exchanger heat loads. 7. Supply external heating only above the pinch and external cooling only below the pinch.

3.5.4 Minimum Number of Exchangers The network shown in Figure 3.25 was designed to give the maximum heat recovery, and will therefore give the minimum consumption, and cost, of the hot and cold utilities. This will not necessarily be the optimum design for the network. The optimum design will be that which gives the lowest total annualized cost, taking into account the capital cost of the system, in addition to the utility and other operating costs. The number of exchangers in the network, and their size, will determine the capital cost. In Figure 3.25 it is clear that there is scope for reducing the number of exchangers. The 30 kW exchanger between streams 2 and 3 can be deleted and the heat loads of the cooler and heater increased to bring streams 2 and 3 to their target temperatures. Heat would cross the pinch and the consumption of the utilities would be increased. Whether the revised network would be better, or more economic, depends on the relative cost of capital and utilities and the operability of each design. For any network, there will be an optimum design that gives the least annual cost: capital charges plus utility and other operating costs. The estimation of capital and operating costs are covered in Chapters 7 and 8. To find the optimum design it is necessary to cost a number of alternative designs, seeking a compromise between the capital costs, determined by the number and size of the exchangers, and the utility costs, determined by the heat recovery achieved. For simple networks Holmann (1971) has shown that the minimum number of exchangers is given by Zmin = N′ − 1 where Zmin = minimum number of exchangers needed, including heaters and coolers N′ = the number of streams, including the utilities

(3.6)

3.5 Heat-exchanger Networks

139

1 2

C H

3 4

FIGURE 3.26 Loop in network.

For complex networks a more general expression is needed to determine the minimum number of exchangers: Zmin = N′ + L′ − S

(3.7)

where L′ = the number of internal loops present in the network S = the number of independent branches (subsets) that exist in the network A loop exists where a closed path can be traced through the network. There is a loop in the network shown in Figure 3.25. The loop is shown in Figure 3.26. The presence of a loop indicates that there is scope for reducing the number of exchangers. For a full discussion of Equation 3.7 and its applications see Linnhoff, Mason, Wardle (1979), Smith (2005), or Kemp (2007). In summary, to seek the optimum design for a network: 1. Start with the design for maximum heat recovery. The number of exchangers needed will be equal to or less than the number for maximum energy recovery. 2. Identify loops that cross the pinch. The design for maximum heat recovery will usually contain loops. 3. Starting with the loop with the least heat load, break the loops by adding or subtracting heat. 4. Check that the specified minimum temperature difference ΔTmin has not been violated. If the violation is significant, revise the design as necessary to restore ΔTmin. If the violation is small then it may not have much impact on the total annualized cost and can be ignored. 5. Estimate the capital and operating costs, and the total annual cost. 6. Repeat the loop breaking and network revision to find the lowest cost design. 7. Consider the safety, operability, and maintenance aspects of the proposed design.

3.5.5 Threshold Problems Problems that show the characteristic of requiring only either a hot utility or a cold utility (but not both) over a range of minimum temperature differences, from zero up to a threshold value, are known as threshold problems. A threshold problem is illustrated in Figure 3.27.

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∆Hhot

∆Tmin = Threshold ∆Hcold = 0 H

FIGURE 3.27 Threshold problem.

To design the heat-exchanger network for a threshold problem, it is normal to start at the most constrained point. The problem can often be treated as one half of a problem exhibiting a pinch. Threshold problems are often encountered in the process industries. A pinch can be introduced in such problems if multiple utilities are used, as in the recovery of heat to generate steam, or if the chosen value of ΔTmin is greater than the threshold value. The procedures to follow in the design of threshold problems are discussed by Smith (2005) and Kemp (2007).

3.5.6 Determining Utility Consumption Pinch analysis can be used to determine targets for process utility consumption. Initial targets for total hot and cold utility use can be calculated directly from the problem table algorithm or read from the composite curves. A more detailed breakdown of the utility needs can be determined from the initial heat-exchanger network. The following guidelines should be followed when using the pinch method to determine utility consumption targets: 1. Do not use cold utilities above the pinch temperature. This means that no process stream should be cooled from a temperature above the pinch temperature using a cold utility. 2. Do not use hot utilities below the pinch. This means no process stream should be heated from a temperature below the pinch temperature using a hot utility. 3. On either side of the pinch, maximize use of the cheapest utility first. Above the pinch this means use LP steam wherever possible before considering MP steam, then HP steam, hot oil, etc. Below the pinch, maximize use of cooling water before considering refrigeration. 4. If the process pinch is at a high temperature, consider boiler feed water preheat and steam generation as potential cold utility streams. 5. If the process pinch is at a low temperature, consider steam condensate and spent cooling water as hot streams.

3.5 Heat-exchanger Networks

141

6. If the process requires cooling to a very low temperature, consider using cascaded refrigeration cycles to improve the overall COP. 7. If the process requires heating to a very high temperature and a fired heater is needed, consider using the convective section heat either for process heating or for steam generation. For process control reasons, it may be necessary to operate the heater with process heating in the radiant section only, but the convective section heat is still available for use. In strict pinch terms, this heat can be used at any temperature above the pinch temperature, but in practice convective section heat recovery is usually limited by the acid-gas dew point of the flue gas or other furnace design considerations (see Section 19.17). 8. If a process condition leads to the use of a more expensive utility, then consider process modifications that would make this unnecessary. For example, if a product must be cooled and sent to storage at 30 ºC, the cooling cannot be carried out using cooling water and refrigeration must be used. The designer should question why 30 ºC was specified for the storage. If it was because a vented tank was selected, then choosing a non-vented (floating roof) tank instead might allow the product to be sent to storage at 40 ºC, in which case the refrigeration system could be eliminated. Graphical methods and numerical approaches have been developed to assist in the optimal design of utility systems. For simple problems, these methods are not needed, as the heaters and coolers that have been identified in the heat-exchange network can be assigned to the appropriate utility stream using the simple rules above. When a stream requires heating or cooling over a broad temperature range, the designer should consider whether it is cheaper to break the duty into several exchangers, each served by the appropriate utility for a given temperature range, or whether it makes more economic sense to use a single exchanger, served by the hottest or coldest utility. The problem of placing multiple utilities is illustrated in Example 3.6.

3.5.7 Process Integration: Integration of Other Process Operations The pinch technology method can give many other insights into process synthesis, beyond the design of heat-exchanger networks. The method can also be applied to the integration of other process units, such as separation columns, reactors, compressors and expanders, boilers, and heat pumps. The wider applications of pinch technology are discussed in the Institution of Chemical Engineers Guide, Kemp (2007) and by El-Halwagi (2006) and Smith (2005). The techniques of process integration have been expanded for use in optimizing mass transfer operations, and have been applied in waste reduction, water conservation, and pollution control; see El-Halwagi (1997) and Dunn and El-Halwagi (2003).

3.5.8 Computer Tools for Heat-exchanger Network Design Most pinch analysis in industry is carried out using commercial pinch analysis software. Programs such as Aspen HX-Net™ (Aspen Technology Inc.), SUPERTARGET™ (Linnhoff March Ltd.) and UniSim™ ExchangerNet™ (Honeywell International Inc.) allow the design engineer to plot composite curves, optimize ΔT min , set targets for multiple utilities, and design the heat-exchanger network.

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Most of these programs are able to automatically extract stream data from process simulation programs, although great care should be taken to check the extracted data. There are many possible pitfalls in data extraction; for example, not recognizing changes in the CP of a stream or partial vaporization or condensation of a stream, any of which could lead to a kink in the stream T-H profile. See Smith (2005) or Kemp (2007) for more information on data extraction. The commercial pinch technology tools also usually include automatic heat-exchanger network synthesis features. The automatic synthesis methods are based on MINLP optimization of superstructures of possible exchanger options (see Chapter 12 for discussion of MINLP methods). These tools can be used to arrive at a candidate network, but the optimization must be properly constrained so that it does not introduce a large number of stream splits and add a lot of small exchangers. Experienced designers seldom use automatic heat-exchanger network synthesis methods, as it usually requires more effort to turn the resulting network into something practical than it would take to design a practical network manually. The NLP optimization capability of the software is widely used though, for fine tuning the network temperatures by exploitation of loops and stream split ratios.

Example 3.5 Determine the pinch temperatures and the minimum utility requirements for the streams set out in the table below, for a minimum temperature difference between the streams of 20 °C. Devise a heat-exchanger network to achieve the maximum energy recovery.

Stream Number

Type

1 2 3 4

hot hot cold cold

Heat Capacity Flow Rate, kW/°C 40.0 30.0 60.0 20.0

Source Temp. °C 180 150 30 80

Solution

Target Temp. °C 40 60 180 160

Heat Load, kW 5600 1800 9000 1600

The problem table to find the minimum utility requirements and the pinch temperature can be built in a spreadsheet. The calculations in each cell are repetitive and the formula can be copied from cell to cell using the cell copy commands. A spreadsheet template for the problem table algorithm is available in MS Excel format in the online material at booksite.Elsevier.com/Towler. The use of the spreadsheet is illustrated in Figure 3.28 and described below. First calculate the interval temperatures, for ΔTmin = 20 °C hot streams Tint = Tact − 10 °C cold streams Tint = Tact + 10 °C

Project Name Project Number

Company Name Address

REV

1 of 1

Sheet

DATE

APVD

REV

DATE

APVD

PROBLEM TABLE ALGORITHM Form XXXXX-YY-ZZ 1. Minimum temperature approach Tmin

20 °C

2. Stream data

Stream No. 1 2 3 4 5 6 7 8

Actual temperature (°C) Source Target 180 40 150 60 30 180 80 160

Interval temperature (°C) Source Target 170 30 140 50 40 190 90 170

Heat capacity flow rate CP (kW/°C) 40 30 60 20

Heat load (kW) 5600 2700 9000 1600 0 0 0 0

Interval

Interval temp (°C)

1 2 3 4 5 6 7 8

190 170 170 140 90 50 40 30

FIGURE 3.28 Problem table algorithm spreadsheet.

Interval T (°C) 20 0 30 50 40 10 10

Sum CPc sum CPh (kW/°C) 60 60 40 10 10 20 40

dH (kW) 1200 0 1200 500 400 200 400

Cascade (kW)

(kW)

0 1200 1200 2400 2900 2500 2700 2300

2900 1700 1700 500 0 400 200 600

3.5 Heat-exchanger Networks

3. Problem table

143

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CHAPTER 3 Utilities and Energy Efficient Design

Actual Temp. °C Stream 1 2 3 4

Interval Temp. °C

Source

Target

Source

Target

180 150 30 80

40 60 180 160

170 140 40 90

30 50 190 170

In the spreadsheet this can be done by using an IF function to determine whether the source temperature is lower than the target temperature, in which case the stream is a cold stream and should have ΔTmin/2 added. Next rank the interval temperatures, ignoring any duplicated values. In the spreadsheet this is done using the LARGE function. Determine which streams occur in each interval. For a stream to be present in a given interval the largest stream interval temperature must be greater than the lower end of the interval range and the lowest stream interval temperature must also be greater than or equal to the lower end of the interval range. This can be calculated in the spreadsheet using IF, AND, and OR functions. Once the streams in each interval have been determined it is possible to calculate the combined stream heat capacities. These calculations are not strictly part of the problem table, so they have been hidden in the spreadsheet (in columns to the right of the table). The sum of CP values for the cold streams minus that for the hot streams can then be multiplied by the interval ΔT to give the interval ΔH, and the interval ΔH values can be cascaded to give the overall heat flow. The amount of heat that must be put in to prevent the heat flow from becoming negative is the lowest value in the column, which can be found using the SMALL function. The final column then gives a cascade showing only positive values, with zero energy cascading at the pinch temperature. In the last column 2900 kW of heat have been added to eliminate the negative values in the previous column; so the hot utility requirement is 2900 kW and the cold utility requirement, the bottom value in the column, is 600 kW. The pinch occurs where the heat transferred is zero, that is at interval number 4, interval temperature 90 °C. So at the pinch hot streams will be at 90 + 10 = 100 °C and the cold streams will be at 90 − 10 = 80 °C Note that in the table both stream 1 and stream 4 had an interval temperature of 170 ºC, which led to a duplicate line in the list of ranked interval temperatures. Strictly, this line could have been eliminated, but since it gave a zero value for the ΔT, it did not affect the calculation. The programming of the spreadsheet is a lot easier if duplicate temperatures are handled in this manner. To design the network for maximum energy recovery, start at the pinch and match streams, following the rules on stream heat capacities for matches adjacent to the pinch. Where a match is made, transfer the maximum amount of heat. The proposed network is shown in Figure 3.29.

1 2

180 °C

100 °C 100 °C

150 °C

100 °C 100 °C

800 kW 180 °C 1250 kW 160 °C H

3.5 Heat-exchanger Networks

145

CP (kW/ °C)

ΔH (kW)

40 °C

5600

60 °C

2700

9000

1600

C 600 kW

80 °C 80 °C

H 3200 kW

750 kW

30 °C 1800 kW

80 °C

1200 kW

850 kW 750 kW

FIGURE 3.29 Proposed heat-exchanger network for Example 3.5.

The methodology followed in devising this network was: Above Pinch

1. CPh ≤ CPc 2. We can match stream 1 or 2 with stream 3 but neither stream can match with stream 4. This creates a problem, since if we match stream 1 with 3 then stream 2 will not be able to make a match at the pinch. Likewise, if we match stream 2 with 3 then stream 1 will not be able to make a match at the pinch. 3. Check the heat available in bringing the hot streams to the pinch temperature. stream 1 ΔH = 40:0ð180 − 100Þ = 3200 kW stream 2 ΔH = 30:0ð150 − 100Þ = 1500 kW 4. Check the heat required to bring the cold streams from the pinch temperature to their target temperatures. stream 3 ΔH = 60:0ð180 − 80Þ = 6000 kW stream 4 ΔH = 20:0ð160 − 80Þ = 1600 kW 5. If we split stream 3 into two branches with CP of 40.0 and 20.0, then we can match the larger branch with stream 1 and transfer 3200 kW, which satisfies (ticks off) stream 1. 6. We now have two cold streams, both with CP of 20.0, and one hot stream (2) with CP of 30.0. We need to split stream 2 into two branches. As an initial guess these can both have CP of 15.0. We can then match one branch of stream 2 with the smaller branch of 4 and transfer 750 kW, and the other branch with stream 3, also for 750 kW, which then ticks off stream 2. 7. Include a heater on the larger branch of stream 3 to bring it to its target temperature: ΔHhot = 40ð100Þ − 3200 = 800 kW 8. Include a heater on the smaller branch of stream 3 to provide the balance of the heat required: ΔHhot = 20ð100Þ – 750 = 1250 kW

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9. Include a heater on stream 4 to provide the balance of the heat required: ΔHhot = 1600 − 750 = 850 kW Check sum of heater duties = 800 + 1250 + 850 = 2900 kW = hot utility target. Below Pinch

10. 11. 12. 13.

CPh ≥ CPc Note that stream 4 starts at the pinch temperature and so cannot provide any cooling below the pinch. We cannot match stream 1 or 2 with stream 3 at the pinch. Split stream 3 to reduce CP. An even split will allow both streams 1 and 2 to be matched with the split streams adjacent to the pinch, so try this initially. 14. Check the heat available from bringing the hot streams from the pinch temperature to their target temperatures: stream 1 ΔH = 40:0ð100 − 40Þ = 2400 kW stream 2 ΔH = 30:0ð100 − 60Þ = 1200 kW 15. Check the heat required to bring the cold streams from their source temperatures to the pinch temperature: stream 3 ΔH = 60:0ð80 − 30Þ = 3000 kW Stream 4 is at the pinch temperature 16. Note that stream 1 cannot be brought to its target temperature of 40 °C by full interchange with stream 3 as the source temperature of stream 3 is 30 °C, so ΔTmin would be violated. So transfer 1800 kW to one leg of the split stream 3. 17. Check temperature at exit of this exchanger: Temp out = 100 − 1800 = 55 °C, satisfactory 40 18. Provide cooler on stream 1 to bring it to its target temperature; the cooling needed is ΔHcold = 2400 − 1800 = 600 kW 19. Transfer the full heat load from stream 2 to second leg of stream 3; this satisfies both streams. Note that the heating and cooling loads, 2900 kW and 600 kW, respectively, match those predicted from the problem table. Note also that in order to satisfy the pinch decomposition and the stream matching rules we ended up introducing a large number of stream splits. This is quite common in heat-exchanger network design. None of the three split fractions was optimized, so substantial savings as well as simplification of the network could be possible. For example, loops exist between the branches of stream 3 and stream 1 and between the branches of stream 3 and stream 2. With the current split ratios these loops cannot be eliminated, but with other ratios it might be possible to eliminate one or two exchangers.

3.5 Heat-exchanger Networks

147

The introduction of multiple stream splits is often cited as a drawback of the pinch method. Stream splits can be problematic in process operation. For example, when an oil or other multicomponent stream is heated and partially vaporized, then the stream is a two-phase mixture. It is difficult to control the splitting of such streams to give the required flow rate in each branch. Experienced designers usually constrain the network to avoid multiple stream splits whenever possible, even if this leads to designs that have higher than minimum utility consumption.

Example 3.6 Determine the mix of utilities to use for the process introduced in Example 3.5, if the following utility streams are available: Utility Stream MP steam (20 bar) LP steam (6 bar) Cooling water Chilled water

Tsupply (ºC) 212 159 30 10

Treturn (ºC) 212 159 40 20

Cost $5.47/1000 lb $4.03/1000 lb $0.10/1000 gal $4.50/GJ

Solution

From the solution to Example 3.5, we have the following heating and cooling duties that require utilities: Cooler on stream 1, duty 600 kW, to cool stream 1 from 55 ºC to 40 ºC Heater on large branch of stream 3, duty 800 kW, to heat from 160 ºC to 180 ºC Heater on small branch of stream 3, duty 1250 kW, to heat from 117.5 ºC to 180 ºC Heater on stream 4, duty 750 kW, to heat from 117.5 ºC to 160 ºC It is obvious by inspection that if we are to maintain an approach temperature of 20 ºC, then we will need to use MP steam and chilled water in at least some of the utility exchangers. We can start by converting the utility costs into annual costs to provide a kW of heating or cooling, based on an assumed 8000 hours per year of operation. For MP steam at 20 bar: Heat of condensation ðby interpolation in steam tablesÞ ≈ 1889 kJ/kg 1 kW = 3600 × 8000 kJ/yr, therefore requires 3600 × 8000/1889 = 15:2 × 103 kg/y Annual cost per kW = 15:2 × 103 × 2:205 ðlb/kgÞ × 5:47 ð$/1000 lbÞ/1000 = $183 /y Similarly for LP steam at 6 bar: Heat of condensation ðby interpolation in steam tablesÞ ≈ 2085 kJ/kg 1 kW = 3600 × 8000 kJ/yr, therefore requires 3600 × 8000/2085 = 13:8 × 103 kg/y Annual cost per kW = 13:8 × 103 × 2:205 ðlb/kgÞ × 4:03 ð$/1000 lbÞ/1000 = $123/y

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For cooling water with a cooling range of 10 ºC: 1 kW of cooling requires CP = 1/10 = 0:1 kW/°C Heat capacity of water ≈ 4.2 kJ/kgºC, so: Annual flow rate of cooling water per kW = 0:1 × 3600 × 8000/4:2 = 686 × 103 kg/y 1000 gal of water = 3785 liters and has mass roughly 3785 kg, so: water flow rate = 686 × 103 /3785 = 181:2 thousand gallons per year, which has annual cost 0:1 × 181:2 = $18:1/y For chilled water: 1 kW of cooling = 3600 × 8000 = 28:8 × 106 kJ/y = 28:8 GJ/y So, annual cost = 28.8 × 4.50 = $129.6/y. It is clearly cheaper to use LP steam rather than MP steam and to use cooling water instead of chilled water whenever it is feasible to do so. Beginning with the design below the pinch, if we are to maintain a minimum temperature difference of 20 ºC, then we cannot use cooling water below 30 + 20 = 50 ºC. The lowest utility cost design would therefore use cooling water to cool stream 1 from 55 ºC to 50 ºC (duty 200 kW). A second cooler would then be needed to cool stream 1 from 50 ºC to 40ºC using chilled water (duty 400 kW). The annual utility cost of this design would be 200(18.1) + 400(129.6) = $55,460. It might reasonably be argued that the utility savings from using the minimum cost of coolant do not justify the capital cost of an extra exchanger. Two possible alternatives can be considered. If all of the cooling is carried out using chilled water, then the minimum temperature difference constraint is not violated and a single cooler of duty 600 kW can be used. The annual utility cost would be 600(129.6) = $77,760. The use of chilled water gives larger log-mean temperature difference in the cooler, so the total surface area required in this design is less than the sum of the areas needed for the two exchangers proposed above. The incremental operating cost would have to be traded against the capital cost savings. Alternatively, if we jettison the 20 ºC minimum temperature difference and allow a 10 ºC minimum temperature difference in the cooler, then we can cool stream 1 using only cooling water in a single cooler of duty 600 kW. The annual utility cost would be 600(18.1) = $10,860. The savings in operating cost would have to be traded against the increased capital cost that would result from having a lower log-mean temperature difference for this exchanger. Turning now to the design above the pinch, LP steam cannot be used for heating any stream that is above a temperature of 159 – 20 = 139 ºC. The minimum utility cost design would therefore use the following heaters: LP steam to heat stream 4 from 117.5 ºC to 139 ºC LP steam to heat the small branch of stream 3 from 117.5 ºC to 139 ºC MP steam to heat the small branch of stream 3 from 139 ºC to 180 ºC MP steam to heat the large branch of stream 3 from 160 ºC to 180 ºC MP steam to heat stream 4 from 139 ºC to 160 ºC

3.6 Energy Management in Unsteady Processes

149

Again, although this design has the minimum utility cost, other designs may be more optimal when capital costs are also considered. For example, there is no reason why the two branches of stream 3 must be sent to separate MP steam heaters. These two heaters could be combined, even though that violates the rule of thumb about not mixing streams at different temperatures, as we are well away from the pinch and have already ensured maximum use of LP steam. This modification would reduce capital cost with no increase in operating cost, so would almost certainly be adopted. Another modification to consider would be to examine allowing a smaller minimum temperature difference for the heaters that use LP steam. This would increase LP steam use at the expense of more capital (reduced temperature difference in the exchangers) and so would require a tradeoff between the additional capital and the energy cost savings. Note that by introducing the lowest cost utilities into the design we went from needing three heaters and one cooler in Figure 3.29 to using two coolers and five heaters in the lowest utility cost design. The introduction of multiple utilities almost always leads to an increase in the number of heat exchangers needed in a design as well as the surface area requirements, and the energy cost savings must justify the resulting increase in capital cost.

3.6 ENERGY MANAGEMENT IN UNSTEADY PROCESSES The energy recovery approaches described above have been for steady-state processes, where the rate of energy generation or consumption did not vary with time. Batch and cyclic processes present multiple challenges for energy management. The designer must not only consider the amount of heat that must be added to or removed from the process, but also the dynamics of heat transfer. Limitations on the rate of heat transfer often cause heating and cooling steps to become the ratelimiting steps in determining the overall cycle time. The sequential nature of batch operations can also reduce the possibilities for heat recovery by heat exchange, unless multiple batches are processed in parallel and sequenced such that heat can be transferred from one batch to the next.

3.6.1 Differential Energy Balances If a batch process is considered, or if the rate of energy generation or removal varies with time, it is necessary to set up a differential energy balance. For batch processes, the total energy requirements can usually be estimated by taking a single batch as the time basis for the calculation; but the maximum rate of heat generation must also be estimated to size any heat-transfer equipment needed. A generalized differential energy balance can be written as Energy out = Energy in + generation − consumption − accumulation

(3.8)

The energy in and energy out terms should include both heat transfer and convective heat flows, while the generation and consumption terms include heat of mixing, heat of reaction, etc. An unsteady state mass balance must usually be solved simultaneously with the differential energy balance. Most batch processing operations are carried out in the liquid phase in stirred tanks. In the simplest case, heat is only added or removed when the vessel is full, and the convective heat flows can

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be neglected. If there is no heat of reaction or mixing, then Equation 3.8 simplifies to Rate of heat accumulation = rate of heat transfer into vessel MCp

dT = UAΔTm dt

(3.9) (3.10)

where M = the mass contained in the vessel, kg Cp = the specific heat capacity of the vessel contents, J/kgºC T = temperature of the vessel contents, ºC t = time, s U = the overall heat-transfer coefficient, W/m2°C A = heat-transfer area, m2 ΔTm = the mean temperature difference, the temperature driving force, °C The mean temperature difference for heat transfer, ΔTm, will generally be a function of the temperature of the vessel contents, T, as well as depending on the nature of the heating or cooling medium (isothermal or nonisothermal) and the type of heat transfer surface used. Batch tanks are usually heated or cooled using internal coils, jacketed vessels, or external heat exchangers. Heat transfer to vessels is discussed in more detail in Section 19.18. In more complex cases, it is usually a good idea to set up a dynamic simulation model of the process. The use of dynamic simulation allows the designer to include additional heat source and sink terms such as losses to the environment. The designer can also use the dynamic model to investigate the interaction between the process, the heat transfer equipment, and the process control system, and hence to develop control algorithms that ensure rapid heating or cooling but do not cause excessive overshoot of the target temperature. The application of differential energy balances to simple problems is illustrated in Examples 3.7 and 15.6.

3.6.2 Energy Recovery in Batch and Cyclic Processes Most batch processes operate at relatively low temperatures, below 200 ºC, where use of steam or hot oil will give high heat transfer rates for process heating. High heat transfer rates allow shorter heating times and enable use of internal coils and jacketed vessels, reducing the number of pieces of equipment in the plant. If the energy cost is a very small fraction of the total cost of production then recovering heat from the process may not be economically attractive, as the resulting increase in capital cost will not be justified. Many batch processes need cooling to temperatures that require some degree of refrigeration. Fermentation processes are often operated at temperatures below 40 ºC, where use of cooling water can be problematic and chilled water or other refrigerants are used instead. Food processes often require refrigeration or freezing of the product. Recovery of “cooling” from chilled streams is not possible when the product must be delivered in chilled form. Three of the most commonly used methods for recovering heat in batch and cyclic processes are described below. Energy optimization in batch plants has been the subject of much research, and is discussed in more detail in the papers by Vaselenak, Grossman, and Westerberg (1986), Kemp and

3.6 Energy Management in Unsteady Processes

151

Deakin (1989), and Lee and Reklaitis (1995) and the books by Smith (2005), Kemp (2007), and Majozi (2010).

Semi-continuous Operation The simplest approach to allow some degree of heat recovery in a batch process is to operate part of the plant in a continuous mode. The use of intermediate accumulation tanks can allow sections of the plant to be fed continuously or to accumulate product for batching into other operations. Semi-continuous operation is often deployed for feed sterilizers and pasteurizers in food processing and fermentation plants. In a pasteurization operation, the feed must be heated to a target temperature, held at that temperature for long enough to kill unwanted species that may be present in the feed, and then cooled to the process temperature. The high temperature residence time is usually obtained by passing the process fluid through a steam-traced or well-insulated pipe coil. The initial heating of the feed can be accomplished by heat exchange with the hot fluid leaving the coil, allowing the use of a smaller steam heater to reach the target temperature, as shown in Figure 3.30. This design is common in food-processing plants, but care must be taken to ensure that there is no leakage across the heat exchanger, which could potentially lead to contamination of the “sterile” feed with components from the raw feed. Another situation where semi-continuous operation is often adopted is in the separation section of a batch plant. Some energy-intensive separations such as distillation and crystallization are easier to control to high recovery and tight product specifications when operated in continuous mode. In these cases a surge tank can feed the continuous section of the plant and typical heat recovery schemes such as feed-bottoms heat exchange can be considered. If a batch plant is designed so that batches are transferred from one vessel to another (as opposed to undergoing successive steps in the same vessel), then heat can be transferred between streams as they are pumped from one vessel to the next. During the pumping operation the flow is at a pseudo-steady state, and a heat exchanger between two streams behaves the same as a heat exchanger in a continuous plant. Figure 3.31 shows such an arrangement in which a hot stream flows from vessel R1 to vessel R2, while a cold stream flows from vessel R3 to vessel R4. The flowing streams exchange heat in a heat exchanger that is shown as being countercurrent, but could equally well be cross-flow or cocurrent if the temperatures were suitable. This arrangement is sometimes referred to as a “countercurrent” heat integration, although it should be stressed that the exchanger can be cocurrent or cross-flow. Steam heater Coil Raw feed Sterilized feed

FIGURE 3.30 Heat integration of feed sterilization system.

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FIGURE 3.31 Stream-to-stream (“countercurrent”) heat integration of batch vessels.

When stream-to-stream heat transfer is used, a high degree of heat recovery can be obtained. The exchanger will perform well and maintain roughly constant stream outlet temperatures during the period when the vessels are being pumped out. When the liquid level in the vessels becomes too low for pump operation, the flow rates in the exchanger become too low for the exchanger to function effectively. If batch-to-batch contamination is not important and there are no safety hazards, product quality issues, or fouling concerns, then the exchanger can be isolated (“blocked in”) while the remaining tank contents are drained through bypass lines, and the exchanger is then ready to be reused when tanks R1 and R3 are again ready to be drained. In the case where batchto-batch mixing is not desired, or where there are other reasons why the exchanger cannot be left full of process fluid, provision must be made to flush, drain, and clean the exchanger once the upstream tanks are empty.

Sequencing Multiple Batches If a plant contains several batches that are undergoing different steps of a process at the same time, or if several different batch plants are grouped close to each other, then the batches can sometimes be sequenced so that heat can be transferred from one batch to another. Suppose a batch process contains the steps of heating reagents, reacting them at a desired temperature and then cooling the products before sending them for further processing. If two reactors are used, a heat exchanger can be employed to exchange heat from the reactor that is being cooled to the reactor that is being heated. For example, in Figure 3.32, hot fluid from vessel R5 is pumped through an exchanger where it transfers heat to cold fluid that is pumped from vessel R6. The fluid from each vessel is returned to the vessel that it came from. The heat exchanger in Figure 3.31 is shown as being countercurrent, but cocurrent or cross-flow heat exchange could be used if the temperatures were appropriate. The graph on the right of Figure 3.32 is a schematic of the temperature-time profile for both vessels. As time progresses, they become closer in temperature, and would eventually reach thermal equilibrium. In practice, it is usually not economical to run the exchanger for very long times, and heat transfer is

3.6 Energy Management in Unsteady Processes

153

T TR5 ΔTmin TR6

FIGURE 3.32 Tank-to-tank (“cocurrent”) heat integration of batch vessels.

TA TR9 TR8

R9 ΔTmin t

FIGURE 3.33 Stream-to-tank (“cocurrent/countercurrent”) heat integration of batch vessels.

stopped when an acceptable minimum temperature difference between the vessels is reached, shown as ΔTmin in the figure. Tank-to-tank heat transfer does not allow as efficient heat recovery as stream-tostream, as the hottest temperatures in the hot tank are matched with the coldest temperatures in the cold tank, as they would be in a cocurrent heat exchanger, hence Vaselenak, et al. (1986) named this type of batch heat integration “cocurrent” heat integration. It should again be stressed that the heat exchanger is usually designed to be countercurrent or cross-flow. An improvement on this scheme is to use stream-to-tank heat transfer, shown in Figure 3.33, in which a stream that is transferred from one vessel to another exchanges heat with a stream that is returned to the tank from which it originated. In Figure 3.33, hot fluid flows from R7 to R8 and transfers heat to a cold stream that is pumped from R9 and returned to R9. The graph on the right of Figure 3.33 is a schematic of the temperature behavior of R9, R8, and the location marked as A on the line entering R8. The temperature of the cold fluid in R9 increases over time as heat is transferred to it. The temperature at A is the temperature of the hot fluid at the exit of the heat exchanger. The heat exchanger will usually be designed to pinch at the cold end, since the recirculating flow from R9 can be much greater than the pump-out flow from R7. Consequently, the temperature at A will be equal to the temperature in R9 plus the temperature

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approach of the heat exchanger, and so the temperature at A has a profile offset above the R9 temperature profile. The temperature in R8 is the time-averaged integral of the temperature of the feed to the vessel, i.e., the time-averaged integral of the temperature at A. Although the fluid entering R8 becomes hotter with time, it is mixed with an accumulating volume of colder fluid, so the temperature in R8 does not increase so rapidly as the temperature in R9, and R8 can even be colder than R9 when the heat transfer is complete. This process is therefore intermediate in thermal efficiency between tank-to-tank heat transfer and stream-to-stream heat transfer. It is sometimes known as “cocurrent/countercurrent” heat integration. The derivation of the equations needed to accurately describe the temperature profiles for this arrangement is given by Vaselenak, et al. (1986). When tank-to-tank or tank-to-stream heat transfer is selected, care must be taken to ensure that the heat exchanger doesn’t cause problems when not in use. If the designer anticipates that there could be problems with fouling, corrosion, batch-to-batch contamination, product degradation, safety issues, or any other issue with leaving the exchanger filled, then the design must include means to drain, flush, and clean the exchanger between batches. When considering the use of stream-to-stream, stream-to-tank, or tank-to-tank heat transfer in a batch process, the designer must ensure that the batch schedules allow both streams to be available at the same time and for a sufficient time to accomplish the desired heat recovery. When draining, flushing, and cleaning of the heat exchanger are necessary, these steps must also be taken into account. For a process that handles multiple batches simultaneously or a site with multiple batch plants, the resulting scheduling problem becomes too large to optimize by hand and numerical methods must be used. See Vaselenak, et al. (1986), Kemp and Deakin (1989), and Lee and Reklaitis (1995) for approaches to solving such problems.

Indirect Heat Recovery An alternative method of heat recovery that can be used in batch processing is to recover heat indirectly through the utility system or using a heat storage system. Although less thermally efficient than process-to-process heat recovery, this method eliminates problems from sequencing of operations. In indirect heat recovery, heat from a hot process stream is transferred to a utility stream, such as a reservoir of heat-transfer fluid. The heat-transfer fluid can then be used for heating elsewhere in the process. Indirect heat recovery can be used in any of the flow schemes described above, but in all cases the use of an intermediate stream will reduce the thermal efficiency and the amount of heat that can be recovered. Heat storage systems can only be used when there is a large enough temperature difference between the process heat source and process heat sink to allow for the thermal inefficiency of transfer of heat to the storage medium, cooling losses during storage, and transfer of heat to the process heat sink.

Example 3.7: Differential Energy Balance In the batch preparation of an aqueous solution, the water is first heated to 80 °C in a jacketed, agitated vessel; 1000 Imp. gal. (4545 kg) is heated from 15 °C. If the jacket area is 300 ft2 (27.9 m2) and the overall heattransfer coefficient can be taken as 50 Btu ft−2 h−1 °F−1 (285 W m−2 K−1), estimate the heating time. Steam is supplied at 25 psig (2.7 bar).

References

155

Solution

The rate of heat transfer from the jacket to the water will be given by Equation 3.10: MCp dT = UAΔTm dt

(3.10)

Since steam is used as the heating medium, the hot side is isothermal and we can write ΔTm = Ts − T where Ts = the steam saturation temperature. Integrating: tðB

MCp dt = UA

Tð2

dT ðTs − TÞ

Batch heating time, tB: tB = −

MCp Ts − T2 ln UA Ts − T1

For this example, MCp = 4:18 × 4545 × 103 JK−1 UA = 285 × 27 WK−1 T1 = 15 °C, T2 = 80 °C, Ts = 130 °C tB = −

4:18 × 4545 × 103 130 − 80 ln 285 × 27:9 130 − 15

= 1990 s = 33:2 min In this example the heat capacity of the vessel and the heat losses have been neglected for simplicity. They would increase the heating time by 10 to 20 percent.

References Balmer, R. (2010). Thermodynamic tables to accompany modern engineering thermodynamics. Academic Press. Barnwell, J., & Morris, C. P. (1982). Heat pump cuts energy use. Hyd. Proc., 61(July), 117. Bloch, H. P., Cameron, J. A., Danowsky, F. M., James, R., Swearingen, J. S., & Weightman, M. E. (1982). Compressors and expanders: Selection and applications for the process industries. Dekker.

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Buse, F. (1981). Using centrifugal pumps as hydraulic turbines. Chem. Eng., NY, 88(Jan 26th), 113. Chada, N. (1984). Use of hydraulic turbines to recover energy. Chem. Eng., NY, 91(July 23rd), 57. Dincer, I. (2003). Refrigeration systems and applications. Wiley. Douglas, J. M. (1988). Conceptual design of chemical processes. McGraw-Hill. Dryden, I. (Ed.). (1975). The efficient use of energy. IPC Science and Technology Press. Dunn, R. F., & El-Halwagi, M. M. (2003). Process integration technology review: background and applications in the chemical process industry. J. Chem. Technol. Biot., 78, 1011. Dunn, K. S., & Tomkins, A. G. (1975). Waste heat recovery from the incineration of process wastes. Inst. Mech. Eng. Conference on Energy Recovery in the Process Industries, London. El-Halwagi, M. M. (1997). Pollution prevention through process integration: Systematic design tools. Academic Press. El-Halwagi, M. M. (2006). Process integration. Academic Press. Green, D. W., & Perry, R. H. (Eds.). (2007). Perry’s chemical engineers’ handbook (8th ed.). McGraw-Hill. Gundersen, T., & Naess, L. (1988). The synthesis of cost optimal heat-exchanger networks an industrial review of the state of the art. Comp. and Chem. Eng., 12(6), 503. Hinchley, P. (1975). Waste heat boilers in the chemical industry. Inst. Mech. Eng. Conference on Energy Recovery in the Process Industries, London. Holmann, E. C. (1971). PhD Thesis, Optimum networks for heat exchangers. University of South California. Holland, F. A., & Devotta, S. (1986). Prospects for heat pumps in process applications. Chem. Eng., London, 425(May), 61. Jenett, E. (1968). Hydraulic power recovery systems. Chem. Eng., NY, 75(April 8th), 159, (June 17th) 257 (in two parts). Kemp, I. C. (2007). Pinch analysis and process integration (2nd ed.). A user guide on process integration for efficient use of energy. Butterworth-Heinemann. Kemp, I. C., & Deakin, A. W. (1989). The cascade analysis for energy and process integration of batch processes. Chem. Eng. Res. Des., 67, 495. Kenney, W. F. (1984). Energy conversion in the process industries. Academic Press. Lee, B., & Reklaitis, G. V. (1995). Optimal scheduling of cyclic batch processes for heat integration – I. Basic formulation. Comp. and Chem. Eng., 19(8), 883. Linnhoff, B., & Flower, J. R. (1978). Synthesis of heat exchanger networks. AIChE J., 24(633) (in two parts). Linnhoff, B., Mason, D. R., & Wardle, I. (1979). Understanding heat exchanger networks. Comp. and Chem. Eng., 3, 295. Linnhoff, B., Townsend, D. W., Boland, D., Hewitt, G. F., Thomas, B. E. A., Guy, A. R., & Marsland, R. H. (1982). User guide on process integration for the efficient use of energy (1st ed.). London: Institution of Chemical Engineers. Luckenbach, E. C. (1978). U.S. 4,081,508, to Exxon Research and Engineering Co. Process for reducing flue gas contaminants from fluid catalytic cracking regenerator. Majozi, T. (2010). Batch chemical process integration: Analysis, synthesis and optimization. Springer. Meili, A. (1990). Heat pumps for distillation columns. Chem. Eng. Prog., 86(6), 60. Miles, F. D. (1961). Nitric Acid Manufacture and Uses. Oxford U.P. Miller, R. (1968). Process energy systems. Chem. Eng., NY, 75(May 20th), 130. Moser, F., & Schnitzer, H. (1985). Heat pumps in industry. Elsevier. Perry, R. H., & Chilton, C. H. (Eds.). (1973). Chemical engineers handbook (5th ed.). McGraw-Hill. Reay, D. A., & Macmichael, D. B. A. (1988). Heat pumps: Design and application (2nd ed.). Pergamon Press. Santoleri, J. J. (1973). Chlorinated hydrocarbon waste disposal and recovery systems. Chem. Eng. Prog., 69(Jan.), 69.

Nomenclature

157

Silverman, D. (1964). Electrical design. Chem. Eng., NY, 71(May 25th), 131, (June 22nd) 133, (July 6th) 121, (July 20th), 161 (in four parts). Singh, J. (1985). Heat transfer fluids and systems for process and energy applications. Marcel Dekker. Smith, R. (2005). Chemical process design and integration. Wiley. Stoecker, W. F. (1998). Industrial refrigeration handbook. McGraw-Hill. Trott, A. R., & Welch, T. C. (1999). Refrigeration and air conditioning. Butterworth-Heinemann. Vaselenak, J. A., Grossman, I. E., & Westerberg, A. W. (1986). Heat integration in batch processing. Ind. Eng. Chem. Proc. Des. Dev., 25, 357.

American and International Standards NFPA 70. (2006). National electrical code. National Fire Protection Association.

NOMENCLATURE Dimensions in $MLTθ A CP CPc CPh Cp ΣCPc ΣCPh COP COPh dHb H ΔH ΔHcold ΔHex ΔHhot ΔHn ΔHxp −ΔH°c ΔH°f hg L′ M m N N′ PBFW

Area Stream heat capacity flow rate Stream heat capacity flow rate, cold stream Stream heat capacity flow rate, hot stream Specific heat at constant pressure Sum of heat capacity flow rates of cold streams Sum of heat capacity flow rates of hot streams Coefficient of performance for a refrigeration cycle Coefficient of performance for a heat pump Boiler heating rate Enthalpy Change in enthalpy Heat transfer from cold utility Heat transfer in exchanger Heat transfer from hot utility Net heat required in nth interval Cross-pinch heat transfer Standard heat of combustion Standard enthalpy of formation Specific enthalpy of steam Number of internal loops in network Mass Mass flow-rate Number of cold streams, heat-exchanger networks Number of streams Price of boiler feed water

L2 ML2T−2θ−1 ML2T−2θ−1 ML2T−2θ−1 L2T−2θ−1 ML2T−2θ−1 ML2T−2θ−1 — — L−2T2 ML2T−2 ML2T−2 ML2T−3 ML2T−3 ML2T−3 ML2T−3 ML2T−3 L2T−2 L2T−2 L2T−2 — M MT−1 — — $M−1

(Continued )

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CHAPTER 3 Utilities and Energy Efficient Design

Dimensions in $MLTθ PF PHPS S sg T T1 T2 Tact Tc Te Tint Tn Tpinch Treturn Ts Tsupply Ts Tt ΔTm ΔTmin ΔTn t tB U Zmin ηB

Price of fuel Price of high pressure steam Number of independent branches Specific entropy Temperature, absolute Initial temperature Final temperature Actual stream temperature Condenser temperature Evaporator temperature Interval temperature Temperature in nth interval Pinch temperature Return temperature for utility Source temperature Supply temperature for utility Steam saturation temperature Target temperature Mean temperature difference Minimum temperature difference (minimum approach) in heat exchanger Interval temperature difference Time Batch heating time Overall heat transfer coefficient Minimum number of heat exchangers in network Boiler efficiency

$M−1L−2T2 $M−1 — L2T−2θ−1 θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ T T MT−3θ−1 — —

PROBLEMS 3.1. A process heater uses Dowtherm A heat transfer fluid to provide 850 kW of heat. Estimate the annual operating cost of the heater if the Dowtherm evaporator is 80% efficient and the price of natural gas is $4.60/MMBtu. Assume 8000 operating hours per year. 3.2. A site steam system consists of HP steam at 40 bar, MP steam at 18 bar, and LP steam at 3 bar. If natural gas costs $3.50/MMBtu and electricity is worth $0.07/ kWh, estimate the cost of steam at each level in $/metric ton. 3.3. Make a rough estimate of the cost of steam per ton, produced from a packaged boiler. 10,000 kg per hour of steam are required at 15 bar. Natural gas will be used as the fuel, calorific value 39 MJ/m3 (roughly 1 MMBtu/1000 scf). Take the boiler efficiency as 80%. No condensate will be returned to the boiler.

Problems

159

3.4. A crystallization process requires operation at −5º C. The refrigeration system can reject heat to cooling water that is available at 35º C. If a single refrigeration cycle has an efficiency of 60% of Carnot cycle performance then estimate the cost of providing 1 kW of cooling to this process using a single-stage cycle and using a cascaded-two stage cycle (in which the colder cycle rejects heat to the warmer cycle). Electricity costs $0.07/kWh and the cost of cooling water can be neglected. 3.5. A gas produced as a by-product from the carbonization of coal has the following composition, mole %: carbon dioxide 4, carbon monoxide 15, hydrogen 50, methane 12, ethane 2, ethylene 4, benzene 2, balance nitrogen. Using the data given in Appendix C (available online at booksite .Elsevier.com/Towler), calculate the gross and net calorific values of the gas. Give your answer in MJ/m3, at standard temperature and pressure. 3.6. Determine the pinch temperature and the minimum utility requirements for the process set out below. Take the minimum approach temperature as 15 °C. Devise a heat-exchanger network to achieve maximum energy recovery.

Stream Number

Type

1 2 3 4

hot hot cold cold

Heat Capacity kW/°C 13.5 27.0 53.5 23.5

Source Temp. °C

Target Temp. °C

180 135 60 35

80 45 100 120

3.7. Determine the pinch temperature and the minimum utility requirements for the process set out below. Take the minimum approach temperature as 15 °C. Devise a heat-exchanger network to achieve maximum energy recovery.

Stream Number

Type

1 2 3 4 5

hot hot hot cold cold

Heat Capacity kW/°C 10.0 20.0 40.0 30.0 8.0

Source Temp. °C 200 155 90 60 35

Target Temp. °C 80 50 35 100 90

3.8. To produce a high purity product two distillation columns are operated in series. The overhead stream from the first column is the feed to the second column. The overhead from the second column is the purified product. Both columns are conventional distillation columns fitted with reboilers and total condensers. The bottom products are passed to other processing units, which do not form part of this problem. The feed to the first column passes through a

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preheater. The condensate from the second column is passed through a product cooler. The duty for each stream is summarized below: No.

Stream

Type

Source Temp. °C.

1 2 3 4 5 6

Feed preheater First condenser Second condenser First reboiler Second reboiler Product cooler

cold hot hot cold cold Hot

20 70 65 85 75 55

Target Temp. °C 50 60 55 87 77 25

Duty, kW 900 1350 1100 1400 900 30

Find the minimum utility requirements for this process, for a minimum approach temperature of 10 °C. Note: the stream heat capacity is given by dividing the exchanger duty by the temperature change. 3.9. At what value of the minimum approach temperature does the problem in Example 3.5 become a threshold problem? Design a heat-exchanger network for the resulting threshold problem. What insights does this give into the design proposed in Example 3.5?

CHAPTER

Process Simulation

KEY LEARNING OBJECTIVES • How to use commercial process simulation software to build a process heat and material balance model • How to select thermodynamic models for prediction of phase equilibrium and stream properties • How to use user-specified models and components when the simulator does not have what you need • How to converge flowsheets that include recycles and overcome convergence problems • How to optimize converged flowsheets

4.1 INTRODUCTION This chapter addresses the use of process simulation tools in developing an overall process mass and energy balance. A process flow diagram or flowsheet typically includes material balances made over the complete process and each individual unit. Energy balances are also made to determine the energy flows and the utility requirements. Most flowsheet calculations are carried out using commercial process simulation programs. The process simulation programs contain models for most unit operations as well as thermodynamic and physical property models. All the commercial programs feature some level of custom modeling capability that allows the designer to add models for nonstandard operations. Many companies developed proprietary flowsheeting programs between 1960 and 1980. The cost of maintaining and updating proprietary software is high; consequently, very few of the proprietary flowsheeting programs are still in use, and most companies now rely entirely on commercially-available software. Each of the commercial process simulation programs has its own unique idiosyncrasies, but they share many common features. The discussion in this chapter addresses general problems of process simulation and flowsheeting rather than software-specific issues. The latter are usually thoroughly documented in the user manuals and online help that come with the software. Examples have been provided in this chapter using both Aspen Plus ® (Aspen Technology Inc.) and UniSim™ Design Suite (Honeywell International Inc.). UniSim Design is

161

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CHAPTER 4 Process Simulation

based on the Hysys™ software that was originally developed by Hyprotech Ltd. and is now owned and licensed by Honeywell. Cyclic and batch process operations that do not run at steady state require dynamic simulation models. Several of the steady state process simulation programs can be modified to run as dynamic simulators. Specialized programs have also been developed for batch processing, such as SuperPro Batch Designer™, which has many features tailored to the simulation of biological processes. Simulation of batch processes is discussed in Section 4.9. Because flowsheeting is usually carried out using computer programs, it is necessary for the design engineer to have a good understanding of how to set up and solve computer models. The flowsheet model that is solved on the computer to generate a mass and energy balance is often not an exact representation of the process flow diagram. The designer may need to use combinations of simulation library models and user models to capture the performance of process equipment. Spreadsheet or hand calculations are also often helpful in setting up process simulation models and providing good initial estimates, so as to accelerate convergence.

4.2 PROCESS SIMULATION PROGRAMS The most commonly-used commercial process simulation programs are listed in Table 4.1. Most of these programs can be licensed by universities for educational purposes at nominal cost. Detailed discussion of the features of each of these programs is beyond the scope of this book. For a general review of the requirements, methodology, and application of process simulation programs the reader is referred to the books by Husain (1986), Wells and Rose (1986), Leesley (1982), Benedek (1980), and Westerberg, Hutchinson, Motard, and Winter (1979). The features of the individual programs are described in their user manuals and online help. Two of these simulators have been used to generate the examples in this chapter: Aspen Plus® (v.11.1) and UniSim Design (R360.1). More recent versions of these programs are now available with additional features, but the screen appearance has not changed significantly since the examples were developed. Process simulation programs can be divided into two basic types: Sequential-modular programs: in which the equations describing each process unit (module) are solved module-by-module in a stepwise manner. Iterative techniques are then used to solve the problems arising from the recycle of information. Simultaneous (also known as equation-oriented) programs: in which the entire process is described by a set of equations, and the equations are solved simultaneously, not stepwise as in the sequential approach. Simultaneous programs can simulate the unsteady-state operation of processes and equipment, and can give faster convergence when multiple recycles are present. In the past, most simulation programs available to designers were of the sequential-modular type. They were simpler to develop than the equation-oriented programs, and required only moderate computing power. The modules are processed sequentially, so essentially only the equations for a particular unit are in the computer memory at one time. Also, the process conditions, temperature, pressure,

4.2 Process Simulation Programs

163

Table 4.1 Simulation Packages Name

Type

Source

Aspen Plus

steady-state

CHEMCAD

steady-state

DESIGN II

steady-state

HYSYS

steady-state and dynamic

PRO/II and DYNSIM

steady-state and dynamic

UniSim Design

steady-state and dynamic

Aspen Technology Inc. Ten Canal Park Cambridge, MA 02141-2201, USA Chemstations Inc. 2901 Wilcrest, Suite 305 Houston, TX 77042 USA WinSim Inc. P.O. Box 1885 Houston, TX 77251-1885, USA Aspen Technology Inc. Ten Canal Park Cambridge, MA 02141-2201, USA SimSci-Esscor 5760 Fleet Street Suite 100, Carlsbad, CA 92009, USA Honeywell 300-250 York Street London, Ontario N6A 6K2, Canada

Internet Address http// www.— Aspentech.com

Chemstations.net

Winsim.com

Aspentech.com

Simsci.com

Honeywell.com

Note: Contact the web site to check the full features of the most recent versions of the programs.

flow rate, etc., are fixed in time. With the sequential modular approach, computational difficulties can arise due to the iterative methods used to solve recycle problems and obtain convergence. A major limitation of sequential-modular simulators is the inability to simulate the dynamic, time dependent, behavior of a process. Simultaneous, dynamic simulators require appreciably more computing power than steady-state simulators to solve the thousands of differential equations needed to describe a process, or even a single item of equipment. With the development of fast, powerful computers, this is no longer a restriction. By their nature, simultaneous programs do not experience the problems of recycle convergence inherent in sequential simulators; however, as temperature, pressure, and flow rate are not fixed and the input of one unit is not determined by the calculated output from the previous unit in the sequence, simultaneous programs demand more computer time. This has led to the development

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CHAPTER 4 Process Simulation

Data input

Thermodynamic subroutines Convergence promotion sub-routines Physical property data files Cost data files

Executive program (organization of the problem)

Equipment sub-routines library and specials

Data output

FIGURE 4.1 A typical simulation program.

of hybrid programs in which the steady-state simulator is used to generate the initial conditions for the equation-oriented or dynamic simulation. The principal advantage of simultaneous, dynamic simulators is their ability to model the unsteady-state conditions that occur at start-up and during fault conditions. Dynamic simulators are being increasingly used for safety studies and in the design of control systems, as discussed in Section 4.9. The structure of a typical simulation program is shown in Figure 4.1. The program consists of: 1. A main executive program that controls and keeps track of the flowsheet calculations and the flow of information to and from the subroutines. 2. A library of equipment performance subroutines (modules) that simulate the equipment and enable the output streams to be calculated from information on the inlet streams. 3. A data bank of physical properties. To a large extent, the utility of a sophisticated flowsheeting program depends on the comprehensiveness of the physical property data bank. The collection of the physical property data required for the design of a particular process and its transformation into a form suitable for a particular flowsheeting program can be very timeconsuming. 4. Subroutines for thermodynamics, such as the calculation of vapor-liquid equilibrium and stream enthalpies. 5. Subprograms and data banks for equipment sizing and costing. Process simulation programs enable the designer to consider alternative processing schemes, and the cost routines allow quick economic comparisons to be made. Some programs include optimization routines. To make use of a costing routine, the program must be capable of producing at least approximate equipment designs.

4.3 Specification of Components

165

In a sequential-modular program, the executive program sets up the flowsheet sequence, identifies the recycle loops, and controls the unit operation calculations, while interacting with the unit operations library, physical property data bank, and the other subroutines. The executive program also contains procedures for the optimum ordering of the calculations and routines to promote convergence. In an equation-oriented simulator, the executive program sets up the flowsheet and the set of equations that describe the unit operations, and then solves the equations using data from the unit operations library and the physical property data bank and calling on the file of thermodynamics subroutines. All process simulators use graphical user interfaces to display the flowsheet and facilitate the input of information to the package. The entry of data is usually intuitive to anyone familiar with the MS Windows™ operating systems.

4.3 SPECIFICATION OF COMPONENTS The first step in building a process simulation is usually establishing the chemical basis for the model. This consists of choosing the components that will be included in the mass balance and deciding which models to use for the prediction of physical properties and phase equilibrium. This section focuses on the selection of suitable components, and the selection of physical property models is discussed in Section 4.4.

4.3.1 Pure Components Each of the commercial process simulation programs contains a large data bank of pure component compounds. Most of the pure components are organic compounds, but inorganic compounds and electrolytes are also included. The fact that a pure component is listed in a simulator data bank does not guarantee that any of the properties given for that component are based on measured data. If the properties of a compound are critical to process performance, then the scientific literature should be consulted to confirm that the values used in the simulation are realistic. The most important decision when building a pure component model is choosing the right number of components. The design engineer needs to consider carefully which components will have a significant impact on process design, operation, and economics. If too few components are used, the model will be inadequate for process design, as it will not correctly predict the performance of reactors and separation equipment. Conversely, if too many components are used, the model can become difficult to converge, particularly if there are multiple recycles in the design. Some guidelines to keep in mind when building a component list include: 1. Always include any component that has a specified limit in any of the products if that component is present in any of the feeds or could be formed in the process. This is critical to determining whether the separations are meeting product specifications.

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CHAPTER 4 Process Simulation

2. Always include any component that has a specified limit in any of the feeds. These components can be a source of by-products or can act as catalyst or enzyme inhibitors. They must be tracked to ensure that they do not accumulate in the process or make it difficult to meet product specifications. In some cases, an additional separation may be needed to remove a feed contaminant. 3. Always include components that are expected to be formed in side reactions or consecutive reactions. It is important to understand where these components will accumulate or leave the process, even if their yield is not yet known. 4. Always include any compounds that are expected to be present and are known to have significant health, safety, or environmental concerns, such as compounds with high toxicity or explosivity, known carcinogens, or listed hazardous air pollutants (see Chapter 10). These compounds must be tracked to make sure that they do not reach unsafe levels in any stream and to understand where they might be released to the environment. 5. Usually include any compound that might be present at a mass or mole fraction greater than 2% in any stream in the process. 6. Do not include isomers unless the process specifically requires distinction between isomers (for example, if the process is selective for one isomer, gives different products for different isomers, or is designed to separate isomers). Considering all of the possible isomers of organic compounds becomes combinatorially explosive at high carbon numbers. For fuels and bulk petrochemical processes that are carried out at relatively high temperatures it is often reasonable to assume an equilibrium distribution of isomers. For fine chemical and pharmaceutical processes it is usually important to track isomers separately, particularly enantiomers, as the desired product is often only one of the isomers. In general, pure component models solve more efficiently with less than about 40 components. If the number of components becomes too large and there are many recycles, then it may be necessary to build two models. The first is a high-level model that contains only the main bulk components. This model is then used to initialize a second, more detailed model that has the full component list.

4.3.2 Pseudocomponents Pseudocomponents (hypocomponents) are components created by the simulator to match the boiling curves of petroleum mixtures. Crude oil, fuels such as gasoline, kerosene, and diesel, and most intermediate streams in an oil refinery consist of many different hydrocarbon compounds. The number of possible hydrocarbon isomers present depends on the carbon number, and both increase with boiling range. For diesel, crude oil and heavy fuel oils, the number of possible compounds can be from 104 to >106. At the time of writing, there is no analytical method that can uniquely identify all of these compounds, so it would be impossible to include them all in a model even if the resulting model could be solved. Instead, a large number of possible compounds with boiling points in a given range are “lumped” together and represented by a single pseudocomponent with a boiling point in the middle of that range. A set of 10 to 30 pseudocomponents can then be fitted to any petroleum assay and used to model that oil.

4.3 Specification of Components

167

Pseudocomponent models are very useful for oil fractionation and blending problems. They can also be used to characterize heavy products in some chemical processes such as ethane cracking. Pseudocomponents are treated as inert in most of the reactor models, but they can be converted or produced in yield shift reactors (see Section 4.5.1). Some of the commercial simulation programs use a standard default set of pseudocomponents and fit the composition of each to match a boiling curve of the oil that is entered by the user. This can sometimes lead to errors when predicting ASTM D86 or D2887 curves for products from a feed that has been defined based on a true boiling point (TBP) curve, or when making many sub-cuts or cuts with tight distillation specifications. It is often better to work back from the product distillation curves and add extra pseudocomponents around the cut points to make sure that the recoveries and 5% and 95% points on the product distillation curves are predicted properly. All of the simulators have the option to add pseudocomponents to the default set or use a user-generated curve.

4.3.3 Solids and Salts Most chemical and pharmaceutical processes involve some degree of solids handling. Examples of solids that must be modeled include: • • • • • • • • • • •

Components that are crystallized for separation, recovery, or purification Pharmaceutical products that are manufactured as powders or tablets Insoluble salts formed by the reaction of acids and bases or other electrolytes Hydrates, ice, and solid carbon dioxide that can form in cryogenic processes Cells, bacteria, and immobilized enzymes in biological processes Pellets or crystals of polymer formed in polymerization processes Coal and ash particles in power generation Catalyst pellets in processes in which the catalyst is fluidized or transported as a slurry Mineral salts and ores that are used as process feeds Fertilizer products Fibers in paper processing

Some solid phase components can be characterized as pure components and can interact with other components in the model through phase and reaction equilibrium. Others, such as cells and catalysts, are unlikely to equilibrate with other components, although they can play a vital role in the process. In Aspen Plus, solid components are identified as different types. Pure materials with measurable properties such as molecular weight, vapor pressure, and critical temperature and pressure are known as conventional solids and are present in the MIXED sub-stream with other pure components. They can participate in any of the phase or reaction equilibria specified in any unit operation. If the solid phase participates only in reaction equilibrium but not in phase equilibrium (for example, when the solubility in the fluid phase is known to be very low), then it is called a conventional inert solid and is listed in a sub-stream CISOLID. If a solid is not involved in either phase or reaction equilibrium, then it is a nonconventional solid and is assigned to sub-stream NC. Nonconventional solids are defined by attributes rather than molecular properties

168

CHAPTER 4 Process Simulation

and can be used for coal, cells, catalysts, bacteria, wood pulp, and other multicomponent solid materials. In UniSim Design, nonconventional solids can be defined as hypothetical components (see Section 4.3.4). The solid phases of pure components are predicted in the phase and reaction equilibrium calculations and do not need to be identified separately. Many solids-handling operations have an effect on the particle size distribution (PSD) of the solid phase. The particle size distribution can also be an important product property. Aspen Plus allows the user to enter a particle size distribution as an attribute of a solid substream. In UniSim Design, the particle size distribution is entered on the “PSD Property” tab, which appears under “worksheet” on the stream editor window for any stream that contains a pure or hypothetical solid component. Unit operations such as yield shift reactor, crusher, screen, cyclone, electrostatic precipitator, and crystallizer can then be set up to modify the particle size distribution; typically by using a conversion function or a particle capture efficiency in each size range. When inorganic solids and water are present, an electrolyte phase-equilibrium model must be selected for the aqueous phase, to properly account for the dissolution of the solid and formation of ions in solution.

4.3.4 User Components The process simulators were originally developed for petrochemical and fuels applications; consequently, many molecules that are made in specialty chemical and pharmaceutical processes are not listed in the component data banks. All of the simulators allow the designer to overcome this drawback by adding new molecules to customize the data bank. In UniSim Design, new molecules are added as hypothetical components. The minimum information needed to create a new hypothetical pure component is the normal boiling point, although the user is encouraged to provide as much information as is available. If the boiling point is unknown, then the molecular weight and density are used instead. The input information is used to tune the UNIFAC correlation to predict the physical and phase equilibrium properties of the molecule, as described in Section 4.4. User-defined components are created in Aspen Plus using a “user-defined component wizard”. The minimum required information is the molecular weight and normal boiling point. The program also allows the designer to enter molecular structure, specific gravity, enthalpy and Gibbs energy of formation, ideal gas heat capacity, and Antoine vapor pressure coefficients, but for complex molecules usually only the molecular structure is known. It is often necessary to add user components to complete a simulation model. The design engineer should always be cautious when interpreting simulation results for models that include user components. Phase equilibrium predictions for flashes, decanters, extraction, distillation, and crystallization operations should be carefully checked against laboratory data to ensure that the model is correctly predicting the component distribution between the phases. If the fit is poor, the binary interaction parameters in the phase-equilibrium model can be tuned to improve the prediction.

4.4 Selection of Physical Property Models

169

4.4 SELECTION OF PHYSICAL PROPERTY MODELS The process simulation programs all contain subroutines for calculating component and stream physical properties and for determining phase equilibrium in process operations. The user must select a thermodynamic model that provides a sufficiently accurate representation of the system for design purposes. When the design is sensitive to the choice of thermodynamic model, the models should be checked against measured data and the most accurate model selected. In some cases, it may be necessary to tune the library models in the simulator by adjusting some of the parameters to provide a better fit to the data.

4.4.1 Sources of Physical Property Data It is always a good practice to benchmark the physical properties predicted using a process simulation program against measured data. There are many good literature sources of data for properties of individual compounds, but much less data is available for mixtures. Caution should be exercised when taking data from the literature, as typographical errors often occur. If a value looks suspicious, it should be cross-checked in an independent reference or by estimation. The values of some properties are dependent on the method of measurement; for example, surface tension and flash point, and the method used should be checked, by reference to the original paper if necessary, if an accurate value is required. International Critical Tables (ICT) (Washburn, 1933) is still probably the most comprehensive compilation of physical properties, and is available in most reference libraries. Though it was first published in 1933, physical properties do not change, except in as much as experimental techniques improve, and ICT is still a useful source of engineering data. ICT is now available as an e-book and can be referenced on the Internet through Knovel (2003). Tables and graphs of physical properties are given in many handbooks and textbooks on chemical engineering and related subjects. Many of the data given are duplicated from book to book, but the various handbooks do provide quick, easy access to data on the more commonly-used substances. An extensive compilation of thermophysical data has been published by Plenum Press, Touloukian (1970–77). This multiple-volume work covers conductivity, specific heat, thermal expansion, viscosity, and radiative properties (emittance, reflectance, absorptance, and transmittance). The Engineering Sciences Data Unit (ESDU, www.ihsesdu.com) was set up to provide validated data for engineering design, developed under the guidance and approval of engineers from industry, the universities, and research laboratories. ESDU data include equipment design data and extensive highquality physical property data—mostly for pure fluids that are in use in the oil and process industries. The results of research work on physical properties are reported in the general engineering and scientific literature. The Journal of Chemical Engineering Data specializes in publishing physical property data for use in chemical engineering design. A quick search of the literature for data can be made by using the abstracting journals, such as Chemical Abstracts (American Chemical Society) and Engineering Index (Engineering Index Inc., New York). Engineering Index is now called Engineering Information (Ei) and is a web-based reference source owned by Elsevier (www .ei.org). Chemical Abstracts can be searched using the ACS SciFinder® service.

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CHAPTER 4 Process Simulation

Experimental phase-equilibrium data have been published for several thousand binary and many multicomponent systems. Virtually all the published experimental data has been collected together in the volumes comprising the DECHEMA vapor-liquid and liquid-liquid data collection, DECHEMA (1977). The books by Chu, Wang, Levy, and Paul (1956), Hala, Wichterle, and Linek (1973), Hala, Wichterle, Polak, and Boublik (1968), Hirata, Ohe, and Nagahama (1975), and Ohe (1989, 1990) are also useful sources. Computerized physical property data banks have been set up by various organizations to provide a service to the design engineer. They can be incorporated into computer-aided design programs and are increasingly being used to provide reliable, authenticated, design data. Examples of such programs are the PPDS and the DIPPR™ databases. PPDS (Physical Property Data Service) was originally developed in the United Kingdom by the Institution of Chemical Engineers and the National Physical Laboratory. It is now available as a Microsoft™ Windows version from NEL, a division of the TUV Suddeutschland Group (www.tuvnel.com). PPDS is made available to universities at a discount. The DIPPR™ databases were developed by the Design Institute for Physical Properties of the AIChE. The DIPPR™ projects are aimed at providing evaluated process design data for the design of chemical processes and equipment (www.aiche.org/TechnicalSocieties/DIPPR/index. aspx). The DIPPR Project 801 has been made available to university departments; see Rowley, Wilding, Oscarson, Yang, and Zundel (2004). Many of the important sources of engineering information are subscription services. The American Chemical Society’s Chemical Abstracts Service is the best source for chemical properties and reaction kinetics data. Chemical abstracts can be searched online through the SciFinder subscription service (www.cas.org). This is available in most university libraries. Another important source of information is Knovel. Knovel provides online access to most standard reference books. It is a subscription service but can be accessed through many libraries, including those of professional engineering institutions and most universities. At the time of writing, Knovel is available for free to members of the AIChE. In addition to having many reference books in .pdf format, Knovel has interactive graphs and look-up tables for books such as Perry’s Chemical Engineers Handbook and the International Critical Tables.

4.4.2 Prediction of Physical Properties The process simulation programs contain subroutines that predict the physical properties of pure compounds and mixtures as functions of temperature, pressure, and composition. The algorithms used have been developed based on decades of research in thermodynamics and property estimation. Techniques are available for the prediction of most physical properties with sufficient accuracy for use in process and equipment design; however, the accuracy of the predictions should always be assessed by comparing the model output with data from experiments, pilot plants, or operating units. A detailed review of all the different methods available is beyond the scope of this book. If accurate values are required, then specialized texts on physical property estimation should be consulted, such as those by Reid, Prausnitz, and Poling (1987), Poling Prausnitz, and O’Connell (2000), Bretsznajder (1971), Sterbacek, Biskup, and Tausk (1979), and AIChE (1983, 1985), and the data should be confirmed experimentally. The techniques used for prediction are also useful for the correlation, and extrapolation and interpolation, of experimental values.

4.4 Selection of Physical Property Models

171

The two most common approaches used in predicting properties are group contribution methods and the use of reduced properties.

Group Contribution Methods Group contribution techniques are based on the concept that a particular physical property of a compound can be considered to be made up of contributions from the constituent atoms, groups, and bonds; the contributions being determined from experimental data. They provide the designer with simple, convenient methods for physical property estimation, requiring only a knowledge of the structural formula of the compound. Group contribution methods are used to predict a wide range of physical properties when no data are available for regression. For example, the group contribution method proposed by Chueh and Swanson (1973a,b) gives reasonably accurate predictions of specific heat capacity for organic liquids. The contributions to be assigned to each molecular group are given in Table 4.2 and the method is illustrated in Example 4.1. The most widely used group contribution model is the UNIFAC method for predicting the parameters for phase-equilibrium models.

Example 4.1 Using Chueh and Swanson’s method, estimate the specific heat capacity of ethyl bromide at 20 °C.

Solution

Ethyl bromide CH3CH2Br

Group

Contribution

—CH3 —CH2— —Br

36.84 30.40 37.68

No. of 1 1 1 Total

= 36.84 = 30.40 = 37.68 104.92 kJ/kmol°C

mol. wt. = 109 Specific heat capacity =

104:92 = 0:96 kJ=kg°C 109

Experimental value 0.90 kJ/kg°C

Reduced Properties Reduced property models (also known as method of corresponding states models) predict properties based on knowledge of the critical conditions of a compound. They are useful if values for the critical properties are available, or can be estimated with sufficient accuracy; see Sterbacek et al. (1979). An example of a reduced property model is the method for estimating latent heat of

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CHAPTER 4 Process Simulation

Table 4.2 Group Contributions for Liquid Heat Capacities at 20 °C, kJ/kmol°C (Chueh and Swanson, 1973a,b) Group

Value

Group

Alkane

––CH3

36.84

––CH2–– CH C

60.71

30.40

––CH2OH

73.27

20.93

CHOH

76.20

COH

111.37

21.77

––OH ––ONO2

44.80 119.32

21.35

15.91

Alkyne ––C≡H ––C≡

7.37 Olefin

CH2

24.70 24.70

Halogen ––Cl (first or second on a carbon) ––Cl (third or fourth on a carbon)

36.01 25.12

––Br ––F ––I

37.68 16.75 36.01

In a ring

Nitrogen

18.42

Value

58.62

N H

12.14

43.96

22.19

31.40

––CH2––

25.96

Oxygen ––O–– C C

––C≡N 35.17

O O

53.00 53.00

58.70 Sulphur

––SH

44.80

––S––

33.49 Hydrogen

O C

18.84

(in a ring)

79.97

H–– (for formic acid, formates, hydrogen cyanide, etc.)

14.65

Add 18.84 for any carbon group that fulfils the following criterion: a carbon group which is joined by a single bond to a carbon group connected by a double or triple bond with a third carbon group. In some cases a carbon group fulfils the above criterion in more ways than one; 18.84 should be added each time the group fulfils the criterion. Exceptions to the above 18.84 rule: 1. No such extra 18.84 additions for ––CH3 groups. 2. For a ––CH2–– group fulfilling the 18.84 addition criterion add 10.47 instead of 18.84. However, when the ––CH2–– group fulfils the addition criterion in more ways than one, the addition should be 10.47 the first time and 18.84 for each subsequent addition. 3. No such extra addition for any carbon group in a ring.

4.4 Selection of Physical Property Models

173

vaporization developed by Haggenmacher (1946), which is derived from the Antoine vapor pressure equation: Lv =

8:32 BT 2 Δz ðT + CÞ2

(4.1)

where Lv = latent heat at the required temperature, kJ/kmol T = temperature, K B, C = coefficients in the Antoine equation (Antoine, 1888): ln P = A − where P A, B, C T Δz

= = = =

B T +C

(4.2)

vapor pressure, mmHg the Antoine coefficients temperature, K and zgas − zliquid (where z is the compressibility constant), calculated from the equation: 0:5 P (4.3) Δz = 1 − 3r Tr

where Pr = reduced pressure = P/Pc Tr = reduced temperature = T/Tc

Example 4.2 Estimate the latent heat of vaporization of acetic anhydride, C4H6O3, at its boiling point, 139.6°C (412.7 K), and at 200°C (473 K).

Solution

For acetic anhydride Tc = 569.1 K, Pc = 46 bar, Antoine constants A = 16:3982 B = 3287:56 C = −75:11 The experimental value at the boiling point is 41,242 kJ/kmol. From Haggenmacher’s equation: at the b:p: Pr = 1 = 0:02124 46 412:7 = 0:7252 Tr = 569:1 0:5 0:02124 = 0:972 Δz = 1 − 0:72523 Lv,b =

8:32 × 3287:6 × ð412:7Þ2 × 0:972 ð412:7 − 75:11Þ2

= 39,733 kJ/mol

174

CHAPTER 4 Process Simulation

At 200°C, the vapor pressure must first be estimated, from the Antoine equation: ln P = A −

B T +C

3287:56 = 8:14 473 − 75:11 P = 3421:35 mmHg = 4:5 bar Pr = 4:5 = 0:098 46 473 = 0:831 Tr = 569:1 0:5 Δz = 1 − 0:0983 = 0:911 0:831

ln P = 16:3982 −

Lv =

8:32 × 3287:6 × ð473Þ2 × 0:911 ð473 − 75:11Þ2

= 35,211 kJ=kmol

If reliable experimental values of the critical constants cannot be found, techniques are available for estimating the critical constants with sufficient accuracy for most design purposes. For organic compounds Lydersen’s method is normally used, Lydersen (1955): Tc =

Tb ½0:567 + ΣΔT − ðΣΔTÞ2

(4.4)

M ð0:34 + ΣΔPÞ2

(4.5)

Pc =

Vc = 0:04 + ΣΔV where Tc Pc Vc Tb M ΔT ΔP ΔV

= = = = = = = =

(4.6)

critical temperature, K critical pressure, atm (1.0133 bar) molar volume at the critical conditions, m3/kmol normal boiling point, K relative molecular mass critical temperature increments, Table 4.3 critical pressure increments, Table 4.3 molar volume increments, Table 4.3

Lydersen’s method illustrates how process simulation programs can predict the properties of userspecified components using just a molecular structure and a boiling point. Application of Lydersen’s method generates critical constants, which can then be used in reduced parameter models to generate other properties. Although the final values that are predicted may still be suitable for preliminary design purposes, inaccuracy is introduced and propagated at each stage of such calculations, and the predictions should be confirmed against experimental values before detailed design.

Table 4.3 Critical Constant increments (Lydersen, 1955) ΔT

ΔP

ΔV

ΔP

ΔV

0.020

0.227

0.055

0.0

0.198

0.036

CH2

0.020

0.227

0.055

0.0

0.198

0.036

0.012

0.210

0.051

0.005

0.153

0.036*

0.00

0.210

0.041

0.005

0.153

0.036*

CH2

0.018

0.198

0.045

0.018

0.198

0.045

0.013

0.184

0.0445

0.011

0.154

0.037

0.012

0.192

0.046

0.011

0.154

0.036

−0.007*

0.154*

0.031*

0.011

0.154

0.036

0.018 0.017

0.224 0.320

0.018 0.049

—Br —I

0.010 0.012

0.50* 0.83*

0.070* 0.095*

Non-ring increments —CH3

Ring increments —CH2— CH

Halogen increments —F —Cl

(Continued )

4.4 Selection of Physical Property Models

ΔT

175

176

Table 4.3 Critical Constant increments (Lydersen, 1955) —Cont’d ΔT

ΔP

ΔV

ΔP

ΔV

0.033*

0.2*

0.050*

0.048

0.33

0.073

Oxygen increments —OH (alcohols)

0.082

0.06

0.018*

—OH (phenols)

0.031

−0.02*

0.030*

—O— (non-ring)

0.021

0.16

0.020

—COOH (acid)

0.085

0.4*

0.080

—O— (ring)

0.014*

0.12*

0.080*

—COO— (ester)

0.047

0.47

0.080

O (non-ring)

0.040

0.29

0.060

==O (except for combinations above)

0.02*

0.12*

0.011*

Nitrogen increments —NH2

0.031

0.095

0.028

0.007*

0.013*

0.032*

NH (non-ring)

0.031

0.135

0.037*

—CN

0.060*

0.36*

0.080*

NH (ring)

0.024*

0.09*

0.027*

—NO2

0.055*

0.42*

0.078*

0.014

0.17

0.042*

0.015 0.015

0.27 0.27

0.055 0.055

—S— (ring) S

0.008* 0.003*

0.24* 0.24*

0.045* 0.047*

(non-ring)

Sulphur increments —SH —S— (non-ring)

CO (ring) O (aldehyde)

(ring)

Miscellaneous Si

0.03

0.54*

Dashes represent bonds with atoms other than hydrogen. Values marked with an asterisk are based on too few experimental points to be reliable.

0.03*

CHAPTER 4 Process Simulation

ΔT

4.4 Selection of Physical Property Models

177

Example 4.3 Estimate the critical constants for diphenylmethane using Lydersen’s method; normal boiling point 537.5 K, molecular mass 168.2, structural formula: H C

H C

C C H

H C

C H

H C

CH C H

C H

Solution Total Contribution Group jj H—C—ðringÞ j ¼ C—ðringÞ —CH2—

No. of

ΔT

ΔP

ΔV

0.11

1.54

0.37

0.022

0.308

0.072

0.02

0.227

0.055

Σ 0.152

2.075

0.497

Tc =

537:5 = 772 k ð0:567 + 0:152 − 0:1522 Þ experimental value 767 K,

Pc =

168:2 = 28:8 atm ð0:34 + 2:075Þ2 experimental value 28:2 atm,

Vc = 0:04 + 0:497 = 0:537 m3 /kmol

4.4.3 Phase-equilibrium Models The choice of the best method for deducing vapor-liquid and liquid-liquid equilibria for a given system will depend on three factors: 1. The composition of the mixture (the system chemistry) 2. The operating pressure (low, medium, or high) 3. The experimental data available

178

CHAPTER 4 Process Simulation

The criterion for thermodynamic equilibrium between two phases of a multicomponent mixture is that for every component, i: fiv = fiL

(4.7)

where fiv is the vapor-phase fugacity and fiL the liquid-phase fugacity of component i: fiv = Pϕi yi

(4.8)

fiL = fiOL γi xi

(4.9)

and where P = total system pressure ϕi = vapor fugacity coefficient yi = concentration of component i in the vapor phase fiOL = standard state fugacity of the pure liquid γi = liquid-phase activity coefficient xi = concentration of component i in the liquid phase Substitution from Equations 4.8 and 4.9 into Equation 4.7, and rearranging gives Ki =

γ f OL yi = i i xi Pϕi

where Ki = is the distribution coefficient (the K value), ϕi = can be calculated from an appropriate equation of state, and fiOL = can be computed from the following expression: ðP − Poi Þ L OL o s vi fi = Pi ϕi exp RT

(4.10)

(4.11)

where Poi = the pure component vapor pressure (which can be calculated from the Antoine equation, Equation 4.2), N/m2 s ϕi = the fugacity coefficient of the pure component i at saturation vLi = the liquid molar volume, m3/mol The exponential term in Equation 4.11 is known as the Poynting correction, and corrects for the effect of pressure on the liquid-phase fugacity. ϕsi is calculated using the same equation of state used to calculate ϕi. For systems in which the vapor phase imperfections are not significant, Equation 4.10 reduces to the familiar Raoult’s law equation: Ki =

γi Poi P

(4.12)

Vapor phase nonideality is usually modeled using an equation of state. An equation of state is a model for the molar volume of a real gas or liquid as a function of temperature and pressure. The features and limitations of the most commonly used equations of state are given in Table 4.4.

4.4 Selection of Physical Property Models

179

Table 4.4 Equations of State Model

Features

References

Redlich-Kwong Equation (R-K)

Extension of Van der Waal’s equation, where constants are calculated from critical pressure and temperature. Not suitable for use near the critical pressure (Pr > 0.8) or for liquids. Modification to the R-K equation to extend its usefulness to the critical region and for use with liquids. An eight-parameter empirical model that gives accurate predictions for vapor and liquid-phase hydrocarbons. It can also be used for mixtures of light hydrocarbons with carbon dioxide and water. Lee and Kesler extended the B-W-R equation to a wider variety of substances using the principle of corresponding states. The method was modified further by Plocker et al. Gives accurate predictions for hydrogen and light hydrocarbons, but limited to temperatures below 530K. Extended the C-S equation for use with hydrogenrich mixtures and for high-pressure and hightemperature systems. It can be used up to 200 bar and 4700K. Extension of the R-K-S equation to overcome instability in the R-K-S equation near the critical point.

Redlich and Kwong (1949)

Redlich-KwongSoave Equation (R-K-S) Benedict-WebbRubin Equation (B-W-R) Lee-Kesler-Plocker Equation (L-K-P) Chao-Seader Equation (C-S) Grayson-Streed Equation (G-S) Peng-Robinson Equation (P-R)

Soave (1972) Benedict, Webb, and Rubin (1951) Lee and Kesler (1975), Plocker Knapp, and Prausnitz (1978) Chao and Seader (1961) Grayson and Streed (1963)

Peng and Robinson (1976)

For low-pressure systems with no known chemical interactions in the vapor phase, it is often acceptable to assume ideal gas behavior. For details of the equations the reader should consult the reference cited, or the books by Reid et al. (1987), Prausnitz, Lichtenthaler, and Azevedo (1998), and Walas (1985). To select the best equation to use for a particular process design refer to Figure 4.2. Liquid phase nonideality is encountered much more often than vapor phase nonideality, and is modeled using activity coefficient models. The most frequently-used activity coefficient models are the Wilson, NRTL, and UNIQUAC models summarized in Table 4.5. The simpler models that are taught in undergraduate thermodynamics classes are rarely adequate for design purposes. Activity coefficient models generally give good prediction of liquid phase fugacity for binary mixtures and can be extended to multicomponent mixtures if all the binary interaction parameters are known. The models become less reliable as the number of components increases, and the accuracy can be improved by fitting some data from ternary or higher-order mixtures. The selection of the most appropriate liquid-phase activity coefficient model for a given design is discussed in Section 4.4.5 and illustrated in Figure 4.2. The liquid-phase activity coefficient, γi, is a function of pressure, temperature, and liquid composition. At conditions remote from the critical conditions it is virtually independent of pressure and, in the

180

CHAPTER 4 Process Simulation

Table 4.5 Activity Coefficient Models Model

Features

References

Wilson Equation

Uses 2 adjustable parameters to model binary interactions between molecules. Can be extended to multicomponent systems using only binary parameters. Cannot predict formation of a second liquid phase. Uses 3 parameters for each binary pair, where two are energies of interaction (similar to the Wilson parameters) and the third is a randomness factor that characterizes the tendency of molecules i and j to be distributed randomly in the mixture. Can predict liquid-liquid or vapor-liquid equilibrium. Mathematically more complex than NRTL, but uses fewer adjustable parameters. Can predict liquid-liquid and vapor-liquid equilibrium. In the absence of experimental data, the parameters can be predicted by the UNIFAC method. Probably the most widely-used model.

Wilson (1964)

NRTL (NonRandom TwoLiquid) Equation

UNIQUAC (Universal QuasiChemical) Equation

Renon and Prausnitz (1969)

Abrams and Prausnitz (1975) Anderson and Prausnit(1978a) Anderson and Prausnitz (1978b)

range of temperature normally encountered in distillation, can be taken as independent of temperature. For a detailed discussion of the equations for activity coefficients and their relative merits the reader is referred to the books by Reid et al. (1987), Prausnitz et al. (1998), Walas (1985), and Null (1970). Most of the commercial process simulation programs contain subroutines that allow the user to enter phase-equilibrium data and perform a localized regression to better tune the binary interaction parameters in any of the activity coefficient models. The binary interaction parameters are not unique constants and locally adjusted parameters will provide more accurate prediction of phase equilibrium for a given design problem. Details of how to fit phase-equilibrium data are given in the simulation program manuals.

4.4.4 Prediction of Phase-equilibrium Constants The designer will often be confronted with the problem of how to proceed with the design of a separation process without adequate experimentally-determined equilibrium data. Some techniques are available for the prediction of vapor-liquid equilibrium (VLE) data and for the extrapolation of experimental values. The process simulation programs include libraries of measured data and interaction parameters for mixtures, as well as predictive methods. Caution must be used in the application of these techniques in design and the predictions should be confirmed against experimentally-determined values whenever practicable.

Group Contribution Methods Group contribution methods have been developed for the prediction of liquid-phase activity coefficients. The objective has been to enable the prediction of phase-equilibrium data for the tens of thousands of possible mixtures of interest to the process designer to be made from the contributions of the relatively few functional groups that made up the compounds. The UNIFAC method, Fredenslund,

4.4 Selection of Physical Property Models

181

Gmehling, Michelsen, Rasmussen, and Prausnitz (1977a), is probably the most useful for process design. Its use is described in detail in a book by Fredenslund, Gmehling, and Rasmussen (1977b). A method was also developed to predict the parameters required for the NRTL equation: the ASOG method, Kojima and Tochigi (1979). More extensive work has been done to develop the UNIFAC method, to include a wider range of functional groups; see Gmehling, Rasmussen, and Frednenslund (1982) and Magnussen, Rasmussen, and Frednenslund (1981). The UNIFAC method can be used to estimate binary interaction parameters for the UNIQUAC model, and by extension the NRTL and Wilson models. Care must be exercised in applying the UNIFAC method. The specific limitations of the method are: 1. 2. 3. 4.

Pressure not greater than a few bar (say, limit to 5 bar). Temperature below 150°C. No noncondensable components or electrolytes. Components must not contain more than 10 functional groups.

Sour-water Systems The term sour water is used for water containing carbon dioxide, hydrogen sulfide, and ammonia encountered in refinery operations. Special correlations have been developed to handle the vapor-liquid equilibrium of such systems, and these are incorporated in most design and simulation programs. Newman (1991) gives the equilibrium data required for the design of sour water systems, as charts.

Electrolyte Systems When water and salts are present in a mixture then the salts can dissociate into ions in aqueous solution. The phase-equilibrium model must account for dissociation and the presence of long-range interactions between charges on ions as well as vapor-liquid or liquid-liquid equilibrium. Special electrolyte models and databases such as the OLI model have been developed for electrolyte systems. These models are available in the commercial process simulation programs, but sometimes require an additional fee.

Vapor-liquid Equilibrium at High Pressures At pressures above a few atmospheres, the deviations from ideal behavior in the gas phase will be significant and must be taken into account in process design by use of a suitable equation of state for the vapor phase. The effect of pressure on the liquid-phase activity coefficient must also be considered. A discussion of the methods used to correlate and estimate vapor-liquid equilibrium data at high pressures is beyond the scope of this book. The reader should refer to the texts by Null (1970), Prausnitz et al. (1998), or Prausnitz and Chueh (1968). Prausnitz and Chueh also discuss phase equilibrium in systems containing components above their critical temperature (super-critical components).

Liquid-liquid Equilibrium Experimental data, or predictions, that give the distribution of components between the two solvent phases are needed for the design of liquid-liquid extraction processes, and mutual solubility limits are needed for the design of decanters, and other liquid-liquid separators.

182

CHAPTER 4 Process Simulation

Green and Perry (2007) give a useful summary of solubility data. Liquid-liquid equilibrium (LLE) compositions can be predicted from vapor-liquid equilibrium data, but the predictions are rarely accurate enough for use in the design of liquid-liquid extraction processes. The DECHEMA data collection includes liquid-liquid equilibrium data for several hundred mixtures, DECHEMA (1977). The UNIQUAC equation can be used to estimate activity coefficients and liquid compositions for multicomponent liquid-liquid systems. The UNIFAC method can be used to estimate UNIQUAC parameters when experimental data are not available. Some process simulation programs require the user to enable three-phase calculation or switch from a VLE mode to a VLLE mode when solving liquid-liquid equilibrium calculations. It must be emphasized that extreme caution should be exercised when using predicted values for liquid-liquid equilibrium in design calculations.

4.4.5 Choice of Phase-equilibrium Model for Design Calculations There is no universal algorithm for the selection of a phase-equilibrium model. Although general rules can be given for the applicability of different equations of state, the models for liquid-phase activity coefficients are semi-empirical and it is often impossible to determine a priori which will provide the best fit to a set of experimental phase-equilibrium data. The flowchart shown in Figure 4.2 has been adapted from a similar chart published by Wilcon and White (1986) and can be used as a preliminary guide to model selection. The abbreviations used in the chart for the equations of state and activity coefficient models correspond to those given in Tables 4.4 and 4.5. It must be emphasized that the best activity coefficient model is the model that provides the best fit to the experimental data over the range of interest. If no experimental data are available, then the best model is probably that for which the fewest interaction parameters must be estimated. If a phase-equilibrium model is created using estimated interaction parameters, the designer should highlight this as a source of uncertainty in the design. Before proceeding to detailed design, the design team should ensure that sufficient data is collected to confirm the model, and an expert on thermodynamics should be consulted to give advice on model selection and parameter estimation.

4.4.6 Validation of Physical Property Models The physical properties and phase equilibrium predicted by a process simulation program should always be validated by comparison with experimental measurements. It is not necessary to compare every parameter predicted by the model with real data, but any parameter that has a significant influence on the design should be confirmed. In some cases, it may also be necessary to confirm the accuracy of a physical property over a range of temperature or pressure. In a revamp design, model validation is relatively straightforward, though usually not easy. A simulation model of the existing process can be built and tuned to match the current plant performance. Once the model is successfully benchmarked against the plant data, it can be used to evaluate new cases for the proposed design modifications. Although this sounds simple, the effort involved in matching a model to plant data can be considerable. It is often worthwhile to use a few independent laboratory experiments under more controlled conditions to reduce the number of parameters that are adjusted in the plant-based model.

N Use G-S

Start

T < 250 K Y H2 present

Use P-R or R-K-S

Hydrocarbon C5 or lighter

N Use B-W-R or L-K-P

Use G-S

H2 present

Electrolytes

N Y

P < 200 bar

Use R-K-S

0 < T < 750 K N

P < 350 bar N Need more experimental data

FIGURE 4.2 Flow chart for the selection of phase-equilibrium model.

Use sour water system

Use electrolyte

N N

P < 4 bar T < 150 °C Y Use UNIFAC to estimate interaction parameters

γi experimental data Y Two liq phases

Use Wilson, NRTL or UNIQUAC

Y Use NRTL or UNIQUAC

Select model that gives best fit to data

4.4 Selection of Physical Property Models

Sour water N

T < 250 K

Use G-S or P-R

Polar or hydrogen bonding

183

184

CHAPTER 4 Process Simulation

Pilot plants and laboratory experiments can be a good source of data for model validation. When designing a pilot plant, consideration should be given to the need for collecting data to validate phase-equilibrium models. Care must be taken to ensure that samples are taken when streams are at steady state and have had time to equilibrate. If no experimental data are available then it is usually a good idea to make an independent estimate of any parameters that have a strong influence on the design, to be satisfied that the results from the simulator are credible. If the independent estimate does not agree with the simulation result then it may be worthwhile to conduct some experiments to collect real data. Methods for estimating physical properties are given in the book by Poling et al. (2000). A flash calculation can be used as a simple technique for validating a phase-equilibrium model when there are no data available. The designer should set up a simulation model of a flash calculation using the temperature, pressure, and composition of interest. This simulation can then be run using different models for liquid- and vapor-phase nonideality that might be expected to be applicable to the system of interest. If the model predicts essentially the same stream flows and compositions regardless of the thermodynamic models selected, then the models are equally valid. This does not mean that the models are accurate, but at least they give the same results. If the flash calculation gives substantially different stream flows or compositions with different thermodynamic models, the designer should seek more experimental data with which to determine which model is most applicable.

4.5 SIMULATION OF UNIT OPERATIONS A process simulation is built up from a set of unit operation models connected by mass and energy streams. The commercial simulators include many unit operation subroutines, sometimes referred to as library models. These operations can be selected from a palette or menu and then connected together using the simulator graphical user interface. Table 4.6 gives a list of the main unit operation models available in Aspen Plus and UniSim Design. Details of how to specify unit operations are given in the simulator manuals. This section provides general advice on unit operations modeling and modeling of nonstandard unit operations.

4.5.1 Reactors The modeling of real industrial reactors is usually the most difficult step in process simulation. It is usually easy to construct a model that gives a reasonable prediction of the yield of main product, but the simulator library models are not sophisticated enough to fully capture all the details of hydraulics, mixing, mass transfer, catalyst and enzyme inhibition, cell metabolism, and other effects that often play a critical role in determining the reactor outlet composition, energy consumption, rate of catalyst deactivation, and other important design parameters. In the early stages of process design, the simulator library models are usually used with simplistic reaction models that give the design engineer a good enough idea of yields and enthalpy changes to allow design of the rest of the process. If the design seems economically attractive, then more detailed models can be built and substituted into the flowsheet. These detailed models are usually built as user models, as described in Section 4.6 and Section 15.11.

4.5 Simulation of Unit Operations

185

Table 4.6 Unit Operation Models in Aspen Plus™ and UniSim™ Design Suite Unit Operation

Aspen Plus Models

UniSim Design Models

Stream mixing Component splitter Decanter Flash Piping components Piping Valves & fittings Hydrocyclone Reactors Conversion reactor Equilibrium reactor Gibbs reactor Yield reactor CSTR Plug flow reactor Columns Shortcut distillation Rigorous distillation Liquid-liquid extraction Absorption and stripping

Mixer Sep, Sep2 Decanter Flash2, Flash3

Mixer Component Splitter 3-Phase Separator Separator, 3-Phase Separator

Pipe, Pipeline Valve HyCyc

Pipe Segment, Compressible Gas Pipe Valve, Tee, Relief Valve Hydrocyclone

RStoic REquil RGibbs RYield RCSTR RPlug

Conversion Reactor Equilibrium Reactor Gibbs Reactor Yield Shift Reactor Continuous Stirred Tank Reactor Plug Flow Reactor

DSTWU, Distl, SCFrac RadFrac, MultiFrac Extract RadFrac

Shortcut Column Distillation, 3-Phase Distillation Liquid-Liquid Extractor Absorber, Refluxed Absorber, Reboiled Absorber 3 Stripper Crude, 4 Stripper Crude, Vacuum Resid Column, FCCU Main Fractionator

Fractionation Rate-based distillation Batch distillation Heat transfer equipment Heater or cooler Heat exchanger Air cooler Fired heater Multi-stream exchanger Rotating equipment Compressor Turbine Pump, hydraulic turbine Solids handling Size reduction Size selection

PetroFrac RATEFRAC™ BatchFrac Heater HeatX, HxFlux, Hetran, HTRI-Xist Aerotran Heater MheatX

Heater, Cooler Heat Exchanger

Compr, MCompr Compr, MCompr Pump

Compressor Expander Pump

Crusher Screen

Screen

Air Cooler Fired Heater LNG Exchanger

(Continued )

186

CHAPTER 4 Process Simulation

Table 4.6 Unit Operation Models in Aspen Plus™ and UniSim™ Design Suite —Cont’d Unit Operation

Aspen Plus Models

UniSim Design Models

Crystallizer Neutralization Solids washing Filter Cyclone Solids decanting Solids transport Secondary recovery User models

Crystallizer

Crystallizer, Precipitation Neutralizer

SWash Fabfl, CFuge, Filter HyCyc, Cyclone CCD ESP, Fabfl, VScrub User, User2, User3

Rotary Vacuum Filter Hydrocyclone, Cyclone Simple Solid Separator Conveyor Baghouse Filter User Unit Op

Most of the commercial simulation programs have variants on the following reactor models:

Conversion Reactor (Stoichiometric Reactor) A conversion reactor requires a reaction stoichiometry and an extent of reaction, which is usually specified as an extent of conversion of a limiting reagent. No reaction kinetics information is needed, so it can be used when the kinetics are unknown (which is often the case in the early stages of design) or when the reaction is known to proceed to full conversion. Conversion reactors can handle multiple reactions, but care is needed in specifying the order in which they are solved if they use the same limiting reagent.

Equilibrium Reactor An equilibrium reactor finds the equilibrium product distribution for a specified set of stoichiometric reactions. Phase equilibrium is also solved. The engineer can enter the outlet temperature and pressure and let the reactor model calculate the duty needed to reach that condition, or else enter a heat duty and let the model predict the outlet conditions from an energy balance. An equilibrium reactor only solves the equations specified, so it is useful in situations where one or more reactions equilibrate rapidly while other reactions proceed much more slowly. An example is the steam reforming of methane to hydrogen. In this process, the water-gas-shift reaction between water and carbon monoxide equilibrates rapidly at temperatures above 450 °C, while methane conversion requires catalysis even at temperatures above 800 °C. This process chemistry is explored in Example 4.5. In some simulation programs, the equilibrium reactor model requires the designer to specify both liquid- and vapor-phase products, even though one of the streams may be calculated to have zero flow. If the real reactor has a single outlet, then the two product streams in the model should be mixed back together.

Gibbs Reactor The Gibbs reactor solves the full reaction and phase equilibrium of all species in the component list by minimization of the Gibbs free energy, subject to the constraint of the feed mass balance.

4.5 Simulation of Unit Operations

187

A Gibbs reactor can be specified with restrictions such as a temperature approach to equilibrium or a fixed conversion of one species. The Gibbs reactor is very useful when modeling a system that is known to come to equilibrium, in particular, high-temperature processes involving simple molecules. It is less useful when complex molecules are present, as these usually have high Gibbs energy of formation; consequently, very low concentrations of these species are predicted unless the number of components in the model is very restricted. The designer must specify the components carefully when using a Gibbs reactor in the model, as the Gibbs reactor can only solve for specified components. If a component that is actually formed is not listed in the component set, then the Gibbs reactor results will be meaningless. Care must be taken to include all isomers, as the absence of isomers can distort the results of a Gibbs reactor. Furthermore, if some of the species have high Gibbs free energy, their concentrations may not be properly predicted by the model. An example is aromatic hydrocarbon compounds such as benzene, toluene, and xylenes, which have Gibbs free energy of formation greater than zero. If these species are in a model component set that also contains hydrogen and carbon, then a Gibbs reactor will predict that only carbon and hydrogen are formed. Although hydrogen and coke are indeed the final equilibrium products, the aromatic hydrocarbons are kinetically stable and there are many processes that convert aromatic hydrocarbon compounds without significant coke yields. In this situation, the designer must either omit carbon from the component list or else use an equilibrium reactor in the model.

Continuous Stirred Tank Reactor (CSTR) The CSTR is a model of the conventional well-mixed reactor. It can be used when a model of the reaction kinetics is available and the reactor is believed to be well mixed, i.e., the conditions everywhere in the reactor are the same as the outlet conditions. By specifying forward and reverse reactions, the CSTR model can model equilibrium and rate-based reactions simultaneously. The main drawback of using the CSTR model is that a detailed understanding of kinetics is necessary if by-products are to be predicted properly.

Plug-flow Reactor (PFR) A plug-flow reactor models the conventional plug flow behavior, assuming radial mixing, but no axial dispersion. The reaction kinetics must be specified and the model has the same limitations as the CSTR model. Most of the simulators allow heat input or removal from a plug-flow reactor. Heat transfer can be with a constant wall temperature (as encountered in a fired tube, steam-jacketed pipe, or immersed coil) or with counter-current flow of a utility stream (as in a heat exchanger tube or jacketed pipe with cooling water).

Yield Shift Reactor The yield shift reactor overcomes some of the drawbacks of the other reactor models by allowing the designer to specify a yield pattern. Yield shift reactors can be used when there is no model of the kinetics, but some laboratory or pilot plant data are available, from which a yield correlation can be established.

188

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Yield shift reactors are particularly useful when modeling streams that contain pseudocomponents, solids with a particle size distribution or processes that form small amounts of many by-products. These can all be described easily in yield correlations, but can be difficult to model with the other reactor types. The main difficulty in using the yield shift reactor is in establishing the yield correlation. If a single point, for example from a patent, is all that is available, then entering the yield distribution is straightforward. If, on the other hand, the purpose is to optimize the reactor conditions, then a substantial set of data must be collected to build a model that accurately predicts yields over a wide enough range of conditions. If different catalysts can be used, the underlying reaction mechanism may be different for each, and each will require its own yield model. The development of yield models can be an expensive process and is usually not undertaken until corporate management has been satisfied that the process is likely to be economically attractive.

Modeling Real Reactors Industrial reactors are usually more complex than the simple simulator library models. Real reactors usually involve multiple phases and have strong mass transfer, heat transfer, and mixing effects. The residence time distributions of real reactors can be determined by tracer studies, and seldom exactly match the simple CSTR or PFR models; see Section 15.12. Sometimes a combination of library models can be used to model the reaction system. For example, a conversion reactor can be used to establish the conversion of main feeds, followed by an equilibrium reactor that establishes an equilibrium distribution among specified products. Similarly, reactors with complex mixing patterns can be modeled as networks of CSTR and PFR models, as described in Sections 12.11.2 and 15.11.2 and illustrated in Figure 12.14. When using a combination of library models to simulate a reactor, it is a good idea to group these models in a sub-flowsheet. The sub-flowsheet can be given a suitable label such as “reactor” that indicates that all the unit operations it contains are modeling a single piece of real equipment. This makes it less likely that someone else using the model will misinterpret it as containing additional distinct operations. Detailed models of commercial reactors are usually written as user models. User models are described in Section 4.6. Detailed modeling of reactors is discussed in more detail in Section 15.11.

Example 4.4 When heavy oils are cracked in a catalytic or thermal cracking process, lighter hydrocarbon compounds are formed. Most cracking processes on heavy oil feeds form products with carbon numbers ranging from two to greater than twenty. How does the equilibrium distribution of hydrocarbon compounds with five carbons (C5 compounds) change as the temperature of the cracking process is increased at 200kPa?

Solution

This problem was solved using UniSim Design. The problem asks for an equilibrium distribution, so the model should contain either a Gibbs reactor or an equilibrium reactor. A quick glance at the component list in UniSim Design shows that there are 22 hydrocarbon species with five carbons. To model the equilibrium among these species, we also need to include hydrogen to allow for the

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formation of alkenes, dienes, and alkynes. Although it would be possible to enter 21 reactions and use an equilibrium reactor, it is clearly easier to use a Gibbs reactor for this analysis. Figure 4.3 shows the Gibbs reactor model. To specify the feed we must enter the temperature, pressure, flow rate, and composition. The temperature, pressure, and flow rate are entered in the stream editor window, Figure 4.4. The feed composition can be entered as 100% of any of the C5 paraffin species, for example normal pentane. The results from a Gibbs reactor would be the same if 100% isopentane was entered. It should be noted, however, that if a mixture of a pentane and a pentene was specified, then the overall ratio of hydrogen to carbon would be different and different results would be obtained. A spreadsheet was also added to the model, as illustrated in Figure 4.3, to make it easier to capture and download the results. The spreadsheet was set up to import component mole fractions from the simulation, Figure 4.5. The simulation was then run for a range of temperatures, and after each run a new column was entered in the spreadsheet (Figure 4.6). When the results are examined, many of the individual species are present at relatively low concentrations. It thus makes sense to group some compounds together by molecular type, for example, adding all the dienes together and adding all the alkynes (acetylenes) together.

FIGURE 4.3 Gibbs reactor model.

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FIGURE 4.4 Stream entry.

The spreadsheet results were corrected to give the distribution of C5 compounds by dividing by one minus the mole fraction of hydrogen, and then plotted to give the graph in Figure 4.7. It can be seen from the graph that the equilibrium products at temperatures below 500 °C are mainly alkanes (also known as paraffins or saturated hydrocarbons), with the equilibrium giving roughly a 2:1 ratio of isopentane to normal pentane. As the temperature is increased from 500 °C to 600 °C, there is increased formation of alkene compounds (also known as olefins). At 700 °C, we see increased formation of cyclopentene and of dienes, and above 800 °C dienes are the favored product. Of course this is an incomplete picture, as the relative fraction of C5 compounds would be expected to decrease as the temperature is raised and C5 species are cracked to lighter compounds in the C2 and C3 range. The model also did not contain carbon (coke), and so could not predict the temperature at which coke would become the preferred product. A more rigorous equilibrium model of a cracking process might include all of the possible hydrocarbon compounds up to C7 or higher. A real reactor might give a very different distribution of C5 compounds from that calculated using the Gibbs reactor model. Dienes formed at high temperatures might recombine with hydrogen during cooling, giving a mixture that looks more like the equilibrium product at a lower temperature. There might also be formation of C5 compounds by condensation reactions of C2 and C3 species during cooling, or loss of dienes and cyclopentene due to coke formation.

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FIGURE 4.5 Product composition spreadsheet.

Example 4.5 Hydrogen can be made by steam reforming of methane, which is a highly endothermic process: CH4 + H2 O ↔ CO + 3H2

ΔH°rxn = 2:1 × 105 kJ/kgmol

Steam reforming is usually carried out in fired tubular reactors, with catalyst packed inside the tubes and fuel fired on the outside of the tubes to provide the heat of reaction. The product gas mixture contains carbon dioxide and water vapor as well as carbon monoxide and hydrogen and is conventionally known as synthesis gas or syngas. Hydrogen can also be made by partial oxidation of methane, which is an exothermic process, but yields less product per mole of methane feed: CH4 + ½ O2 → CO + 2H2

ΔH°rxn = −7:1 × 104 kJ/kgmol

When steam, oxygen, and methane are combined, heat from the partial oxidation reaction can be used to provide the heat for steam reforming. The combined process is known as autothermal reforming. Autothermal reforming has the attraction of requiring less capital investment than steam reforming (because it does not need a fired-heater reactor), but giving higher yields than partial oxidation.

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FIGURE 4.6

Fraction

Spreadsheet results.

FIGURE 4.7 Product distribution.

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 400.00 500.00 600.00 700.00 800.00 900.00 1000.00 Temperature (°C)

22M propane cyclopentane cyclopentene i-pentane n-pentane dienes acetylenes pentenes methyl butenes

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The yield of hydrogen can be further increased by carrying out the water gas shift reaction: CO + H2 O ↔ CO2 + H2

ΔH°rxn = −4:2 × 104 kJ/kgmol

The water gas shift reaction equilibrates rapidly at temperatures above about 450 °C. At high temperatures this reaction favors the formation of carbon monoxide, while at low temperatures more hydrogen is formed. When hydrogen is the desired product, the shift reaction is promoted at lower temperatures by using an excess of steam and providing a medium- or low-temperature shift catalyst. In an autothermal reforming process, 1000 kmol/h of methane at 20 °C is compressed to 10 bar, mixed with 2500 kmol/h of saturated steam, and reacted with pure oxygen to give 98% conversion of the methane. The resulting products are cooled and passed over a medium-temperature shift catalyst that gives an outlet composition corresponding to equilibrium at 350 °C. i. ii. iii. iv.

How much heat is required to vaporize the steam? How much oxygen is needed? What is the temperature at the exit of the autothermal reforming reactor? What is the final molar flow rate of each component of the synthesis gas?

Solution

This problem was solved using Aspen Plus. The model must simulate the high temperature reforming reaction and also the re-equilibration of the water-gas-shift reaction as the product gas is cooled. A Gibbs reactor can be used for the high-temperature reaction, but an equilibrium reactor must be specified for the shift reactor, as only the water-gas-shift reaction will re-equilibrate at 350°C. Because the methane compressor supplies some heat to the feed, it should be included in the model. Since the question asks how much heat is needed to vaporize the steam, a steam boiler should also be included. The oxygen supply system can also be included, giving the model shown in Figure 4.8. The heat duty to the reforming reactor is specified as zero. The oxygen flow rate can then be adjusted until the desired methane conversion is achieved. For 98% conversion, the flow rate of methane in the autothermal reactor product (stream 502) is 2% of the flow rate in the reactor feed (stream 501), i.e., 20 kmol/h. For the purpose of this example, the oxygen flow rate was adjusted manually, although a controller could have been used, as described in Section 4.8. The results are shown in Figure 4.9. When the simulation model was run, the following values were calculated: i. ii. iii. iv.

The steam heater requires 36MW of heat input. 674 kmol/h of oxygen are needed. The temperature at the exit of the reforming reactor is 893 °C. The molar flow rates at the outlet of the shift reactor (stream 504) are: H2 H2O CO CO2 CH4

2504 1956 68 912 20

It should be immediately apparent from the model output that the process as simulated is far from optimal. The oxygen consumption is larger than the 500 kmol/h that would have been needed for partial oxidation. The excess

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FIGURE 4.8 Authothermal reforming model.

oxygen is needed because the additional steam that is being fed must also be heated to the reactor outlet temperature, which requires more of the feed methane to be burned. The corollary of this result is that the hydrogen yield, at roughly 2.5 moles per mole methane, is not much better than could have been obtained with partial oxidation followed by shift, despite the large excess of steam used. The designer has several options that could be examined to improve this process: 1. Increase heat recovery from the product gas to the feed streams to preheat the reactor feed and reduce the amount of oxygen that is needed. 2. Reduce the amount of steam fed with the methane. 3. Bypass a part of the steam from the reformer feed to the shift reactor feed, so as to obtain the benefit of driving the equilibrium in the shift reactor without the cost of providing extra heat to the reformer. 4. Reduce the conversion of methane so that a lower reactor conversion and lower outlet temperature are required. In practice, all of these options are implemented to some extent to arrive at the optimal autothermal reforming conditions. This optimization is explored further in Problem 4.13.

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FIGURE 4.9 Autothermal reactor model results.

4.5.2 Distillation The commercial process simulators contain a range of distillation models with different degrees of sophistication. The design engineer must choose a model that is suitable for the purpose, depending on the problem type, the extent of design information available, and the level of detail required in the solution. In some cases, it may make sense to build different versions of the flowsheet, using different levels of detail in the distillation models, so that the simpler model can be used to initialize a more detailed model.

Shortcut Models The simplest distillation models to set up are the shortcut models. These models use the FenskeUnderwood-Gilliland or Winn-Underwood-Gilliland method to determine the minimum reflux and number of stages or to determine the required reflux given a number of trays or the required number of trays for a given reflux ratio. These methods are described in Chapter 17. The shortcut models can also estimate the condenser and reboiler duties and determine the optimum feed tray. The minimum information needed to specify a shortcut distillation model is: • • •

The component recoveries of the light and heavy key components The condenser and reboiler pressures Whether the column has a total or partial condenser

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In some cases, the designer can specify the purities of the light and heavy key components in the bottoms and distillate respectively. Care is needed when using purity as a specification, as it is easy to specify purities or combinations of purity and recovery that are infeasible. The easiest way to use a shortcut distillation model is to start by estimating the minimum reflux and number of stages. The optimum reflux ratio is usually between 1.05 and 1.25 times the minimum reflux ratio, Rmin, so 1.15 × Rmin is often used as an initial estimate. Once the reflux ratio is specified, the number of stages and optimum feed stage can be determined. The shortcut model results can then be used to set up and initialize a rigorous distillation simulation. Shortcut models can also be used to initialize fractionation columns (complex distillation columns with multiple products), as described below. Shortcut distillation models are robust and are solved quickly. They do not give an accurate prediction of the distribution of non-key components, and they do not perform well when there is significant liquid-phase nonideality, but they are an efficient way of generating a good initial design for a rigorous distillation model. In processes that have a large number of recycle streams, it is often worthwhile to build one model with shortcut columns and a second model with rigorous columns. The simple model will converge more easily and can be used to provide good initial estimates of column conditions and recycle streams for the detailed model. The main drawback of shortcut models is that they assume constant relative volatility, usually calculated at the feed condition. If there is significant liquid- or vapor-phase nonideality, constant relative volatility is a very poor assumption and shortcut models should not be used.

Rigorous Models Rigorous models carry out full stage-by-stage mass and energy balances. They give better predictions of the distribution of components than shortcut models, particularly when the liquid phase behaves nonideally, as the flash calculation is made on each stage. Rigorous models allow many more column configurations, including use of side streams, intermediate condensers and reboilers, multiple feeds, and side strippers and rectifiers. Rigorous models can be much harder to converge, particularly if poor initial estimates are used or if the column is improperly specified. The two main types of rigorous distillation models are equilibrium-stage models and rate-based models. Equilibrium-stage models assume either full vapor-liquid equilibrium on each stage or else an approach to equilibrium based on a stage efficiency entered by the designer. When using an equilibrium-stage model for column sizing, the stage efficiencies must be entered. Stage efficiency is typically less than 0.8, and is discussed in more detail in Chapter 17. Rate-based models do not assume phase equilibrium, except at the vapor-liquid interface, and instead solve the interphase mass transfer and heat transfer equations. Rate-based models are more realistic than the idealized equilibrium-stage models, but because it can be difficult to predict the interfacial area and mass transfer coefficients, rate-based models are less widely used in practice. Rigorous distillation models can be used to model absorber columns, stripper columns, refluxed absorbers, three-phase systems such as extractive distillation columns, many possible complex column configurations, and columns that include reactions such as reactive distillation and reactive absorption columns. The formation of a second liquid phase (usually a water phase) in the column can be predicted if the designer has selected a liquid phase activity model that allows for the prediction of two liquid phases.

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One of the most useful features of the rigorous distillation models in the commercial simulation programs is that most include a tool for plotting column profiles. The design engineer can generate plots showing the molar composition of each species in either phase versus tray number. These plots can be helpful in troubleshooting column designs. For example, Figures 4.10 to 4.15 show column profiles for the distillation problem introduced in Examples 4.6 and 4.7, which is optimized in Example 12.1. The column was simulated in UniSim Design. •

In Figure 4.10, the feed stage was moved up to tray 10, which is too high. The column profiles show a broad flat region between trays 20 and 45, indicating that nothing much is going on over this part of the column. There are too many trays in the stripping section and the feed tray should be moved lower. Sections with very small change in composition can also be indicative of pinched regions where an azeotropic mixture is being formed.

FIGURE 4.10 Feed tray too high.

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In Figure 4.11, the feed tray has been moved down to tray 63, which is too low. The column profiles for benzene and toluene, the light components, are flat between trays 30 and 60 in the rectifying section, indicating that the feed tray should be moved higher. In Figure 4.12, the column specification was changed from toluene recovery to reflux ratio and a low value of reflux ratio (2.2) was entered. This is less than the minimum reflux required for the specified separation; consequently, the desired recovery of toluene cannot be achieved. The recovery of toluene is reduced to 72%. In Figure 4.13, the reflux ratio was increased to 4.0. The recovery of toluene is now 100%, which is greater than the 99% required. This represents a suboptimal use of energy and capital. Figure 4.14 shows the column profiles when the number of trays was reduced to 25, with the feed on tray 8. The column profile for toluene shows that there are insufficient stages (and or reflux). Although the profile is changing smoothly, the recovery in the distillate is only 24.5%. The column profiles with the optimum conditions determined in Example 12.1 are shown in Figure 4.15. The poor features shown in the other profiles are absent.

FIGURE 4.11 Feed tray too low.

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Toluene in bottoms

FIGURE 4.12 Reflux ratio too low: toluene recovery 72%.

Column Convergence Convergence of distillation column models is probably the most common problem in process simulation for novice engineers. There are many reasons why rigorous distillation models (and models of other multistage operations) may fail to converge. The most common causes of convergence problems are as follows: •

•

Infeasible specifications: In multicomponent distillation, care must be taken when using purity as a specification. It will not be possible to make a 99% pure distillate if the feed contains 2% of a component that boils lighter than the light key. The choice of column specifications is discussed in more detail in Section 17.6.2. Poor initialization: If the simulation model is set up with fewer than the minimum number of trays or less than the minimum reflux then it will not converge. Shortcut models can be used to provide an initial design that is feasible, which can then be used as a starting point for a rigorous model.

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FIGURE 4.13 Reflux ratio too high: toluene recovery 100%.

•

Poor initial estimates: The faster distillation column solution algorithms (such as the widelyused inside-out algorithm discussed in Section 17.8.2) run much better when provided with a good initial estimate of tray temperatures.

A good practice is to start by using simple hand calculations to check that the column specifications are feasible. A shortcut model can then be used to determine the minimum reflux and the number of trays and feed tray location when the reflux is increased to about 1.1 times minimum reflux. The rigorous model should then be initialized with the reboiler and condenser temperatures found from the shortcut simulation, a linear temperature profile, and a pressure gradient that makes an approximate allowance for the pressure drop per tray (about 2 inches of liquid is typical). If the inside-out algorithm is used, the rigorous model should initially be run with easy specifications, such as reflux ratio and either distillate rate or bottoms rate. These will guarantee convergence and generate a realistic column temperature profile that can then be stored as the estimate for future runs. The model specifications can then be changed to the desired design specifications

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FIGURE 4.14 Too few trays: toluene recovery 24.5%.

(purity or recovery specifications) and now that the model has a good initialization and set of estimates, convergence will usually be rapid. In the event that this method fails to give quick convergence, the designer should check the specifications are feasible, check for existence of azeotropes, try adding trays, and examine the column profiles for clues to the problem.

Complex Columns for Fractionation Several of the commercial simulation programs offer preconfigured complex column rigorous models for petroleum fractionation. These models include charge heaters, several side strippers, and one or two pump-around loops. These fractionation column models can be used to model refinery distillation operations such as crude oil distillation, vacuum distillation of atmospheric residue oil, fluidized catalytic cracking (FCC) process main columns, and hydrocracker or coker main columns. Aspen Plus also has a shortcut fractionation model SCFrac, which can be used to configure fractionation columns in the same way that shortcut distillation models are used to initialize multicomponent rigorous distillation models.

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FIGURE 4.15 Optimized column profiles.

A typical crude oil distillation column is illustrated in Figure 4.16, which shows a simulation using an Aspen Plus PetroFrac model. The crude oil is preheated in a heat-exchange network and charge heater and is then fed to the flash zone at the bottom of the column. Stripping steam is also added at the bottom of the column to provide additional vapor flow. Products with different boiling ranges are withdrawn from the column. The intermediate products are withdrawn from the bottom of side-stripper columns, so as to minimize loss of lighter products in the side stream. Although the exact distillation ranges can vary depending on the local fuels specifications and the sophistication of the refinery, the typical products taken in a crude oil distillation unit are (from the bottom up): 1. Atmospheric residue oil (Residue), containing compounds that boil above about 340 °C (650 °F). This is normally sent to a vacuum distillation unit to recover more light products, but parts of it may be blended into high sulfur fuels such as heating oil or bunker fuel (marine fuel). 2. Atmospheric gas oil (AGO), containing compounds that boil in the range 275 °C to 340 °C (530 °F to 650 °F). This material is too high-boiling for use as a transportation fuel and is usually sent to a hydrocracker or FCC unit for conversion to lighter products.

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FIGURE 4.16 Crude oil fractionation.

3. Heavy distillate (straight-run distillate or SRD), containing compounds that boil in the range 205 °C to 275 °C (400 °F to 530 °F). This material is hydrotreated to remove sulfur compounds and can then be blended into heating oils and diesel fuels for trucks, railroad engines, and offroad applications such as tractors and mining equipment. 4. Light distillate (straight-run kerosene or SRK), containing compounds that boil in the range 175 °C to 230 °C (350 °F to 450 °F). Light distillate is hydrotreated to remove sulfur and can then be blended into jet fuel or sold as kerosene (sometimes called paraffin) for lamp and cooking fuel. 5. Naphtha, boiling in the range 25 °C to 205 °C (80 °F to 400 °F). Naphtha is usually sent to an additional column for separation into a light naphtha boiling below 80 °C (180 °F) and a heavy naphtha. Heavy naphtha has the right boiling range for gasoline, but usually has very low octane number. It is typically upgraded by catalytic reforming using noble metal catalysts, to increase the concentration of aromatic hydrocarbons in the naphtha and raise the octane number. Catalytic reforming is also the first step in the production of aromatic hydrocarbons for petrochemicals manufacture. Light naphtha also boils in a suitable range for blending into gasoline, and often has an acceptable octane number. It is usually treated to oxidize odiferous

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mercaptan sulfur compounds. Light naphtha is also widely used as a petrochemical feedstock for steam cracking to produce olefin compounds such as ethylene and propylene. 6. The overhead product of the crude unit contains hydrogen, methane, carbon dioxide, hydrogen sulfide, and hydrocarbons up to butanes and some pentanes. It is usually sent to a set of distillation columns known as a “saturate gas plant” for recovery of propane and butane for sale. The lighter gases are then used as refinery fuel. The design of refinery fractionation columns can be complex. The pump-around streams function as intermediate condensers and remove surplus heat from the column. This heat is usually recovered by heat exchange with the cold crude oil feed. Oil refineries are often designed to handle many different crude oils with different boiling assays. The refinery may make different product slates at different times of the year, or in response to market conditions. The crude oil distillation and associated heat-exchange network must be flexible enough to handle all of these variations, while still achieving tight specifications on the boiling point curves of every product.

Column Sizing The rigorous column models allow the design engineer to carry out tray sizing and hydraulics calculations for the basic types of distillation trays and for some types of random and structured packing. Different commercial simulators use different tray sizing correlations, but they all follow a method similar to that described in Chapter 17. The tray sizing tools are not always enabled when running the distillation models. In some of the simulation programs, the design engineer must enable a tray sizing program and/or enter default values for tray type and tray spacing before the sizing algorithm will work properly. If the column diameter does not change when the reflux rate is significantly changed (or if all the columns in the simulation appear to have the same diameter), then the designer should check to make sure that the tray sizing part of the program is properly configured. The tray sizing options in the simulators are restricted to standard internals such as sieve trays, valve trays, bubble-cap trays, random packings, and structured packings. They do not include highcapacity trays, high-efficiency trays, or the latest packing designs. When designing a column that has many stages or a large diameter, it is always worth contacting the column internals vendors for estimates, as use of high-capacity, high-efficiency internals can lead to substantial savings. Advanced internals are also usually used when revamping an existing column to a higher throughput or tighter product specifications. The design engineer should always allow for tray inefficiency when using column sizing tools in conjunction with an equilibrium-stage model. Failure to do so would underpredict the number of stages and hence have an impact on the column pressure drop and hydraulics. Estimation of stage efficiency is discussed in Chapter 17. For initial design purposes, a stage efficiency of 0.7 to 0.8 is usually used. For detailed design, stage efficiencies depend on the type of tray used and are often provided by the column internals vendor. The design engineer must remember to allow a suitable design factor or design margin when sizing columns. Design factors are discussed in Section 1.6. It may be necessary to create two versions of the flowsheet. One version will have the design basis flow rates for producing the mass and energy balances, while the second will have flow rates that are 10% larger for purposes of sizing equipment. The simulation of distillation processes is discussed in more detail by Luyben (2006).

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Example 4.6 Design a distillation column to separate 225 metric tons per hour of an equimolar mixture of benzene, toluene, ethylbenzene, paraxylene, and orthoxylene with minimum total annualized cost. The feed is a saturated liquid at 330 kPa. The recovery of toluene in the distillate should be greater than 99%, and the recovery of ethylbenzene in the bottoms should be greater than 99%. In this example, a column simulation should be set up using a shortcut model. The shortcut model results will be used to initialize a rigorous model in the example that follows. Determine: i. ii. iii. iv.

The The The The

minimum reflux ratio minimum number of trays actual number of trays when the reflux is 1.15 Rmin optimum feed tray

Solution

This problem was solved using UniSim Design. The problem was set up as a shortcut column as shown in Figure 4.17.

FIGURE 4.17 Shortcut distillation.

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UniSim Design requires the designer to specify the mole fraction of the light key component in the bottoms and the heavy key component in the distillate. We have an equimolar feed, so if we take a basis of 100 mol/hr of feed, then the molar flow rate of each component is 20 mol/hr. A 99% recovery of each key component corresponds to allowing 0.2 mol/hr of that component into the other stream. The mole fractions are then Ethylbenzene in distillate = 0:2/40 = 0:005 Toluene in bottoms = 0:2/60 = 0:00333 When these are entered into the shortcut column as specifications, the minimum reflux is calculated to be Rmin = 2.130. The actual reflux ratio can then be specified as 2.13 × 1.15 = 2.45, as shown in Figure 4.18. The shortcut column results are shown in Figure 4.19. The minimum number of stages is calculated as 16.4, which should be rounded up to 17. The actual number of trays required is 39, with feed at stage 18.

Example 4.7 Continuing the problem defined in Example 4.6, use a rigorous simulation to carry out tray sizing and estimate the required column diameter.

FIGURE 4.18 Shortcut column specifications.

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FIGURE 4.19 Shortcut column results.

Solution

Since we are now sizing the column, the first step is to increase the flow rate to allow for a design factor. The process design basis is 225 metric tons per hour of feed. The equipment design should include at least a 10% safety factor, so the equipment design basis was set at 250 metric tons per hour of feed (rounding up from 247.5 for convenience). This flow rate is used in simulating the process for the purpose of sizing equipment, but energy consumption must be based on the reboiler and condenser duties expected for a 225 t/h feed rate. Figure 4.20 shows the rigorous column simulation. UniSim Design allows the designer to enter any two specifications for the column, so instead of entering the reflux ratio as a specification, we can enter the required recoveries and provide the value of reflux ratio found in the shortcut model as an initial estimate, as shown in Figure 4.21. The column converges quickly with the good estimate provided from the shortcut model. The column profiles can be checked by selecting the Performance tab in the column environment and then selecting Plots from the menu on the left and Composition from the list of possible plots, as shown in Figure 4.22. This generates composition profiles like those presented in Figures 4.10 to 4.15. To size the trays in UniSim Design, the tray sizing utility must be activated (from the tools menu via tools/ utilities/tray sizing). When sieve trays are selected with the default spacing of 609.6 mm (2 ft) and the other default parameters shown in Figure 4.23, then the results in Figure 4.24 are obtained. The column diameter is found to be 4.42 m (14.5 ft).

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FIGURE 4.20 Rigorous distillation.

The data on column size, number of trays, reboiler, and condenser duty can then be extracted from the simulation and put into a cost model or spreadsheet to carry out optimization of the total annual cost of production. The results of the optimization are described in Example 12.1.

4.5.3 Other Separations Other multistage vapor-liquid separations such as absorption and stripping can be modeled using variations of the rigorous distillation models, as can multistage liquid-liquid extraction. Single-stage liquid-liquid or vapor-liquid separation can be modeled as a flash vessel, but some caution is needed. The simulation programs assume perfect separation in a flash unless the designer specifies otherwise. If there is entrainment of droplets or bubbles, the outlet compositions of a real flash vessel will be different from those predicted by the simulation. If the flash is critical to process performance, the designer should make an allowance for entrainment. Most of the simulation

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FIGURE 4.21 Rigorous column specifications.

FIGURE 4.22 Generating column profiles.

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FIGURE 4.23 Default tray sizing options.

programs allow the designer to specify a fraction of each phase that is entrained with the other phases. This is illustrated in Figure 4.25, which shows the data entry sheet for entrained flows for UniSim Design. In UniSim Design, the entrained fractions are entered on the Rating tab of the flash model window. Users can also use built-in correlation models with their specified information such as vessel dimensions and nozzle locations. More sophisticated real separator modeling can be found in the three-phase separator model in UniSim Design. The fraction that is entrained depends on the design of the vessel, as described in Chapter 16. Most of the simulators contain several models for fluid-solid separation. These models can be used to manipulate the particle size distribution when solids are present. None of the commercial process simulators contains a good library model for adsorptive separations or membrane separations at the time of writing. These separation methods are important for gas-gas separations, chromatographic separations, and size-exclusion or permeation-based

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FIGURE 4.24 Tray sizing results.

separations, and are described in more detail in Chapter 16. All of these processes must be modeled using component splitters, as described below.

Component Splitter Models A component splitter is a subroutine in the simulation that allows a set of components from a stream to be transferred into another stream with a specified recovery. Component splitters are

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FIGURE 4.25 Flash model with entrainment.

convenient for modeling any separation process that cannot be described using one of the library models. Examples of real operations that are usually modeled as component splitters include: • • • • • • •

Pressure-swing adsorption Temperature-swing adsorption Chromatography Simulated-moving-bed adsorption Membrane separation Ion exchange Guard beds (irreversible adsorption)

When a component splitter is used in a model, it is a good practice to give the splitter a label that identifies the real equipment that is being modeled. Component splitters are sometimes used in place of distillation columns when building simple models to provide initial estimates for processes with multiple recycles. There is little advantage to this approach compared with using shortcut distillation models, as the component splitter will not calculate the distribution of non-key components unless a recovery is entered for each. Estimating and entering the recoveries for every component is difficult and tedious and poor estimates of

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recoveries can lead to poor estimates of recycle flows, so the use of component splitters in this context effectively adds another layer of iteration to the model.

4.5.4 Heat Exchange All of the commercial simulators include models for heaters, coolers, heat exchangers, fired heaters, and air coolers. The models are easy to configure and the only inputs that are usually required on the process side are the estimated pressure drop and either the outlet temperature or the duty. A good initial estimate of pressure drop is 0.3 to 0.7 bar (5 to 10 psi). The heater, cooler, and heat exchanger models allow the design engineer to enter estimates of film transfer coefficients, and hence calculate the exchanger area. As with distillation columns, the designer must remember to add a design factor to the sizes predicted by the model. Design factors are discussed in Section 1.6. Problems often arise when using heat-exchanger models to simulate processes that have a high degree of process-to-process heat exchange. Whenever a process-to-process heat exchanger is included in a simulation, it sets up an additional recycle of information; consequently, an additional loop must be converged. A common situation is where the effluent from a reactor or the bottoms from a distillation column is used to preheat the reactor or column feed, as illustrated in Figure 4.26. If these process flow schemes are simulated using heat exchangers, a recycle of energy is set up between the product and the feed. This recycle must be converged every time the flowsheet is calculated (i.e., at every iteration of any other recycle loop in the process). If more than a few of these exchangers are present, the overall flowsheet convergence can become difficult. Instead, it is usually a good practice to model the process using only heaters and coolers, and then set up subproblems to model the heat exchangers. This facilitates data extraction for pinch analysis, makes it easier for the designer to recognize when exchangers might be internally pinched or have low F factors (see Chapter 19), and improves convergence. Another problem that is often encountered when simulating heat exchangers and heat exchange networks is temperature cross. A temperature cross occurs when the cold stream outlet temperature is hotter than the hot stream outlet temperature (Section 19.6). When temperature cross occurs, many types of shell and tube heat exchanger give a very poor approximation of counter-current flow, and consequently have low F factors and require large surface areas. In some of the commercial simulation programs, the heat exchanger models will indicate if the F factor is low. If this is the case, the designer should split the exchanger into several shells in series so that temperature cross is avoided. Some of the simulation

(a)

(b)

FIGURE 4.26 Common feed heating schemes: (a) feed-effluent exchange; (b) feed-bottoms exchange.

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programs allow the designer to plot profiles of temperature versus heat flow in the exchanger. These plots can be useful in identifying temperature crosses and internal pinches. Example 4.8 A mixture of 100 kgmol/h of 80 mol% benzene and 20 mol% ethylene at 40 °C and 100 kPa is fed to a feedeffluent exchanger, where it is heated to 300 °C and fed to a reactor. The reaction proceeds to 100% conversion of ethylene, and the reactor products are withdrawn, cooled by heat exchange with the feed, and sent to further processing. Estimate the outlet temperature of the product after heat exchange and the total surface area required if the average heat transfer coefficient is 200 Wm−2K−1.

Solution

This problem was solved using UniSim Design. The reaction goes to full conversion, so a conversion reactor can be used. The simulation model is shown in Figure 4.27. When the temperature at the outlet of the exchanger on the feed side is specified, the duty of the exchanger is defined and there is no recycle of information. The model thus solves very quickly, but it is necessary to check the results to see that the exchanger design makes sense.

FIGURE 4.27 Feed-effluent heat exchange model for Example 4.8.

4.5 Simulation of Unit Operations

215

The outlet temperature of the product (stream 6) is found to be 96.9 °C, so there is enough heat in the product mixture to give an approach temperature of nearly 60 °C, which seems perfectly adequate. If we open the exchanger worksheet though, there is a warning that the F factor is too low. Figure 4.28 shows the exchanger worksheet, and the F factor is only 0.2, which is not acceptable. When we examine the temperature-heat duty plot shown in Figure 4.29 (generated from the Performance tab of the exchanger worksheet), it is clear that there is a substantial temperature cross. This temperature cross causes the exchanger to have such a low F factor and gives a UA value of 78.3 × 103 WK−1, where U is the overall heat transfer coefficient in Wm−2K−1 and A is the area in m2. If UA = 78.3 × 103 WK−1 and U = 200 Wm−2K−1, then the exchanger area is A = 392 m2. This would be a feasible size of exchanger, but is large for the duty and is not acceptable because of the low F factor. We should add more shells in series. By examining the temperature-heat duty plot in Figure 4.29, we can see that if we break the exchanger into two shells, with the first shell heating the feed up to the dew point (the kink in the lower curve), then the first shell will not have a temperature cross. This design corresponds to an outlet temperature of about 70 °C for the first exchanger. The second exchanger would still have a temperature cross though. If we break this second exchanger into two more exchangers, then the temperature cross is eliminated. We thus need at least three heat exchangers in series to avoid the temperature cross. This result could have been obtained by “stepping off” between the temperature-duty plots, as illustrated in Figure 4.30.

FIGURE 4.28 Exchanger worksheet for a single-shell design.

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CHAPTER 4 Process Simulation

450.0 Tube side

400.0

Shell side

Temperature (°C)

350.0 300.0 250.0 200.0 150.0 100.0 50.0 0.0 0.0

1000000.0 2000000.0 3000000.0 4000000.0 5000000.0 6000000.0 Heat flow (kJ/h)

FIGURE 4.29 Temperature-heat flow plot for a single-shell design.

450.0 Tube side

400.0

Shell side

Temperature (°C)

350.0

300.0 250.0 2

200.0 150.0 100.0 1 50.0 0.0 0.0

1000000.0 2000000.0 3000000.0 4000000.0 5000000.0 6000000.0 Heat flow (kJ/h)

FIGURE 4.30 Stepping between heat profiles to avoid temperature cross.

4.5 Simulation of Unit Operations

217

FIGURE 4.31 Feed-effluent heat exchange with three shells in series.

Figure 4.31 shows a modified flowsheet with two additional heat exchangers added in series. The outlet temperature of the second exchanger was specified as 200 °C, to divide the duty of the second and third exchangers roughly equally. The results are given in Table 4.7. Temperature-heat flow plots for the three exchangers are given in Figure 4.32. The modified design achieved a reduction in surface area from 392 m2 to 68 m2 at the price of having three shells instead of the original one. More importantly, the modified design is more practical than the original design and is less likely to suffer from internal pinch points. The modified design is not yet optimized. Optimization of this problem is explored in Problem 4.11.

4.5.5 Hydraulics Most of the commercial simulation programs contain models for valves, pipe segments, tees, and elbows. These models can be used to make an initial estimate of system pressure drop for the purposes of sizing pumps and compressors.

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Table 4.7 Heat Exchanger Results Design Case

Original (Single Shell)

Exchanger

E100

E101

E102

Duty (MW) UA (W/K) F ΔTmin ΔTlmtd A (m2) Total area (m2)

1.44 78,300 0.2 56.9 18.4 392 392

0.53 6,310 0.93 56.9 83.6 32

0.57 4,780 0.82 139.7 118.7 24 68

0.35 2,540 0.93 134.3 138.4 13

Modified (Multiple Shell)

220.0

400.0

200.0

350.0

180.0 Temperature (°C)

Temperature (°C)

300.0 160.0 140.0 120.0 100.0

250.0

200.0

150.0 80.0 100.0

60.0 40.0 xx

50.0 xxxxxxx xxxxxx xxxxxxx xxxxxxx xxxxxxx xxxxxxx xxxxxx xxxxxxx xxxxxxxx xxxxxxx

0.0

500000.0

Heat flow (kJ/h) E100

1000000.0

1500000.0

Heat flow (kJ/h) E101

(a)

(b) 450.0

Temperature (°C)

400.0

350.0

300.0

250.0

200.0 0.0

200000.0

400000.0 600000.0 800000.0 1000000.0 1200000.0 1400000.0 Heat flow (kJ/h) E102

Shell side

FIGURE 4.32 Temperature-heat flow profiles for the three exchangers in series: (a) E100; (b) E101; (c) E102.

2000000.0 2500000.0

4.6 User Models

219

If a process hydraulic model is built, care must be taken to specify pressure drop properly in the unit operation models. Rules of thumb are adequate for initial estimates, but in a hydraulic model these should be replaced with rigorous pressure drop calculations. Sufficient allowance must be made for pressure drop across control valves, as discussed in Chapter 5 and Chapter 20. A hydraulic model will not be accurate unless some consideration has been given to plant layout and piping layout. Ideally, the hydraulic model should be built after the piping isometric drawings have been produced, when the designer has a good idea of pipe lengths and bends. The designer should also refer to the piping and instrumentation diagram for isolation valves, flow meters, and other obstructions that cause increased pressure drop. These subjects are discussed in Chapter 5 and Chapter 20. Care is needed when modeling compressible gas flows, flows of vapor-liquid mixtures, slurry flows, and flows of non-Newtonian liquids. Some simulators use different pipe models for compressible flow. The prediction of pressure drop in multiphase flow is inexact at best and can be subject to very large errors if the extent of vaporization is unknown. In most of these cases, the simulation model should be replaced by a computational fluid dynamics (CFD) model of the important parts of the plant.

4.5.6 Solids Handling The commercial simulation programs were originally developed mainly for petrochemical applications and none of them has a complete set of solids-handling operations. Although models for filters, crystallizers, decanters, and cyclones are present in most of the simulators, the designer may have to add user models for operations such as • • • • • • • • • •

hoppers belt conveyors elevators pipe conveyors screw conveyors kneaders extruders slurry pumps fluidized bed heaters fluidized bed reactors

• • • • • • • • • •

washers flocculators spray driers prill towers rotary driers rotary kilns belt dryers centrifuges falling film evaporators moving bed reactors

• • • • • • • • •

crushers and pulverizers jet mills ball mills agglomerators granulators tableting presses paper machines classifiers electrostatic precipitators

Because solids are handled in many commodity chemical processes as well as pharmaceuticals, polymers, and biological processes, the simulation software vendors are under pressure from their customers to enhance the capability of the programs for modeling solids operations. This continues to be an area of evolution of the commercial software.

4.6 USER MODELS When the design engineer needs to specify a unit operation that is not represented by a library model and cannot be approximated by a simple model such as a component splitter or a combination of library models, then it is necessary to construct a user model. All of the commercial simulators allow the user to build add-in models of varying sophistication.

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4.6.1 Spreadsheet Models Models that require no internal iteration are easily coded as spreadsheets. Most of the simulators offer some degree of spreadsheet capability, ranging from simple calculation blocks to full Microsoft Excel™ functionality. In UniSim Design, spreadsheets can be created by selecting the spreadsheet option on the unit operations palette. The spreadsheet is easy to configure and allows data to be imported from streams and unit operations. The functionality of the UniSim Design spreadsheet is rather basic at the time of writing, but is usually adequate for simple input-output models. Values calculated by the spreadsheet can be exported back to the simulation model. The spreadsheet can thus be set up to act as a unit operation. The use of a spreadsheet as a unit operation is illustrated in Example 4.9. Aspen Plus has a similar simple spreadsheet capability using Microsoft Excel, which can be specified as a calculator block (via Data/Flowsheet Options/Calculator). The Excel calculator block in Aspen Plus requires a little more time to configure than the UniSim Design spreadsheet, but at the time of writing it can perform all of the functions available in MS Excel 97. For more sophisticated spreadsheet models, Aspen Plus allows the user to link a spreadsheet to a simulation via a user model known as a USER2 block. The designer can create a new spreadsheet or customize an existing spreadsheet to interact with an Aspen Plus simulation. The USER2 block is much easier to manipulate when handling large amounts of input and output data, such as streams with many components or unit operations that involve multiple streams. The procedure for setting up a USER2 MS Excel model is more complex than using a calculator block, but avoids having to identify every number required from the flowsheet individually. Instructions on how to build USER2 spreadsheet models are given in the Aspen Plus manuals and online help (Aspen Technology, 2001).

4.6.2 User Subroutines Models that require internal convergence are best written as subroutines rather than spreadsheets, as more efficient solution algorithms can be used. Most user subroutines are written in FORTRAN or Visual Basic, though some of the simulators allow other programming languages to be used. It is generally a good practice to compile and test a user model in a simplified flowsheet or as a standalone program before adding it to a complex flowsheet with recycles. It is also a good practice to check the model carefully over a wide range of input values, or else constrain the inputs to ranges where the model is valid. Detailed instructions on how to write user models to interface with commercial simulation programs can be found in the simulator manuals. The manuals also contain specific requirements for how the models should be compiled and registered as extensions or shared libraries (.dll files in Microsoft Windows). In Aspen Plus, user models can be added as USER or USER2 blocks, following the instructions in the Aspen Plus manuals. In UniSim Design, it is very easy to add user models using the User Unit Operation, which can be found on the object palette or under the Flowsheet/Add Operation menu. The UniSim Design User Unit Operation can be linked to any program without requiring an extension file to be registered. The User Unit Operation is not documented in the UniSim Design manual, but instructions on setting it up and adding code are given in the online help.

4.6 User Models

221

Example 4.9 A gas turbine engine is fueled with 3000 kg/hr of methane at 15 °C and 1000 kPa, and supplied with ambient air at 15 °C. The air and fuel are compressed to 2900 kPa and fed to a combustor. The air flow rate is designed to give a temperature of 1400 °C at the outlet of the combustor. The hot gas leaving the combustor is expanded in the turbine. Shaft work produced by the turbine is used to power the two compressors and run a dynamo for generating electricity. If the efficiency of the compressors is 98% and that of the turbine is 88% and 1% of the shaft work is lost due to friction and losses in the dynamo, estimate the rate of power production and the overall cycle efficiency.

Solution

This problem was solved using UniSim Design. A gas turbine engine should run with a large excess of air to provide full combustion of the fuel, so the combustor can be modeled as a conversion reactor. There is no model for a dynamo in UniSim Design, so the dynamo and shaft losses can be modeled using a spreadsheet operation, as shown in Figure 4.33.

FIGURE 4.33 Gas turbine model.

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CHAPTER 4 Process Simulation

Figure 4.33 also illustrates the use of an “Adjust” controller to set the air flow rate so as to give the desired reactor outlet temperature. The specifications for the Adjust are shown in Figures 4.34 and 4.35. The Adjust was specified with a minimum air flow rate of 60,000 kg/hr to ensure that the solver did not converge to a solution in which the air flow did not give full conversion of methane. The stoichiometric requirement is 3000 × 2 × (32/16)/0.21 = 57,000 kg/hr of air. The spreadsheet model of the dynamo is relatively simple, as illustrated in Figure 4.36. The model takes the turbine shaft work and compressor duties as inputs. The friction losses are estimated as 1% of the turbine shaft work. The friction losses and compressor duties are then subtracted from the shaft work to give the net power from the dynamo, which is calculated to be 17.7 MW.

FIGURE 4.34 Adjust specifications.

4.7 Flowsheets With Recycle

223

FIGURE 4.35 Adjust solving parameters.

The cycle efficiency is the net power produced divided by the heating rate of the fuel. The heating rate is the molar flow of fuel multiplied by the standard molar heat of combustion: Heating rate ðkWÞ = molar flow ðmol/hrÞ × ΔH°c ðkJ/molÞ/3600

(4.13)

The cycle efficiency is calculated to be 42.7%.

4.7 FLOWSHEETS WITH RECYCLE Recycles of solvents, catalysts, unconverted feed materials, and by-products are found in many processes. Most processes contain at least one material recycle, and some may have six or more. Furthermore, when energy is recovered by process-to-process heat transfer energy recycles are created, as discussed in Section 4.5.4.

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CHAPTER 4 Process Simulation

FIGURE 4.36 Spreadsheet model of dynamo.

4.7.1 Tearing the Flowsheet For a sequential-modular simulation program to be able to solve a flowsheet with a recycle, the design engineer needs to provide an initial estimate of a stream somewhere in the recycle loop. This is known as a “tear” stream, as the loop is “torn” at that point. The program can then solve and update the tear stream values with a new estimate. The procedure is repeated until the difference between values at each iteration becomes less than a specified tolerance, at which point the flowsheet is said to be converged to a solution. The procedure for tearing and solving a simulation can be illustrated by a simple example. Figure 4.37 shows a process in which two feeds, A and B, are combined and fed to a fixed bed reactor. The reactor product is sent to a stripping column to remove light ends and is then sent to a column that separates heavy product from unreacted feed B. The unreacted feed B is recycled to the reactor. To solve the reactor model, we need to specify the reactor feeds, streams 2 and 4. Stream 4 is made by adding fresh feed stream 1 to recycle stream 3, so a logical first approach might be to make an estimate of the recycle stream, in which case stream 3 is the tear stream. Figure 4.38

4.7 Flowsheets With Recycle

Feed B Feed A

3 4

Recycle of B

Reactor

Lights 5

Product 7

FIGURE 4.37 Example process with recycle.

Iterate to convergence

Estimate Feed B

Update

Feed A 2

Recycle of B

Reactor

Lights 5

Product 7

FIGURE 4.38 Tearing the recycle loop.

225

226

CHAPTER 4 Process Simulation

shows the flowsheet torn at stream 3. The designer provides an initial estimate of stream 3a. The flowsheet then solves and calculates stream 3b. The design engineer specifies a recycle operation connecting streams 3a and 3b, and the simulator then updates stream 3a with the values from stream 3b (or with other values if an accelerated convergence method is used, as discussed in Section 4.7.2). The calculation is then repeated until the convergence criteria are met. The choice of tear stream can have a significant impact on the rate of convergence. For example, if the process of Figure 4.37 were modeled with a yield shift reactor, then tearing the flowsheet at stream 5 would probably give faster convergence. Some of the simulation programs automatically identify the best tear stream.

4.7.2 Convergence Methods The methods used to converge recycle loops in the commercial process simulation programs are similar to the optimization methods described in Chapter 12. Most of the commercial simulation programs include the following methods.

Successive Substitution (Direct Substitution) In this method, an initial estimate, xk, is used to calculate a new value of the parameter, f(xk). The estimate is then updated using the calculated value: xk+1 = f ðxk Þ xk+2 = f ðxk+1 Þ, etc:

(4.14)

This method is simple to code, but is computationally inefficient and convergence is not guaranteed.

Bounded Wegstein The bounded Wegstein method is the default method in most of the simulation programs. It is a linear extrapolation of successive substitution. The Wegstein method initially starts out with a direct substitution step: x1 = f ðx0 Þ An acceleration parameter, q, can then be calculated: s q= s−1

(4.15)

(4.16)

where s=

f ðxk Þ − f ðxk−1 Þ xk − xk−1

(4.17)

and the next iteration is then xk +1 = q xk + ð1 – qÞ f ðxk Þ

(4.18)

If q = 0, the method is the same as successive substitution. If 0 < q < 1, then convergence is damped, and the closer q is to 1.0, the slower convergence becomes. If q is less than 0, then the convergence is accelerated. The bounded Wegstein method sets bounds on q, usually keeping it in the range −5 < q < 0, so as to guarantee acceleration without overshooting the solution too widely.

4.7 Flowsheets With Recycle

227

The bounded Wegstein method is usually fast and robust. If convergence is slow, then the designer should consider reducing the bounds on q. If convergence oscillates, then consider damping the convergence by setting bounds such that 0 < q < 1.

Newton and Quasi-Newton Methods The Newton method uses an estimate of the gradient at each step to calculate the next iteration, as described in Section 12.7.4. Quasi-Newton methods such as Broyden’s method use linearized secants rather than gradients. This approach reduces the number of calculations per iteration, although the number of iterations may be increased. Newton and quasi-Newton methods are used for more difficult convergence problems, for example, when there are many recycle streams, or many recycles that include operations that must be converged at each iteration, such as distillation columns. The Newton and quasi-Newton methods are also often used when there are many recycles and control blocks (see Section 4.8.1). The Newton method should not normally be used unless the other methods have failed, as it is more computationally intensive and can be slower to converge for simple problems.

4.7.3 Manual Calculations The convergence of recycle calculations is almost always better if a good initial estimate of the tear stream is provided. If the tear stream is chosen carefully, it may be easy for the design engineer to generate a good initial estimate. This can be illustrated by returning to the problem of Figure 4.37. We can tear the recycle loop at the reactor effluent, as shown in Figure 4.39. We can then state the following about the reactor effluent: 1. The reactor effluent must contain the net production rate of product (which is known), plus any product that is in the recycle. Recycling product to the reactor is not a good idea, as it is likely to lead to by-product formation. A reasonable estimate of product recovery in the separation section is probably 99% or greater, so a good initial estimate of the amount of product in stream 5b is the net production rate divided by the separation recovery, or roughly 101% of the net production rate. Feed B Feed A

3 4

Recycle of B

Reactor 6

Lights 5a

FIGURE 4.39 Tearing at the reactor outlet.

Product

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CHAPTER 4 Process Simulation

2. Since feed B is recycled and feed A is not, it looks like we are using an excess of B to drive full conversion of A. A good initial estimate of the flow rate of component A in stream 5b is therefore zero. If we have conversion data in terms of A, then we could produce a better estimate. 3. Feed B is supplied to the reactor in excess. The amount of B consumed in the reactor must be equal to the amount required by stoichiometry to produce the product. The amount of B remaining in the reactor effluent is given by moles B fed −1 stoichiometric moles B per mole product 1 −1 = conversion of B

moles B remaining per mole product =

(4.19)

So, knowing the flow rate of product, we can get a good initial estimate of the flow rate of B if we know either the conversion of B or the ratio in excess of the stoichiometric feed rate of B that we want to supply. We can thus make good estimates of the three major components that are present in stream 5b. If light or heavy by-products are formed in the reactor but not recycled, then a single successive substitution step will provide good estimates for these components, as well as a better estimate of the conversion of B and the amount of A that is required in excess of stoichiometric requirements. Manual calculations are also very useful when solving flowsheets that use recycle and purge. Purge streams are often withdrawn from recycles to prevent the accumulation of species that are difficult to separate, as described in Section 2.3.4. A typical recycle and purge flow scheme is illustrated in Figure 4.40. A liquid feed and a gas are mixed, heated, reacted, cooled, and separated to give a liquid product. Unreacted gas from the separator is recycled to the feed. A make-up stream is added to the gas recycle to make up for consumption of gas in the process. If the make-up gas contains any inert gases, then over time these would accumulate in the recycle and eventually the reaction would be slowed down when the partial pressure of reactant gas fell. To prevent this situation from occurring, we withdraw a purge stream to maintain the inerts at an acceptable level. We can provide a good initial estimate of the recycle stream by noting: 1. The flow rate of inerts in the purge is equal to the flow rate of inerts in the make-up gas. 2. The required partial pressure of reactant gas at the reactor outlet sets the concentration of reactant gas and inerts in the recycle and the unconverted gas flow rate if the reactor pressure is specified. We can then write a mass balance on inerts: F M yM = F P yR

(4.20)

FM ð1 − yM Þ = G + FP ð1 − yR Þ

(4.21)

and on reactant gas: hence FM ð1 − yM Þ = G + FM

yM ð1 − yR Þ yR

4.7 Flowsheets With Recycle

Make-up gas

229

Purge

Feed Reactor Product

FIGURE 4.40 Process with gas recycle and purge.

where FM FP yM yR G

= = = = =

make-up molar flow rate purge molar flow rate mole fraction of inerts in make-up mole fraction of inerts in recycle and purge molar rate of consumption of gas in reactor

Hence we can solve for FM and FP if G is known. The temperature of the recycle gas at the outlet of the compressor is not easily estimated, so the logical place to tear the recycle is between the purge and the compressor, as indicated in Figure 4.40.

4.7.4 Convergence Problems If a flowsheet is not converged, or if the process simulation software runs and gives a statement “converged with errors”, then the results cannot be used for design. The designer must take steps to improve the simulation so that a converged solution can be found. The first steps that an experienced designer would usually take would be: 1. 2. 3. 4. 5.

Make sure that the specifications are feasible. Try increasing the number of iterations. Try a different convergence algorithm. Try to find a better initial estimate. Try a different tear stream.

If one or more unit operations have been given infeasible specifications, then the flowsheet will never converge. This problem also occurs with multicomponent distillation columns, particularly when purity specifications or flow rate specifications are used, or when nonadjacent key components are chosen; see Section 17.6. A quick manual mass balance around the column can usually determine whether the specifications are feasible. Remember that all the components in the feed must exit the column somewhere. The use of recovery specifications is usually more robust, but care is still needed to make sure that the reflux ratio and number of trays are greater than the minimum required. A similar problem is encountered in recycle loops if a component accumulates

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because of the separation specifications that have been set. Adding a purge stream usually solves this problem. For large problems with multiple recycles, it may be necessary to increase the number of iterations to allow the flow sheet time to converge. This strategy can be effective, but is obviously inefficient if underlying problems in the model are causing the poor convergence. In some cases, it may be worthwhile to develop a simplified simulation model to arrive at a first estimate of tear stream composition, flow rate, and conditions (temperature and pressure). Models can be simplified by using faster and more robust unit operation models, for example, substituting shortcut column models for rigorous distillation models. Models can also be simplified by reducing the number of components in the model. Reducing the number of components often leads to a good estimate of the bulk flows and stream enthalpies, which can be useful if there are interactions between the mass and energy balances. Another simplification strategy that is often used is to model heat exchangers using a dummy stream on one side (usually the side that is downstream in the process). The recycle of energy from downstream to upstream is then not converged until after the rest of the flowsheet has been converged. Alternatively, heaters and coolers can be used in a simplified model, or even in the rigorous model, as long as the stream data is then extracted and used to design the real exchangers. Another approach that is widely used is to “creep up on” the converged solution. This entails building up the model starting from a simplified version and successively adding detail while reconverging at each step. As more complexity is added, the values from the previous run are used to initialize the next version. This is a slow, but effective, method. The design engineer must remember to save the intermediate versions every so often, in case later problems are encountered. A similar strategy is often used when running sensitivity analyses or case studies that require perturbations of a converged model. The designer changes the relevant parameters in small steps to reach the new conditions, while reconverging at each step. The results of each step then provide a good initial estimate for the next step and convergence problems are avoided. When there are multiple recycles present, it is sometimes more effective to solve the model in a simultaneous (equation-oriented) mode rather than in a sequential modular mode. If the simulation program allows simultaneous solution of the equation set, this can be attempted. If the process is known to contain many recycles, the designer should anticipate convergence problems and should select a process simulation program that can be run in a simultaneous mode. Example 4.10 Light naphtha is a mixture produced by distillation of crude oil. Light naphtha primarily contains alkane compounds (paraffins) and it can be blended into gasoline. The octane value of methyl-substituted alkanes (iso-paraffins) is higher than that of straight-chain compounds (normal paraffins), so it is often advantageous to isomerize the light naphtha to increase the proportion of branched compounds. A simple naphtha isomerization process has a feed of 10,000 barrels per day (bpd) of a 50 wt% mixture of n-hexane and methyl pentane. The feed is heated and sent to a reactor where it is brought to equilibrium at 1300 kPa and 250 °C. The reactor products are cooled to the dew point and fed to a distillation column operated at 300 kPa. The bottoms product of the distillation is rich in n-hexane and is recycled to the reactor feed. An overall conversion of n-hexane of 95% is achieved. Simulate the process to determine the recycle flow rate and composition.

4.7 Flowsheets With Recycle

231

Solution

This problem was solved using UniSim Design. The first step is to convert the volumetric flow rate into a mass flow rate in metric units. We can set up a stream that has a 50:50 mixture by weight of n-hexane and methyl pentane. This stream has a density of 641 kg/m3 at 40 °C, so the required flow rate is 10,000 bpd = 10,000 × 641 ðkg/m3 Þ × 0:1596 ðm3 /bblÞ/24 = 42:627 metric tons/h In a real isomerization process, a part of the feed will be lost due to cracking reactions; however, in our simplified model the only reactions that occur are isomerization reactions. Because we only consider isomerization reactions, all of the product and feed components have the same molecular weight (C6H14, Mw = 86). The feed flow rate of nhexane is thus 42.627 × 0.5 = 21.31 metric tons/h. So for 95% conversion of n-hexane, the amount of n-hexane in the product is 0.05 × 21.31 = 1.0655 metric tons/h, or 1065.5/86 = 12.39 kgmol/h. The mole fraction of n-hexane in the product is 5% of 50%, or 2.5 mol%. To get an initial estimate of the distillation column conditions, the process was first simulated using a shortcut column model, as shown in Figure 4.41. If we assume that no cyclic compounds are formed in the

FIGURE 4.41 Isomerization process model using shortcut distillation.

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process, then the component list includes all of the available C6 paraffin compounds, i.e., n-hexane, 2-methyl pentane, 3-methyl pentane, 2,3-methyl butane, and 2,2-methyl butane. The reactor achieves complete equilibrium between these species and so can be modeled using a Gibbs reactor. The shortcut column model requires a second specification, given in terms of the heavy key component. We can define either of the methyl pentane species as the heavy key. In the simplified model that we have built, the level of methyl pentane in the recycle is not important to the process performance. Increasing the recycle of methyl pentane species increases the process yield of dimethyl butane species, which would lead to an improvement in the product octane number. In reality, the presence of side reactions that cause cracking to less valuable light hydrocarbons would establish a trade-off that would set the optimum level of methyl pentane recycle. For now, we will assume that the mole fraction of 2-methyl pentane in the bottoms is 0.2. With these conditions, and with the recycle not closed, the shortcut column model predicts a minimum reflux of 3.75. The reflux ratio is then set at 1.15 × Rmin = 4.31, as shown in Figure 4.42. The shortcut model then calculates that we need 41 theoretical trays, with optimal feed tray 26, as shown in Figure 4.43. The column bottoms flow rate is 18,900 kg/h, which can be used as an initial estimate for the recycle flow. The recycle loop can now be closed and run. The converged solution still has Rmin = 3.75, so the reflux ratio does not need to be adjusted. The converged recycle flow rate is 18.85 metric tons/h or 218.7 kgmol/h, as shown in Figure 4.44. The shortcut column design of the converged flowsheet still has 41 trays with the feed on tray 26. The results from the shortcut model can now be used to provide a good initial estimate for a rigorous model. The shortcut column is replaced with a rigorous column, as shown in Figure 4.45. The rigorous column model can

FIGURE 4.42 Shortcut column specifications.

4.7 Flowsheets With Recycle

FIGURE 4.43 Shortcut column results.

FIGURE 4.44 Converged recycle results for the shortcut column model.

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FIGURE 4.45 Isomerization process model using rigorous distillation.

be set up with the number of stages and feed stage predicted by the shortcut model, Figure 4.46. If we specify the reflux ratio and bottoms product rate as column specifications, as in Figure 4.47, then the flowsheet converges quickly. The results from the rigorous model with the inputs specified as above show a flow rate of 1084.5 kg/hr of n-hexane in the distillate product. This exceeds the requirements calculated from the problem statement (1065.5 kg/h). The simplest way to get back to the required specification is to use it directly as a specification for the column. From the Design tab on the column window we can select Monitor and then Add spec to add a specification on the distillate flow rate of n-hexane, as shown in Figure 4.48. This specification can then be made active and the bottoms flow rate specification can be relaxed. When the simulation is reconverged, the bottoms flow rate increases to 19,350 kg/h and the n-hexane in the distillate meets the specification flow rate of 1065.5 kg/h. The column profiles for the rigorous distillation model are shown in Figure 4.49. The profiles do not show any obvious poor design of the column, although the design is not yet optimized. The simulation was converged to achieve the target conversion of n-hexane with a recycle of 19.35 metric tons/h. The recycle composition is 50.0 mol% n-hexane, 21.1 mol% 2-methyl pentane, 25.1 mol%

4.7 Flowsheets With Recycle

FIGURE 4.46 Design parameters for the rigorous distillation column.

FIGURE 4.47 Specifications for the rigorous distillation column.

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FIGURE 4.48 Adding a specification on n-hexane mass flow.

3-methyl pentane, 3.6 mol% 2,3-methyl butane, and 0.2 mol% 2,2-methyl butane. This is a converged solution, but it is only one of many possible converged solutions. No attempt has yet been made to optimize the design. The optimization of this process is examined in Problem 4.14. For more realistic information on isomerization process conditions, the reader should consult Meyers (2003).

4.8 FLOWSHEET OPTIMIZATION After achieving a converged simulation of the process, the designer will usually want to carry out some degree of optimization. The commercial simulation programs have a limited optimization capability that can be used with suitable caution.

4.8.1 Use of Controllers The simplest form of optimization is to impose additional constraints on the simulation so that it meets requirements specified by the designer. For example, if the designer made estimates of the feed rates, then the production rate of product that is predicted by the model may be less (or more)

4.8 Flowsheet Optimization

237

FIGURE 4.49 Column profiles for the rigorous distillation model.

than the desired rate. The designer could correct this by calculating the appropriate ratio, multiplying all the feed streams by this ratio, and then reconverging the model, but this approach would soon become tedious. Instead, the simulation programs allow the designer to impose constraints on the model. In the example above, this would be a constraint that the product flow rate is equal to a target value. Constraints are imposed using controller functions, known as a “Design Spec” in Aspen Plus or a “Set” or “Adjust” in UniSim Design. Controllers are specified either as Set variable x to value z or Adjust variable x to value y bymanipulating variable z where z is an unknown variable or set of variables that will be calculated by the simulation and x is the variable that the designer wants to specify.

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Controllers can be used to capture all kinds of design constraints and specifications. They are particularly useful for setting feed ratios and controlling purge rates and recycle ratios to achieve target compositions. Some care is needed to ensure that they are used sparingly, otherwise too many recycles of information can be introduced and convergence becomes difficult. Controllers behave much like recycles, and it is usually a good idea to generate a converged simulation to act as a good initial estimate before adding controllers. This does not apply to simple controller functions such as feed ratio controllers. In a dynamic simulation, controllers are used to model the real control valves of the process. When converting a steady state simulation to a dynamic simulation, some care is needed to ensure that the controller functions correspond to physically achievable control structures.

4.8.2 Optimization Using Process Simulation Software The commercial process simulation programs all have the ability to solve optimization problems that can be posed as nonlinear programming (NLP) problems. At the time of writing, only Aspen Plus allows the designer to carry out discrete optimization using integer variables. It is, therefore, not possible to optimize integer parameters such as feed tray location, while simultaneously optimizing continuous variables in any commercial process simulation program other than Aspen Plus. Likewise, only Aspen Plus can be used to carry out superstructure optimization. Note that this discrete optimization functionality is not included in the general license of Aspen Plus, is only available in versions more recent than release 2006.5, and may not be available to all academic users. The other simulation program vendors are expected to add this capability in future releases. Optimization of a large process simulation model is intrinsically difficult, particularly if there are multiple recycles. As noted in Section 12.10, the solution algorithms for NLP problems require multiple solutions of the model, which must be converged at each solution. An additional complication of flowsheet optimization is the formulation of the objective function. The objective function for industrial design is always a measure of economic performance. The design parameters calculated by the simulation program can be used to give relatively good estimates of equipment cost, but this typically requires exporting the parameters into a specialized cost-estimating program, such as Aspen Icarus, as described in Section 7.10. Furthermore, the equipment must usually be oversized by a suitable design factor compared to the design flow rates, as discussed in Section 1.6. The simplest way to address this problem is to generate two or three simulation runs with variations of the key design parameters. These designs can then be costed to develop approximate cost curves, which can then be used in the optimization tool of the simulation program. The Aspen Plus manual provides several useful recommendations for specifying optimization problems (Aspen Technology, 2001): 1. Start by converging a simulation of the flowsheet. This helps the designer detect errors, ensures that specifications are feasible, and provides good estimates for tear streams. 2. Carry out a sensitivity analysis to determine which variables have the most impact on the objective function. These are the variables that should be used as decision variables. It is also important to determine reasonable ranges for these variables and set upper and lower bound constraints. If the ranges set are too narrow, then the optimum may not be found. If they are too wide, then convergence may be difficult.

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3. While carrying out the sensitivity analysis, see if the optimum is broad or sharp. If there are only small changes in the objective function, further optimization may not be justified. Another approach that is often used is to carry out optimization using simplified models to fix the process structure and determine the approximate values of key decision variables. A final NLP optimization can then be carried out using a rigorous model.

4.9 DYNAMIC SIMULATION Most continuous processes are only simulated in steady-state mode. Some of the simulation programs allow a steady-state simulation to be converted to run in a dynamic mode. Dynamic simulation is useful for: 1. Simulating batch and semi-continuous processes to determine rate-controlling steps and investigate batch-to-batch recycles and heat recovery. 2. Simulating process start-up and shutdown. 3. Simulating cyclic processes. 4. Simulating process disturbances to evaluate control system performance and tune controllers. 5. Simulating emergency conditions to evaluate alarm system and relief system responses and ensure that they are adequate. For a good dynamic simulation, the designer must specify the actual control system from the piping and instrumentation diagram (see Chapter 5) and also all of the vessel designs so that hold-ups can be calculated. Mass transfer rates and reaction rates must also be known or assumed. Dynamic simulation is more computationally intensive than steady-state simulation. Dynamic simulation is usually applied to parts of a process (or even single unit operations) rather than an entire process. Different simulation strategies are needed to give a robust dynamic model. Good introductions to dynamic simulation are given in the books by Luyben (2006), Ingham et al. (2007), Seborg et al. (2003), and Asprey and Machietto (2003) and the paper by Pantelides (1988).

References Abrams, D. S., & Prausnitz, J. M. (1975). Statistical thermodynamics of liquid mixtures. New expression for the excess Gibbs energy of partly or completely miscible systems. AIChE J., 21(1), 116. AIChE, 1983. Design institute for physical property data, manual for predicting chemical process design data. AIChE. AIChE, 1985. Design institute for physical property data, data compilation, part II. AIChE. Anderson, T. F., & Prausnitz, J. M. (1978a). Application of the UNIQUAC equation to calculation of multicomponent phase equilibriums. 1. Vapor-liquid equilibrium. Ind. Eng. Chem. Proc. Des. Dev., 17(4), 552. Anderson, T. F., & Prausnitz, J. M. (1978b). Application of the UNIQUAC equation to calculation of multicomponent phase equilibriums. 2. Liquid-liquid equilibrium. Ind. Eng. Chem. Proc. Des. Dev., 17(4), 562. Antoine, C. (1888). Tensions des vapeurs: nouvelle relation entre les tensions et les températures. Compte rend., 107, 681 and 836. Aspen Technology, 2001. Aspen plus® 11.1 user guide. Aspen Technology Inc. Asprey, S. P., & Machietto, S. (2003). Dynamic model development: methods, theory and applications. Elsevier.

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Benedek, P. (Ed.). (1980). Steady-state flow-sheeting of chemical plants. Elsevier; 1980. Benedict, M., Webb, G. B., & Rubin, L. C. (1951). An experimental equation for thermodynamic properties of light hydrocarbons. Chem. Eng. Prog., 47, 419, 449, 571, 609 (in four parts). Bretsznajder, S. (1971). Prediction of transport and other physical properties of fluids. Pergamon Press. Chao, K. C., & Seader, J. D. (1961). A generalized correlation for vapor-liquid equilibria in hydrocarbon mixtures. AIChE J., 7, 598. Chu, J. C., Wang, S. L., Levy, S. L., & Paul, R. (1956). Vapor-liquid equilibrium data. Ann Arbor, MI: J. W. Edwards Inc. Chueh, C. F., & Swanson, A. C. (1973a). Estimation of liquid heat capacity. Can. J. Chem. Eng., 51, 576. Chueh, C. F., & Swanson, A. C. (1973b). Estimating liquid heat capacity. Chem. Eng. Prog., 69(July), 83. DECHEMA, (1977ff). DECHEMA chemistry data series. DECHEMA. Fredenslund, A., Gmehling, J., Michelsen, M. L., Rasmussen, P., & Prausnitz, J. M. (1977a). Computerized design of multicomponent distillation columns using the UNIFAC group contribution method for calculation of activity coefficients. Ind. Eng. Chem. Proc. Des. Dev., 16, 450. Fredenslund, A., Gmehling, J., & Rasmussen, P. (1977b). Vapor-liquid equilibria using UNIFAC: A group contribution method. Elsevier. Gmehling, J., Rasmussen, P., & Frednenslund, A. (1982). Vapor liquid equilibria by UNIFAC group contribution, revision and extension. Ind. Eng. Chem. Proc. Des. Dev, 21, 118. Grayson, H. G., & Streed, C. W. (1963). Vapor-liquid equilibrium for high temperature, high pressure hydrogenhydrocarbon systems. Proc. 6th World Petroleum Congress, Frankfurt, Germany, paper 20, Sec. 7, 233. Green, D. W., & Perry, R. H. (Eds.). (2007). Perry’s chemical engineers’ handbook. (8th ed.). McGraw-Hill. Haggenmacher, J. E. (1946). Heat of vaporization as a function of temperature. J. Am. Chem. Soc., 68, 1633. Hala, E., Wichterle, I., & Linek, J. (1973). Vapor-liquid equilibrium data bibliography. Elsevier. Supplements: 1, 1976; 2, 1979; 3, 1982, 4, 1985. Hala, E., Wichterle, I., Polak, J., & Boublik, T. (1968). Vapor-liquid equilibrium data at normal pressure. Pergamon. Hirata, M., Ohe, S., & Nagahama, K. (1975). Computer aided data book of vapor-liquid equilibria. Elsevier. Husain, A. (1986). Chemical process simulation. Wiley. Ingham, J., Dunn, I. J., Heinzle, E., Prenosil, J. E., & Snape, J. B. (2007). Chemical engineering dynamics (3rd ed.). Wiley-VCH. Knovel (2003). International Tables of Numerical Data, Physics, Chemistry and Technology (1st electronic ed.). Knovel. Kojima, K., & Tochigi, K. (1979). Prediction of vapor-liquid equilibria by the asog method. Elsevier. Lee, B. I., & Kesler, M. G. (1975). A generalized thermodynamic correlation based on three-parameter corresponding states. AIChemEJL., 21, 510. Leesley, M. E. (Ed.). (1982). Computer aided process plant design. Gulf; 1982. Luyben, W. L. (2006). Distillation design and control using aspen™ Simulation. Wiley. Lydersen, A.L., (1955). Estimation of critical properties of organic compounds. University of Wisconsin Coll. Eng. Exp. Stn. Report 3, University of Wisconsin. Magnussen, T., Rasmussen, P., & Frednenslund, A. (1981). UNIFAC parameter table for prediction of liquidliquid equilibria. Ind. Eng. Chem. Proc. Des. Dev., 20, 331. Meyers, R. A. (2003). Handbook of petroleum refining processes (3rd ed.). McGraw-Hill. Newman, S. A. (1991). Sour water design by charts. Hyd. Proc., 70 (Sept.), 145 (Oct.) 101 (Nov.) 139 (in three parts). Null, H. R. (1970). Phase equilibrium in process design. Wiley. Ohe, S. (1989). Vapor-liquid equilibrium. Elsevier. Ohe, S. (1990). Vapor-liquid equilibrium at high pressure. Elsevier. Pantelides, C. C. (1988). SpeedUp—recent advances in process engineering. Comp. and Chem. Eng., 12, 745. Peng, D. Y., & Robinson, D. B. (1976). A new two constant equation of state. Ind. Eng. Chem. Fund., 15, 59.

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Plocker, U., Knapp, H., & Prausnitz, J. (1978). Calculation of high-pressure vapor-liquid equilibria from a corresponding-states correlation with emphasis on asymmetric mixtures. Ind. Eng. Chem. Proc. Des. Dev., 17, 243. Poling, B. E., Prausnitz, J. M., & O’Connell, J. P. (2000). The properties of gases and liquids (5th ed.). McGraw-Hill. Prausnitz, J. M., & Chueh, P. L. (1968). Computer calculations for high-pressure vapor-liquid equilibria. Prentice-Hall. Prausnitz, J. M., Lichtenthaler, R. N., & Azevedo, E. G. (1998). Molecular thermodynamics of fluid-phase equilibria (3rd ed.). Prentice-Hall. Redlich, O., & Kwong, J.N.S. (1949). The thermodynamics of solutions, V. An equation of state. Fugacities of gaseous solutions. Chem. Rev., 44, 233. Reid, R. C., Prausnitz, J. M., & Poling, B. E. (1987). Properties of liquids and gases (4th ed.). McGraw-Hill. Renon, H., & Prausnitz, J. M. (1969). Estimation of parameters for the non-random, two-liquid equation for excess Gibbs energies of strongly non-ideal liquid mixtures. Ind. Eng. Chem. Proc. Des. Dev, 8(3), 413. Rowley, R.L.,Wilding, W.V., Oscarson, J.L., Yang, W., Zundel, N.A., 2004. DIPPR™ data compilation of pure chemical properties. Design Institute for Physical Properties, AIChE. Seborg, D. E., Edgar, T. F., & Mellichamp, D. A. (2003). Process dynamics and control. Prentice Hall. Soave, G. (1972). Equilibrium constants from modified Redlich-Kwong equation of state. Chem. Eng. Sci., 27, 1197. Sterbacek, Z., Biskup, B., & Tausk, P. (1979). Calculation of properties using corresponding-state methods. Elsevier. Touloukian, Y. S. (Ed.). (1970-77). Thermophysical properties of matter, TPRC Data Services. Plenum Press. 1970-77. Walas, S. M. (1985). Phase equilibrium in chemical engineering. Butterworths. Washburn, E. W. (Eds.). (1933). International critical tables of numerical data, physics, chemistry, and technology (Vols. 8.). McGraw-Hill. Wells, G. L., & Rose, L. M. (1986). The art of chemical process design. Elsevier. Westerberg, A. W., Hutchinson, H. P., Motard, R. L., & Winter, P. (1979). Process flow-sheeting. Cambridge U.P. Wilcon, R. F., & White, S. L. (1986). Selecting the proper model to stimulate vapor-liquid equilibrium. Chem. Eng., NY, 93(Oct. 27th), 142. Wilson, G. M. (1964). A new expression for excess energy of mixing. J. Am. Chem. Soc., 86, 127.

American Standards ASTM D 86, 2007. Standard test method for distillation of petroleum products at atmospheric pressure. ASTM International. ASTM D 2887, 2006. Standard test method for boiling range distribution of petroleum fractions by gas chromatography. ASTM International.

NOMENCLATURE Dimensions in MLT θ A A B

Heat exchanger area Coefficient in the Antoine equation Coefficient in the Antoine equation

L2 — θ

(Continued )

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Dimensions in MLT θ C Cp F FM FP fi fiOL G K Lv Lv,b M P Pc P0i Pr ΔPc q s T Tc Tr ΔTc U ΔVc vLi x x xk y y yM yR z z γ ϕ ϕs

Coefficient in the Antoine equation Specific heat capacity at constant pressure Shell and tube exchanger factor (for non-counter-current flow) Make-up gas molar flow rate Purge gas molar flow rate Fugacity coefficient for component i Standard state fugacity coefficient of pure liquid Molar rate of consumption of gas in reactor Equilibrium constant (ratio) Latent heat of vaporization Latent heat at normal boiling point Molecular mass (weight) Pressure Critical pressure Vapor pressure of component i Reduced pressure Critical constant increment in Lydersen equation (Equation 4.5) Wegstein method acceleration parameter Wegstein method estimate of gradient Temperature, absolute scale Critical temperature Reduced temperature Critical constant increment in Lydersen equation (Equation 4.4) Overall heat transfer coefficient Critical constant increment in Lydersen equation (Equation 4.6) Liquid molar volume Mol fraction, liquid phase Controlled parameter Estimate of parameter x at kth iteration Target value Mol fraction, vapor phase Mole fraction of inerts in make-up Mole fraction of inerts in recycle and purge Target value or unknown variable calculated by simulation program Compressibility factor Liquid activity coefficient Fugacity coefficient Fugacity coefficient of pure component

θ L2T−2θ−1 — MT−1 MT−1 — — MT−1 — L2T−2 L2T−2 M ML−1T−2 ML−1T−2 ML−1T−2 or L — M−1/2L1/2T — — θ θ θ — MT−3θ−1 M−1L3 M−1L3 — — — — — — — — — — — —

(Continued )

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Dimensions in MLT θ Suffixes a, b ) i, j, k 1, 2

Components

—

L V

Liquid Vapor

— —

PROBLEMS 4.1. Monochlorobenzene is produced by the reaction of benzene with chlorine. A mixture of monochlorobenzene and dichlorobenzene is produced, with a small amount of trichlorobenzene. Hydrogen chloride is produced as a by-product. Benzene is fed to the reactor in excess to promote the production of monochlorobenzene. The reactor products are fed to a condenser where the chlorobenzenes and unreacted benzene are condensed. The condensate is separated from the noncondensable gases in a separator. The noncondensables, hydrogen chloride and unreacted chlorine, pass to an absorption column where the hydrogen chloride is absorbed in water. The chlorine leaving the absorber is recycled to the reactor. The liquid phase from the separator, containing chlorobenzenes and unreacted benzene, is fed to a distillation column, where the chlorobenzenes are separated from the unreacted benzene. The benzene is recycled to the reactor. Using the data given below, calculate the stream flows and draw up a preliminary flowsheet for the production of 1.0 tonne (metric ton) of monochlorobenzene per day. Data: Reactor Reactions: C6H6 + Cl2 → C6H5 + HCl C6H6 + 2Cl2 → C6H4 Cl2 + 2HCl mol ratio Cl2 : C6H6 at inlet to reactor = 0.9 overall conversion of benzene = 55.3% yield of monochlorobenzene = 73.6% yield of dichlorobenzene = 27.3% The production of other chlorinated compounds can be neglected. Separator Assume 0.5% of the liquid stream is entrained with the vapor.

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Absorber Assume 99.99% absorption of hydrogen chloride, and that 98% of the chlorine is recycled, the remainder being dissolved in the water. The water supply to the absorber is set to produce a 30% w/w strength hydrochloric acid. Distillation Column Take the recovery of benzene to be 95 per cent, and 99.99% recovery of the chlorobenzenes. Note: This problem can be solved without using process simulation software. Start the mass balance at the reactor inlet (after the recycle streams have been added) and assume 100 kgmol/h of benzene at this point. 4.2. Methyl tertiary butyl ether (MTBE) is used as an antiknock additive in gasoline. It is manufactured by the reaction of isobutene with methanol. The reaction is highly selective and practically any C4 stream containing isobutene can be used as a feedstock CH2 = CðCH3 Þ2 + CH3 OH → ðCH3 Þ3 –C–O–CH3 A 10% excess of methanol is used to suppress side reactions. In a typical process, the conversion of isobutene in the reactor stage is 97%. The product is separated from the unreacted methanol and any C4 compounds by distillation. The essentially pure, liquid, MTBE leaves the base of the distillation column and is sent to storage. The methanol and C4 compounds leave the top of the column as vapor and pass to a column where the methanol is separated by absorption in water. The C4 compounds leave the top of the absorption column, saturated with water, and are used as a fuel gas. The methanol is separated from the water solvent by distillation and recycled to the reactor stage. The water, which leaves the base of the column, is recycled to the absorption column. A purge is taken from the water recycle stream to prevent the build-up of impurities. a. Draw up a block flow diagram for this process. b. Estimate the feeds for each stage. c. Draw a flowsheet for the process. Treat the C4 compounds, other than isobutene, as one component. Data: a. b. c. d. e. f. g.

Feedstock composition, mol%: n-butane = 2, butene-1 = 31, butene-2 = 18, isobutene = 49. Required production rate of MTBE, 7000 kg/h. Reactor conversion of isobutene, 97%. Recovery of MTBE from the distillation column, 99.5%. Recovery of methanol in the absorption column, 99%. Concentration of methanol in the solution leaving the absorption column, 15%. Purge from the water recycle stream, to waste treatment, 10% of the flow leaving the methanol recovery column. h. The gases leave the top of the absorption column saturated with water at 30 °C. i. Both columns operate at essentially atmospheric pressure.

Problems

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4.3. Ethanol can be produced by fermentation of sugars and is used as a gasoline blending component. Because the sugars can be derived from biomass, ethanol is potentially a renewable fuel. In the fermentation of cane sugar to ethanol, sucrose (C11H22O11) is converted by yeast (Saccharomyces cerevisae) to yield ethanol and CO2. Some sucrose is also consumed in maintaining the cell culture in the fermentation reactor. The fermentation reaction can be carried out in a continuous reactor as long as the ethanol concentration does not exceed about 8 wt%, at which point the productivity of the yeast declines significantly. The sucrose is fed as a 12.5 wt% solution in water, which must be sterilized before it can be fed to the reactor. The sterilization is usually accomplished by heating with steam. Carbon dioxide is vented from the fermentation reactor. The liquid product of the fermentation reactor is sent to a hydrocyclone to concentrate the yeast for recycle to the reactor. The remaining liquid is sent to a distillation column known as a “beer column,” which concentrates the alcohol to about 40 mol% ethanol and 60 mol% water in the distillate. The recovery of ethanol in the beer column is 99.9%. The bottoms stream from the beer column contains the remaining components of the fermentation broth and can be processed for use as animal feed. a. Draw a flowsheet for this process. b. Estimate the stream flow rates and compositions for a production rate of 200,000 US gal/d of dry (100%) ethanol. c. Estimate the ethanol lost in the CO2 vent gas. d. Estimate the reboiler duty of the beer column. Data: a. Yield per kg sucrose: ethanol 443.3g, CO2 484g, non-sugar solids 5.3g, yeast 21g, fermentation by-products 43.7g, higher alcohols (fusel oil) 2.6g. b. Conversion of sucrose, 98.5%. c. Yeast concentration in fermentation reactor at steady state, 3 wt%. d. Fermenter temperature, 38 °C. 4.4. In an ethanol plant, the mixture of water and ethanol from the beer column distillate contains about 40% ethanol (molar basis) in water, together with the fusel oils described in the previous problem. This mixture is distilled to give an azeotropic mixture of ethanol and water (89% ethanol) overhead, with 99.9% recovery of ethanol. The fusel oil can cause blending problems if it is allowed to accumulate in the distillate. Fusel oil is a mixture of higher alcohols and ethers that can be approximated as a mixture of n-butanol and diethyl ether. This mixture is usually removed as a side stream from the column. When the side stream is contacted with additional water, a two-phase mixture can be formed and the oil phase can be decanted to leave an ethanol-water phase that is returned to the column. 1. Draw a flowsheet for this process. 2. Estimate the stream flow rates and compositions for a production rate of 200,000 US gal/d of dry (100%) ethanol. 3. Optimize the distillation column using the cost correlations given in Section 6.3 and assuming that reboiler heat costs $5/MMBtu. Minimize the total annualized cost of the column.

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4.5. Water and ethanol form a low boiling point azeotrope; hence, water cannot be completely separated from ethanol by conventional distillation. To produce absolute (100%) ethanol, it is necessary to add an entraining agent to break the azeotrope. Benzene is an effective entrainer and is used where the product is not required for food products. Three columns are used in the benzene process. Column 1. This column separates the ethanol from the water. The bottom product is essentially pure ethanol. The water in the feed is carried overhead as the ternary azeotrope of ethanol, benzene, and water (roughly 24% ethanol, 54% benzene, 22% water). The overhead vapor is condensed and the condensate separated in a decanter into a benzene-rich phase (22% ethanol, 74% benzene, 4% water) and a water-rich phase (35% ethanol, 4% benzene, 61% water). The benzene-rich phase is recycled to the column as reflux. A benzene make-up stream is added to the reflux to make up any loss of benzene from the process. The water-rich phase is fed to the second column. Column 2. This column recovers the benzene as the ternary azeotrope and recycles it as vapor to join the overhead vapor from the first column. The bottom product from the column is essentially free of benzene (29% ethanol, 51% water). This stream is fed to the third column. Column 3. In this column, the water is separated and sent to waste treatment. The overhead product consists of the azeotropic mixture of ethanol and water (89% ethanol, 11% water). The overheads are condensed and recycled to join the feed to the first column. The bottom product is essentially free of ethanol. 1. Draw a flowsheet for this process. 2. Estimate the stream flow rates and compositions for a production rate of 200,000 US gal/d of dry (100%) ethanol. 3. Estimate the ethanol lost in the CO2 vent gas. Take the benzene losses to total 0.1 kmol/h. All the compositions given are molar percentages. 4.6. A plant is required to produce 10,000 tonnes per year of anhydrous hydrogen chloride from chlorine and hydrogen. The hydrogen source is impure: 90 mol% hydrogen, balance nitrogen. The chlorine is essentially pure chlorine, supplied in rail tankers. The hydrogen and chlorine are reacted in a burner at 1.5 bar pressure. H2 + Cl2 → 2HCl Hydrogen is supplied to the burner in 3% excess over the stoichiometric amount. The conversion of chlorine is essentially 100%. The gases leaving the burner are cooled in a heat exchanger. The cooled gases pass to an absorption column where the hydrogen chloride gas is absorbed in dilute hydrochloric acid. The absorption column is designed to recover 99.5% of the hydrogen chloride in the feed. The unreacted hydrogen and inerts pass from the absorber to a vent scrubber where any hydrogen chloride present is neutralized by contact with a dilute, aqueous solution of sodium hydroxide. The solution is recirculated around the scrubber. The concentration of sodium hydroxide is maintained at 5% by taking a purge from the recycle loop and introducing a make-up stream of 25% concentration. The maximum concentration of hydrogen chloride discharged in the gases vented from the scrubber to atmosphere must not exceed 200 ppm (parts per million) by volume.

Problems

247

The strong acid from the absorption column (32% HCl) is fed to a stripping column where the hydrogen chloride gas is recovered from the solution by distillation. The diluted acid from the base of this column (22% HCl) is recycled to the absorption column. The gases from the top of the stripping column pass through a partial condenser, where the bulk of the water vapor present is condensed and returned to the column as reflux. The gases leaving the column will be saturated with water vapor at 40 °C. The hydrogen chloride gas leaving the condenser is dried by contact with concentrated sulfuric acid in a packed column. The acid is recirculated over the packing. The concentration of sulfuric acid is maintained at 70% by taking a purge from the recycle loop and introducing a make-up stream of strong acid (98% H2SO4). The anhydrous hydrogen chloride product is compressed to 5 bar and supplied as a feed to another process. Using the information provided, calculate the flow rates and compositions of the main process streams, and draw a flowsheet for this process. All compositions are wt%, except where indicated. 4.7. Ammonia is synthesized from hydrogen and nitrogen. The synthesis gas is usually produced from hydrocarbons. The most common raw materials are oil or natural gas, though coal and even peat can be used. When produced from natural gas, the synthesis gas will be impure, containing up to 5% inerts, mainly methane and argon. The reaction equilibrium and rate are favored by high pressure. The conversion is low, about 15%, and so, after removal of the ammonia produced, the gas is recycled to the converter inlet. A typical process consists of: a converter (reactor) operating at 350 bar; a refrigerated system to condense out the ammonia product from the recycle loop; and compressors to compress the feed and recycle gas. A purge is taken from the recycle loop to keep the inert concentration in the recycle gas at an acceptable level. Using the data given below, draw a flow diagram of the process and calculate the process stream flow rates and compositions for the production of 600 t/d ammonia. Data: Composition of synthesis gas, mol fraction: N2 24.5

H2 73.5

CH4 1.7

A 0.3

Temperature and operating pressure of liquid ammonia—gas separator, 340 bar and −28°C. Inert gas concentration in recycle gas, not greater than 15 mol%. 4.8. Methyl ethyl ketone (MEK) is manufactured by the dehydrogenation of 2-butanol. A simplified description of the process listing the various units used is given below: 1. A reactor in which the butanol is dehydrated to produce MEK and hydrogen, according to the reaction CH3 CH2 CH3 CHOH → CH3 CH2 CH3 CO + H2 The conversion of alcohol is 88% and the selectivity to MEK can be taken as 100%.

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2. A cooler-condenser, in which the reactor off-gases are cooled and most of the MEK and unreacted alcohol are condensed. Two exchangers are used but they can be modeled as one unit. Of the MEK entering the unit, 84% is condensed, together with 92% of the alcohol. The hydrogen is noncondensable. The condensate is fed forward to the final purification column. 3. An absorption column, in which the uncondensed MEK and alcohol are absorbed in water. Around 98% of the MEK and alcohol can be considered to be absorbed in this unit, giving a 10 wt% solution of MEK. The water feed to the absorber is recycled from the next unit, the extractor. The vent stream from the absorber, containing mainly hydrogen, is sent to a flare stack. 4. An extraction column, in which the MEK and alcohol in the solution from the absorber are extracted into trichloroethane (TCE). The raffinate, water containing around 0.5 wt% MEK, is recycled to the absorption column. The extract, which contains around 20 wt% MEK, and a small amount of butanol and water, is fed to a distillation column. 5. A distillation column, which separates the MEK and alcohol from the solvent TCE. The recovery of MEK is 99.99%. The solvent containing a trace of MEK and water is recycled to the extraction column. 6. A second distillation column, which produces a 99.9% pure MEK product from the crude product from the first column. The residue from this column, which contains the bulk of the unreacted 2-butanol, is recycled to the reactor. For a production rate of 1250 kg/h MEK: 1. 2. 3. 4.

Draw a flowsheet for the process. Estimate the stream flow rates and compositions. Estimate the reboiler and condenser duties of the two distillation columns. Estimate the number of theoretical trays required in each column.

4.9. In the problem of Example 4.4, the feed was specified as pentane (C5H12) with a hydrogen to carbon ratio of 2.4:1. If the feed to the process were a heavy oil, the hydrogen to carbon ratio would be more like 2:1. How would the distribution of C5 carbon compounds change if the feed had a 2:1 carbon ratio? 4.10. Example 4.4 examined the equilibrium distribution of hydrocarbon compounds within a single carbon number (C 5 ). In reality, cracking reactions to ethylene, propylene, and other light alkenes and alkynes will have a significant effect on the yield of a cracking process. 1. What is the effect of including C2 and C3 compounds on the equilibrium distribution? 2. What is the effect of including coke (carbon) as well as the C2 and C3 compounds? 3. What do these results tell you about cracking processes? 4.11. Optimize the heat exchanger design of Example 4.8 to minimize the total surface area required.

Problems

249

4.12. A stream containing 4 metric tons/h of a 20 wt% mixture of benzene in toluene is heated from 20 °C to the bubble point at 4 atm pressure. The mixture is separated in a distillation column to give 99.9% recovery of benzene overhead and toluene in the bottoms. 1. If the toluene product must be cooled to 20 °C, how much of the feed heat can be supplied by heat exchange with the bottoms? 2. How many heat exchange shells are needed? 3. What is the minimum total heat exchange area? 4. What is the distillation column diameter? 5. How many sieve trays are needed if the tray efficiency is 70%? 4.13. The autothermal reforming of methane to hydrogen was described in Example 4.5. The solution in the example was not optimized, and suggestions were given for how to improve the results. Optimize the process to minimize the cost of production of hydrogen, assuming: 1. 2. 3. 4. 5. 6.

Cost of methane = 16 ¢/lb Cost of oxygen = 2 ¢/lb Cost of water = 25 ¢/1000 lb Annualized cost of heat exchangers = $ 30,000 + 3 A, where A is the area in ft2 Cost of electric power = 6 ¢/kWh Reactor and catalyst costs are the same in all cases.

Hint: First determine the optimal heat recovery and steam and oxygen to methane ratios for a given methane conversion. Repeat for different methane conversions to find the overall optimum. 4.14. The light naphtha isomerization process is more complex than the description given in Example 4.10. 1. Hydrogen is flowed through the plant to reduce catalyst deactivation. The hydrogen flow rate is typically about 2 moles per mole of hydrocarbon on a pure hydrogen basis. The hydrogen make-up gas is typically about 90 mol% hydrogen, with the balance methane. 2. Light hydrocarbon compounds are formed by cracking reactions. These compounds accumulate in the hydrogen recycle and are controlled by taking a purge stream. A stabilizer column is also required, upstream of the distillation column, to remove light hydrocarbons and hydrogen before the distillation. 3. Each of the C6 isomers has a different blending octane value. The total octane value of the product can be found by summing the products of the mole fraction of each component and the component blending value. The blending values are: n-hexane 60; 2-methyl pentane 78.5; 3-methyl pentane 79.5; 2,2-dinethyl butane 86.3; 2,3-dimethyl butane 93. Optimize the design of Example 4.10, subject to the following: 1. The selectivity loss due to cracking reactions can be approximated as 1% conversion of C6 compounds to propane per reactor pass. 2. The wholesale value of gasoline can be assumed to be 2.0 + 0.05 (octane number – 87) $/US gal.

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3. The cost of hydrogen is $6/1000 scf, and the fuel value of the hydrogen and propane purge stream is $5/MMBtu. 4. The reactor plus catalyst total installed cost can be taken as $0.5 MM per 1000 bpd of liquids processed. 5. Other costs can be estimated using the cost correlations given in Table 7.2. 4.15. The composition of the feed to a debutanizer is given below. The column will operate at 14 bar and below 750 K. The process is to be modeled using a commercial simulation program. Suggest a suitable phase-equilibrium method to use in the simulation. Feed composition: kg/h Propane Isobutane n-butane Isopentane normal pentane normal hexane

C3 i-C4 n-C4 i-C5 n-C5 n-C6

910 180 270 70 90 20

4.16. The product specifications for Problem 4.15 are 99.5% recovery of C5+ in the bottoms and 99% recovery of C4 and lighter compounds in the distillate. Your company’s corporate engineering standard is to design for a reflux ratio of 1.15 times the minimum reflux and to assume a stage efficiency of 60%. Using rigorous simulation, determine the number of trays, feed tray, and reboiler duty for this column. 4.17. In the manufacture of methyl ethyl ketone from butanol, the product is separated from unreacted butanol by distillation. The feed to the column consists of a mixture of methyl ethyl ketone, 2-butanol, and trichloroethane. What would be a suitable phase equilibrium correlation to use in modeling this process? Additional flowsheeting problems are given in the form of design projects in Appendices E and F. Additional reaction and distillation simulation problems are given in Chapters 15 and 17, respectively.

CHAPTER

Instrumentation and Process Control

KEY LEARNING OBJECTIVES • How to read a piping and instrument diagram drawn using ISA 5.1 symbols • How to design control schemes for common unit operations and whole processes

5.1 INTRODUCTION The process flowsheet shows the arrangement of the major pieces of equipment and their interconnection. It is a description of the nature of the process. The piping and instrument diagram (P&I diagram or PID) shows the engineering details of the equipment, instruments, piping, valves, and fittings and their arrangement. It is often called the engineering flowsheet or engineering line diagram. This chapter covers the preparation of the preliminary P&I diagrams at the process design stage of the project. Some process control information is also indicated on the process flow diagram (PFD). It is common practice to show control valves on the PFD, but to omit isolation valves, relief valves, and instrumentation details. Control valves require a significant pressure drop to operate effectively, so the location of control valves will often indicate a need for additional pumps or compressors. In some cases, process control considerations may even lead to the addition of vessels to the flowsheet; for instance, when a surge tank is added to smooth out operation between batch and continuous sections of the plant. The design of piping systems, and the specification of the process instrumentation and control systems, is usually done by specialist design groups, and a detailed discussion of control systems is beyond the scope of this book. Only general guide rules are given. The piping handbook edited by Nayyar (2000) and the process automation handbook by Love (2007) are particularly recommended for guidance on the detailed design of piping systems and process instrumentation and control. The references cited in the text and listed at the end of the chapter should also be consulted. The detailed design of piping systems, valves, and plant hydraulics and the sizing and selection of control valves are discussed in more detail in Chapter 20.

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5.2 THE P&I DIAGRAM The P&I diagram shows the arrangement of the process equipment, piping, pumps, instruments, valves, and other fittings. It should include: 1. All process equipment identified by an equipment number. The equipment should be drawn roughly in proportion, and the location of nozzles shown. 2. All pipes, identified by a line number. The pipe size and material of construction should be shown. The material may be included as part of the line identification number. 3. All valves: control and block valves, with an identification number. The type and size should be shown. The type may be shown by the symbol used for the valve or included in the code used for the valve number. 4. Ancillary fittings that are part of the piping system, such as inline sight-glasses, strainers, and steam traps, with an identification number. 5. Pumps, identified by a suitable code number. 6. All control loops and instruments, with an identification number. For simple processes, the utility (service) lines can be shown on the P&I diagram. For complex processes, separate diagrams should be used to show the service lines, so the information can be shown clearly, without cluttering up the diagram. The service connections to each unit should, however, be shown on the P&I diagram. The P&I diagram will resemble the process flowsheet, but the process information is not shown. The same equipment identification numbers should be used on both diagrams.

5.2.1 Symbols and Layout The symbols used to show the equipment, valves, instruments, and control loops will depend on the practice of the particular design office. The equipment symbols are usually more detailed than those used for the process flowsheet. A typical example of a P&I diagram is shown in Figure 5.22 at the end of this chapter. The most widely-used international standard symbols for instruments, controllers, and valves are those given by the Instrumentation Systems and Automation Society design code ISA 5.1-1984 (R1992). Some companies use their own symbols though, and different standards are followed in some countries, such as BS 1646 in the United Kingdom and DIN 19227 and DIN 2429 in Germany. When laying out the diagram, it is only necessary to show the relative elevation of the process connections to the equipment where these affect the process operation; for example, the net positive suction head (NPSH) of pumps, barometric legs, siphons, and the operation of thermosiphon reboilers. Full details of pipe layout are usually shown in a different drawing, known as a piping isometric drawing. See Figure 20.21 for an example. Computer aided drafting programs are available for the preparation of P&I diagrams. Microsoft Visio™ Professional edition contains a library of P&I diagram symbols.

5.2.2 Basic Symbols The symbols illustrated below in Figures 5.1 to 5.7 are those given in ISA 5.1-1984 (R1992).

5.2 The P&I Diagram

253

Control Valves Different types of valves are shown in Figure 5.1 and discussed in Section 20.5.

General

Three-way

Globe

Diaphragm

FIGURE 5.1 Control valves.

Actuators Actuator symbols are illustrated in Figure 5.2. Most modern control valves (final control elements) are actuated by electric motors, but older valves are actuated by pneumatic signals using instrument air. Pneumatic actuators are preferred in situations where electronic controllers might cause a process hazard or where electric power is not available or reliable. Pneumatic controllers are also found in many older plants where replacement with electronic controllers has not yet occurred. Motor actuators are used for larger valves, while digital and solenoid actuators are used for valves that switch from open to closed, as often occurs in batch processing. Many newer controllers use a combination of these approaches. For example, a digital signal can be sent to a solenoid that opens or shuts an instrument air line that then actuates a pneumatically-driven control valve.

Diaphragm or unspecified actuator

Solenoid

Digital

Rotary motor

FIGURE 5.2 Actuators.

Instrument Lines The instrument connecting lines are drawn in a manner to distinguish them from the main process lines, as shown in Figure 5.3. Process lines are drawn as solid lines and are usually drawn thicker. The undefined signal symbol is often used when indicating controllers in a PFD, as the instrument design may not have been specified when the PFD was first drawn.

Failure Mode The direction of the arrow shows the position of the valve on failure of the power supply; see Figure 5.4.

General Instrument and Controller Symbols General instrument symbols are shown in Figure 5.5. Locally mounted means that the controller and display are located out on the plant near the sensing instrument location. Main panel means that they are located on a panel in the control room. Except on small plants, most controllers would be mounted in the control room.

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Instrument supply or connection to process Undefined signal Pneumatic signal

Electric signal

Electric binary (on-off) signal

Internal system link (software or data link) All lines should be drawn fine in relation to process piping lines

FIGURE 5.3 Instrument lines.

Fails open

Fails closed

Fails locked in current position

Panel mounted in primary location

Panel mounted in auxiliary location (local panel)

Failure mode indeterminate

FIGURE 5.4 Valve failure modes.

Field mounted

Dual function instrument

FIGURE 5.5 General instrument and controller symbols.

Distributed Control—Shared Display Symbols Symbols for shared displays and programmable logic controllers are shown in Figure 5.6. A distributed control system is a system that is functionally integrated, but consists of subsystems that may be physically separate and remotely located from one another. A shared display is an operator interface device such as a computer screen or video screen that is used to display process

5.2 The P&I Diagram

255

Field mounted shared display device with limited access to adjustments

Shared display device with operator access to adjustments *AH *AL

Shared display device with software alarms (* is measured variable)

Programmable logic controller accessible to operator

Field mounted programmable logic controller

FIGURE 5.6 Shared display symbols for distributed control and logic control.

control information from a number of sources at the command of the operator. Most plants built since 1990 (and many older plants) use shared displays instead of instrument panels. Programmable logic controllers are used to control discrete operations, such as steps in a batch or semi-continuous process, and to program interlock controls that guard against unsafe or uneconomic conditions. For example, a logic controller could be used to ensure that an operator cannot open an air vent line to a vessel unless the feed valves are closed and nitrogen purge is open.

Other Common Symbols Other symbols commonly encountered on a P&I diagram are shown in Figure 5.7.

Restriction orifice

Pressure relief or safety valve

Self-contained backpressure regulator

Stop check (nonreturn) valve

Hand control valve

Gate valve or isolation valve

FIGURE 5.7 Other common symbols.

Type of Instrument This is indicated on the circle representing the instrument-controller by a letter code (see Table 5.1).

256

Initiating or Measured Variable Analysis (composition) Flow rate Flow ratio Power Level Pressure, vacuum Pressure differential Quantity Radiation Temperature Temperature differential Weight

Controllers

First Letter

Indicating Only

Recording

Indicating

Blind

Transmitters

Final Control Element

A F FF J L P PD Q R T TD W

AI FI FFI JI LI PI PDI QI RI TI TDI WI

ARC FRC FFRC JRC LRC PRC PDRC QRC RRC TRC TDRC WRC

AIC FIC FFIC JIC LIC PIC PDIC QIC RIC TIC TDIC WIC

AC FC FFC

AT FT FFT JT LT PT PDT QT RT TT TDT WT

AV FV FFV JV LV PV PDV QZ RZ TV TDV WZ

Notes: (1) The letters C, D, G, M, N and O are not defined and can be used for any user-specified property. (2) The letter S as second or subsequent letter indicates a switch. (3) The letter Y as second or subsequent letter indicates a relay or a compute function. (4) The letter Z is used for the final control element when this is not a valve. Consult the standard for the full set of letter codes.

LC PC PDC RC TC TDC WC

CHAPTER 5 Instrumentation and Process Control

Table 5.1 Letter Code for Instrument Symbols (Based on ISA-5.1-1984 (R1992))

5.3 Process Instrumentation and Control

PAH PAL

257

PIC

FIGURE 5.8 A typical control loop.

The first letter indicates the property measured; for example, F = flow. Subsequent letters indicate the function; for example, I = indicating RC = recorder controller The letters AH or AL indicate high or low alarms. The P&I diagram shows all the components that make up a control loop. For example, Figure 5.8 shows a field located pressure transmitter connected to a shared display pressure indicator-controller with operator access to adjustments and high and low alarms. The pressure controller sends an electric signal to a fail-closed diaphragm-actuated pressure control valve.

5.3 PROCESS INSTRUMENTATION AND CONTROL 5.3.1 Instruments

Instruments are provided to monitor the key process variables during plant operation. They may be incorporated in automatic control loops, or used for manual monitoring of process operation. In most modern plants, the instruments will be connected to a computer control and data logging system. Instruments monitoring critical process variables will be fitted with automatic alarms to alert the operators to critical and hazardous situations. Details of process instruments and control equipment can be found in various handbooks, such as Green and Perry (2007), Love (2007), and Liptak (2003). Reviews of process instruments and control equipment are published periodically in the journals Chemical Engineering and Hydrocarbon Processing. These reviews give details of instruments and control hardware available commercially. Table 5.2 summarizes some of the more commonly-used types of instruments encountered in chemical plants. It is desirable that the process variable that is to be monitored should be measured directly; however, this is often impractical and some dependent variable that is easier to measure is monitored in its place. For example, in the control of distillation columns the continuous, online, analysis of the overhead product is desirable but is difficult and expensive to achieve reliably, so temperature is

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Table 5.2 Commonly Used Process Instruments Measured Variable

Instrument Type

Pressure (gauge)

Differential pressure (DP) cell

Pressure difference Temperature

DP cell

Volumetric flow

Orifice meter

Volumetric flow

Venturi meter

Mass flow

Coriolis meter

Level

DP cell

Level

Capacitance probe

Interface level

DP cell

Glass electrode

Composition

Chromatograph

Thermocouple

Operating Principle Pressure difference causes displacement of a diaphragm. The displacement can be transmitted mechanically to a bellows to register a pneumatic signal or converted to an electrical signal by a strain gauge or by movement of the diaphragm relative to a static capacitor plate. Gauge pressure is measured relative to atmospheric pressure. As above. Pressure difference is measured between two points in the process. Wires of different metals joined together to form a circuit with one joint hotter than the other will develop an EMF through the Seebeck effect. If one joint is at a reference temperature the other temperature can be found from the EMF. The reference temperature is usually ambient temperature, which is determined by measuring the electrical resistance of a platinum wire. Different combinations of metal wire are used depending on the temperature range. See Love (2007) for details of thermocouple types. Flow passes through a restriction orifice. Pressure difference across the orifice is measured with a DP cell. Flow rate is calculated from pressure drop. Flow passes through a shaped pipe restriction. Pressure difference across the restriction is measured with a DP cell. Flow rate is calculated from pressure drop. Flow through a shaped vibrating pipe loop causes it to twist due to the Coriolis effect. The extent of twist is measured optically. These instruments can be used for multiphase flow, but are expensive, particularly for large flow rates. A DP cell placed between the top and bottom of a vessel can indicate level if there is no internal pressure drop in the vessel. The capacitance between a probe in the center of the vessel and the wall is affected by the dielectric constant of the material between them, and so varies with level. A DP cell can determine the interface level between immiscible fluids if they are in a vessel that has an internal weir (so that overall level remains constant). The glass electrode and a reference electrode (usually silver/silver chloride) form an electrochemical circuit allowing EMF to be measured. Gas chromatography (GC) can be used to separate simple mixtures and generate a signal through a thermal conductivity detector (TCD) or flame ionization detector (FID). GC methods are difficult to use for online control because the chromatography typically takes a few minutes, but they can be used in cascade control schemes to adjust set points on other controllers.

5.3 Process Instrumentation and Control

259

often monitored as an indication of composition. The temperature instrument may form part of a control loop controlling, say, reflux flow, with the composition of the overheads checked frequently by automated sampling and online GC analysis.

5.3.2 Instrumentation and Control Objectives The primary objectives of the designer when specifying instrumentation and control schemes are: 1. Safe plant operation: a. To keep the process variables within known safe operating limits. b. To detect dangerous situations as they develop and to provide alarms and automatic shutdown systems. c. To provide interlocks and alarms to prevent dangerous operating procedures. 2. Production rate: To achieve the design product output. 3. Product quality: To maintain the product composition within the specified quality standards. 4. Cost: To operate at the lowest production cost, commensurate with the other objectives. 5. Stability: To maintain steady, automatic plant operation with minimal operator intervention. These are not separate objectives and must be considered together. The order in which they are listed is not meant to imply the precedence of any objective over another, other than that of putting safety first. Product quality, production rate, and the cost of production will be dependent on sales requirements. For example, it may be a better strategy to produce a better-quality product at a higher cost. In a typical chemical processing plant these objectives are achieved by a combination of automatic control, manual monitoring, and laboratory and online analysis.

5.3.3 Automatic Control Schemes The detailed design and specification of the automatic control schemes for a large project is usually done by specialists. The basic theory underlying the design and specification of automatic control systems is covered in several texts: Coughanowr (1991), Shinskey (1984), (1996), Luyben, Tyreus, and Luyben (1999), Henson, Seborg, and Hempstead (1996), Seborg, Edgar, and Mellichamp (2004), Love (2007), and Green and Perry (2007). The books by Murrill (1988), Shinskey (1996), Kalani (2002), and Love (2007) cover many of the more practical aspects of process control system design, and are recommended. In this chapter only the first step in the specification of the control systems for a process will be considered: the preparation of a preliminary scheme of instrumentation and control, developed from the process flowsheet. This can be drawn up by the process designer based on experience with similar plants and critical assessment of the process requirements. Many of the control loops will be conventional and a detailed analysis of the system behavior will not be needed, nor justified. Judgment, based on experience, must be used to decide which systems are critical and need detailed analysis and design.

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Some examples of typical (conventional) control systems used for the control of specific process variables and unit operations are given in the next section, and can be used as a guide in preparing preliminary instrumentation and control schemes.

Guide Rules The following procedure can be used when drawing up preliminary P&I diagrams: 1. Identify and draw in those control loops that are obviously needed for steady plant operation, such as a. level controls, b. flow controls, c. pressure controls, d. temperature controls. 2. Identify the key process variables that need to be controlled to achieve the specified product quality. Include control loops using direct measurement of the controlled variable, where possible; if not practicable, select a suitable dependent variable. 3. Identify and include those additional control loops required for safe operation, not already covered in steps 1 and 2. 4. Decide and show those ancillary instruments needed for the monitoring of plant operation by the operators and for troubleshooting and plant development. It is well worth including additional connections for instruments that may be needed for future troubleshooting and development, even if the instruments are not installed permanently. These would include extra thermowells, pressure taps, orifice flanges, and sample points. 5. Decide on the location of sample points. 6. Decide on the type of control instrument that will be used, including whether it will be a local instrument or tied into the plant computer control system. Also decide on the type of actuator that can be used, the signal system, and whether the instrument will record data. This step should be done in conjunction with steps 1 to 4. 7. Decide on the alarms and interlocks needed; this should be done in conjunction with step 3 (see Chapter 10). In step 1 it is important to remember the following basic rules of process control: • • • • • •

There can only be a single control valve on any given stream between unit operations. A level controller is needed anywhere a vapor-liquid or liquid-liquid interface is maintained. Pressure control is more responsive when the pressure controller actuates a control valve on a vapor stream. Two operations cannot be controlled at different pressures unless there is a valve or other restriction (or a compressor or pump) between them. Temperature control is usually achieved by controlling the flow of a utility stream (such as steam or cooling water) or a bypass around an exchanger. The overall plant material balance is usually set by flow controllers or flow ratio controllers on the process feeds. There cannot be an additional flow controller on an intermediate stream unless there is provision for accumulation (surge), such as an intermediate storage tank.

Some simple examples of control schemes for common unit operations are given in the next section.

5.4 Conventional Control Schemes

261

5.4 CONVENTIONAL CONTROL SCHEMES 5.4.1 Level Control

In any equipment where an interface exists between two phases (e.g. a liquid and a vapor), some means of maintaining the interface at the required level must be provided. This may be incorporated in the design of the equipment, for example by providing an internal weir, or by automatic control of the flow from the equipment. Figure 5.9 shows a typical arrangement for the level control at the base of a column. The control valve should be placed on the discharge line from the pump.

5.4.2 Pressure Control Pressure control will be necessary for most systems handling vapor or gas. The method of control depends on the nature of the process. Typical schemes are shown in Figures 5.10(a), (b), (c), and (d). The scheme shown in Figure 5.10(a) would not be used where the vented gas was toxic or valuable. In these circumstances the vent should be taken to a vent recovery system, such as a scrubber. The controls shown in Figure 5.10(b), (c), and (d) are commonly used for controlling the pressure of distillation columns. In processes that have a high-pressure reaction section and low-pressure separation section, the highpressure section is usually pressure controlled by expanding the product from the high-pressure section across a control valve. If the process fluid does not change phase, then a more economical scheme is to expand the product through a turbine or turbo-expander and recover shaft work from the expansion.

5.4.3 Flow Control Flow control is usually associated with inventory control in a storage tank or other equipment or with feeds to the process. There must be a reservoir upstream of the control valve to take up the changes in flow rate.

FIGURE 5.9 Level control.

LAH LAL

LIC

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CHAPTER 5 Instrumentation and Process Control

PV PV

PIC

(a)

(b) PIC

Coolant

PT Process

PV (c)

PIC

Process vapor

Coolant (d)

FIGURE 5.10 (a) Pressure control by direct venting; (b) venting of noncondensables after a condenser; (c) condenser pressure control by controlling coolant flow; (d) pressure control of a condenser by varying the heat-transfer area, area dependent on liquid level.

To provide flow control on a compressor or pump running at a fixed speed and supplying a near constant volume output, a bypass control would be used, as shown in Figure 5.11(a). The use of variable speed motors as shown in Figure 5.11(c) is more energy efficient than the traditional arrangement shown in Figure 5.11(b), and is becoming increasingly common; see Hall (2010). The overall process material balance is usually set by flow controllers on the feed streams. These will often control feeds in ratio to a flow of valuable feed, a solid stream flow (which is difficult to change quickly), or a measured flow of process mixture. Flow rates of small streams are often controlled using special metering pumps that deliver a constant mass flow rate. The design of pump and control valve systems to assure a desired process flow rate and range of controllability is discussed in more detail in Chapter 20.

5.4.4 Heat Exchangers Figure 5.12(a) shows the simplest arrangement, the temperature being controlled by varying the flow of the cooling or heating medium.

5.4 Conventional Control Schemes

263

FIC FY FV FI

(a) FIC

FIC FV PI

M (b)

(c)

FIGURE 5.11 (a) Spill-back flow control for a reciprocating pump; (b) flow control for a centrifugal pump; (c) centrifugal pump with variable speed drive.

If the exchange is between two process streams whose flows are fixed, bypass control will have to be used, as shown in Figure 5.12(b). For air coolers, the coolant temperature may vary widely on a seasonal (or even hourly) basis. A bypass on the process side can be used as shown in Figure 5.12(c), or else a variable speed motor can be used as shown in Figure 5.12(d).

Condenser Control Temperature control is unlikely to be effective for condensers, unless the liquid stream is subcooled. Pressure control is often used, as shown in Figure 5.10(d), or control can be based on the outlet coolant temperature.

Reboiler and Vaporizer Control As with condensers, temperature control is not effective, as the saturated vapor temperature is constant at constant pressure. Level control is often used for vaporizers; the controller controls the steam supply to the heating surface, with the liquid feed to the vaporizer on flow control, as shown in Figure 5.13. An increase in the feed results in an automatic increase in steam to the vaporizer to vaporize the increased flow and maintain the level constant.

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Hot or cold utility

Process TE

TIC

TV (a)

TIC

(b)

TO VARIABLE SPEED MOTOR CONTROL CIRCUIT

TIC

(c)

TIC

(d)

FIGURE 5.12 (a) Temperature control of one fluid stream; (b) bypass control; (c) air cooler with bypass control; (d) air cooler with variable speed drive.

Vapor

FIC LIC FT

FV LV LT

Feed Steam Trap Condensate

FIGURE 5.13 Vaporizer control.

5.4 Conventional Control Schemes

265

Reboiler control systems are selected as part of the general control system for the distillation column and are discussed in Section 5.4.7.

5.4.5 Cascade Control With this arrangement, the output of one controller is used to adjust the set point of another. Cascade control can give smoother control in situations where direct control of the variable would lead to unstable operation. The “slave” controller can be used to compensate for any short-term variations in, say, a utility stream flow, which would upset the controlled variable, the primary (“master”) controller controlling long-term variations. Typical examples are shown in Figures 5.18 and 5.19.

5.4.6 Ratio Control Ratio control can be used where it is desired to maintain two flows at a constant ratio; for example, reactor feeds or distillation column reflux. A typical scheme for ratio control is shown in Figure 5.14.

5.4.7 Distillation Column Control The primary objective of distillation column control is to maintain the specified composition of the top and bottom products and any side streams, correcting for the effects of disturbances in: 1. 2. 3. 4.

Feed flow rate, composition, and temperature Steam or other hot utility supply Cooling water or air cooler conditions Ambient conditions, which can cause cooling of the column shell and changes in internal reflux (see Chapter 17).

The feed flow rate is often set by the level controller on a preceding column. It can be independently controlled if the column is fed from a storage or surge tank. Feed temperature is not normally controlled, unless a feed preheater is used.

FFC FFV FT

FIGURE 5.14 Ratio control.

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CHAPTER 5 Instrumentation and Process Control

In the usual case where the feed rate is set by upstream operations and the column produces a liquid distillate product, there are five control valves, and hence five degrees of freedom; see Figure 5.15. One degree of freedom is used to set the column pressure, usually by control of the condenser using one of the schemes shown in Figure 5.10. Column pressure is normally controlled at a constant value, which then sets the vapor inventory in the column. The use of variable pressure control to conserve energy has been discussed by Shinskey (1976). Two degrees of freedom are needed to control the liquid inventories by controlling the vapor-liquid level in the column sump and the reflux drum (or condenser if no reflux drum is used). The remaining two degrees of freedom can be used to achieve the desired separation, either in terms of product purity or recovery, by adjusting two flow rates. One of these flows is controlled by a flow or flow ratio controller to achieve the desired split between distillate and bottoms, while the other is usually controlled by a column temperature to achieve a desired composition in one of the products. The flow controller cannot be on the distillate or bottoms stream if the designer intends to control composition, as it would then be impossible to maintain product composition if there were changes in feed composition. The temperature controller can, however, control either the distillate or bottoms flow rate. The usual practice is to control a top temperature by varying the reflux ratio or distillate flow rate if the overhead product purity is more important (Figure 5.16), or control a bottom temperature by varying the boil-up rate or bottoms flow if bottoms purity is more important (Figure 5.17).

Coolant Distillate Reflux

Feed

Steam

Bottoms

FIGURE 5.15 Control valves and degrees of freedom for a simple distillation column.

5.4 Conventional Control Schemes

267

LC LC

LC FC

(a)

(b)

FIGURE 5.16 Material balance control schemes for controlling overhead product composition. Flow control on reboiler can be in ratio to feed if feed rate varies. (a) Direct control of distillate by composition; (b) indirect control of distillate, composition controls reflux.

Control schemes of this type are commonly referred to as material balance control schemes, as they achieve the desired product purity by manipulating the column material balance. These schemes are very robust for processes where the feed flow rate to the column is relatively constant but the composition varies and close control must be maintained on one product composition. Temperature is usually used as an indication of composition. The temperature sensor should be located at a position in the column where the rate of change of temperature with change in composition of the key component is a maximum; see Parkins (1959). Near the top and bottom of the column the change is usually small. When designing the column, it is a good idea to allow for thermowells on several trays, so that the best control point can be found when the column is actually operating. If reliable online composition analyzers are available they can be incorporated in the control loop, but more complex control equipment will be needed and composition analyzers are usually used to cascade onto simpler temperature control loops. With multicomponent systems, temperature is not a unique function of composition.

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CHAPTER 5 Instrumentation and Process Control

TC LC LC

(a)

(b)

FIGURE 5.17 Material balance control schemes for controlling bottoms product composition. Flow control on reflux can be in ratio to feed if feed rate varies. (a) Direct control of bottoms by composition; (b) indirect control of bottoms, composition controls boil-up.

Flow ratio controllers are sometimes used in distillation control, controlling the reflux or boil-up in ratio to the feed, distillate, or bottoms rate. The same effect can be accomplished using cascade control, with the feed rate adjusting the set point of the flow controller on reflux or boil-up. Shinskey (1984) has shown that there are 120 ways of connecting the five main pairs of measured and controlled variables, in single loops. A variety of control schemes has been devised for distillation column control. Some typical schemes are shown in Figures 5.16 to 5.18; ancillary control loops and instruments are not shown. The choice of control scheme may be influenced by many other factors. For example, the control scheme of Figure 5.17(b) controls boil-up by composition and gives the fastest control response to variations in composition of any of the schemes. Kister (1990) discusses the advantages and drawbacks of the material balance control schemes shown in Figures 5.16 and 5.17. An older control scheme that is often encountered is similar to Figure 5.16(b), but has the steam to the reboiler controlled by a temperature in the stripping section of the column. This scheme is

5.4 Conventional Control Schemes

269

FIC

TE TT

FIC

Steam Intermittent charge

Trap

FIGURE 5.18 Batch distillation, reflux flow controlled based on temperature to infer composition.

known as temperature-pattern control or dual composition control, and in principle allows both top and bottom compositions to be controlled. The drawback of this scheme is that there is a tendency for the controllers to fight each other, leading to unstable operation. Distillation column control is discussed in detail by Parkins (1959), Bertrand and Jones (1961), Shinskey (1984) and Buckley, Luyben, and Shunta (1985). Additional temperature indicating or recording points should be included up the column for monitoring column performance and for troubleshooting.

5.4.8 Reactor Control The schemes used for reactor control depend on the process and the type of reactor. If a reliable online composition analyzer is available and the reactor dynamics are suitable, the product composition can be monitored continuously and the reactor conditions and feed flows controlled automatically to maintain the desired product composition and yield. More often, the operator is the final link in the control loop, adjusting the controller set points to maintain the product within specification, based on periodic laboratory analyses. For small stirred-tank reactors, temperature will normally be controlled by regulating the flow of the heating or cooling medium. For larger reactors, temperature is often controlled by recycling a part of the product stream or adding inert material to the feed to act as a heat sink. Pressure is usually held constant. For liquid-phase reactors, pressure is often controlled by maintaining a vapor space above the liquid reagents. This space can be pressurized with nitrogen or other suitable gases.

270

CHAPTER 5 Instrumentation and Process Control

PIC

To vent system M FIC

Feed A TIC

FIC

FV LT

TE FT

FIC

LAH LIC LAL

Feed B

Coolant

Product

FIGURE 5.19 A typical stirred-tank reactor control scheme, temperature cascade control of coolant flow, and flow control of reagents.

Material balance control will be necessary to maintain the correct flow of reactants to the reactor and the flow of products and unreacted materials from the reactor. A typical control scheme for a simple liquid-phase reactor is shown in Figure 5.19. The control of biological reactions is more complex, because it is necessary to maintain many parameters within relatively tight ranges. Control of biological reactors is discussed in Section 15.9.7.

5.5 ALARMS, SAFETY TRIPS, AND INTERLOCKS Alarms are used to alert operators to serious, and potentially hazardous, deviations in process conditions. Key instruments are fitted with switches and relays or software alarms to operate audible and visual alarms on the control panels and shared display screens. Where delay or lack of response by the operator is likely to lead to the rapid development of a hazardous situation, the instrument would be fitted with a trip system to take action automatically to avert the hazard, such as shutting down pumps, closing valves, and operating emergency systems. The basic components of an automatic trip system are: 1. A sensor to monitor the control variable and provide an output signal when a preset value is exceeded (the instrument)

5.5 Alarms, Safety Trips, and Interlocks

LIC

LAL

271

LAL

TRIP LAL

LSL

UC A

(a)

(b)

FIGURE 5.20 (a) Trip as part of control system; (b) separate shutdown trip.

2. A link to transfer the signal to the actuator, usually consisting of a system of pneumatic or electric relays 3. An actuator to carry out the required action; close or open a valve, switch off a motor. A description of some of the equipment (hardware) used is given by Rasmussen (1975). A safety trip can be incorporated in a control loop, as shown in Figure 5.20(a). In this system the level control instrument has a built-in software alarm that alerts the operator if the level is too low and a programmed trip set for a level somewhat lower than the alarm level. However, the safe operation of such a system will be dependent on the reliability of the control equipment, and for potentially hazardous situations it is better practice to specify a separate trip system, such as that shown in Figure 5.20(b), in which the trip is activated by a separate low level switch. Provision must be made for the periodic checking of the trip system to ensure that the system operates when needed. The effective operation of instrumented safety systems depends on the reliable operation of all the components in the system. Because no component is perfectly reliable, designers increase the system reliability by building in redundancy and adding duplicate instruments, switches, relays, etc., so that if one component fails the rest of the system will still operate correctly. More information on the design of safety instrumented systems is given in Section 10.8.

5.5.1 Interlocks Where it is necessary to follow a fixed sequence of operations—for example, during a plant start-up and shutdown, or in batch operations—interlocks are included to prevent operators from departing

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from the required sequence. They may be incorporated in the control system design, as pneumatic or electric relays, or may be mechanical interlocks. Various proprietary special lock and key systems are also available. In most plants, programmable logic controllers are used and the interlocks are coded into the control algorithms. Care should be taken to test all of the interlocks in the plant automation during commissioning or whenever changes are made to the plant control and automation.

5.6 BATCH PROCESS CONTROL Batch processes necessarily involve dynamic variation in process parameters, so the design of control systems for batch plants is more complex than for plants that operate continuously. In addition to conventional regulatory control functions that maintain temperatures, pressures, flows, and levels at desired values, the designer must consider discrete (on-off) control functions that start and stop operations, as well as the overall recipe or sequence of operations. In a plant that has several batch processes or that makes multiple products, the automation system may also include production planning, batch sequencing, and tracking and logging of batch data for quality control purposes. The international standard for the design of control systems for batch plants is IEC 61512, which is based on the set of standards developed by the ISA S88 committee. These standards define an architecture for batch process control systems that regulates the flow of information from high-level decisions such as recipe management and production scheduling down to low-level regulatory process control functions. A detailed description of the S88 standards is beyond the scope of this book, and for more information the reader should consult ISA 88.01 (1995) or the books by Fleming and Pillai (1998), Parshall and Lamb (2000), or Love (2007). When developing a PFD or P&I diagram for a batch plant, the design team must consider all of the controllers that are needed to regulate the dynamic operation of the plant. The regulatory controllers will be controlling the same variables that would be controlled in a continuous process. Indeed, during some phases of the batch recipe, the regulatory control loops function in the same way as they would for a continuous process. In addition to the regulatory control systems, the designer must then add the discrete control functions that change the set points of the regulatory controllers and activate the opening and closing of isolation valves to start and stop flows to the process. Microprocessor-based programmable logic controllers are usually used to control the sequence of phases that makes up the batch recipe.

5.7 COMPUTER CONTROL SYSTEMS Almost all process control systems installed on new plants use programmable electronic devices based on microprocessors. These range from simple digitally actuated single-loop controllers that produce a single output signal (Single Input – Single Output or SISO devices) up to complex distributed control systems that carry out control, real-time optimization, and data logging and archiving for multiple process plants across a site or even an enterprise (Multiple Input – Multiple Output or MIMO devices). The use of microprocessors in controllers allows the controllers to perform more complex control algorithms than could previously be achieved using analog systems based on pneumatic signals.

5.7 Computer Control Systems

273

FIC

FV FT

FIGURE 5.21 Gas mass flow controller.

A microprocessor can take input from several instruments and use a sophisticated model to calculate the outputs to multiple actuators. A simple example of a multiple input device is a gas mass-flow controller, Figure 5.21, in which the gas mass flow is computed based on inputs from temperature, pressure, and flow instruments. The conventional control schemes described in Section 5.4 mainly make use of SISO controllers, since the schemes were developed for single unit operations. At the unit operation level, the primary focus of process control is usually on safe and stable operation, and it is difficult to take advantage of the capability of advanced microprocessor-based control systems. When several unit operations are put together to form a process then the scope for use of MIMO devices increases, particularly when the devices are able to communicate with each other rapidly. The digital control system can then make use of more complex algorithms and models that enable feed-forward control (modelbased or multivariable predictive control) and allow data collected from upstream in the process to guide the selection of operating conditions and controller set points for downstream operations. This allows for better response to process dynamics and more rapid operation of batch, cyclic, and other unsteady state processes. Model-based predictive control is also often used as a means of controlling product quality. This is because devices for measuring product quality typically require analytical procedures that take several minutes to hours to run, making effective feedback control difficult to accomplish. The use of instruments that log and archive data facilitates remote monitoring of process performance and can improve plant troubleshooting and optimization, as well as providing high-level data for enterprise-wide supply chain management. The electronic equipment and systems technology available for process control continues to evolve rapidly. Because of the pace of innovation, industry-wide standards have not been able to keep up, and consequently different manufacturers’ systems usually use proprietary technology and are often not fully compatible with each other. The implementation of the ISA 50 and HART Foundation Fieldbus standards has substantially improved digital communications between control devices, leading to improved control, faster setup, better reliability through higher redundancy, and even greater distribution of functions between devices. The ISA recently published the ISA 100 standard for wireless transmission. Wireless systems are beginning to be used in inventory control and maintenance management, but are not widely used yet in plant control. The control systems vendors appear to have overcome problems with interference, signal blocking, and signal loss and have demonstrated robust error checking and transmission protocols. As experience is gained with wireless instrumentation it is likely to be much more widely

274 FIGURE 5.22 Piping and instrumentation diagram.

References

275

adopted in the future, as wireless systems are more convenient to install and can be more robust in the event of incidents such as small fires. A recent survey of wireless control was given by McKeon-Slattery (2010), but this area is currently evolving rapidly. A detailed treatment of digital technology for process control is beyond the scope of this book. Kalani (1988), Edgar et al. (1997), Liptak (2003), and Love (2007) all provide excellent reviews of the subject. Mitchell and Law (2003) give a good overview of digital bus technologies.

References Bertrand, L., & Jones, J. B. (1961). Controlling distillation columns. Chem. Eng., NY, 68(Feb. 20th), 139. Buckley, P. S., Luyben, W. L., & Shunta, J. P. (1985). Design of distillation column control systems. Arnold. Coughanowr, D. R. (1991). Process systems analysis and control (2nd ed.). MacGraw-Hill. Edgar, T. F., Smith, C. L., Shinskey, F. G., Gassman, G. W., Schafbuch, P. J., McAvoy, T. J., & Seborg, D. E. (1997). Process control. In: Perry’s chemical engineers handbook (7th ed.). McGraw-Hill. Fleming, D. W., & Pillai, V. (1998). S88 implementation guide. McGraw Hill. Green, D. W., & Perry, R. H. (Eds.). (2007). Perry’s chemical engineers’ handbook (8th ed.). McGraw-Hill. Hall, J. (2010). Process pump control. Chem. Eng., 117(12), 30. Henson, M., Seborg, D. E., & Hempstead, H. (1996). Nonlinear process control. Prentice Hall. Kalani, G. (1988). Microprocessor based distributed control systems. Prentice Hall. Kalani, G. (2002). Industrial process control: advances and applications. Butterworth Heinemann. Kister, H. Z. (1990). Distillation operation. McGraw-Hill. Liptak, B. G. (2003). Instrument engineers’ handbook, vol 1: process measurement and analysis (4th ed.). CRC Press. Love, J. (2007). Process automation handbook. A Guide to Theory and Practice. Springer. Luyben, W. L., Tyreus, B. D., & Luyben, M. L. (1999). Plantwide process control. McGraw-Hill. McKeon-Slattery, M. (2010). The world of wireless. Chem. Eng. Prog., 106(2), 6. Mitchell, J. A., & Law, G. (2003). Get up to speed on digital buses. Chem. Eng., NY, 110(2), (Feb 1). Murrill, P. W. (1988). Application concepts of process control. ISA. Nayyar, M. L. (2000). Piping handbook (7th ed.). McGraw-Hill. Parkins, R. (1959). Continuous distillation plant controls. Chem. Eng. Prog., 55(July), 60. Parshall, J., & Lamb, L. (2000). Applying S88: Batch control from a user’s perspective. ISA. Rasmussen, E. J. (1975). Alarm and shut down devices protect process equipment. Chem. Eng., NY, 82 (May 12th), 74. Seborg, D. E., Edgar, T. F., & Mellichamp, D. A. (2004). Process dynamics and control (2nd ed.). Wiley. Shinskey, F. G. (1976). Energy-conserving control systems for distillation units. Chem. Eng. Prog., 72(May), 73. Shinskey, F. G. (1984). Distillation control (2nd ed.). McGraw-Hill. Shinskey, F. G. (1996). Process control systems (4th ed.). McGraw-Hill.

American and International Standards IEC 61512-1. (1997). Batch control part 1: Models and terminology (1st ed.). ISA 5.1-1984. R1992. Instrumentation symbols and identification. ISA 50.00.01. (1975). Compatibility of Analog Signals for Electronic Industrial Process Instruments – formerly ANSI/ISA 50.1-1982 (R1992); formerly ANSI/ISA-50.1-1975 (R1992) per ANSI had to revert to 1975 doc. ISA 88.01-1995. R2006. Batch Control Part 1: Models and Terminology. ISA 100.11A. (2009). Wireless systems for industrial automation: Process control and related applications.

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Other Standards BS 1646:1984. (1984). Symbolic representation for process measurement control functions and instrumentation. DIN 2429-2. (1988). Symbolic representation of pipework components for use on engineering drawings; functional representation. DIN 19227-1. (1993). Control technology; graphical symbols and identifying letters for process control engineering; symbolic representation for functions. DIN 19227-2. (1991). Control technology; graphical symbols and identifying letters for process control engineering; representation of details.

PROBLEMS 5.1. How would you measure: a. b. c. d. e.

The The The The The

temperature of a fermentation broth. mass flow of a gas at high temperature and pressure. volumetric flow rate of a slurry of diced carrots in water. level of liquid in a crystallizer. feed rate of solids to a mixing tank.

5.2. a. What alarms would you add to the vaporizer control scheme shown in Figure 5.13? Indicate whether the alarm would signal high or low conditions, what the alarm would signify, and what operator response would be required in each case. b. Which alarms should activate a shutdown trip, and which valves should be closed? 5.3. Sketch a control scheme for the reactor section shown in Figure 2.17. The feeds are liquids and the reactors operate under pressure with inert nitrogen in the vapor space above the reagents. The objective is to achieve full conversion of feed A by the outlet of the last reactor. 5.4. A fermentation reactor is charged with a sterile feed of growth media at 35 °C and inoculated with a batch of microorganisms. The batch is allowed to grow for 10 days. During the growth period the temperature is maintained at 37 °C by circulating cold water through a jacket on the vessel. Sterile air is sparged into the fermenter to maintain a desired dissolved oxygen concentration. The pH of the fermenter is controlled by periodic addition of a dilute solution of sodium hydroxide. At the end of the growth period the batch is discharged from the reactor to the harvesting section of the process. a. Sketch a P&I diagram of the reactor and feed section. b. What pressure would you choose for operation of the fermenter, and how would you control it? 5.5. A polymer is produced by the emulsion polymerization of acrylonitrile and methyl methacrylate in a stirred vessel. The monomers and an aqueous solution of catalyst are fed to the polymerization reactor continuously. The product is withdrawn from the base of the vessel as a slurry.

Problems

277

Devise a control system for this reactor, and draw up a preliminary piping and instrument diagram. The following points need to be considered: 1. 2. 3. 4. 5. 6.

Close control of the reactor temperature is required. The reactor runs 90% full. The water and monomers are fed to the reactor separately. The emulsion is a 30% mixture of monomers in water. The flow of catalyst will be small compared with the water and monomer flows. Accurate control of the catalyst flow is essential.

5.6. Devise a control system for the distillation column described in Chapter 17, Example 17.2. The flow to the column comes from a storage tank. The product, acetone, is sent to storage and the waste to an effluent pond. It is essential that the specifications on product and waste quality are met.

CHAPTER

Materials of Construction

KEY LEARNING OBJECTIVES • Mechanical and chemical properties that must be considered when selecting materials of construction for a chemical plant • Relative costs of common materials of construction • Properties of alloys commonly used in engineering • When to use polymers or ceramic materials

6.1 INTRODUCTION This chapter covers the selection of materials of construction for process equipment and piping. The selection of materials of construction must be made before the capital cost of a process can be estimated, as plant costs can vary significantly with materials selection. Many factors have to be considered when selecting engineering materials, but for chemical process plant the overriding considerations are usually high temperature strength and the ability to resist corrosion. The process designer will be responsible for recommending materials that will be suitable for the process conditions. The process engineer must also consider the requirements of the mechanical design engineer; the material selected must have sufficient strength and be easily worked. The most economical material that satisfies both process and mechanical requirements should be selected; this will be the material that gives the lowest cost over the working life of the plant, allowing for maintenance and replacement. Other factors, such as product contamination and process safety, must also be considered. The mechanical properties that are important in the selection of materials are discussed briefly in this chapter. Several books have been published on the properties of materials, and the metal-working processes used in equipment fabrication, and a selection suitable for further study is given in the list of references at the end of this chapter. The mechanical design of process equipment is discussed in Chapter 14. A detailed discussion of the theoretical aspects of corrosion is not given in this chapter, as this subject is covered comprehensively in several books: Revie (2005), Fontana (1986), Dillon (1994), and Schweitzer (1989). An extensive set of corrosion data for different materials is given by Craig and Anderson (1995).

279

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CHAPTER 6 Materials of Construction

6.2 MATERIAL PROPERTIES The most important characteristics to be considered when selecting a material of construction are: 1. Mechanical properties a. Strength: tensile strength b. Stiffness: elastic modulus (Young’s modulus) c. Toughness: fracture resistance d. Hardness: wear resistance e. Fatigue resistance f. Creep resistance 2. The effect of high temperature, low temperature, and thermal cycling on the mechanical properties 3. Corrosion resistance 4. Any special properties required, such as thermal conductivity, electrical resistance, and magnetic properties 5. Ease of fabrication: forming, welding, casting (see Table 6.1) 6. Availability in standard sizes—plates, sections, tubes 7. Cost

6.3 MECHANICAL PROPERTIES Typical values of the mechanical properties of the more common materials used in the construction of chemical process equipment are given in Table 6.2. Table 6.1 A Guide to the Fabrication Properties of Common Metals and Alloys Machining Mild steel Low alloy steel Cast iron Stainless steel (18Cr, 8Ni) Nickel Monel Copper (deoxidized) Brass Aluminum Dural Lead Titanium

Cold Working

Hot Working

Casting

Welding

Annealing Temp. °C

S S S S

S D U S

S S U S

D D S D

S S D/U S

750 750 — 1050

S S D

S S S

S S D

1150 1100 800

S S S — S

D S S S S

S S S — U

S D — — U

S S S S D

700 550 350 — —

S—Satisfactory, D—Difficult, special techniques needed. U—Unsatisfactory.

6.3 Mechanical Properties

281

Table 6.2 Mechanical Properties of Common Metals and Alloys (Typical Values at Room Temperature)

Mild steel Low alloy steel Cast iron Stainless steel (18Cr, 8Ni) Nickel (>99% Ni) Monel Copper (deoxidized) Brass (Admiralty) Aluminum (>99%) Dural Lead Titanium

Tensile Strength (N/mm2)

0.1% Proof Stress (N/mm2)

Modulus of Elasticity (kN/mm2)

430 420–660 140–170 >540

220 230–460 — 200

210 210 140 210

100–200 130–200 150–250 160

7.9 7.9 7.2 8.0

500 650 200 400–600 80–150 400 30 500

130 170 60 130 — 150 — 350

210 170 110 115 70 70 15 110

80–150 120–250 30–100 100–200 30 100 5 150

8.9 8.8 8.9 8.6 2.7 2.7 11.3 4.5

Hardness Brinell

Specific Gravity

Note: Tensile stress and proof stress are not the same as the maximum allowable stress permitted by design code. See Tables 6.5 and 6.7 for maximum allowable stress values.

6.3.1 Tensile Strength The tensile strength (tensile stress) is a measure of the basic strength of a material. It is the maximum stress that the material will withstand, measured by a standard tensile test. The older name for this property, which is more descriptive of the property, was Ultimate Tensile Strength (UTS). Proof stress is the stress to cause a specified permanent extension, usually 0.1%. The maximum allowable stress specified by the ASME Boiler and Pressure Vessel (BPV) Code is calculated from these and other material properties at the design temperature, and allowing for suitable safety factors. The basis for establishing maximum allowable stress values is discussed in Chapter 14 and is described in detail in the ASME BPV Code Section II Part D, Mandatory Appendix 1.

6.3.2 Stiffness Stiffness is the ability to resist bending and buckling. It is a function of the elastic modulus of the material and the shape of the cross-section of the member (the second moment of area).

6.3.3 Toughness Toughness is associated with tensile strength, and is a measure of the material’s resistance to crack propagation. The crystal structure of ductile materials, such as steel, aluminum, and copper, is such that they stop the propagation of a crack by local yielding at the crack tip. In other materials, such as the cast irons and glass, the structure is such that local yielding does not occur and

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CHAPTER 6 Materials of Construction

the materials are brittle. Brittle materials are weak in tension but strong in compression. Under compression any incipient cracks present are closed up. Various techniques have been developed to allow the use of brittle materials in situations where tensile stress would normally occur, for example, the use of prestressed concrete, and glass-fiber-reinforced plastics in pressure vessel construction. A detailed discussion of the factors that determine the fracture toughness of materials can be found in the books by Institute of Metallurgists (1960) and Boyd (1970). Gordon (1976) gives an elementary, but very readable, account of the strength of materials in terms of their macroscopic and microscopic structure.

6.3.4 Hardness The surface hardness, as measured in a standard test, is an indication of a material’s ability to resist wear. This will be an important property if the equipment is being designed to handle abrasive solids, or liquids containing suspended solids that are likely to cause erosion.

6.3.5 Fatigue Fatigue failure is likely to occur in equipment subject to cyclic loading; for example, rotating equipment, such as pumps and compressors, and equipment subjected to temperature or pressure cycling. A comprehensive treatment of this subject is given by Harris (1976).

6.3.6 Creep Creep is the gradual extension of a material under a steady tensile stress, over a prolonged period of time. It is usually only important at high temperatures, for instance, with steam and gas turbine blades. For a few materials, notably lead, the rate of creep is significant at moderate temperatures. Lead will creep under its own weight at room temperature and lead linings must be supported at short intervals. The creep strength of a material is usually reported as the stress to cause rupture in 100,000 hours, at the test temperature.

6.3.7 Effect of Temperature on the Mechanical Properties The tensile strength and elastic modulus of metals decrease with increasing temperature. For example, the tensile strength of mild steel (low carbon steel, C < 0.25 %) is 450 N/mm2 at 25 °C falling to 210 N/mm2 at 500 °C, and the value of Young’s modulus is 200,000 N/mm2 at 25 °C falling to 150,000 N/mm 2 at 500 °C. The ASME BPV Code Section II Part D specifies maximum temperatures for each material. For example, SA-285 plain carbon steel plate cannot be used to construct a pressure vessel that meets the specifications of ASME BPV Code Section VIII Div. 1 with a design temperature greater than 900 °F (482 °C). Any pressure vessel that is designed for use above this temperature must be made from killed steel or alloy. The maximum allowable stress used in design is always based on the design temperature. Materials must be chosen that have sufficient strength at the design temperature to give an economic and mechanically feasible wall thickness. The stainless steels are superior in this respect to plain carbon steels.

6.4 Corrosion Resistance

283

Creep resistance will be important if the material is subjected to high stresses at elevated temperatures. Special alloys, such as Inconel 600 (UNS N06600) or Incoloy 800 (UNS N08800) (both trademarks of International Nickel Co.) are used for high-temperature equipment such as furnace tubes in environments that do not contain sulfur. The selection of materials for high-temperature applications is discussed by Day (1979) and Lai (1990). At low temperatures, less than 10 °C, metals that are normally ductile can fail in a brittle manner. Serious disasters have occurred through the failure of welded carbon steel vessels at low temperatures. The phenomenon of brittle failure is associated with the crystalline structure of metals. Metals with a body-centered-cubic (bcc) lattice are more liable to brittle failure than those with a face-centered-cubic (fcc) or hexagonal lattice. For low-temperature equipment, such as cryogenic plant and liquefied-gas storages, austenitic stainless steel (fcc) or aluminum alloys (hex) should be specified; see Wigley (1978). V-notch impact tests, such as the Charpy test, are used to test the susceptibility of materials to brittle failure: see Wells (1968) and ASME BPV Code Sec. VIII Div. 1 Part UG-84. The brittle fracture of welded structures is a complex phenomenon and is dependent on plate thickness and the residual stresses present after fabrication, as well as the operating temperature. A comprehensive discussion of brittle fracture in steel structures is given by Boyd (1970).

6.4 CORROSION RESISTANCE The conditions that cause corrosion can arise in a variety of ways. For this brief discussion on the selection of materials it is convenient to classify corrosion into the following categories: 1. 2. 3. 4. 5. 6. 7. 8. 9.

General wastage of material—uniform corrosion Galvanic corrosion—dissimilar metals in contact Pitting—localized attack Intergranular corrosion Stress corrosion Erosion-corrosion Corrosion fatigue High temperature oxidation and sulfidation Hydrogen embrittlement

Metallic corrosion is essentially an electrochemical process. Four components are necessary to set up an electrochemical cell: 1. 2. 3. 4.

Anode—the corroding electrode Cathode—the passive, noncorroding electrode The conducting medium—the electrolyte—the corroding fluid Completion of the electrical circuit—through the material Cathodic areas can arise in many ways:

1. Dissimilar metals 2. Corrosion products 3. Inclusions in the metal, such as slag

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CHAPTER 6 Materials of Construction

4. Less well-aerated areas 5. Areas of differential concentration 6. Differentially strained areas

6.4.1 Uniform Corrosion This term describes the more or less uniform wastage of material by corrosion, with no pitting or other forms of local attack. If the corrosion of a material can be considered to be uniform, the life of the material in service can be predicted from experimentally-determined corrosion rates. Corrosion rates are usually expressed as a penetration rate in inches per year, or mills per year (mpy) (where a mill = 10−3 inches). They are also expressed as a weight loss in milligrams per square decimeter per day (mdd). Most of the published data on corrosion rates are in imperial units. In corrosion testing, the corrosion rate is measured by the reduction in weight of a specimen of known area over a fixed period of time. ipy =

12w tAρ

where w = mass loss in time t, lb t = time, years A = surface area, ft2 ρ = density of material, lb/ft3 In SI units 1 ipy = 25 mm per year. When judging corrosion rates expressed in mdd it must be remembered that the penetration rate depends on the density of the material. For ferrous metals 100 mdd = 0.02 ipy. What can be considered as an acceptable rate of attack will depend on the cost of the material; the duty, particularly with regard to safety; and the economic life of the plant. For the more commonly used inexpensive materials, such as the carbon and low alloy steels, a guide to what is considered acceptable is given in Table 6.3. For the more expensive alloys, such as the high alloy steels, the brasses, and aluminum, the figures given in Table 6.3 should be divided by 2. If the predicted corrosion rate indicates only short exposures, the design engineer should allow for frequent inspection of the plant and periodic replacement of the affected equipment. This affects process economics in two ways, as it reduces the on-stream factor (number of days of production per year) and increases the maintenance costs. Usually the economic impact of frequent shutdown and replacement is so negative that use of a more expensive alloy with better corrosion resistance can be justified. Allowances for expected corrosion over the plant life or time between replacements must be added to the minimum vessel wall thicknesses calculated to comply with the ASME BPV Code. These corrosion allowances can be economically or mechanically prohibitive if the corrosion rate is high. Guidance on corrosion allowances is given in the ASME BPV Code Sec. VIII Div. 1 Nonmandatory Appendix E. The corrosion allowance should at least equal the expected corrosion loss during the desired life of the vessel. The corrosion rate will be dependent on the temperature and concentration of the corrosive fluid. An increase in temperature usually results in an increased rate of corrosion, though not always. The rate will depend on other factors that are affected by temperature, such as oxygen solubility.

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Table 6.3 Acceptable Corrosion Rates Corrosion Rate

Completely satisfactory Use with caution Use only for short exposures Completely unsatisfactory

ipy

mm/y

159

Light Moderate Intermediate Heavy Severe

Adapted from the Dow F&EI guide (1994).

10.6 Safety Indices

457

Only a brief outline of the method used to calculate the Dow F&EI will be given in this section. The full guide should be studied before applying the technique to a particular process. Judgment, based on experience with similar processes, is needed to decide the magnitude of the various factors used in the calculation of the index, and the loss control credit factors.

10.6.1 Calculation of the Dow F&EI The procedure for calculating the index and the potential loss is set out in Figure 10.2. Select pertinent process unit Determine material factor

Calculate F1 General process hazards factor

Calculate F2 Special process hazards factor

Determine process unit hazards factor F3 = F1 × F2 Calculate loss control credit factor = C1 × C2 × C3

Determine F&EI F&EI = F3 × material factor Determine area of exposure Determine replacement value in exposure area

Determine base MPPD

Determine damage factor

Determine actual MPPD

Determine MPDO

Determine BI

FIGURE 10.2 Procedure for calculating the Fire and Explosion Index and other risk analysis information. From Dow (1994) reproduced by permission of the American Institute of Chemical Engineers. © 1994 AIChE. All rights reserved.

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FIGURE 10.3 Dow Fire and Explosion Index calculation form. From Dow (1994) reproduced by permission of the American Institute of Chemical Engineers. © 1994 AIChE. All rights reserved. Note: The figure numbers refer to the Dow guide. Gallons are US gallons. Note: 1 m3 = 264.2 US gal; 1 kN/m2 = 0.145 psi; 1 kg = 2.2 lbs; 1 kJ/Kg = 0.43 BTU/lb.

10.6 Safety Indices

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The first step is to identify the units that would have the greatest impact on the magnitude of any fire or explosion. The index is calculated for each of these units. The basis of the F&EI is a Material Factor (MF). The MF is then multiplied by a Unit Hazard Factor, F3, to determine the F&EI for the process unit. The Unit Hazard Factor is the product of two factors that take account of the hazards inherent in the operation of the particular process unit: the general and special process hazards (Figure 10.3).

Material Factor The material factor is a measure of the intrinsic rate of energy release from the burning, explosion, or other chemical reaction of the material. Values for the MF for over 300 of the most commonly used substances are given in the guide. The guide also includes a procedure for calculating the MF for substances not listed from knowledge of the flash points (for dusts, dust explosion tests) and a reactivity value, N r. The reactivity value is a qualitative description of the reactivity of the substance, and ranges from 0 for stable substances, to 4 for substances that are capable of unconfined detonation. Some typical material factors are given in Table 10.7. In calculating the F&EI for a unit the value for the material with the highest MF that is present in significant quantities is used.

General Process Hazards The general process hazards are factors that play a primary role in determining the magnitude of the loss following an incident. Six factors are listed on the calculation form, Figure 10.3. A. Exothermic chemical reactions: the penalty varies from 0.3 for a mild exotherm, such as hydrogenation, to 1.25 for a particularly sensitive exotherm, such as nitration. Table 10.7 Some Typical Material Factors MF Acetaldehyde Acetone Acetylene Ammonia Benzene Butane Chlorine Cyclohexane Ethyl alcohol Hydrogen Nitroglycerine Sulfur Toluene Vinyl Chloride

24 16 40 4 16 21 1 16 16 21 40 4 16 21

Flash Point °C −39 −20 Gas Gas −11 Gas – −20 13 Gas – – 40 Gas

Heat of Combustion MJ/kg 24.4 28.6 48.2 18.6 40.2 45.8 0.0 43.5 26.8 120.0 18.2 9.3 31.3 18.6

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B. Endothermic processes: a penalty of 0.2 is applied to reactors, only. It is increased to 0.4 if the reactor is heated by the combustion of a fuel. C. Materials handling and transfer: this penalty takes account of the hazard involved in the handling, transfer, and warehousing of the material. D. Enclosed or indoor process units: accounts for the additional hazard where ventilation is restricted. E. Access of emergency equipment: areas not having adequate access are penalized. The minimum requirement is access from two sides. F. Drainage and spill control: penalizes design conditions that would cause large spills of flammable material adjacent to process equipment, such as inadequate design of drainage.

Special Process Hazards The special process hazards are factors that are known from experience to contribute to the probability of an incident involving loss. Twelve factors are listed on the calculation form, Figure 10.3. A. Toxic materials: the presence of toxic substances after an incident will make the task of the emergency personnel more difficult. The factor applied ranges from 0 for nontoxic materials, to 0.8 for substances that can cause death after short exposure. B. Sub-atmospheric pressure: allows for the hazard of air leakage into equipment. It is only applied for pressure less than 500 mmHg (0.66 bara). C. Operation in or near flammable range: covers the possibility of air mixing with material in equipment or storage tanks, under conditions where the mixture will be within the explosive range. D. Dust explosion: covers the possibility of a dust explosion. The degree of risk is largely determined by the particle size. The penalty factor varies from 0.25 for particles above 175 μm, to 2.0 for particles below 75 μm. E. Relief pressure: this penalty accounts for the effect of pressure on the rate of leakage, should a leak occur. Equipment design and operation becomes more critical as the operating pressure is increased. The factor to apply depends on the relief device setting and the physical nature of the process material. It is determined from Figure 2 in the Dow Guide. F. Low temperature: this factor allows for the possibility of brittle fracture occurring in carbon steel, or other metals, at low temperatures (see Chapter 6 of this book). G. Quantity of flammable material: the potential loss will be greater the greater the quantity of hazardous material in the process or in storage. The factor to apply depends on the physical state and hazardous nature of the process material, and the quantity of material. It varies from 0.1 to 3.0, and is determined from Figures 3, 4, and 5 in the Dow Guide. H. Corrosion and erosion: despite good design and materials selection, some corrosion problems may arise, both internally and externally. The factor to be applied depends on the anticipated corrosion rate. The severest factor is applied if stress corrosion cracking is likely to occur (see Chapter 6 of this book). I. Leakage—joints and packing: this factor accounts for the possibility of leakage from gaskets, pump and other shaft seals, and packed glands. The factor varies from 0.1 where there is the possibility of minor leaks, to 1.5 for processes that have sight glasses, bellows, or other expansion joints.

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461

J. Use of fired heaters: the presence of boilers or furnaces, heated by the combustion of fuels, increases the probability of ignition should a leak of flammable material occur from a process unit. The risk involved will depend on the siting of the fired equipment and the flash point of the process material. The factor to apply is determined with reference to Figure 6 in the Dow Guide. K. Hot oil heat exchange system: most special heat exchange fluids are flammable and are often used above their flash points, so their use in a unit increases the risk of fire or explosion. The factor to apply depends on the quantity and whether the fluid is above or below its flash point; see Table 5 in the Guide. L. Rotating equipment: this factor accounts for the hazard arising from the use of large pieces of rotating equipment: compressors, centrifuges, and some mixers.

10.6.2 Potential Loss The procedure for estimating the potential loss that would follow an incident is set out in Table 10.8: the Process Unit Risk Analysis Summary. The first step is to calculate the damage factor for the unit. The damage factor depends on the value of the material factor and the process unit hazards factor (F3 in Figure 10.3). It is determined using Figure 8 in the Dow Guide. An estimate is then made of the area (radius) of exposure. This represents the area containing equipment that could be damaged following a fire or explosion in the unit being considered. It is evaluated from Figure 7 in the Guide and is a linear function of the Fire and Explosion Index. An estimate of the replacement value of the equipment within the exposed area is then made, and combined with by the damage factor to estimate the base maximum probable property damage (Base MPPD). The maximum probable property damage (MPPD) is then calculated by multiplying the Base MPPD by a loss control credit factor. The loss control credit factors, see Table 10.9, allow for the reduction in the potential loss given by the preventative and protective measures incorporated in the design. The Dow Guide should be consulted for details of how to calculate the credit factors. The MPPD is used to predict the maximum number of days which the plant will be down for repair, the maximum probable days outage (MPDO). The MPDO is used to estimate the financial loss due to the lost production: the business interruption (BI). The financial loss due to lost business opportunity can often exceed the loss from property damage.

10.6.3 Basic Preventative and Protective Measures The basic safety and fire protective measures that should be included in all chemical process designs are listed below. This list is based on that given in the Dow Guide, with some minor amendments. 1. 2. 3. 4. 5. 6.

Adequate and secure water supplies for firefighting. Correct structural design of vessels, piping, steel work. Pressure-relief devices. Corrosion-resistant materials, and/or adequate corrosion allowances. Segregation of reactive materials. Grounding of electrical equipment.

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Table 10.8 Loss Control Credit Factors Feature

Credit Factor Range

1. Process Control Credit Factor (C1) a. Emergency Power b. Cooling c. Explosion Control d. Emergency Shutdown e. Computer Control f. Inert Gas g. Operating Instructions/Procedures h. Reactive Chemical Review i. Other Process Hazard Analysis C1 Value(3)

0.98 0.97 0.84 0.96 0.93 0.94 0.91 0.91 0.91

2. Material Isolation Credit Factor (C2) a. Remote Control Valves b. Dump/Blowdown c. Drainage d. Interlock C2 Value(3)

0.96 to 0.98 0.96 to 0.98 0.91 to 0.97 0.98

3. Fire Protection Credit Factor (C3) a. Leak Detection b. Structural Steel c. Fire Water Supply d. Special Systems e. Sprinkler Systems f. Water Curtains g. Foam h. Hand Extinguishers/Monitors i. Cable Protection C3 Value(3)

0.94 0.95 0.94 0.91 0.74 0.97 0.92 0.93 0.94

Loss Control Credit Factor = C1 × C2 × C3 =

to to to to to to to to

Credit Factor Used(2)

0.99 0.98 0.99 0.99 0.96 0.99 0.98 0.98

to 0.98 to 0.98 to 0.97 to to to to to

0.97 0.98 0.97 0.98 0.98

(enter on line 7 Table 10.9)

7. 8. 9. 10. 11.

Safe location of auxiliary electrical equipment, transformers, switchgear. Provision of backup utility supplies and services. Compliance with national codes and standards. Fail-safe instrumentation. Provision for access of emergency vehicles and the evacuation of personnel.

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Table 10.9 Process Unit Risk Analysis Summary 1. Fire & Explosion Index (F&El) 2. Radius of Exposure 3. Area of Exposure 4. Value of Area of Exposure 5. Damage Factor 6. Base Maximum Probable Property Damage—(Base MPPD) [4 × 5] 7. Loss Control Credit Factor 8. Actual Maximum Probable Property Damage—(Actual MPPD) [6 × 7] 9. Maximum Probable Days Outage—(MPDO) 10. Business Interruption—(Bl)

(Figure 7)* ft or m ft2 or m2 $MM (Figure 8)* $MM (See Above) $MM (Figure 9)* days $MM

12. Adequate drainage for spills and firefighting water. 13. Insulation of hot surfaces. 14. No glass equipment used for flammable or hazardous materials, unless no suitable alternative is available. 15. Adequate separation of hazardous equipment. 16. Protection of pipe racks and cable trays from fire. 17. Provision of block valves on lines to main processing areas. 18. Protection of fired equipment (heaters, furnaces) against accidental explosion and fire. 19. Safe design and location of control rooms. Note: The design and location of control rooms, particularly as regards protection against an unconfined vapor explosion, is covered in a publication of the Chemical Industries Association, CIA (1979).

10.6.4 Mond Fire, Explosion, and Toxicity Index The Mond index was developed from the Dow F&EI by personnel at the ICI Mond division. The third edition of the Dow index, Dow (1973), was extended to cover a wider range of process and storage installations; the processing of chemicals with explosive properties; and the evaluation of a toxicity hazards index. Also included was a procedure to allow for the offsetting effects of good design, and of control and safety instrumentation. Their revised Mond fire, explosion, and toxicity index was discussed in a series of papers by Lewis (1979a, 1979b), which included a technical manual setting out the calculation procedure. An extended version of the manual was issued in 1985, and an amended version published in 1993, ICI (1993).

Procedure The basic procedures for calculating the Mond indices are similar to those used for the Dow index. The process is first divided into a number of units that are assessed individually.

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The dominant material for each unit is then selected and its material factor determined. The material factor in the Mond index is a function of the energy content per unit weight (the heat of combustion). The material factor is then modified to allow for the effect of general and special process and material hazards; the physical quantity of the material in the process step; the plant layout; and the toxicity of process materials. Separate fire and explosion indices are calculated. An aerial explosion index can also be estimated, to assess the potential hazard of aerial explosions. An equivalent Dow index can also be determined. The individual fire and explosion indices are combined to give an overall index for the process unit. The overall index is the most important in assessing the potential hazard. The magnitude of the potential hazard is determined by reference to rating tables, similar to that shown for the Dow index in Table 10.6. After the initial calculation of the indices (the initial indices), the process is reviewed to see what measures can be taken to reduce the rating (the potential hazard). The appropriate offsetting factors to allow for the preventative features included in the design are then applied, and final hazard indices calculated.

Preventative Measures Preventative measures fall into two categories: 1. Those that reduce the number of incidents, such as sound mechanical design of equipment and piping, operating and maintenance procedures, and operator training. 2. Those that reduce the scale of a potential incident, such as measures for fire protection and fixed firefighting equipment. Many measures will not fit neatly into individual categories but will apply to both.

Implementation The Mond technique of hazard evaluation is fully explained in the ICI technical manual, ICI (1993), to which reference should be made to implement the method. The calculations are made using a standard form, similar to that used for the Dow index.

10.6.5 Summary The Dow and Mond indices are useful techniques that can be used in the early stages of a project design to evaluate the hazards and risks of the proposed process. Calculation of the indices for the various sections of the process will highlight any particularly hazardous sections and indicate where a detailed study is needed to reduce the hazards. Example 10.1 Evaluate the Dow F&EI for the nitric acid plant illustrated in Chapter 2, Figure 2.8.

Solution

The calculation is set out on the special form shown in Figure 10.3a. Notes on the decisions taken and the factors used are given below.

10.6 Safety Indices

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CHAPTER 10 Safety and Loss Prevention

Unit: consider the total plant, no separate areas, but exclude the main storages. Material factor: for ammonia, from Dow Guide, and Table 10.6: MF = 4:0 Note: Hydrogen is present, and has a larger material factor (21) but the concentration is too small for it to be considered the dominant material. General Process Hazards

A. B. C. D. E. F.

Oxidizing reaction, factor = 0.5 Not applicable Not applicable Not applicable Adequate access would be provided, factor = 0.0 Adequate drainage would be provided, factor = 0.0

Special Process Hazards

A. B. C. D. E.

F. G.

H. I. J. K. L.

Ammonia is highly toxic, likely to cause serious injury, factor = 0.6 Not applicable Operation always is within the flammable limits, factor = 0.8 Not applicable Operation pressure 8 atm = 8 × 14.7 − 14.7 = 103 psig. Set relief valve at 20% above the operating pressure (see Chapter 14 of this book) = 125 psig. From Figure 2 in the guide, factor = 0.35. Note: psig = pounds force per square inch, gauge. Not applicable The largest quantity of ammonia in the process will be the liquid in the vaporizer, say around 500 kg. Heat of combustion, Table 10.3 = 18.6 MJ/kg Potential energy release = 500 × 18.6 = 9300 MJ = 9300 × 106/(1.05506 × 103) = 8.81 × 106 Btu which is too small to register on Figure 3 in the Guide, factor = 0.0 Corrosion resistant materials of construction would be specified, but external corrosion is possible due to nitric oxide fumes, allow minimum factor = 0.1. Welded joints would be used on ammonia service and mechanical seals on pumps. Use minimum factor as full equipment details are not known at the flowsheet stage, factor = 0.1. Not applicable Not applicable Large turbines and compressors used, factor = 0.5

The index works out at 21: classified as “Light”. Ammonia would not normally be considered a dangerously flammable material; the danger of an internal explosion in the reactor is the main process hazard. The toxicity of ammonia and the corrosiveness of nitric acid would also need to be considered in a full hazard evaluation. The Process Unit Risk Analysis would be completed when the site for the plant had been determined.

10.7 Hazard and Operability Studies

467

10.7 HAZARD AND OPERABILITY STUDIES A hazard and operability study is a systematic procedure for critical examination of the operability of a process. When applied to a process design or an operating plant, it indicates potential hazards that may arise from deviations from the intended design conditions. The technique was developed by the Petrochemicals Division of ICI, see Lawley (1974), and is now in general use in the chemical and process industries. The term “operability study” should more properly be used for this type of study, though it is usually referred to as a hazard and operability study, or HAZOP study. This can cause confusion with the term “hazard analysis,” or “process hazard analysis” (PHA), which is a similar but somewhat less rigorous method. Numerous books have been written illustrating the use of HAZOP. Those by Hyatt (2003), CCPS (2000), Taylor et al. (2000), and Kletz (1999a) give comprehensive descriptions of the technique, with examples. A brief outline of the technique is given in this section to illustrate its use in process design. It can be used to make a preliminary examination of the design at the flowsheet stage and for a detailed study at a later stage, when a full process description, final flowsheets, P&I diagrams, and equipment details are available. An “as-built” HAZOP is often carried out after construction and immediately before commissioning a new plant.

10.7.1 Basic Principles A formal operability study is the systematic study of the design, vessel by vessel and line by line, using “guide words” to help generate thought about the way deviations from the intended operating conditions can cause hazardous situations. The seven guide words recommended are given in Table 10.10. In addition to these words, the following words are also used in a special way, and have the precise meanings given below: Intention: the intention defines how the particular part of the process was intended to operate; the intention of the designer. Deviations: these are departures from the designer’s intention that are detected by the systematic application of the guide words. Causes: reasons why, and how, the deviations could occur. Only if a deviation can be shown to have a realistic cause is it treated as meaningful. Consequences: the results that follow from the occurrence of a meaningful deviation. Hazards: consequences that can cause damage (loss) or injury. The use of the guide words can be illustrated by considering a simple example. Figure 10.4 shows a chlorine vaporizer, which supplies chlorine at 2 bar to a chlorination reactor. The vaporizer is heated by condensing steam. Consider the steam supply line and associated control instrumentation. The designer’s intention is that steam shall be supplied at a pressure and flow rate to match the required chlorine demand. Apply the guide word NO: Possible deviation—no steam flow. Possible causes—blockage, valve failure (mechanical or power), failure of steam supply (fracture of main, boiler shutdown).

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Table 10.10 A List of Guide Words Guide Words NO or NOT MORE LESS AS

WELL AS

Meanings

Comments

The complete negation of these intentions Quantitative increases or decreases A qualitative increase

No part of the intentions is achieved but nothing else happens.

PART OF REVERSE

A qualitative decrease The logical opposite of the intention

OTHER

Complete substitution

THAN

These refer to quantities and properties such as flow rates and temperatures, as well as activities like “HEAT” and “REACT”. All the design and operating intentions are achieved together with some additional activity. Only some of the intentions are achieved; some are not. This is mostly applicable to activities, for example reverse flow or chemical reaction. It can also be applied to substances, e.g., “POISON instead of “ANTIDOTE” or “D” instead of “L” optical isomers. No part of the original intention is achieved. Something quite different happens.

PIC

PV Vapor to reactor

FIC

Chlorine feed

S/D FV

LIC

LAH

LV LT Steam

Trap

FIGURE 10.4 Chlorine vaporizer instrumentation.

Clearly this is a meaningful deviation, with several plausible causes. Consequences—the main consequence is loss of chlorine flow to the chlorination reactor. The effect of this on the reactor operation would have to be considered. This would be brought out in the operability study on the reactor; it would be a possible cause of no chlorine flow. Since the flow controller does not know that steam flow has been lost, chlorine will continue to be pumped into the vessel until the high level alarm sounds and the high level shutdown closes the control valve. A secondary consequence is that the vessel is now filled with liquid chlorine that must be drained to a safe level before operation can be resumed. The operating procedures must include instructions on how to deal with this scenario.

10.7 Hazard and Operability Studies

469

Apply the guide word MORE: Possible deviation—more steam flow. Possible cause—valve stuck open. Consequences—low level in vaporizer (this should activate the low level alarm), higher rate of flow to the reactor. Note: To some extent the level will be self-regulating, because as the level falls the heating surface is uncovered. Hazard—depends on the possible effect of high flow on the reactor. Possible deviation—more steam pressure (increase in mains pressure). Possible causes—failure of pressure-regulating valves. Consequences—increase in vaporization rate. Need to consider the consequences of the heating coil reaching the maximum possible steam system pressure. Hazard—rupture of lines (unlikely), effect of sudden increase in chlorine flow on reactor. A more detailed illustration of the HAZOP method is given in Example 10.2.

10.7.2 Explanation of Guide Words It is important to understand the intended meaning of the guide words in Table 10.10. The meaning of the words NO/NOT, MORE, and LESS are easily understood; the NO/NOT, MORE, and LESS could, for example, refer to flow, pressure, temperature, level, and viscosity. All circumstances leading to NO flow should be considered, including reverse flow. The other words need some further explanation: AS WELL AS: something in addition to the design intention, such as impurities, side reactions, ingress of air, extra phases present. P ART OF : something missing, only part of the intention realized, such as the change in composition of a stream, a missing component. REVERSE: the reverse of, or opposite to, the design intention. This could mean reverse flow if the intention was to transfer material. For a reaction, it could mean the reverse reaction. In heat transfer, it could mean the transfer of heat in the opposite direction to what was intended. OTHER THAN: an important and far-reaching guide word, but consequently more vague in its application. It covers all conceivable situations other than that intended, such as start-up, shutdown, maintenance, catalyst regeneration and charging, and failure of plant services. When referring to time, the guide words SOONER

THAN

and LATER

THAN

can also be used.

10.7.3 Procedure An operability study would normally be carried out by a team of experienced people, who have complementary skills and knowledge; led by a team leader who is experienced in the technique. The team would include a similar set of experts to an FMEA team, as described in Section 10.5. The team examines the process vessel by vessel, and line by line, using the guide words to detect any hazards. The information required for the study will depend on the extent of the investigation. A preliminary study can be made from a description of the process and the process flow diagrams. For a detailed,

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final, study of the design, the flowsheets, piping and instrument diagrams, equipment specifications, and layout drawings would be needed. For a batch process, information on the sequence of operation will also be required, such as that given in operating instructions, logic diagrams, and flow charts. A typical sequence of events is shown in Figure 10.5. After each line has been studied it is marked on the flowsheet as checked. Beginning 1

Select a vessel

Explain the general intention of the vessel and its lines

Select a line

Explain the intention of the line

Apply guide word

Develop a meaningful deviation

Examine possible causes

Examine consequences

Detect hazards or operating problems

Make suitable record

11 12

Repeat 6–10 for all meaningful deviations derived from the guide word Repeat 5–11 for all the guide words

Mark line as having been examined

Repeat 3–13 for each line

Select an auxiliary (e.g., heating system)

Explain the intention of the auxiliary

Repeat 5–12 for the auxiliary

Mark auxiliary as having been examined

Repeat 15–18 for all auxiliaries

Explain intention of the vessel

Repeat 5–12 for the vessel

Mark vessel as completed

Repeat 1–22 for all vessels on flowsheet

Mark flowsheet as completed

Repeat 1–24 for all flowsheets

End

FIGURE 10.5 Detailed sequence of an operability study.

10.7 Hazard and Operability Studies

471

A written record is not normally made of each step in the study; only those deviations that lead to a potential hazard are recorded. If possible, the action needed to remove the hazard is decided by the team and recorded. If more information, or time, is needed to decide the best action, the matter is referred to the design group for action, or taken up at another meeting of the study team. When using the operability study technique to vet a process design, the action to be taken to deal with a potential hazard will often be modifications to the control systems and instrumentation: the inclusion of additional alarms, trips, or interlocks. If major hazards are identified, major design changes may be necessary; alternative processes, materials, or equipment should be considered.

Example 10.2 This example illustrates how the techniques used in an operability study can be used to decide the instrumentation required for safe operation. Figure 10.6(a) shows the basic instrumentation and control systems required for the steady-state operation of the reactor section of the nitric acid process introduced in Figure 2.8. Figure 10.6(b)

FV 1

FIC 1

105

104

103 Air

FT 1

Filter

PAL TI 1

FFC 1

Compressor FT 2

FFV 1

102 PIC 1 LIC 1

LV 1

PV 1

101 NH3 from storage

106

109 NRV2

Steam Vaporizer TI 2

To scrubber

Reactor 107

FIGURE 10.6(a) Nitric acid plant reactor section before HAZOP.

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CHAPTER 10 Safety and Loss Prevention

FV 1

FIC 1

105

PDI 1

103

104

Air

NRV1

FT 1

Filter

TI 1

PSL 1

FFC 1

Compressor

PI 1

PAL

FFV 1

FT 2

102 NRV3 PIC 1

LSH 1 LAH LV 1

LAL

NRV4

AI 2

AAH

AAH ASH 1

S LIC 1

LT 1

LT 2

101

NH3 from storage

AI 1

SV1

LAH LAL

PV 1

SV3

SV2

109

106

NRV2

Steam Vaporizer TI 2

To scrubber

TAHL

Reactor 107

FIGURE 10.6(b) After HAZOP.

shows the additional instrumentation and safety trips added after making the operability study set out below. The instrument symbols used are explained in Chapter 5. The most significant hazard of this process is the probability of an explosion if the concentration of ammonia in the reactor is inadvertently allowed to reach the explosive range, >14%. Note that this is a simplified flow diagram and a HAZOP based on the full P&I diagram would go into considerably more detail.

Operability Study

The sequence of steps shown in Figure 10.4 is followed. Only deviations leading to action, and those having consequences of interest, are recorded.

10.7 Hazard and Operability Studies

473

Vessel—Air Filter Intention—to remove particles that would foul the reactor catalyst Guide Word

Deviation

Cause

Consequences and Action

Line No. 103 Intention—transfers clear air at atmospheric pressure and ambient temperature to compressor LESS OF Flow Partially blocked filter Possible dangerous increase in NH3 concentration: measure and log pressure differential AS WELL AS Composition Filter damaged, Impurities, possible poisoning of catalyst: incorrectly installed proper maintenance Vessel—Compressor Intention—to supply air at 8 bar, 12,000 kg/h, 250 °C, to the mixing tee Line No. 104 Intention—transfers air to reactor (mixing tee) NO/NONE Flow Compressor failure MORE

Flow

Failure of compressor controls

REVERSE

Flow

Fall in line press. (compressor fails) high pressure at

Line No. 105 Intention—transfer secondary air to absorber NO Flow Compressor failure FV1 failure LESS Flow FV1 plugging failure, FIC1

Possible dangerous NH3 conc.: pressure indicator with low pressure alarm (PI1) interlocked to shut down NH3 flow High rate of reaction, high reactor temperature: high-temperature alarms added to TI2 NH3 in compressor—explosion hazard: fit non-return valve (NRV1); hot wet acid reactor gas-corrosion; fit second valve (NRV4)

Incomplete oxidation, air pollution from absorber vent: operating procedures As no flow

Vessel—Ammonia vaporizer Intention—evaporate liquid ammonia at 8 bar, 25 °C, 731 kg/h Guide Word

Deviation

Cause

Line No. 101 Intention—transfer liquid NH3 from storage NO Flow Pump failure LV1 fails LESS

Flow

Partial failure pump/ valve

Consequences and Action

Level falls in vaporizer: fit low-level alarm on LIC1 LIC1 alarms

(Continued )

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Flow

LV1 sticking, LIC1 fails

AS WELL AS

Water brine

REVERSE

Flow

Leakage into storages from refrigeration Pump fails, vaporizer press. higher than delivery

Line No. 102 Intention—transfers vapor to mixing tee NO Flow Failure of steam flow, FFV1 fails closed, LESS

Flow

Partial failure or blockage FFV1 LIC1 fails FT2/ratio control misoperation

Level Flow

REVERSE

Level Flow

LIC1 fails Steam failure

Line 109 (auxiliary) NO

Flow

PV1 fails, trap frozen

Vaporizer floods, liquid to reactor: fit highlevel alarm on LIC1 with automatic pump shutdown. Add independent level transmitter and alarm LT2. Concentration of NH4OH in vaporizer: routine analysis, maintenance Flow of vapor into storages: LIC1 alarms; fit non-return valve (NRV2)

LIC1 alarms, reaction ceases: considered low flow alarm, rejected—needs resetting at each rate As no flow LT2 backup system alarms. Danger of high ammonia concentration: fit alarm, fit analyzers (duplicate) with high alarm 12% NH3 (AI1, AI2) LT2 backup system alarms Hot, acid gases from reactor—corrosion: fit non-return valve (NRV3) High level in vaporizer: LIC1 actuated

Vessel—Reactor Intention—oxidizes NH3 with air, 8 bar, 900 °C Line No. 106 Intention—transfers mixture to reactor, NO Flow LESS Flow NH3 conc. MORE

NH3 conc.

250 °C NRV4 stuck closed NRV4 partially closed Failure of ratio control Failure of ratio control, air flow restricted

Flow Control systems failure Line No. 107 Intention—transfers reactor products to waste-heat boiler AS WELL AS Composition Refractory particles from reactor

Fall in reaction rate: fit low temp. alarm on TI2 As NO Temperatures fall: TI2 alarms (consider low conc. alarm on AI1, AI2) High reactor temp.: TI2 alarms 14% explosive mixture enters reactor—potential for disaster: include automatic shutdown bypass actuated by AI1, AI2, SV2 closes, SV3 opens High reactor temp.: TI2 alarms

Possible plugging of boiler tubes: install filter upstream of boiler

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475

10.8 QUANTITATIVE HAZARD ANALYSIS Methods such as FMEA, HAZOP, and use of safety indices will identify potential hazards, but give only qualitative guidance on the likelihood of an incident occurring and the loss suffered; these are left to the intuition of the team members. In a quantitative hazard analysis, the engineer attempts to determine the probability of an event occurring and the potential cost in terms of injuries, financial loss, etc. The international standard IEC 61508 (1998) defines the risk of a hazard as the probable rate of occurrence (typically expressed as events per year) multiplied by the degree of severity of the harm caused. If there are no protective systems in place, the inherent risk, Rnp, is Rnp = Fnp × C

(10.2)

where Fnp = is the inherent frequency of the hazard with no protective system (number of events per year) C = is the impact of the hazard (impact per loss event) The impact can be stated in terms of injuries, serious injuries, emissions, financial loss, or other measures. The analysis is sometimes repeated with different measures of impact, as the organization may have a different tolerance for risk of injuries than for financial risk. In most designs, protective systems are added to reduce the risk of a hazard to a tolerable level. The tolerable risk is defined as: Rt = Ft × C

(10.3)

where Ft = is the tolerable frequency of the hazard (number of events per year) Rt = is the tolerable risk, also sometimes called the acceptable risk The risk reduction factor of the protective system, ΔR, is defined as the ratio of inherent frequency to tolerable frequency: Fnp ΔR = (10.4) Ft It can be seen that the risk reduction factor is the inverse of the average probability that the protective system will fail when it is called upon to operate (average probability of failure on demand), PFDav: F 1 PFDav = t = (10.5) Fnp ΔR The quantitative hazard analysis can thus be used to set targets for the reliability of the protective system. The reliability of the protective system can then be increased until the desired risk reduction factor is attained. Methods that are used to improve the reliability of the protective system are discussed in Section 10.8.2. The design of safety instrumented systems for maintaining safe operation of processes is discussed in the international standard IEC 61511, which is adopted as ANSI/ISA-84.00.01-2004 in the United States. For a safety system that must operate on demand (i.e., in response to an initiating event), IEC 61511 states that each safety instrumented function (SIF) must have a safety integrity level (SIL) specified to give the required risk reduction or average probability of failure on demand shown in Table 10.11. A good introduction to the application of the functional safety standards IEC 61508 and 61511 and the development of safety instrumented systems is given by King (2007). The book by Cameron and Raman (2005) is an extensive guide to risk management systems.

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Table 10.11 Safety Integrity Levels in Demand Mode of Operation (IEC 61511) Safety Integrity Level (SIL)

Target Average Probability of Failure on Demand (PFDav)

4 3 2 1

≥ ≥ ≥ ≥

10−5 10−4 10−3 10−2

to to to to

< < <
10,000 to ≤ 100,000 >1000 to ≤ 10,000 >100 to ≤ 1000 >10 to ≤ 100

10.8.1 Fault Trees Incidents usually occur through the coincident failure of two or more items; failure of equipment, control systems, and instruments; and misoperation. The sequence of events leading to a hazardous incident can be shown as a fault tree (logic tree), such as that shown in Figure 10.7. This figure shows the set of events that could lead to a pressure vessel rupture. The AND symbol is used where all the inputs are necessary before the system fails, and the OR symbol where failure of any input, by itself, would cause failure of the system. A fault tree is analogous to the type of logic diagram used to represent computer operations, and the symbols are analogous to logic AND and OR gates (Figure 10.8). It can be seen from Figure 10.7 that failure of the vessel will only occur if there is a cause of overpressure AND a failure of the pressure relief valve (PRV) to respond adequately. These in turn have several possible causes, which may also have possible causes. Each chain of causality should be pursued to the root cause, and the diagram in Figure 10.7 is incomplete. PRV back pressure too high PRV sized incorrectly Dirt

PRV fails to give adequate discharge at pressure danger level

PRV blocked Other

Vessel Explodes

Other

Downstream equipment plugged Inlet valve failed open Pressure surge on feed line Other

FIGURE 10.7 Fault tree for failure of a pressure vessel.

Flow in > flow out at pressure danger level

10.8 Quantitative Hazard Analysis

A B C

477

AND Gate

OR Gate

Z = ABC = 1 iff A, B and C = 1

Z = A + B + C = 1 if A, B or C = 1

FIGURE 10.8 Logic symbols for

AND

and

OR.

The fault trees for even a simple process unit will be complex, with many branches. Fault trees are used to make a quantitative assessment of the likelihood of failure of a system, using data on the reliability of the individual components of the system. Once the fault tree for a subsection of the process has been developed, it can be used to improve the reliability of the design by introducing additional, redundant, instrumentation. Since a hazardous condition usually requires the failure of one or more devices, introducing additional parallel devices reduces the likelihood of a failure as long the devices do not have a common mode of failure. The quantitative analysis of the likelihood of an event can be used to determine the level of system redundancy that is required to reduce the likelihood to an acceptably low value. Event trees are a similar way of representing the same information, but there is not sufficient space to present both methods here; see Mannan (2004) or CCPS (2008).

10.8.2 Equipment Reliability When a fault tree has been constructed, it can be used to estimate the probability of the system failing if the probabilities of the events in the fault tree can be estimated. In most cases, this requires a good understanding of the reliability of instruments, alarms, and safety devices, since these devices would be expected to maintain the process in a safe condition. If the failure rate, λ, is the number of occasions per year that a protective system develops a fault (yr−1) and the time interval between tests of the device is τ years, then intuitively, the device on average fails halfway between tests. The probability that the device is inactive and will fail on demand (also known as the fractional dead time) is then approximately ϕ=

λτ 2

(10.6)

If the demand rate, δ, is the number of occasions per year that the protective device is actuated then the hazard rate, F, is δλτ (10.7) F = δϕ = 2 The intuitive result in Equation 10.7 is true if and only if δλ, λτ, and δτ are all ≪ 1. For a more rigorous analysis of reliability see Chapters 7 and 13 of Mannan (2004). It can be seen that for a simple system with a single device, the demand rate is the inherent frequency of the hazard, δ = Fnp, and the probability of the device being inactive is the average probability of failure on demand, ϕ = PFDav. Equations 10.7 and 10.5 are therefore equivalent.

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The hazard rate can be reduced by using more reliable equipment (lower value of λ), more frequent testing (lower τ), or making improvements that lead to steadier operation (lower δ). Alternatively, two protective systems in parallel can be installed, in which case the hazard rate becomes F=

4 δϕ ϕ 3 A B

(10.8)

where ϕA = is the fractional dead time for system A. ϕB = is the fractional dead time for system B, and subject to the same conditions listed above.

Example 10.3 Laboratory test data for a trip system shows a failure rate of 0.2 per year. If the demand rate is once every two years and the test interval is six months, what is the hazard rate? Should a parallel system be installed? Fractional dead time, ϕ =

λ δ 0:2 × 0:5 = = 0:05 2 2

(10.5)

Hazard rate for single system, F = δϕ = 0:5 × 0:05 = 0:025 , i:e:, once in every 40 years Many plants operate for more than 20 years, so this is probably too high a failure rate to be acceptable. If two systems are used in parallel then F = 4 δ ϕA ϕB = 4 × 0:5 × 0:05 × 0:05 = 1:67 × 10−3 or once in 600 years 3 3 Two systems in parallel should be used, or alternatively, the test frequency could be increased to, say, once every two months, giving a more acceptable failure rate of once in every 120 years. Whether the test frequency could be increased will depend on the extent to which testing the device disrupts plant operations. On a large plant with many safety trips and interlocks it may not be possible to test every system on a frequent basis. The data on probabilities given in this example are for illustration only, and do not represent actual data for these components. Some quantitative data on the reliability of instruments and control systems is given by Mannan (2004). Examples of the application of quantitative hazard analysis techniques in chemical plant design are given by Wells (1996) and Prugh (1980).

The Center for Chemical Process Safety (CCPS) of the American Institute of Chemical Engineers has published a comprehensive and authoritative guide to quantitative risk analysis, CCPS (1999). The CCPS has also collected extensive data on device reliability; see CCPS (1989). Several other texts are available on the application of risk analysis techniques in the chemical process industries; see CCPS (2000), Frank and Whittle (2001), Cameron and Raman (2005), Crowl and Louvar (2002), Arendt and Lorenzo (2000), Kales (1997), Dodson and Nolan (1999), Green (1983), and Kletz (1999b).

10.8.3 Tolerable Risk and Safety Priorities If the consequences of an incident can be predicted quantitatively (property loss and the possible number of fatalities), then a quantitative assessment can be made of the risk using Equation 10.2.

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479

If the loss can be measured in money, the cash value of the risk can be compared with the cost of safety equipment or design changes to reduce the risk. In this way, decisions on safety can be made in the same way as other design decisions: to give the best return of the money invested. Hazards invariably endanger life as well as property, and any attempt to make cost comparisons will be difficult and controversial. It can be argued that no risk to life should be tolerated; however, resources are always limited and some way of establishing safety priorities is needed. One approach is to compare the risks, calculated from a hazard analysis, with risks that are generally considered acceptable, such as the average risks in the particular industry, and the kind of risks that people accept voluntarily. One measure of the risk to life is the “Fatal Accident Frequency Rate” (FAFR), defined as the number of deaths per 108 working hours. This is equivalent to the number of deaths in a group of 1000 people over their working lives. The FAFR can be calculated from statistical data for various industries and activities; some of the published values are shown in Tables 10.12 and 10.13. Table 10.12 shows the relative position of the chemical industry compared with other industries; Table 10.13 gives values for some of the risks that people accept voluntarily. In the chemical process industries, it is generally accepted that risks with an FAFR greater than 0.4 (one-tenth of the average for industry) should be eliminated as a matter of priority, with the elimination of lesser risks depending on the resources available; see Kletz (1977a). This criterion is for risks to employees; for risks to the general public (undertaken involuntarily) a lower criterion must be used. In the U.K., the Health and Safety Executive has developed the “as low as reasonably practicable” (ALARP) principle, under which owners can operate a plant in a region defined

Table 10.12 FAFR for Some Industries for the Period 1978–90 Industry Chemical industry UK manufacturing Deep sea fishing

FAFR 1.2 1.2 4.2

Table 10.13 FAFR for Some Nonindustrial Activities Activity Staying at home Travelling by rail Travelling by bus Travelling by car Travelling by air Travelling by motorcycle Rock climbing Source: Brown (2004).

FAFR 3 5 3 57 240 660 4000

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CHAPTER 10 Safety and Loss Prevention

as tolerable risk, as long as they can demonstrate that they have achieved the lowest risk possible taking into account cost versus risk reduction. The tolerable risk region is defined as a fatality frequency of 10−3 to 10−6 per person per year for workers and 10−4 to 10−6 per person per year for the general public; see Schmidt (2007). The level of risk to which the public outside the factory gate should be exposed by plant operations will always be a matter of debate and controversy. Kletz (1977b) suggested that a hazard can be considered acceptable if the average risk is less than one in 10 million, per person, per year. This is an order of magnitude lower than the UK HSE guideline and is equivalent to a FAFR of 0.001; about the same as the chance of being struck by lightning. Additional guidelines on setting tolerable risk are given by Schmidt (2007). There is currently no accepted national guideline on tolerable risk in the United States or Canada. For further reading on the subject of tolerable risk and risk management, see Cox and Tait (1998) and Lowrance (1976).

10.8.4 Computer Software for Quantitative Risk Analysis The assessment of the risks and consequences involved in the planning and operation of a major plant site is a daunting task. In industrial practice, the safety instrumented systems that are used are more complex than the simple systems described above. If two instruments are used in parallel, with either instrument able to activate a shutdown (a “one out of two” system, denoted 1oo2) then the probability of failure on demand is reduced, as illustrated in Example 10.3, but the likelihood of a spurious shutdown due to instrument failure is doubled. The instrument engineer can overcome this problem by using three instruments with a voting policy that requires two out of three of the instruments to activate before a shutdown is caused (2oo3 voting). The use of programmable logic controllers, distributed control systems, and device communication methods such as Fieldbus means that the reliability of many electrical, electronic, and software components must also be considered in the analysis. Credit can also be taken for the performance of the basic process control system (BPCS) as a layer of safety protection (IEC 61511). The calculations soon become too complex to be carried out without using a computer. The methodology of the classical method of quantitative risk analysis is shown in Figure 10.9. First, the likely frequency of failure of equipment, pipelines, and storage vessels must be predicted using the techniques described above. The probable magnitude of any discharges must then be estimated, and the consequences of failure evaluated: fire, explosion, or toxic fume release. Other factors, such as site geography, weather conditions, site layout, and safety management practices, must be taken into consideration. The dispersion of gas clouds can be predicted using suitable models. This methodology enables the severity of the risks to be assessed. Limits have to be agreed on the acceptable risks, such as the permitted concentrations of toxic gases. Decisions can then be made on the location of plant equipment (see Chapter 11), on the suitability of a site location, and on emergency planning procedures. The comprehensive and detailed assessment of the risks required for a “safety-case” can only be satisfactorily carried out for major installations with the aid of computer software. Programs for quantitative risk analysis have been developed by consulting firms that specialize in safety and environmental protection. Typical of the software available is the SAFETI (Suite for Assessment of Flammability Explosion and Toxic Impact) suite of programs developed by DNV Technica Ltd. (www.dnv.com). These programs were initially developed for the authorities in the Netherlands, as a response to the Seveso Directives of the EU. The programs have subsequently been developed

10.9 Pressure Relief

481

Plant data

Management factors

Generate failure cases

Failure rate data

Calculate consequences Meteorological data Population data

Calculate risks Ignition sources Assess risks

FIGURE 10.9 Quantitative risk assessment procedure.

further and extended, and are widely used in the preparation of safety cases; see Pitblado, Shaw, and Stevens (1990). Other examples include PHAWorks and FaultrEASE from Chempute Inc. (www .chempute.com); FTA-Pro and PHA-Pro from Dyadem (www.dyadem.com); RENO and BlockSim7 from Reliasoft (www.risk-analysis-software.org) and LOGAN from Reliass (www.reliability-safetysoftware.com). These and other programs for fault tree analysis, HAZOP, process hazard analysis, and quantitative risk analysis are easily found by searching online, and most chemical companies license one of these programs. Some of the programs offer free trial versions and reduced-cost student subscriptions. Computer programs can be used to investigate a range of possible scenarios for a site; but, as with all computer software used in design, they should not be used without caution and judgment. They would normally be used with the assistance and guidance of the consulting firm supplying the software. With intelligent use, guided by experience, such programs can indicate the magnitude of the likely risks at a site, and allow sound decisions to be made when licensing a process operation or granting planning permission for a new installation.

10.9 PRESSURE RELIEF Pressure relief devices are an essential requirement for the safe use of pressure vessels. Pressure relief devices provide a mechanical means of ensuring that the pressure inside a vessel cannot rise to an unsafe level. All pressure vessels within the scope of Section VIII of the ASME Boiler and

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CHAPTER 10 Safety and Loss Prevention

Pressure Vessel Code must be fitted with a pressure relief device. The purpose of the pressure relief device is to prevent catastrophic failure of the vessel by providing a safe means of relieving overpressure if the pressure inside the vessel exceeds the maximum allowable working pressure. Three different types of relief device are commonly used: • • •

Directly actuated valves: weight or spring-loaded valves that open at a predetermined pressure, and that normally close after the pressure has been relieved. The system pressure provides the motive power to operate the valve. Indirectly actuated valves: pneumatically- or electrically-operated valves that are activated by pressure-sensing instruments. Bursting discs: thin discs of material that are designed and manufactured to fail at a predetermined pressure.

Relief valves are normally used to regulate minor excursions of pressure and bursting discs as safety devices to relieve major overpressure. Bursting discs are often used in conjunction with relief valves to protect the valve from corrosive process fluids during normal operation. The design and selection of relief valves is discussed by Morley (1989a,b), and is also covered by the pressure vessel standards; see below. Bursting discs are discussed by Mathews (1984), Asquith and Lavery (1990), and Murphy (1993). The discs are manufactured in a wide range of common engineering steels and alloys as well as a variety of materials for use in corrosive conditions, such as impervious carbon, gold, and silver, and suitable discs can be found for use with all process fluids. Bursting discs and relief valves are proprietary items and the vendors should be consulted when selecting suitable types and sizes. Selection and sizing of the relief device are the responsibility of the end user of the pressure vessel. Rules for the selection and sizing of pressure relief devices are given in the ASME BPV Code Sec. VIII D.1 Parts UG-125 to UG-137 and D.2 Part AR. Under the rules given in ASME BPV Code Sec. VIII D.1, the primary pressure relief device must have a set pressure not greater than the maximum allowable working pressure of the vessel. The primary relief device must be sized to prevent the pressure from rising 10% or 3 psi (20 kPa), whichever is greater, above the maximum allowable working pressure. If secondary relief devices are used, their set pressure must be not greater than 5% above the maximum allowable working pressure. When multiple relief devices are used, their combined discharge must be adequate to prevent the vessel pressure from rising more than 16% or 4 psi (30 kPa), whichever is greater, above the maximum allowable working pressure. In a relief scenario where the pressure vessel is exposed to an external fire, the relief device or devices must prevent the vessel pressure from increasing to more than 21% above the maximum allowable working pressure. Pressure relief devices must be constructed, located, and installed such that they can be easily inspected and maintained. They are normally located at the top of a vessel in a clean, free-draining location. They must be located on or close to the vessel that they are protecting.

10.9.1 Pressure Relief Scenarios Overpressure will occur whenever mass, moles, or energy accumulate in a contained volume or space with a restricted outflow. The rate at which material or energy accumulates determines the pressure rise. If the process control system is not able to respond quickly enough, the pressure relief

10.9 Pressure Relief

483

device must be activated before the vessel ruptures, explodes, or suffers some other catastrophic loss of containment. The first step in designing a pressure relief system is to evaluate the possible causes of overpressure to determine the rate of pressure accumulation associated with each and hence estimate the relief load (the flow rate that must be discharged through the relief device). The API Recommended Practice (RP) 521 suggests the following causes: Blocked Outlet Utility failure

Chemical Reaction External fire

Cooling or reflux failure Inadvertent valve opening Loss of fans Steam or water hammer Adsorbent flow failure

Abnormal heat input Operator error Check valve failure Internal explosion Overheating a liquid full system

Electric Power Loss Accumulation of noncondensable species Failure of automatic controls Loss of heat in series fractionation Volatile material entering system Heat exchanger tube failure

This list is not exhaustive, and the design engineers should always brainstorm for additional scenarios and review the results of FMEA, HAZOP, HAZAN, or other process safety analyses. In evaluating relief scenarios, the design engineer should consider sequential events that result from the same root cause event, particularly when these can increase the relief load. For example, the loss of electric power in a plant that carries out a liquid phase exothermic reaction could have the following impacts: 1. Failure of all or part of the automatic control system 2. Loss of cooling due to failure of cooling water pumps or air coolers 3. Loss of mixing in the reactor due to failure of the stirrer, leading to localized runaway reaction Since these have a common cause they should be considered as simultaneous events for that cause. If two events do not share a common cause then the probability that they will occur simultaneously is remote and is not usually considered (API RP 521, 3.2). Root cause events such as power loss, utility loss, and external fire will often cause multiple other events and hence large relief loads. The rate at which pressure accumulates is also affected by the response of the process control system. API RP 521 recommends that instrumentation should be assumed to respond as designed if it increases the relieving requirement, but no credit should be taken for instrumentation response if it reduces the relieving requirement. For example in Figure 10.10(a), if the outlet control valve becomes blocked and the pressure in the vessel rises, the flow from the pump will initially decrease because of the higher back-pressure. The flow controller will compensate for this by opening the flow control valve to try to maintain a constant flow rate, and will consequently increase the relieving load. The design engineer should assume that the instrumentation responds as designed and the flow rate remains constant. In Figure 10.10(b), if the outlet control valve becomes blocked the pressure controller will continue opening the pressure control valve until it is fully open. This provides an alternative outflow and reduces the relieving load, but according to API RP 521 this response should not be considered.

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PIC

FIC LIC

LIC

(a)

(b)

FIGURE 10.10 Instrumentation response to pressure relief scenarios: (a) Instrumentation response increases relieving load; (b) instrumentation response would reduce relieving load, but API RP 521 recommends taking no credit for instrumentation response.

Heat exchangers and other vessels with internal compartments must also be protected from overpressure in the case of an internal failure. This is of particular importance for shell and tube type exchangers, as the common design practice is to put the higher pressure fluid on the tube side. This saves costs in constructing the shell and also obviates sizing the tubes to withstand a high compressive load due to external pressure. If the tube side is at higher pressure, then in the event of a tube or tubesheet failure the shell will be exposed to the higher tube-side pressure. Both API RP 521 and ASME BPV Code Section VIII allow multiple vessels connected together to be considered as a single unit for relief scenarios, provided that there are no valves or restriction orifices between the vessels and that the design considers the full relieving load of the system (ASME BPV Code Sec. VIII D.1 UG-133).

10.9.2 Pressure Relief Loads The rate at which pressure accumulates can be estimated by making unsteady-state mass, mole, and energy balances around the vessel or system: in + formed by reaction = out + accumulation

(10.9)

Because liquids have very low compressibility, pressure vessels are seldom operated entirely filled with liquid, since small accumulations of material would cause large surges in pressure. Instead, it is common practice to operate with a “bubble” of vapor (often nitrogen) at the top of the vessel. The mass balance equation can then be rearranged into an equation for the rate of change of pressure of this gas with time. For example, consider a vessel of total volume V m3 that is normally operated 80% full of liquid on level control (as in Figure 10.10(a)) and is fed with a flow rate v m3/s of liquid. If the volume of

10.9 Pressure Relief

485

liquid in the vessel is VL, then if the outlet becomes blocked and the liquid is assumed to be incompressible then the change in the volume of the liquid is: d VL =v dt

(10.10)

where t = time, s. The volume occupied by vapor VG = V − VL, so d VG dV = − L = −v dt dt

(10.11)

If there is no vapor flow in or out of the vessel then assuming the vapor behaves as an ideal gas: VG = nRT/P

(10.12)

where n = number of moles in of gas in the vessel, mol R = ideal gas constant, J/mol.K T = temperature, K P = pressure, N/m2 If the temperature is constant (which is valid for a blocked outlet relief scenario) then until the relief valve opens: dP d 1 nRT dVG P2 v =− 2 = = nRT (10.13) dt dt VG nRT VG dt Equation 10.13 can be used to estimate the rate of pressure accumulation. When the relief valve opens it allows vapor to discharge at a flow rate w kg/s. The number of moles of vapor in the vessel is then given by dn = − 1000 w dt Mw where Mw is the average molecular weight of the vapor, g/mol. The equation for the rate of change of pressure becomes dP = RT d n RT dn − n dVG = 2 VG dt dt VG dt dt VG 2 P 1000 RTw v− = Mw P nRT

(10.14)

(10.15)

If the relief valve is sized correctly then the maximum pressure that can accumulate is 110% of the maximum allowable working pressure, Pm (ASME BPV Code Sec. VIII D.1 UG-125). At this point there is no further accumulation of pressure and dP/dt = 0, hence 1000 RTw =v Mw × 1:1Pm

(10.16)

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CHAPTER 10 Safety and Loss Prevention

and the required relief load is w=

1:1Pm Mw v 1000 RT

(10.17)

Equation 10.17 applies as long as only vapor is vented from the vessel. Once the vapor has been displaced by liquid then the relief load must be the liquid flow rate. If a two-phase mixture is vented then the calculation becomes more complex. In most cases the governing relief scenario includes both material and heat input into the system and typically also includes vaporization of material, reaction, and two-phase flow. Such systems are much more difficult to describe using simple differential algebraic models and the current industrial practice is to use dynamic simulation models for these cases. Dynamic models can be built in any of the commercial process simulators that have this capability. The AIChE Design Institute for Emergency Relief Systems (DIERS) also licenses software called SuperChems™ (formerly SAFIRE) that is written specifically for pressure relief system design and incorporates the DIERS recommended methods and research findings for multiphase, reacting, and highly nonideal systems. For some relief scenarios, correlations have been established for the relieving load. For the external fire case API RP 521 (Section 3.15.2) gives Q = 21000 Fe Aw 0:82 = wf ΔHvap

(10.18)

where Q = heat input due to fire, BTU/hr Fe = environmental factor Aw = internal wetted surface area, ft2 wf = fire case relieving load, lb/hr ΔHvap = heat of vaporization, BTU/lb The environmental factor Fe allows for insulation on the vessel. It is equal to 1.0 for a bare vessel or if the insulation can be stripped off by a liquid jet. The correlation in Equation 10.18 assumes good general design practice and site layout, including use of sewers and trenches or the natural slope of the land to control runoff so that pools do not form. Other formulae for the rate of heat input and relief load are given by ROSPA (1971) and NFPA 30 (2003). Local safety regulations and fire codes should be consulted to determine the appropriate method to use in any particular design. Design codes and standards such as API RP 521 and the DIERS Project Manual (Fisher et al. 1993) should be consulted for other correlations and recommended methods for calculating relief loads. The DIERS Project Manual also discusses calculation of relief loads for underpressure scenarios (see Section 10.9.5).

10.9.3 Design of Pressure Relief Valves Spring-loaded Relief Valves The most commonly used relief device is the conventional spring-loaded relief valve shown in Figure 10.11. This design of valve is available in the widest range of sizes and materials (API Standard 526, BS EN ISO 4126-1:2004). In a conventional relief valve the pressure force acts on a disk that is held against a seating surface by a spring. The compression of the spring can be adjusted using an adjusting screw so that the spring force is equal to the pressure force at the valve set pressure.

10.9 Pressure Relief

487

FIGURE 10.11 Conventional spring-loaded relief valve. Reproduced with permission from API Recommended Practice 520.

The pressure flow response of a conventional relief valve is illustrated schematically in Figure 10.12. When the pressure in the vessel reaches 92% to 95% of the set pressure, a spring-loaded relief valve in a gas or vapor service begins to “simmer” and leak gas. Leakage can be reduced by lapping the disk and seating surface to a high degree of polish, using elastomeric seals (at low

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CHAPTER 10 Safety and Loss Prevention

Flow rate

Secondary lift

Blowdown

Initial “pop”

Leakage −10% of MAWP Normal operating point

Set pressure = Maximum allowable working pressure

+10% of MAWP Maximum relieving pressure

+21% of MAWP Maximum relieving pressure fire scenario

FIGURE 10.12 Pressure–flow response of a conventional spring-loaded relief valve.

temperatures only) or using a high pressure differential between the operating pressure and set pressure. When the set pressure is reached the valve “pops” and the disk lifts from the seat. The disk and seat are shaped such that the force on the disk continues to increase until the valve is fully open, at which point the flow rate is limited only by the bore area of the seating surface and not by the gap between the seating surface and the disk. At this point the design flow rate is achieved and there should be no further pressure accumulation. When the pressure falls sufficiently, the spring force can overcome the forces due to the flowing fluid and the valve reseats. Reseating usually occurs at a lower pressure than the set pressure, giving a different curve for blowdown. The capacity and lift pressure of a conventional spring-loaded relief valve are affected by the back-pressure in the downstream relief system. The back-pressure exerts forces that are additive to the spring force. Where back-pressure is known to fluctuate or accumulate, balanced pressure relief valves that incorporate a bellows or other means of compensating for back-pressure should be used (see API RP 520 for details). This is particularly important when multiple devices are relieved into the same vent or flare system, as common-cause relief scenarios such as power loss can trigger

10.9 Pressure Relief

489

multiple relief events and send a lot of material into the vent or flare system, increasing the back-pressure acting on the relief valves.

Pilot-operated Relief Valves Pilot-operated relief valves are designed to overcome some of the major drawbacks of conventional spring-loaded relief valves. In a pilot-operated relief valve the spring and disk are replaced by a piston, as shown in Figure 10.13. A narrow bore pipe known as a pilot supply line connects from the top of the piston to the relief valve inlet via a secondary (pilot) valve of the spring-loaded type. In normal operation both sides of the valve see the same pressure, but because the top surface area of the piston is greater than the area of the seat, the downward force is greater and the valve remains closed. When the pressure exceeds the set pressure, the pilot valve opens and pressure above the piston is lost. This causes the piston to lift and the valve opens. The pilot valve vent can be exhausted to atmosphere or to the main valve outlet, depending on the containment requirements for the process fluid. The pressure-flow response of a pilot-operated relief valve is illustrated schematically in Figure 10.14. Leakage is eliminated and there is no blowdown.

FIGURE 10.13 Pop-action pilot-operated relief valve. Reproduced with permission from API Recommended Practice 520.

CHAPTER 10 Safety and Loss Prevention

Secondary lift

Flow rate

490

Initial “pop”

−10% of MAWP Normal operating point

Set pressure = Maximum allowable working pressure

+10% of MAWP Maximum relieving pressure

+21% of MAWP Maximum relieving pressure fire scenario

FIGURE 10.14 Pressure–flow response of a pilot-operated relief valve.

Pilot-operated relief valves are used in applications that require a low differential between operating pressure and set pressure (for example, revamps where the vessel is now operated closer to the maximum allowable working pressure or vessels operating below 230 kPa or 20 psig); high pressure services (above 69 bara or 1000 psig); and cases where low leakage is required. They are not available in as broad a range of metallurgies as spring-loaded relief valves. Pilot-operated relief valves are also restricted to lower temperature applications, as they typically use elastomeric materials to make a seal between the piston and its housing. More details of pilot-operated relief valves are given in BS EN ISO 4126-4:2004.

Sizing Relief Valves Guidelines for sizing relief valves are given in API RP 520 and BS EN ISO 4126. Different design equations are recommended for vapor, liquid, steam, or two-phase flows. Sizing methods are also discussed in the DIERS Project Manual (Fisher et al. 1993) and the book by CCPS (1998). When the fluid flowing through the valve is a compressible gas or a vapor, the design must consider whether critical flow is achieved in the nozzle of the valve. The critical flow rate is the maximum flow rate that can be achieved and corresponds to a sonic velocity at the nozzle. If critical flow occurs, the pressure at the nozzle exit cannot fall below the critical flow pressure Pcf, even if a lower pressure exists downstream. The critical flow pressure can be estimated from the upstream pressure for an ideal gas using the equation γ/ðγ−1Þ Pcf 2 = (10.19) γ+1 P1

10.9 Pressure Relief

491

where γ = ratio of specific heats = Cp/Cv P1 = absolute pressure upstream Pcf = critical flow pressure Any consistent set of units may be used for pressure as long as the absolute pressure is used, not the gauge pressure. The ratio Pcf /P1 is called the critical pressure ratio. Typical values of this ratio are given in Table 10.14. If the downstream pressure is less than the critical flow pressure, critical flow will occur in the nozzle. It can be seen from the table that this will be the case whenever the upstream pressure is more than two times the downstream pressure. Since most relief systems are operated close to atmospheric pressure, critical flow is the usual case. For critical flow, API RP 520 (Section 3.6.2) gives the following equation for valve area, Ad: rffiffiffiffiffiffiffi 13, 160 w TZ (10.20) Ad = C Kd P1 Kb Kc Mw where Ad = discharge area, mm2 w = required flow rate,rkg/hr ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðγ+1Þ/ðγ−1Þ C = coefficient = 520 γ γ +2 1 Kd = coefficient of discharge Table 10.14 Critical Flow Pressure Ratios (Adapted from API RP 520) Gas Hydrogen Air Nitrogen Steam Ammonia Carbon dioxide Methane Ethane Ethylene Propane Propylene n-Butane n-Hexane Benzene n-Decane

Specific Heat Ratio γ = Cp /Cv at 60 °F, 1 atm 1.41 1.40 1.40 1.33 1.3 1.29 1.31 1.19 1.24 1.13 1.15 1.19 1.06 1.12 1.03

Critical Flow Pressure Ratio at 60 °F, 1 atm 0.52 0.53 0.53 0.54 0.54 0.55 0.54 0.57 0.57 0.58 0.58 0.59 0.59 0.58 0.60

Notes 1. Taken from API RP 520, Table 7. 2. Some values of critical flow pressure ratio have been determined experimentally and do not necessarily agree with predictions from Equation 10.19.

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CHAPTER 10 Safety and Loss Prevention

P1 = absolute pressure upstream, kPa Kb = back-pressure correction factor Kc = combination correction factor T = relieving temperature, K Z = compressibility at the inlet condition Mw = molecular weight, g/mol For preliminary estimates, the coefficient Kd can be taken as 0.975 for a relief valve and 0.62 for a bursting disk. The back-pressure correction factor, Kb, can initially be assumed to be 1.0 for critical flow. The combination correction factor, Kc, is used when a rupture disk is used upstream of the relief valve (see next section), in which case it is 0.9. If no rupture disk is used then Kc is 1.0. For vessels designed in accordance with ASME BPV Code Sec. VIII, P1 = 1.1 times the maximum allowable working pressure. The relief valve selected should be one with equal or greater area than calculated using Equation 10.20. Relief valve sizes are given in API Standard 526 or BS EN ISO 4126. Sizing equations for subcritical flow of vapors, liquids, steam, and two-phase mixtures are given in API RP 520.

10.9.4 Design of Nonreclosing Pressure Relief Devices Two types of nonreclosing pressure relief devices are used, rupture disks and breaking-pin devices. A rupture disk device consists of a rupture disk and a clamp that holds the disk in position. The disk is made from a thin sheet of metal and is designed to burst if a set pressure is exceeded. Some rupture disks are scored so that they can burst without forming fragments that might damage downstream equipment. Rupture disks are often used upstream of relief valves to protect the relief valve from corrosion or to reduce losses due to relief valve leakage. Large rupture disks are also used in situations that require very fast response time or high relieving load (for example, reactor runaway and external fire cases). They are also used in situations where pressure is intentionally reduced below the operating pressure for safety reasons. The use of bursting disc devices is described in BS EN ISO 4126-2:2004 and BS EN ISO 4126-6:2004. If a rupture disk is used as the primary pressure relief device then when it bursts the operators have no option but to shut down the plant so that the disk can be replaced before the vessel is re-pressured. Rupture disks are therefore most commonly used at the inlets of relief valves or as secondary relief devices. Rupture disks can be sized using Equation 10.20 for compressible gases in sonic flow, with a value of K d = 0.62. The combination of safety valves and rupture discs is discussed in BS EN ISO 4126-3:2004. Breaking-pin devices have a similar construction to spring-loaded relief valves, except the valve disk is held against the seat by a pin that is designed to buckle or break when the set pressure is reached, as illustrated in Figure 10.15. Once the valve has opened the pin must be replaced before the valve can be reset. Both rupture disks and breaking-pin devices are sensitive to temperature. The manufacturer should always be consulted for applications that are not at ambient conditions. Since nonreclosing pressure relief devices can only be used once, the set pressure is determined by testing a sample of the devices out of each manufactured batch. Pressure relief valve test methods are specified in ASME PTC 25-2001.

10.9 Pressure Relief

493

FIGURE 10.15 Buckling-pin relief valve. Reproduced with permission from API Recommended Practice 520.

10.9.5 Design of Pressure Relief Discharge Systems When designing relief venting systems, it is important to ensure that flammable or toxic gases are vented to a safe location. This will normally mean venting at a sufficient height to ensure that the gases are dispersed without creating a hazard. For highly toxic materials it may be necessary to provide a scrubber to absorb and “kill” the material; for instance, the provision of caustic scrubbers for chlorine and hydrochloric acid gases. If flammable materials have to be vented at frequent intervals as, for example, in some refinery operations, flare stacks are used. The rate at which material can be vented will be determined by the design of the complete venting system: the relief device and the associated piping. The maximum venting rate will be limited by the critical (sonic) velocity, whatever the pressure drop. The vent system must be designed such that sonic flow can only occur at the relief valve and not elsewhere in the system, otherwise the design relief load will not be attained. The design of venting systems to give adequate protection against overpressure is a complex and difficult subject, particularly if two-phase flow is likely to occur. When two-phase flow can occur, the relief system must provide for disengagement of liquid from the vapor before the vapor is vented or sent to flare.

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Flare stack

Flare header

Relief valve

Outlet line Water seal pot Knockout drum Liquids to oil recovery or sewer

FIGURE 10.16 Typical relief system design.

Guidelines for relief valve installation and relief system design are given in API RP 520 Part II, API RP 521 Sections 4 and 5, and the DIERS Project Manual (Fisher et al. 1993). API RP 521 also gives design methods for blowdown drums and flare systems. A typical relief system is shown in Figure 10.16. For a comprehensive discussion of the problem of vent system design, and the design methods available, see the papers by Duxbury (1976, 1979) and the guidelines by CCPS (1998).

10.9.6 Protection from Underpressure (Vacuum) Unless designed to withstand external pressure (see Section 14.7) a vessel must be protected against the hazard of underpressure, as well as overpressure. Underpressure will normally mean vacuum on the inside with atmospheric pressure on the outside. It requires only a slight drop in pressure below atmospheric pressure to collapse a storage tank. Though the pressure differential may be small, the force on the tank roof will be considerable. For example, if the pressure in a 10 m diameter tank falls to 10 millibar below the external pressure, the total load on the tank roof will be around 80,000 N (equivalent to 8 metric tons weight). It is not an uncommon occurrence for a storage tank to be sucked in (collapsed) by the suction pulled by the discharge pump, due to the tank vents having become blocked. Where practical, vacuum breakers (valves that open to atmosphere when the internal pressure drops below atmospheric) should be fitted. Example 10.4 A gasoline surge drum has capacity 4 m3 (1060 gal) and is normally operated 50% full at 40 °C (100 °F) under 20 bar absolute pressure (280 psig) of hydrogen in the head space and using a level controlled outflow as shown in Figure 10.10(a). Gasoline of specific gravity 0.7 is pumped into the surge drum at a normal flow rate of 130 m3/hr. Assuming the aspect ratio of the vessel (ratio length/diameter) is 3.0 and the heat of vaporization of gasoline is 180 BTU/lb, evaluate the relief loads for the blocked outflow and external fire cases and hence

10.9 Pressure Relief

495

determine the relief valve size. (In practice, gasoline contains many components that boil over a wide range of temperatures at the design pressure and a more complex calculation is needed than is given here). Blocked Outlet Case

1:1Pm Mw v = 1000 RT

1:1 ×

130 20 × 105 ×2 × 0:9 3600 = 67:8 g/s 1000 × 8:314 × 313

(10.16)

External Fire Case

If the vessel has a hemispherical head then:

2 3 3 volume = π D L + D = 11π D 6 12 4 so D = 1:12 m wetted area = πðDL + D2 Þ/2 = 2πD2 = 7:82 m2 = 84:2 ft2

Assume Fe = 1: 21000 Fe Aw 0:82 21000 × 1 × 84:20:82 = ΔHvap 180 = 4423 lb/hr

wf =

(10.17)

= 0:56 kg/s So the external fire case has the higher relieving load and governs the design. If the vent line discharges to a flare system at atmospheric pressure then Poutlet = 1 2Þ x2 ≥ b ðwhere b < 3Þ hðx1 , x2 Þ = 0

to define a closed search space. It is also possible to overconstrain the problem. For example, if we set the problem Max: s:t:

z = x1 2 + 2x2 2 x 1 + x2 = 5 x2 ≤ 3 x1 ≤ 1

In this case, it can be seen from Figure 12.2 that the feasible region defined by the inequality constraints does not contain any solution to the equality constraint. The problem is therefore infeasible as stated.

12.3.2 Degrees of Freedom If the problem has n variables and me equality constraints then it has n − me degrees of freedom. If n = m e then there are no degrees of freedom and the set of m e equations can be solved for the n variables. If me > n then the problem is overspecified. In most cases, however, me < n and n − me is the number of parameters that can be independently adjusted to find the optimum.

12.3 Constraints and Degrees of Freedom

Max s.t.

x2 5

529

z = x12 + 2 x2 2 x1+ x2 = 5 x2 ≤ 3 x1 ≤ 1

The feasible region defined by the inequalities has no solution for the equality constraint

FIGURE 12.2 An overconstrained problem.

When inequality constraints are introduced into the problem, they generally set bounds on the range over which parameters can be varied and hence reduce the space in which the search for the optimum is carried out. Very often, the optimum solution to a constrained problem is found to be at the edge of the search space, i.e., at one of the inequality constraint boundaries. In such cases, that inequality constraint becomes equal to zero (as written in Equation 12.2) and is said to be “active.” It is often possible to use engineering insight and understanding of chemistry and physics to simplify the optimization problem. If the behavior of a system is well understood, then the design engineer can decide that an inequality constraint is likely to be active. By converting the inequality constraint into an equality constraint, the number of degrees of freedom is reduced by one and the problem is made simpler. This can be illustrated by a simple reactor optimization example. The size and cost of a reactor are proportional to residence time, which decreases as temperature is increased. The optimal temperature is usually a trade-off between reactor cost and the formation of by-products in side reactions; but if there were no side reactions, then the next constraint would be the maximum temperature allowed by the pressure vessel design code. More expensive alloys might allow for operation at higher temperatures. The variation of reactor cost with temperature will look something like Figure 12.3, where TA, TB, and TC are the maximum temperatures allowed by the vessel design code for alloys A, B, and C, respectively. The design engineer could formulate this problem in several ways. It could be solved as three separate problems, one corresponding to each alloy, each with a constraint on temperature T < Talloy. The design engineer would then pick the solution that gave the best value of the objective function. The problem could also be formulated as a mixed integer nonlinear program with integer variables to determine the selection of alloy and set the appropriate constraint (see Section 12.11). The design engineer could also recognize that alloy A costs a lot less than alloy B, and the higher alloys only give a relatively small extension in the allowable temperature range. It is clear that cost decreases with temperature, so the optimum temperature will be TA for alloy A and TB for alloy B. Unless the design engineer is aware of some other effect that has an impact on cost as temperature is increased, it is safe to write T = TA as an equality constraint and solve the resulting problem. If the cost of alloy B is not excessive then it would be prudent to also solve the problem with T = TB, using the cost of alloy B.

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CHAPTER 12 Optimization in Design

Reactor cost

Alloy A

There is a step change in cost when a higher alloy is needed TA

Temperature

FIGURE 12.3 Variation of reactor cost with temperature.

The correct formulation of constraints is the most important step in setting up an optimization problem. Inexperienced engineers are often unaware of many constraints and consequently find “optimal” designs that are dismissed as unfeasible by more experienced designers.

12.4 TRADE-OFFS If the optimal value of the objective is not at a constraint limit, it will usually be determined by a trade-off between two or more effects. Trade-offs are very common in design, because better performance in terms of increased purity, increased recovery, or reduced energy or raw materials use usually comes at the expense of higher capital expense, operating expense, or both. The optimization problem must capture the trade-off between cost and benefit. A well-known example of a trade-off is the optimization of process heat recovery. A high degree of heat recovery requires close temperature approaches in the heat exchangers (see Section 3.5), which leads to high capital cost as the exchangers require more surface area. If the minimum temperature approach is increased, the capital cost is reduced but less energy is recovered. We can plot the capital cost and energy cost against the minimum approach temperature, as shown schematically in Figure 12.4. If the capital cost is annualized (see Section 9.7) then the two costs can be added to give a total cost. The optimum value of the approach temperature, ΔT optimum , is then given by the minimum point in the total cost curve. Some common trade-offs encountered in design of chemical plants include: • • • • • • •

More separations equipment and operating cost versus lower product purity More recycle costs versus increased feed use and waste formation More heat recovery versus cheaper heat-exchange network Higher reactivity at high pressure versus more expensive reactors and higher compression costs Fast reactions at high temperature versus product degradation Marketable by-products versus more plant expense Cheaper steam and electricity versus more offsite capital cost

12.5 Problem Decomposition

531

Total Cost

Cost

Energy Cost

Capital Cost ΔToptimum

Minimum approach temperature

FIGURE 12.4 The capital-energy trade-off in process heat recovery.

Stating an optimization problem as a trade-off between two effects is often useful in conceptualizing the problem and interpreting the optimal solution. For example, in the case of process heat recovery, it is usually found that the shape of the total cost curve in Figure 12.4 is relatively flat over the range 15 °C < ΔToptimum < 40 °C. Knowing this, most experienced designers would not worry about finding the value of ΔToptimum , but would instead select a value for the minimum temperature approach within the range 15 °C to 40 °C, based on knowledge of the customer’s preference for high energy efficiency or low capital expense.

12.5 PROBLEM DECOMPOSITION The task of formally optimizing the design of a complex processing plant involving several hundred variables, usually with highly nonlinear relationships between the variables, is formidable, if not impossible. The task can be reduced by dividing the process into more manageable units, identifying the key variables, and concentrating work where the effort will give the greatest benefit. Some caution is needed when optimizing subproblems. Subdivision, and optimization of the subunits rather than the whole, will not necessarily give the optimum design for the whole process. The optimization of one unit may be at the expense of another. For example, it will usually be satisfactory to optimize the reflux ratio for a distillation column independently of the rest of the plant; but if the column is part of a separation stage following a reactor, in which the product is separated from the unreacted materials, then the design of the column will interact with, and may well determine, the optimization of the reactor design. Care must always be taken to ensure that subcomponents are not optimized at the expense of other parts of the plant. Equipment optimization is usually treated as a subproblem that is solved after the main process variables such as reactor conversion, recycle ratios, and product recoveries have been optimized. For example, the detailed design of heat exchangers is usually a trade-off between pressure drop and heat transfer. Higher shell- or tube-side velocities will give a higher heat-transfer coefficient, leading to a lower area and cheaper exchanger, but will also cause a higher pressure drop. A common practice is to make an allowance for exchanger pressure drop when solving the process

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flowsheet, and then optimize the heat exchanger design subject to not exceeding the constraint of allowable pressure drop during detailed design. If heat exchanger costs are a significant fraction of total capital cost, this approach can lead to poor overall optimization, as the arbitrary assignment of pressure drops and inaccurate estimation of heat transfer coefficients in the process-level model will probably not lead to the optimal design. Another example of a problem decomposition that is often applied is the use of the pinch design method in heat-exchanger network design, described in Sections 3.5.1 and 3.5.3. If we choose to follow the pinch design rule then no heat should be transferred across the pinch and the heatexchanger network design problem is decomposed into two separate, smaller problems above and below the pinch. This is convenient, particularly when solving relatively small problems as hand calculations. Unfortunately, this approach has the drawback that we might miss opportunities to match the same streams above and below the pinch and hence reduce the number of exchangers needed by combining an exchanger from the above pinch problem with one from the below pinch problem. When designing large networks involving many process streams and multiple utility streams, the imposition of utility pinches as well as process pinches can lead to the formation of impractical networks with many small heat exchangers.

12.6 OPTIMIZATION OF A SINGLE DECISION VARIABLE If the objective is a function of a single variable, x, the objective function f(x) can be differentiated with respect to x to give f′(x). Any stationary points in f(x) can then be found as the solutions of f ′(x) = 0. If the second derivative of the objective function is greater than zero at a stationary point then the stationary point is a local minimum. If the second derivative is less than zero then the stationary point is a local maximum and if it is equal to zero then it is a saddle point. If x is bounded by constraints, then we must also check the values of the objective function at the upper and lower limiting constraints. Similarly, if f(x) is discontinuous, then the value of f(x) on either side of the discontinuity should also be checked. This procedure can be summarized as the following algorithm: Min: z = f ðxÞ s:t:

x ≥ xL

(12.3)

x ≤ xU 0 to find values of xS. Solve f ′ = dfdxðxÞ = 2 Evaluate f ″ = d dxf ðxÞ 2 for each value of xS. If f ″> 0 then xS corresponds to a local minimum in f(x). Evaluate f(xS), f(xL), and f(xU). If the objective function is discontinuous then evaluate f(x) on either side of the discontinuity, xD1 and xD2. 5. The overall optimum is the value from the set (xL, xS, xD1, xD2, xU) that gives the lowest value of f(x).

1. 2. 3. 4.

This is illustrated graphically in Figure 12.5(a) for a continuous objective function. In Figure 12.5(a), xL is the optimum point, even though there is a local minimum at xS1. Figure 12.5(b) illustrates the case of

12.7 Search Methods

533

xD2

xS2 xD1

xS1

x (a)

x (b)

FIGURE 12.5 Optimization of a single variable between bounds.

a discontinuous objective function. Discontinuous functions are quite common in engineering design, arising, for example, when changes in temperature or pH cause a change in metallurgy. In Figure 12.5(b) the optimum is at xD1, even though there is a local minimum at xS. If the objective function can be expressed as a differentiable equation then it is usually also easy to plot a graph like those in Figure 12.5 and quickly determine whether the optimum lies at a stationary point or a constraint.

12.7 SEARCH METHODS In design problems, the objective function very often cannot be written as a simple equation that is easily differentiated. This is particularly true when the objective function requires solving large computer models, possibly using several different programs and requiring several minutes, hours, or days to converge a single solution. In such cases, the optimum is found using a search method. The concept of search methods is most easily explained for single variable problems, but search methods are at the core of the solution algorithms for multivariable optimization as well.

12.7.1 Unrestricted Search If the decision variable is not bounded by constraints then the first step is to determine a range in which the optimum lies. In an unrestricted search we make an initial guess of x and assume a step size, h. We then calculate z1 = f(x), z2 = f(x + h), and z3 = f(x − h). From the values of z1, z2, and z3 we determine the direction of search that leads to improvement in the value of the objective, depending on whether we wish to minimize or maximize z. We then continue increasing (or decreasing) x by successive steps of h until the optimum is passed. In some cases, it may be desirable to accelerate the search procedure, in which case the step size can be doubled at each step. This gives the sequence f(x + h), f(x + 3h), f(x + 7h), f(x + 15h), etc. Unrestricted searching is a relatively simple method of bounding the optimum for problems that are not constrained. In engineering design problems it is almost always possible to state upper and lower bounds for every parameter, so unrestricted search methods are not widely used in design. Once a restricted range that contains the optimum has been established, restricted range search methods can be used. These can be broadly classified as direct methods that find the optimum by

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eliminating regions in which it does not lie, and indirect methods that find the optimum by making an approximate estimate of f′(x).

12.7.2 Regular Search (Three-point Interval Search) The three-point interval search starts by evaluating f(x) at the upper and lower bounds, xL and xU, and at the center point (xL + xU)/2. Two new points are then added in the midpoints between the bounds and the center point, at (3xL + xU)/4 and (xL + 3xU)/4, as shown in Figure 12.6. The three adjacent points with the lowest values of f(x) (or the highest values for a maximization problem) are then used to define the next search range. By eliminating two of the four quarters of the range at each step, this procedure reduces the range by half each cycle. To reduce the range to a fraction ε of the initial range therefore takes n cycles, where ε = 0.5n. Since each cycle requires calculating f (x) for two additional points, the total number of calculations is 2n = 2 log ε/log 0.5. The procedure is terminated when the range has been reduced sufficiently to give the desired precision in the optimum. For design problems it is usually not necessary to specify the optimal value of the decision variables to high precision, so ε is usually not a very small number.

12.7.3 Golden-section Search The golden-section search, sometimes called the golden mean search, is as simple to implement as the regular search, but is more computationally efficient if ε < 0.29. In the golden-section search only one new point is added at each cycle. The golden-section method is illustrated in Figure 12.7. We start by evaluating f (xL) and f (xU) corresponding to the upper and lower bounds of the range, labeled A and B in the figure. We then add two new points, labeled C and D, each located a distance ωAB from the bounds A and B, i.e., located at xL + ω(xU − xL) and xU − ω(xU − xL). For a minimization problem, the point that gives the highest value of f (x) is eliminated. In Figure 12.7, this is point B. A single new point, E, is added, such that the new set of points AECD is symmetric with the old set of points ACDB. For the new set of points to be symmetric with the old set of points, AE = CD = ωAD. f(x)

FIGURE 12.6 Regular search.

12.7 Search Methods

535

f (x) ω

A xL

B xU

FIGURE 12.7 Golden-section search.

But we know DB = ωAB, so AD = (1 − ω)AB and CD = (1 − 2ω)AB so ð1 − 2ωÞ = ωð1 − ωÞ pffiffiffi 3± 5 ω= 2 Each new point reduces the range to a fraction (1 − ω) = 0.618 of the original range. To reduce the range to a fraction ε of the initial range therefore requires n = log ε/ log 0.618 function evaluations. The number (1 − ω) is known as the golden mean. The significance of this number has been known since ancient times. Livio (2002) gives a very entertaining account of its history and occurrence in art, architecture, music, and nature.

12.7.4 Quasi-Newton Method Newton’s method is a super-linear indirect search method that seeks the optimum by solving f′(x) and f″(x) and searching for where f′(x) = 0. The value of x at step k + 1 is calculated from the value of x at step k using xk+1 = xk −

f ′ðxk Þ f ″ðxk Þ

(12.4)

and the procedure is repeated until (xk+1 − xk) is less than a convergence criterion or tolerance, ε. If we do not have explicit formulae for f′(x) and f″(x), then we can make a finite difference approximation about a point, in which case xk+1 = xk −

½ f ðxk + hÞ − f ðxk − hÞ/2h ½ f ðxk + hÞ − 2f ðxÞ + f ðxk − hÞ/h2

(12.5)

Care is needed in setting the step size, h, and the tolerance for convergence, ε. The Quasi-Newton method generally gives fast convergence unless f″(x) is close to zero, in which case convergence is poor. All of the methods discussed in this section are best suited for unimodal functions, i.e., functions with no more than one maximum or minimum within the bounded range.

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12.8 OPTIMIZATION OF TWO OR MORE DECISION VARIABLES A two-variable optimization problem can be stated as Min: z = f ðx1 , x2 Þ s:t:

hðx1 , x2 Þ = 0

(12.6)

gðx1 , x2 Þ ≤ 0 For simplicity, all problems will be stated as minimization problems from here on. A maximization problem can be rewritten as Min. z = −f (x1, x2). With two parameters, we can plot contour lines of z on a graph of x1 versus x2 and hence get a visual representation of the behavior of z. For example, Figure 12.8 shows a schematic of a contour plot for a function that exhibits a local minimum of < 30 at about (4,13) and a global minimum of < 10 at about (15,19). Contour plots are useful for understanding some of the key features of multivariable optimization that become apparent as soon as we consider more than one decision variable.

12.8.1 Convexity Constraint boundaries can also be plotted in the (x1, x2) parameter space, as illustrated in Figure 12.9. If the constraints are not linear, then there is a possibility that the feasible region may not be convex. A convex feasible region, illustrated in Figure 12.9(a), is one in which any point on a straight line between any two points inside the feasible region also lies within the feasible region. This can be stated mathematically as x = αxa + ð1 − αÞxb ∈ FR (12.7) ∀xa , xb ∈ FR, 0 < α < 1

Global minimum

50 Contour of z, with value indicated

Local minimum

20 40 10

15 x1

FIGURE 12.8 Optimization of two decision variables.

12.8 Optimization of Two or More Decision Variables

537

x1 (a)

x1 (b)

FIGURE 12.9 Convexity for a two-variable problem. (a) Convex feasible region; (b) nonconvex feasible region.

where xa, xb = any two points belonging to the feasible region FR = the set of points inside the feasible region bounded by the constraints α = a constant If any two points in the feasible region can be found such that some point on a straight line between them lies outside of the feasible region, then the feasible region is nonconvex, as illustrated in Figure 12.9(b). The importance of convexity is that problems with a convex feasible region are more easily solved to a global optimum. Problems with nonconvex feasible regions are prone to convergence to local minima. Nonconvexity is very common in chemical engineering problems, due to the nonlinear nature of many of the equality constraint equations.

12.8.2 Searching in Two Dimensions The procedures for searching in two dimensions are mostly extensions of the methods used for single variable line searches: 1. 2. 3. 4. 5.

Find an initial solution (x1, x2) inside the feasible region. Determine a search direction. Determine step lengths δx1 and δx2. Evaluate z = f(x1 + δx1, x2 + δx2). Repeat steps 2 to 4 until convergence.

If x1 and x2 are varied one at a time then the method is known as a univariate search and is the same as carrying out successive line searches in each parameter. If the step length is determined so as to find the minimum with respect to the variable searched then the calculation steps towards the optimum, as shown in Figure 12.10(a). This method is simple to implement, but can be very slow to converge. Other direct methods include pattern searches such as the factorial designs used in statistical design of experiments (see, for example, Montgomery, 2001), the EVOP method (Box, 1957), and the sequential simplex method (Spendley, Hext, & Himsworth, 1962).

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Start

x1 (a)

(b)

FIGURE 12.10 Search methods. (a) Univariate search; (b) steepest descent.

Indirect methods can also be applied to problems with two or more decision variables. In the steepest descent method (also known as the gradient method), the search direction is along the gradient at point (x1, x2), i.e., orthogonal to the contours of f (x1, x2). A line search is then carried out to establish a new minimum point where the gradient is reevaluated. This procedure is repeated until the convergence criterion is met, as shown in Figure 12.10(b).

12.8.3 Problems in Multivariable Optimization Some common problems that are encountered in multivariable optimization can be described for a two-variable problem and are illustrated in Figure 12.11. In Figure 12.11(a), the shape of the contours is such that a univariate search would be very slow to converge. Using an indirect method such as steepest descent would be more appropriate in this case. Figure 12.11(b) shows the problem of convergence to a local optimum. In this scenario, different answers are obtained for different initial solutions. This problem can be overcome by using pattern searches with a larger grid or by using probabilistic methods such as simulated annealing or genetic algorithms that introduce some possibility of moving away from a local optimum. An introduction to probabilistic methods is given in Diwekar (2003). Probabilistic methods are also useful when faced with a nonconvex feasible region, as pictured in Figure 12.11(c).

12.8.4 Multivariable Optimization When there are more than two decision variables it is much harder to visualize the parameter space, but the same issues of initialization, convergence, convexity, and local optima are faced. The solution of large multivariable optimization problems is at the core of the field of operations research. Operations research methods are widely used in industry, particularly in manufacturing facilities, as discussed in Section 12.12. The following sections give only a cursory overview of this fascinating subject. Readers who are interested in learning more should refer to Hillier and Lieberman (2002) and the other references cited below.

12.9 Linear Programming

539

x2 Start

Start x1

x1 (a)

(b)

x1 (c)

FIGURE 12.11 Common problems in multivariable optimization. (a) Slow convergence; (b) convergence to local optimum; (c) nonconvex feasible region.

12.9 LINEAR PROGRAMMING A set of continuous linear constraints always defines a convex feasible region. If the objective function is also linear and xi > 0 for all xi, then the problem can be written as a linear program (LP). A simple two-variable illustration of a linear program is given in Figure 12.12. Linear programs always solve to a global optimum. The optimum must lie on the boundary at an intersection between constraints, which is known as a vertex of the feasible region. The inequality constraints that intersect at the optimum are said to be active and have h(x) = 0, where x is the vector of decision variables. Many algorithms have been developed for solution of linear programs, of which the most widely used are based on the SIMPLEX algorithm developed by Dantzig (1963). The SIMPLEX method introduces slack and surplus variables to transform the inequality constraints into equalities. For example, if x1 + x2 − 30 ≤ 0 we can introduce a slack variable, S1, and write x1 + x2 − 30 + S1 = 0 The resulting set of equalities is solved to obtain a feasible solution, in which some of the slack and surplus variables will be zero, corresponding to active constraints. The algorithm then searches the vertices of the feasible region, decreasing the objective at each step until the optimum is reached. Details of the SIMPLEX method are given in most optimization or operations research textbooks. See, for example, Hillier and Lieberman (2002) or Edgar and Himmelblau (2001). There have been many improvements to the SIMPLEX algorithm over the years, but it is still the method used in most commercial solvers. Some problems that can occur in solving linear programs are illustrated in Figure 12.13. In Figure 12.13(a), the contours of the objective function are exactly parallel to one of the constraints. The problem is said to be degenerate and has an infinite number of solutions along the line of that constraint. Figure 12.13(b) shows a problem where the feasible region is unbounded. This situation

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CHAPTER 12 Optimization in Design

x2 Contours of z

z x1

FIGURE 12.12 A linear program.

(a)

(b)

(c)

FIGURE 12.13 Problems in linear programming. (a) Objective function parallel to a constraint (degenerate problem); (b) feasible region unbounded; (c) no feasible region.

does not usually occur in engineering design unless the problem has been badly formulated. The situation in Figure 12.13(c) is more common, in which the problem is overconstrained and there is no feasible region. Linear programming can be used to solve very large problems, with thousands of variables and constraints. The method is widely used in operations, particularly in optimization of oil refineries and petrochemical plants. It is used a lot less in design, as design problems almost inevitably contain many nonlinear equations.

12.10 NONLINEAR PROGRAMMING When the objective function and/or the constraints are nonlinear, the optimization must be solved as a nonlinear program (NLP). Three main methods are used for solving a NLP.

12.10 Nonlinear Programming

541

12.10.1 Successive Linear Programming (SLP) In successive linear programming, f (x), g(x), and h(x) are linearized at an initial point. The resulting LP is solved to give an initial solution, and f (x), g(x), and h(x) are linearized again at the new point. The procedure is then repeated until convergence. If the new point is outside the feasible region, the nearest point lying inside the feasible region is used. With SLP there is no guarantee of convergence or global optimality. The method is widely used, nonetheless, as it is a simple extension of linear programming. It should be noted that whenever discontinuous linear functions are used to approximate a nonlinear function, the problem behaves like a SLP. There is no guarantee of convexity or convergence to the optimal solution.

12.10.2 Successive Quadratic Programming (SQP) The SQP algorithm is similar to SLP, but instead approximates f (x) as a quadratic function and uses quadratic programming methods that give faster convergence than SLP. SQP works well for highly nonlinear problems with relatively few variables, for example, optimizing a process simulation or the design of a single piece of equipment. Biegler et al. (1997) suggest SQP is the best method for problems with fewer than fifty variables and where the gradients must be found numerically.

12.10.3 Reduced Gradient Method Reduced gradient methods are related to the SIMPLEX algorithm. The method linearizes the constraints and introduces slack and surplus variables to transform the inequalities into equalities. The n-dimensional vector x is then partitioned into n − m independent variables, where m is the number of constraints. A search direction is determined in the space of the independent variables and a quasi-Newton method is used to determine an improved solution of f (x) that still satisfies the nonlinear constraints. If all the equations are linear, this reduces to the SIMPLEX method (Wolfe, 1962). Various algorithms have been proposed, using different methods for carrying out the search and returning to a feasible solution, for example the generalized reduced gradient (GRG) algorithm (Abadie & Guigou, 1969) and the MINOS algorithm (Murtagh & Saunders, 1978, 1982). Reduced gradient methods are particularly effective for sparse problems with a large number of variables. A problem is said to be sparse if each constraint involves only a few of the variables. This is a common situation in design problems, where many of the constraints are written in terms of only one or two variables. Reduced gradient methods also work better when many of the constraints are linear, as less computational time is spent linearizing constraints and returning the solution to the feasible region. Because of the decomposition of the problem, fewer calculations are required per iteration, particularly if analytical expressions for the gradients are known (which is usually not the case in design). The reduced gradient method is often used in optimizing large spreadsheet models that contain many linear constraints. All of the nonlinear programming algorithms can suffer from the convergence and local optima problems described in Section 12.8.3. Probabilistic methods such as simulated annealing and genetic algorithms can be used if it is suspected that the feasible region is nonconvex or multiple local optima are present.

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12.11 MIXED INTEGER PROGRAMMING Many of the decisions faced in operations involve discrete variables. For example, if we calculate that we need to ship 3.25 trucks of product from plant A to plant B each week, we could send 3 trucks for 3 weeks and then 4 trucks in the fourth week, or we could send 4 trucks each week, with the fourth truck only one-quarter filled, but we cannot send 3.25 trucks every week. Some common operational problems involving discrete variables include: • •

•

Production scheduling: determine the production schedule and inventory to minimize the cost of meeting demand. This is particularly important for batch plants, when the plant can make different products. Transshipment problems and supply chain management: satisfy demands at different producing plants and sales destinations from different supply points, warehouses, and production facilities. Shipping quantities are often constrained to certain size lots corresponding to rail tankers, road tankers, drums, etc. Assignment problems: schedule workers to different tasks.

Discrete variables are also sometimes used in process design, for example, the number of trays or the feed tray of a distillation column, and in process synthesis, to allow selection between flowsheet options, as described below. Discrete decisions are addressed in operations research by introducing integer variables. When integer variables are introduced a linear program becomes a mixed-integer linear program (MILP) and a nonlinear program becomes a mixed-integer nonlinear program (MINLP). Binary integer variables are particularly useful, as they can be used to formulate rules that enable the optimization program to choose between options. For example, if we define y as a binary integer variable such that if y = 1

a feature exists in the optimal solution, and

if y = 0

the feature does not exist in the optimal solution,

then we can formulate constraint equations such as n

∑ yi = 1

choose only one of n options

i=1 n

∑ yi ≤ m

choose at most m of n options

i=1 n

∑ yi ≥ m

choose at least m of n options

i=1

yk − yj ≤ 0 g1 ðxÞ − M y ≤ 0 g2 ðxÞ − Mð1 − yÞ ≤ 0 M is a large scalar value

9 > = > ;

if item k is selected, item j must be selected, but not vice versa either g1 ðxÞ ≤ 0 or g2 ðxÞ ≤ 0

The last rule listed above can be used to select between alternative constraints.

12.11 Mixed Integer Programming

543

12.11.1 Mixed-integer Programming Algorithms Although integer variables are convenient for problem formulation, if too many integer variables are used the number of options explodes in a combinatorial manner and solution becomes difficult. Mixed integer problems can be solved efficiently using methods such as the “branch and bound” algorithm. The branch and bound method starts by treating all integer variables as continuous and solving the resulting LP or NLP to give a first approximation. All integer variables are then rounded to the nearest integer to give a second approximation. The problem is then partitioned into two new integer problems for each integer variable that had a nonintegral solution in the first approximation. In one branch a constraint is added that forces the integer variable to be greater than or equal to the next highest integer, while in the other branch a constraint is added that forces the variable to be equal to or less than the next lowest integer. For example, if a variable was found to have an optimal value y = 4.4 in the first approximation, then the new constraints would be y ≥ 5 in one branch and y ≤ 4 in the other. The branched problems are then solved to give new first approximations, and the branching procedure is repeated until an integer solution is found. When an integer solution is found, it is used to set a bound on the value of the objective. For example, in a minimization problem, the optimal solution must be less than or equal to the bound set by this integral solution. Consequently, all branches with greater values of the objective can be discarded, as forcing the variables in these branches to integer values will lead to deterioration in the objective rather than improvement. The procedure then continues branching on all the nonintegral integer variables from each first approximation, setting new bounds each time an improved integer solution is found, until all of the branches have been bounded and the optimal solution has been obtained. See Hillier and Lieberman (2002) or Edgar and Himmelblau (2001) for details of the algorithm and examples of its application. The branch and bound method can be used for MINLP problems, but it requires solving a large number of NLP problems and is, therefore, computationally intensive. Instead, methods such as the Generalized Benders’ Decomposition and Outer Approximation algorithms are usually preferred. These methods solve a master MILP problem to initialize the discrete variables at each stage and then solve a NLP subproblem to optimize the continuous variables. Details of these methods are given in Floudas (1995), Biegler et al. (1997), and Diwekar (2003).

12.11.2 Superstructure Optimization Binary integer variables can be used to formulate optimization problems that choose between flowsheet options. For example, consider the problem of selecting a reactor. We can set up a unit cell consisting of a well-mixed reactor, a plug-flow reactor, and a bypass in parallel, each with a valve upstream, as illustrated in Figure 12.14(a). If a binary variable is used to describe whether the valve is open or closed and a constraint is introduced such that only one of the valves is open, then the optimization will select the best option. A set of such unit cells can be built into a superstructure, incorporating additional features such as recycles, as shown schematically in Figure 12.14(b). A more rigorous superstructure that encompasses other options such as side-stream feeds to the PFR was developed by Kokossis and Floudas (1990). The optimization of such a superstructure can identify reactor networks or mixing arrangements that would not be intuitively obvious to the design engineer. Similar superstructure formulations have been proposed for other process synthesis problems such as distillation column sequencing,

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Binary variable determines if valve is open or closed 3

Σ y =1 i

i =1

(b)

(a)

FIGURE 12.14 Application of integer programming to reactor design. (a) Unit cell of reactor options; (b) superstructure of unit cells and recycles.

design of heat-exchange networks and design of site utility systems. Biegler et al. (1997) give an excellent overview of the use of superstructure-based methods in process synthesis.

12.12 OPTIMIZATION IN INDUSTRIAL PRACTICE 12.12.1 Optimization of Process Operations

Perhaps not surprisingly, operations research methods are widely used in process operations. Few manufacturing plants do not use LP or MILP tools for planning and scheduling. Supply chain management is very important to economic performance, and is usually carried out using large MILP models. The models used in industry for these purposes are often not very sophisticated, but proper formulation of constraints and the ability to solve robustly with a large number of variables are usually more important features of tools for these applications. The use of operations research methods for plant and supply chain applications is taught as part of the industrial engineering curriculum in most universities. Chemical engineers considering a career in manufacturing would be well advised to develop a solid grounding in these methods.

12.12.2 Optimization of Batch and Semi-continuous Processes In batch operation, there will be periods when product is being produced, followed by nonproductive periods when the product is discharged and the equipment prepared for the next batch. The rate of production will be determined by the total batch time, productive plus nonproductive periods. Batches per year =

8760 × plant attainment batch cycle time

(12.8)

12.12 Optimization in Industrial Practice

545

where the “plant attainment” is the fraction of the total hours in a year (8760) that the plant is in operation. Annual production = quantity produced per batch × batches per year Cost per unit of production =

annual cost of production annual production rate

(12.9)

With many batch operations, the production rate decreases during the production period; for example, batch reactors and plate and frame filter presses. There is then an optimum batch size, or optimum cycle time, that gives the minimum cost per unit of production. For some continuous processes, the period of continuous production will be limited by gradual changes in process conditions. Examples include the deactivation of catalysts or the fouling of heatexchange surfaces. Production is lost during the periods when the plant is shut down for catalyst renewal or equipment cleaning. As with batch processes, there is an optimum cycle time to give the minimum production cost. The optimum time between shutdowns can be found by determining the relationship between cycle time and cost per unit of production (the objective function) and using one of the optimization techniques outlined in this section to find the minimum. With discontinuous processes, the period between shutdowns will usually be a function of equipment size. Increasing the size of critical equipment will extend the production period, but at the expense of increased capital cost. The designer must strike a balance between the savings gained by reducing the nonproductive period and the increased investment required. In some batch plants several trains of identical equipment are operated in a sequence that allows some degree of heat recovery or enables downstream equipment to operate continuously. In this type of plant the time allowed for each operation in the sequence is optimized so that an overall schedule for the plant can be developed. Scheduling of batch processes is described in Biegler et al. (1997).

12.12.3 Optimization in Process Design Few, if any, industrial designs are rigorously optimized. This is because: 1. The cost of building rigorous models of reactor kinetics and hydraulics that give accurate prediction of by-product yields is usually not justified. The amount of time available for the project is usually insufficient for such models to be built. The errors introduced by uncertainty in the process models may be much larger than the differences in performance predicted for different designs. 2. The uncertainty in the forecasts of future prices is usually so large that it dominates most differences between design alternatives. 3. Regardless of the quality of the tools used, or the experience of the estimator, it is usually impossible to make a capital cost estimate within ±15% without completing a substantial amount of design work (see Chapter 7). Many design decisions are thus made on the basis of sketchy cost estimates. The cost of going back and revisiting these design decisions at a later stage in the project when more design detail is available is usually not justified. 4. Criteria such as safety, operability, reliability, and flexibility are of vital importance in process design. These features make the design more robust to variations in the design assumptions and

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operating requirements. A safe, operable, and reliable plant will often require more expense above the cost of the economically “optimal” design. This extra expense is difficult to trade-off against the nonfinancial benefits of having a process that is easier to run. 5. In most cases there are several “near optimal” designs. The difference between the values of the objective obtained for each of these is often not statistically significant, given the errors in prices, cost estimates, and yields. In industrial process design, optimization usually involves carrying out sufficient analysis to be confident that the design is reasonably close to the optimum. The most important things for the design engineer to understand are: 1. What are the constraints on the design? 2. Which constraints are hard (inviolable) and which are soft (can be modified)? 3. Where are the discontinuities in cost? For example, what conditions cause a change to a more costly metallurgy or a different design code? 4. What are the main design trade-offs? 5. How does the objective function vary with the main process parameters? 6. What are the major cost components of the process (both capital and operating costs) and what radical changes could be made to the process to reduce these costs? Experienced design engineers usually think through these questions carefully, to satisfy themselves that their design is “good enough.” Only very occasionally do they formulate an optimization problem and solve it rigorously.

Example 12.1 Optimize the design of a distillation column to separate 225 metric tons per hour of an equimolar mixture of benzene, toluene, ethylbenzene, paraxylene, and orthoxylene with minimum total annualized cost. The feed is a saturated liquid at 330 kPa. The recovery of toluene in the distillate should be greater than 99%, and the recovery of ethylbenzene in the bottoms should be greater than 99%.

Solution

The first step is to determine the design factor. If we assume a design factor of 10%, then the equipment should be designed for a flow rate of 248 metric tons per hour (t/h). This flow rate is used in simulating the process for the purpose of sizing equipment, but energy consumption must be based on the reboiler and condenser duties expected for a 225 t/h feed rate. This is a single distillation column, which is easy to model in any of the commercial simulation programs. UniSim™ (Honeywell Inc.) was used for the purpose of this example. The simulation was set up using the component recoveries of toluene and ethylbenzene as column specifications, which gave rapid convergence. Tray sizing calculations were run using the UniSim™ tray sizing utility. A tray spacing of 0.61 m (2 feet) was assumed, and other tray parameters were left at the UniSim™ default values. Two meters were added to the column height to allow space for a sump and demister. Sieve trays were used and the stage efficiency was assumed to be 80%. Details of the column simulation and design are given in Examples 4.6 and 4.7.

12.12 Optimization in Industrial Practice

547

To optimize the design, we need to formulate an objective function. The distillation column has the following cost components:

• •

Capital costs: column shell, internals, condenser, receiver drum, reboiler, pumps, piping, instrumentation, structure, foundations, etc. Operating costs: cost of heating for the reboiler and cost of cooling for the condenser

The purchased equipment costs can be estimated based on information from the process simulation using the cost correlations given in Chapter 7. The column shell is a pressure vessel and the design can be completed using the methods given in Chapter 14. The details of how to complete these calculations are not important here, but Example 14.2 and Example 7.3 provide detailed explanations of the method followed. Carbon steel construction was assumed. The purchased equipment costs can be converted into an installed capital cost by multiplying by an installation factor. For the purposes of this example, the installation factor can be assumed to be 4.0; see Section 7.6. The installed capital costs can be converted into an annual capital charge by dividing by 3, using a rule of thumb that is developed in Section 9.7. The operating costs are simple to estimate from the condenser and reboiler duties if the cost of energy is known. For this example, the cost of heat is taken as $5.5/GJ and the cost of cooling is $0.2/GJ. The objective function can then be written as Min:: Total annualized cost ðTACÞ = cost of heating + cost of cooling + annualized capital cost = 5:5Qr + 0:2Qc + ð4/3Þð∑ purchased equipment costsÞ where Qr = annual reboiler energy consumption (GJ/yr) Qc = annual condenser energy consumption (GJ/yr) The optimization problem is strictly a MINLP, as we need to consider discrete variables (number of trays, feed tray) as well as continuous variables (reflux ratio, reboiler duty, etc.). This problem is actually relatively easy to formulate and solve rigorously, but instead we will step through the calculation to illustrate how an experienced industrial designer would approach the problem. Table 12.2 gives the results of several iterations of the optimization. 1. To begin, we need to find a feasible solution. As an initial guess we can use 40 trays with the feed on tray 20. The column converges with a reflux ratio of 3.34 and diameter 5.49 m. This is large, but not unreasonable for such a high flow rate. Looking at the components of the total annualized cost, the capital is contributing $0.8 MM/yr and energy is contributing $8.6 MM/yr, so the costs are dominated by energy cost. It is clear that adding more stages and reducing the reflux ratio will reduce the total cost. (If capital costs were dominating then we would reduce the number of stages). There is no upper hard constraint on column height, but there is a soft constraint. At the time of writing there are only 14 cranes in the world that can lift a column taller than 80m. There are 48 cranes that can lift a column up to 60 m. We can therefore expect that the cost of lifting a column > 60 m height will go up as it becomes more expensive to rent the necessary equipment for installation. We can start by assuming a soft constraint that the maximum height must be less than 60m. 2. Using 90 trays with feed on tray 45 gives a reflux ratio of 2.5 and diameter 4.42 m. The column height is 56 m, which allows some space for vessel supports and clearance for piping at the column base and still comes in under the 60 m target. The capital cost increases to $0.95 MM/yr, while energy cost is reduced to $6.96 MM/yr, giving a total annualized cost of $7.91 MM/yr and savings of $1.5 MM/yr relative to the initial design.

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Table 12.2 Optimization Results Iteration Number

Number of trays Feed tray Column height (m) Column diameter (m) Reflux ratio Reboiler duty, Qr (GJ) Condenser duty, Qc (GJ) Annualized capital cost (MM$/y) Annual energy cost (MM$/y) Total annualized cost (MM$/y)

40 20 26.4 5.49 3.34 34.9 33.9 0.82 8.59 9.41

90 45 56.9 4.42 2.50 28.3 27.3 0.95 6.96 7.91

3 120 60 75.2 4.42 2.48 28.2 27.2 1.25 6.93 8.18

4 70 35 44.7 4.42 2.57 28.8 27.8 0.83 7.10 7.93

5 80 40 50.8 4.42 2.52 28.5 27.5 0.89 7.01 7.900

6 76 38 48.4 4.42 2.54 28.6 27.6 0.87 7.04 7.905

7 84 42 53.2 4.42 2.51 28.4 27.4 0.91 6.99 7.904

80 27 50.8 4.42 2.48 28.2 27.2 0.89 6.93 7.82

80 53 50.8 4.57 2.78 30.4 29.4 0.94 7.50 8.44

3. We should explore whether going to an even taller column would make sense. We can investigate this by increasing the installation factor from 4 to 5 for the column shell to allow for the higher cost of using one of the larger cranes. If we increase the number of trays to 120, the column height is 75 m, which will give a total height of close to 80 m when installed. The total annualized cost increases to $8.2 MM/yr, so we can conclude that it is probably not economical to go to a total height above 60 m. We can notice though that the reflux ratio didn’t change much when we added extra trays. This suggests that we are getting close to minimum reflux. It might therefore be worth backing off from the maximum column height constraint to see if there is an optimum number of trays. 4. Adding a design with 70 trays and feed on tray 35 (roughly halfway between 40 and 90) gives reflux ratio 2.57 and total annualized cost $7.94 MM/yr. This is not an improvement on the 90-tray design, so the optimum must be between 70 and 90 trays. 5. A design with 80 trays and feed on tray 40 (half way between 70 and 90) gives reflux ratio 2.52 and total annualized cost $7.90 MM/yr. This is better than 70 or 90 trays. If we wanted to proceed further to establish the optimum we could continue reducing the search space using a regular search until we get to the optimum number of trays. Instead, an experienced designer would note that the difference in cost within the range examined ($0.03 MM/yr) is relatively small compared with the error in the capital cost estimate (±30%, or $0.29 MM/yr). Since the optimum appears to be fairly flat with respect to number of trays over the range 70 to 90, it is reasonable to take the optimum as 80 trays. (As a confirmation, iterations 6 and 7, with 76 and 84 trays indicate that the optimum indeed lies at 80 ±2 trays). 6. Having fixed the number of trays at 80, we should now optimize the feed tray. We start by adding two new points, with the feed tray at trays 27 and 53. These give total annualized costs of $7.82 MM/yr and $8.43 MM/yr, respectively. The minimum cost is given by the lower bound on feed tray location. If we try a higher feed tray (say, tray 26) the UniSim™ tray sizing utility gives a warning “head loss under downcomers is too large.” We could overcome this warning by modifying the tray design, but once again we can notice that the annualized cost savings that we have gained by optimizing feed tray ($0.08 MM/yr) is small compared to the error in the capital cost, so the design with feed tray 27 is close enough to optimum. The column design is thus set at 80 trays, with feed on tray 27, giving a column 50.8 m high and 4.42 m diameter.

Nomenclature

549

The solution obtained is “good enough,” but is not rigorously optimal. Several possible variations in flow scheme were not considered. For example, we could have examined use of feed preheat, intermediate stage condensers, or reboilers, or more efficient column internals such as high-efficiency trays or structured packing. The column cost may also be reduced if different diameters or different internals were used in the rectifying and stripping sections. In the broader context of the process, it may be possible to supply the heat required for the reboiler using heat recovered from elsewhere in the process, in which case the cost of energy will be reduced and the capital energy trade-off will be altered. In the overall process context, we could also question whether the column needs such high recoveries of toluene and ethylbenzene, since the high recoveries clearly lead to a high reflux rate and column energy cost.

References Abadie, J., & Guigou, J. (1969). Gradient réduit generalisé. Électricité de France Note HI 069/02. Biegler, L. T., Grossman, I. E., & Westerberg, A. W. (1997). Systematic methods of chemical process design. Prentice Hall. Box, G. E. P. (1957). Evolutionary operation: a method for increasing industrial productivity. Appl. Statist., 6, 81. Dantzig, G. B. (1963). Linear programming and extensions. Princeton University Press. Diwekar, U. (2003). Introduction to applied optimization. Kluwer Academic Publishers. Edgar, T. E., & Himmelblau, D. M. (2001). Optimization of chemical processes (2nd ed.). McGraw-Hill. Floudas, C. A. (1995). Nonlinear and mixed-integer optimization: fundamentals and applications. Oxford University Press. Hillier, F. S., & Lieberman, G. J. (2002). Introduction to operations research (7th ed.). McGraw-Hill. Kokossis, A. C., & Floudas, C. A. (1990). Optimization of complex reactor networks – 1. Isothermal operation. Chem. Eng. Sci., 45(3), 595. Livio, M. (2002). The golden ratio. Random House. Montgomery, D. C. (2001). Design and analysis of experiments (5th ed.). Wiley. Murtagh, B. A., & Saunders, M. A. (1978). Large-scale linearly constrained optimization. Math. Program., 14, 41. Murtagh, B. A., & Saunders, M. A. (1982). A projected Lagrangian algorithm and its implementation for sparse non-linear constraints. Math. Program. Study, 16, 84. Rudd, D. F., & Watson, C. C. (1968). Strategy of process design. Wiley. Spendley, W., Hext, G. R., & Himsworth, F.R. (1962). Technometrics, 4, 44. Stoecker, W. F. (1989). Design of thermal systems (3rd ed.). McGraw-Hill. Wolfe, P. (1962). Methods of non-linear programming. Notices Am. Math. Soc., 9, 308.

NOMENCLATURE Dimensions in $MLTθ a b f (x) f′(x)

A constant A constant General function of x First derivative of function of x with respect to x

— — — —

(Continued )

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CHAPTER 12 Optimization in Design

Dimensions in $MLTθ f″(x) FR g(x) g(x) h(x) h(x) h M m me mi n Qc Qr S1, S2 … T Talloy TA, TB, TC U x x1, x2 … y1, y2 … z α ε ΔT ΔToptimum δx1, δx2 ω

Second derivative of function of x with respect to x The set of points contained in a feasible region A mi vector of inequality constraints General inequality constraint equation in x A me vector of equality constraints General equality constraint equation in x Step length in a search algorithm A large scalar constant Number of constraints Number of equality constraints Number of inequality constraints Number of variables Condenser duty in distillation Reboiler duty in distillation Slack and surplus variables Temperature Maximum allowed temperature for an alloy Maximum allowed temperature for alloys A, B, and C Overall heat transfer coefficient A vector of n decision variables Continuous variables Integer (discrete) variables The objective (in optimization) A constant between 0.0 and 1.0 Fraction of search range or tolerance for convergence Temperature difference The optimal minimum temperature approach in heat recovery Small increments in x1 and x2 Ratio used in golden-section search (= 0.381966)

— — — — — — — — — — — — ML2T−3 ML2T−3 — θ θ θ MT−3θ−1 — — — — — — θ θ — —

Suffixes D1 D2 i j k L S U

lower side of a discontinuity upper side of a discontinuity ith variable jth variable kth iteration lower bound stationary point upper bound

— — — — — — — —

Problems

551

PROBLEMS 12.1. A separator divides a process stream into three phases: a liquid organic stream, a liquid aqueous stream, and a gas stream. The feed stream contains three components, all of which are present to some extent in the separated steams. The composition and flow rate of the feed stream are known. All the streams will be at the same temperature and pressure. The phase equilibrium constants for the three components are available. a. How many design variables must be specified in order to calculate the output stream compositions and flow rates? b. How would you optimize these variables if the objective of the separator was to maximize recovery of condensable components into the organic liquid stream? What constraints might limit the attainable recovery? 12.2. A rectangular tank with a square base is constructed from 5 mm steel plates. If the capacity required is eight cubic meters determine the optimum dimensions if the tank has: a. A closed top b. An open top 12.3. Estimate the optimum thickness of insulation for the roof of a house given the following information. The insulation will be installed flat on the attic floor. Overall heat transfer coefficient for the insulation as a function of thickness, U values (see Chapter 19): Thickness, mm U, Wm−2K−1

0 20

25 0.9

50 0.7

100 0.3

150 0.25

200 0.20

250 0.15

The cost of insulation, including installation, is $120/m3. Capital charges (see Chapter 9) are 20% per year. The cost of fuel, allowing for the efficiency of the heating system, is $8/GJ. The cost of cooling is $5/GJ. Average temperatures for any region of the United States or Canada can be found online at www.weather.com (under the averages tab). Assume the house is heated or cooled to maintain an internal temperature in the range 70 °F to 80 °F. Note: The rate at which heat is being lost or gained is given by U × ΔT, W/m2, where U is the overall coefficient and ΔT the temperature difference; see Chapter 19. 12.4. What is the optimum practical shape for an above-ground dwelling to minimize the heat losses through the building fabric? When is (or was) this optimum shape used? Why is this optimum shape seldom used in richer societies? 12.5. Hydrogen is manufactured from methane by either steam reforming (reaction with steam) or partial oxidation (reaction with oxygen). Both processes are endothermic. What reactor temperature and pressure would you expect to be optimal for these processes? What constraints might apply?

552

CHAPTER 12 Optimization in Design

12.6. Ethylene and propylene are valuable monomers. A key step in the recovery of these materials is fractionation of the olefin from the corresponding paraffin (ethane or propane). These fractionation steps require refrigeration of the overhead condenser and very large distillation columns with many stages. Raising the pressure at which the column operates improves the performance of the refrigeration system, but increases the number of stages needed. Formulate the objective function for optimizing the recovery of ethylene from an ethylene-ethane mixture. What are the key constraints? What will be the main trade-offs? 12.7. If you had to design a plant for pasteurizing milk, what constraints would you place on the design? 12.8. A catalytic process was designed to make 150,000 metric tons per year of product with a net profit of $0.25/lb of product. The catalyst for the process costs $10/lb and it takes two months to shut down the process, empty the old catalyst, reload fresh catalyst, and restart the process. The feed and product recovery and purification sections can be pushed to make as much as 120% of design basis capacity. The reactor section is sized with sufficient catalyst to make 100% of design basis when operated with fresh catalyst at 500 °F. The reactor can only be operated at temperatures up to 620 °F, for safety reasons. The reactor weight hourly space velocity (lb of product per hour per lb of catalyst) is given by the equation: −8000 expð−8:0 × 10−5 × t × TÞ WHSV = 4:0 × 106 exp T where t = time on stream in months T = temperature Find the optimal temperature versus time profile for the reactor and determine how long the process should be operated before the catalyst is changed out. (Hint: The initial temperature does not have to be 500 °F.) 12.9. The portfolio of investment projects below has been proposed for a company for next year: Project A B C D E F G H I J

Net Present Value (MM$) 100 60 70 65 50 50 45 40 40 30

Cost (MM$) 61 28 33 30 25 17 25 12 16 10

Problems

553

a. Develop a spreadsheet optimization program to select the optimal portfolio of projects to maximize total portfolio net present value (NPV), given a total budget of $100 million. (This is a simple MILP.) b. How would the portfolio and NPV change if the budget was increased to $110 million? c. Because of corporate cost-cutting, the budget is reduced to $80 million. Which projects are now funded and what is the new NPV? d. Based on your answers to parts (a) to (c), can you draw any conclusions on which projects are likely to be funded regardless of the financial situation? e. Can you see any problems with this project selection strategy? If so, how would you recommend they should be addressed?

CHAPTER

Equipment Selection, Specification, and Design

KEY LEARNING OBJECTIVES • Where to find information on process equipment • How to obtain equipment information from vendors

13.1 INTRODUCTION Part I of this book covered process design: the synthesis of the complete process as an assembly of units, each carrying out a specific process operation. In Part II, the selection, specification, and design of the equipment required to carry out these process operations is considered in more detail. In practice, plant design and process design cannot be separated. The selection and specification of one piece of equipment will often require the use of additional equipment and thus have implications on the process flow diagram. For example, if a continuous dryer is selected for drying a solid product, it may be necessary to add a heater to preheat the drying gas, a cyclone or filter to recover solid fines from the off-gas, a cooler and flash drum to cool the off-gas and recover solvent, a vent scrubber to prevent solvent emissions, etc. The design team must understand all the flowsheet implications of equipment selection and design to arrive at an accurate cost estimate and process optimization. This chapter gives a short introduction to the selection and design of process equipment and provides a guide to the following chapters. Most process operations are carried out in closed pressure vessels, which are addressed in Chapter 14. Chapter 15 discusses the design of chemical and biochemical reactors. Separation processes are covered in Chapters 16 and 17. Chapter 18 addresses operations that involve solids handling. Chapter 19 describes the design of equipment for heat transfer and Chapter 20 covers the transport and storage of fluids. Each chapter and section of Part II is intended to be a standalone guide to the design of a particular operation, but in some cases cross references to sections of other chapters are given to avoid duplication. Throughout Part II the emphasis is on selection and sizing of equipment and it is assumed that the reader is familiar with the fundamentals of kinetics, thermodynamics, and transport processes. Further details on the scientific principles and theory that underlie the design and operation of process equipment can be found in the numerous textbooks cited in each section and in general books on unit operations such as McCabe, Smith, and Harriott (2001) and Richardson, Harker, and Backhurst (2002).

557

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CHAPTER 13 Equipment Selection, Specification, and Design

Capital cost correlations for each type of equipment are not given in Part II, as the determination of capital costs for all types of equipment was discussed in Chapter 7. Similarly, materials selection was covered in Chapter 6. Although the role of safety in design was described in Chapter 10, some additional safety issues that are specific to certain unit operations are covered in the relevant sections of Part II.

13.2 SOURCES OF EQUIPMENT DESIGN INFORMATION 13.2.1 Proprietary and Nonproprietary Equipment

The equipment used in the chemical process industries can be divided into two classes: proprietary and nonproprietary. Proprietary equipment, such as pumps, compressors, filters, centrifuges, and dryers, is designed and sold as standard catalog items by specialist manufacturers. Nonproprietary equipment is designed as special, one-off, items for particular processes, for example reactors, distillation columns, and heat exchangers, and is custom-built by specialist fabricators. Unless employed by one of the specialist equipment manufacturers, the chemical engineer is not normally involved in the detailed design of proprietary equipment. The chemical engineer’s job will be to specify the process duty (flowrate, heat load, temperature, pressure, etc.) and then select an appropriate piece of equipment to meet that duty, consulting with the vendors to ensure that the equipment supplied is suitable. Proprietary equipment is often only made in certain standard sizes, and the design engineer must determine which size is best suited for the application, or whether to use multiple units in parallel to accommodate the desired flow. Chemical engineers may be involved with the vendor’s designers in modifying standard equipment for particular applications; for example, a standard tunnel dryer designed to handle particulate solids may be adapted to dry synthetic fibers. As was pointed out in Chapter 1, the use of standard off-the-shelf equipment, whenever possible, will reduce costs. Reactors, columns, flash drums, decanters, and other vessels are usually designed as special items for a given project. In particular, reactor designs are usually unique, except where more or less standard equipment is used, such as an agitated, jacketed vessel. Distillation columns, vessels, and tubular heat exchangers, though nonproprietary items, will be designed to conform to recognized standards and codes; this reduces the amount of design work involved. The chemical engineer’s part in the design of “nonproprietary” equipment is usually limited to selecting and “sizing” the equipment. For example, in the design of a distillation column the design engineer will typically determine the number of plates; the type and design of plate; diameter of the column; and the position of the inlet, outlet, and instrument nozzles. This information would then be transmitted, in the form of sketches and specification sheets, to the specialist mechanical design group, or the fabricator’s design team, for detailed design. It must be emphasized that companies that are engaged in the manufacture of chemicals, fuels, polymers, foods, and pharmaceuticals almost never build their own process equipment. The design engineers from the operating company usually provide specifications to detailed design groups at an Engineering, Procurement, and Construction (EPC) company, who then subcontract the equipment manufacture to specialist equipment fabricators. Even one-of-a-kind items such as reactors, distillation columns, and heat exchangers are built by specialist manufacturers. The accurate transmission of design details is therefore very important, and the process industries have developed many standard specifications to facilitate information exchange with vendors. Standard specifications should be used

13.2 Sources of Equipment Design Information

559

whenever possible, as these lead to cheaper designs and reduce the risk of needing rework during construction.

13.2.2 Published Information on Process Equipment Technical Literature Descriptions and illustrations of most types of process equipment can be found in various handbooks: Green and Perry (2007), Schweitzer (1997), and Walas (1990). Perry’s Chemical Engineers’ Handbook remains the most comprehensive compilation of chemical engineering information. The online version provided by Knovel is the most accessible format. Many specialized books have been written on individual unit operations; these are cited throughout the following chapters. Equipment manufacturers often write articles in the trade journals. Although these are primarily promotional, they can be quite informative. The trade journals also contain advertisements that can help identify manufacturers. Articles by equipment vendors are common in Chemical Engineering and The Chemical Engineer, and appear somewhat less frequently in Chemical Engineering Progress and Hydrocarbon Processing. The journals usually contain a reader response card that can be faxed or mailed in to receive advertisers’ brochures and sales literature. These can be used to build up a library of vendors’ catalogs. Every year the journal Chemical Engineering publishes a buyer’s guide. The Chemical Engineering Buyers’ Guide lists over 500 manufacturers and provides indexes by product type, company name, and trade name, as well as listing web sites and contact information for industry associations. It can be used as a “yellow pages” of chemical industry suppliers, but like other directories it is not fully comprehensive, as not all manufacturers will pay to be listed. In the United Kingdom, a commercial organization, Technical Indexes Ltd., publishes the Process Engineering Index, which contains information from over 3000 manufacturers and suppliers of process equipment globally.

Online Information All equipment vendors now maintain an online presence, but there is a wide variation in the quality of the web sites and the amount of information provided. Several directory sites have been set up to serve the chemical and process industries. Of these, the best at time of writing is www.chemindustry.com, which has links to many vendors. More limited information is also available at www.chemengg.com and www.cheresources.com. A good site for finding new and used equipment for sale is www.equipnet.com. Manufacturers’ web sites are usually easily located using online search engines and often provide details of equipment construction, standard sizes, available metallurgies, specification sheets, and performance information. The Chemical Engineering Buyers’ Guide can also be used to identify vendor web sites for specific equipment types. Manufacturers’ association web sites usually provide the most comprehensive listings of vendors; see for example the web sites of the Valve Manufacturers Association: www.vma.org; Tubular Exchanger Manufacturers Association: http://tema.org; and Conveyor Equipment Manufacturers Association: www.cemanet.org. Other manufacturers’ associations are usually easy to find by searching the Internet. Some equipment types are relatively easy to find using search engines (“crystallizer,” “rotary agglomerator,” “bioreactor,” etc.), but locating the vendors of industrial plant can be more difficult

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CHAPTER 13 Equipment Selection, Specification, and Design

when the equipment name is in common usage (“furnace,” “dryer,” “filter,” “pump,” etc.). In such cases, the best approach is to begin at one of the chemical engineering directory sites listed above.

13.3 GUIDE TO EQUIPMENT SELECTION AND DESIGN Table 13.1 is a guide to the design of the most common types of process equipment. The numbers refer to the section of this book that provides design guidelines. Table 13.2 is a similar guide for separation processes, which have been grouped based on the phases that are separated. Capital cost correlations for most of the equipment listed in these tables can be found in Table 7.2. Table 13.1 Guide to Equipment Design Equipment Type Reactors Basic reactors Bioreactors Catalytic reactors Multiphase reactors Nonisothermal reactors Separation columns Absorption Distillation Extraction Single stage flash Stripping Other separation processes Heat exchange equipment Air coolers Boilers, reboilers, vaporizers Condensers Fired heaters Plate heat exchangers Shell and tube exchangers

Basic Sizing 15.2, 15.5 15.9 15.8 15.7 15.6 16.2.4, 17.14 17.2−17.13 17.16 16.3, 17.3.3 16.2.4, 17.14

Detailed Design As pressure vessels: Chapter 14

Shells as pressure vessels: Chapter 14 Internals: Trays 17.12−17.13 Packing 17.14 See Table 13.2 19.16 19.11 19.10 19.17 19.12 19.1−19.9

Transport equipment Compression of gases Conveying of solids Pumping of liquids

20.6 18.3 20.7

Solids-handling equipment Size reduction (grinding) Size enlargement (forming) Heating and cooling solids

18.9 18.8 18.10

Numbers refer to the sections in this book.

13.3 Guide to Equipment Selection And Design

561

Table 13.2 Separation Processes MINOR COMPONENT

Liquid Gas/Vapor

MAJOR COMPONENT

Solid

Liquid

Gas/Vapor

Sorting

18.4

Pressing

18.6.5

Screening

18.4.1

Drying

18.7

Hydrocyclones

18.4.2

Classifiers

18.4.3

Jigs

18.4.4

Tables

18.4.5

Centrifuges

18.4.6

Dense media

18.4.7

Flotation

18.4.8

Magnetic

18.4.9

Electrostatic

18.4.10

Thickeners

18.6.1

Decanters

16.4.1

Clarifiers

18.6.1

Coalescers

16.4.3

Hydrocyclones

18.6.4

Solvent extraction

16.5.6

Filtration

18.6.2

Leaching

16.5.6

Centrifuges

18.6.3

Chromatography

16.5.7

Crystallizers

16.5.2

Distillation

Chapter 17

Evaporators

16.5.1

Precipitation

16.5.3

Membranes

16.5.4

Reverse osmosis

16.5.4

Ion exchange

16.5.5

Adsorption

16.5.7

Stripping

16.2.4 17.14

Gravity settlers

18.5.1

Separating vessels

16.3

Adsorption

16.2.1

Impingement separators

18.5.2

Demisting pads

16.3

Absorption

Cyclones

18.5.3

16.2.4 17.14

Cyclones

18.5.3

Wet scrubbers

18.5.5

Membranes

16.2.2

Filters

18.5.4

18.5.6

18.5.5

Cryogenic distillation

16.2.3

Wet scrubbers

Electrostatic precipitators

Chapter 17

Electrostatic precipitators

18.5.6

Condensation

16.2.5

Numbers refer to the sections in this book. The terms major and minor component only apply where different phases are to be separated, i.e., not to those on the diagonal. Note that separation processes include processes for separating phases as well as for recovering one or more components from a mixture.

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CHAPTER 13 Equipment Selection, Specification, and Design

References Green, D. W., & Perry, R. H. (Eds.). (2007). Perry’s chemical engineers’ handbook. (8th ed.). McGraw-Hill. McCabe, W. L., Smith, J. C., & Harriott, P. (2001). Unit operations of chemical engineering (6th ed.). McGraw-Hill. Richardson, J. F., Harker, J. H., & Backhurst, J. (2002). Chemical engineering (5th ed., Vol. 2). ButterworthHeinemann. Schweitzer, P. A. (Ed.). (1997). Handbook of separation techniques for chemical engineers. (3rd ed.). McGraw-Hill. Walas, S. M. (1990). Chemical process equipment: Selection and design. Butterworth-Heinemann.

CHAPTER

Design of Pressure Vessels

KEY LEARNING OBJECTIVES • What factors a process engineer must consider when setting specifications for a pressure vessel • How pressure vessels are designed and built and what determines the vessel wall thickness • How to design and size vessels for use as reactors, columns, separators, and other process uses • How codes and standards are used in pressure vessel design

14.1 INTRODUCTION This chapter covers those aspects of the mechanical design of chemical plant that are of particular interest to chemical engineers. The main topic considered is the design of pressure vessels. The design of storage tanks is also discussed briefly. Most reactors, separation columns, flash drums, heat exchangers, surge tanks, and other vessels in a chemical plant will need to be designed as pressure vessels, so this topic is relevant to a broad range of process equipment. The chemical engineer will not usually be called on to undertake the detailed mechanical design of a pressure vessel. Vessel design is a specialized subject, and will be carried out by mechanical engineers who are conversant with the current design codes and methods of stress analysis. However, the chemical engineer will be responsible for developing and specifying the basic design information for a particular vessel, and needs to have a general appreciation of pressure vessel design to work effectively with the specialist designer. Another reason why the process engineer must have an appreciation of methods of fabrication, design codes, and other constraints on pressure vessel design is because these constraints often dictate limits on the process conditions. Mechanical constraints can cause significant cost thresholds in design, for example, when a costlier grade of alloy is required above a certain temperature. The basic data needed by the specialist designer will be: 1. 2. 3. 4. 5.

Vessel function Process materials and services Operating and design temperature and pressure Materials of construction Vessel dimensions and orientation

563

564

6. 7. 8. 9. 10.

CHAPTER 14 Design of Pressure Vessels

Type of vessel heads to be used Openings and connections required Specification of heating and cooling jackets or coils Type of agitator Specification of internal fittings

An elementary understanding of pressure vessel design is needed in the preliminary stages of design, as most correlations for pressure vessel costs are based on the weight of metal required and hence require an estimate of the vessel wall thickness as well as its volume. In many cases, the required wall thickness will be determined by the combination of loads acting on the vessel rather than internal pressure alone. A data sheet for pressure vessel design is given in Appendix G, available online at booksite.Elsevier .com/Towler. Pressure vessel information is also included in the data sheets for fixed-bed reactors, vapor-liquid contactors, and heat exchangers. There is no strict definition of what constitutes a pressure vessel, and different codes and regulations apply in different countries; however, it is generally accepted that any closed vessel over 150 mm diameter subject to a pressure difference of more than 0.5 bar should be designed as a pressure vessel. It is not possible to give a completely comprehensive account of vessel design in one chapter. The design methods and data given should be sufficient for the preliminary design of conventional vessels; for the chemical engineer to check the feasibility of a proposed equipment design; to estimate the vessel cost for an economic analysis; and to determine the vessel’s general proportions and weight for plant layout purposes. For a more detailed account of pressure vessel design the reader should refer to the books by Singh and Soler (1992), Escoe (1994), and Moss (2003). Other useful books on the mechanical design of process equipment are listed in the bibliography at the end of this chapter. An elementary understanding of the principles of the “Strength of Materials” (Mechanics of Solids) will be needed to follow this chapter. Readers who are not familiar with the subject should consult one of the many textbooks available, such as those by Case, Chilver and Ross (1999), Mott (2007), Seed (2001), and Gere and Timoshenko (2000).

14.1.1 Classification of Pressure Vessels For the purposes of design and analysis, pressure vessels are subdivided into two classes depending on the ratio of the wall thickness to vessel diameter: thin-walled vessels, with a thickness ratio of less than 1:10, and thick-walled above this ratio. The principal stresses (see Section 14.3.1) acting at a point in the wall of a vessel, due to a pressure load, are shown in Figure 14.1. If the wall is thin, the radial stress σ3 will be small and can be neglected in comparison with the other stresses, and the longitudinal and circumferential stresses σ1 and σ2 can be taken as constant over the wall thickness. In a thick wall, the magnitude of the radial stress will be significant, and the circumferential stress will vary across the wall. The majority of the vessels used in the chemical and allied industries are classified as thin-walled vessels. Thick-walled vessels are used for high pressures, and are discussed in Section 14.14.

14.2 Pressure Vessel Codes and Standards

σ3

565

σ1

σ2 σ2 σ1 σ3

FIGURE 14.1 Principal stresses in pressure-vessel wall.

14.2 PRESSURE VESSEL CODES AND STANDARDS In all the major industrialized countries the design and fabrication of pressure vessels is covered by national standards and codes of practice. In most countries it is a legal requirement that pressure vessels must be designed, constructed, and tested in accordance with part or all of the design code. The primary purpose of the design codes is to establish rules of safety relating to the pressure integrity of vessels and provide guidance on design, materials of construction, fabrication, inspection, and testing. They form a basis of agreement between the manufacturer, the customer, and the customer’s insurance company. The standard used in North America (and most commonly referenced internationally) is the ASME Boiler and Pressure Vessel Code (the ASME BPV Code). The twelve sections of the ASME BPV Code are listed in Table 14.1. Most chemical plant and refinery vessels fall within the scope of Section VIII of the ASME BPV Code. Section VIII contains three subdivisions: Division 1: contains general rules and is most commonly followed, particularly for low-pressure vessels. Division 2: contains alternative rules that are more restrictive on materials, design temperatures, design details, fabrication methods, and inspection, but allow higher design stresses and hence thinner vessel walls. Division 2 rules are usually chosen for large, high-pressure vessels where the savings in metal cost and fabrication complexity offset the higher engineering and construction costs. Division 3: contains alternative rules intended for vessels with design pressures greater than 10,000 psig. It does not establish a maximum pressure for vessels designed in accordance with Division 1 or Division 2, but provides alternative rules that can be followed for thicker-walled vessels. In the following sections reference will normally be made to the BPV Code Sec. VIII D.1. The scope of the BPV Code Sec. VIII D.1 covers vessels made from iron, steels, and nonferrous metals. It specifically excludes: 1. Vessels within the scope of other sections of the BPV code. For example, power boilers (Sec. I), fiber-reinforced plastic vessels (Sec. X), and transport tanks (Sec. XII).

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Table 14.1 The 2004 ASME Boiler and Pressure Vessel Code SECTIONS I II

Rules for Materials Part A Part B Part C Part D

construction of power boilers Ferrous metal specifications Nonferrous metal specifications Specifications for welding rods, electrodes and filler metals Properties (customary or metric versions)

III

Nuclear power plant components NCA General requirements Division 1 Division 2 Code for concrete containments Division 3 Containments for transport and storage of spent nuclear fuel and high level radioactive material and waste

IV V VI VII VIII

Rules for construction of heating boilers Nondestructive examination Recommended rules for the care and operation of heating boilers Recommended guidelines for the care of power boilers Rules for the construction of pressure vessels Division 1 Division 2 Alternative rules Division 3 Alternative rules for the construction of high pressure vessels

IX X XI XII

Welding and brazing qualifications Fiber-reinforced plastic vessels Rules for in service inspection of nuclear power plant components Rules for construction and continued service of transport tanks

2. Fired process tubular heaters. 3. Pressure containers that are integral parts of rotating or reciprocating devices such as pumps, compressors, turbines, or engines. 4. Piping systems (which are covered by ASME B31.3—see Chapter 20). 5. Piping components and accessories such as valves, strainers, in-line mixers, and spargers. 6. Vessels containing water at less than 300 psi (2 MPa) and less than 210 ºF (99 ºC). 7. Hot water storage tanks heated by steam with heat rate less than 0.2 MMBTU/hr (58.6 kW), water temperature less than 210 ºF (99º C), and volume less than 120 gal (450 liters). 8. Vessels having internal pressure less than 15 psi (100 kPa) or greater than 3000 psi (20 MPa). 9. Vessels of internal diameter or height less than 6 inches (152 mm). 10. Pressure vessels for human occupancy. The ASME BPV Code can be ordered from ASME and is also available online (for example at www.ihs.com). The most recent edition of the code should always be consulted during detailed design.

14.3 Fundamentals of Strength of Materials

567

In addition to the BPV Code Sec. VIII, the process design engineer will frequently need to consult Section II Part D, which lists maximum allowable stress values under Sec. VIII D.1 and D.2, as well as other materials properties. A comprehensive review of the ASME code is given by Chuse and Carson (1992) and Yokell (1986); see also Green and Perry (2007). In the European Union the design, manufacture, and use of pressure systems is covered by the Pressure Equipment Directive (Council Directive 97/23/EC) whose use became mandatory in May 2002. European standard BS EN 13445 provides similar rules and guidelines to the ASME BPV Code. The design of fiber-reinforced plastic vessels is covered by European standard BS EN 13923. The European standards can be obtained from any of the European Union member country national standards agencies; for example, BS EN 13445 can be ordered from www.bsigroup.com. Where national codes are not available, the ASME or European codes would normally be used. Information and guidance on the pressure vessel codes can be found on the Internet at www.ihs .com or www.bsigroup.com. The national codes and standards dictate the minimum requirements and give general guidance for design and construction; any extension beyond the minimum code requirement will be determined by agreement between the manufacturer and customer. The codes and standards are drawn up by committees of engineers experienced in vessel design and manufacturing techniques, and are a blend of theory, experiment, and experience. They are periodically reviewed, and revisions are issued to keep abreast of developments in design, stress analysis, fabrication, and testing. The latest version of the appropriate national code or standard should always be consulted before undertaking the design of any pressure vessel. Several commercial computer programs to aid in the design of vessels to the ASME code and other international codes are available. These programs will normally be used by the specialist mechanical engineers who carry out the detailed vessel design. Some examples include: Pressure Vessel Suite (Computer Engineering Inc.) PVElite and CodeCalc (COADE Inc.) TEMA/ASME and COMPRESS (Codeware Inc.)

14.3 FUNDAMENTALS OF STRENGTH OF MATERIALS This section has been included to provide a basic understanding of the fundamental principles that underlie the design equations given in the sections that follow. The derivation of the equations is given in outline only. A detailed knowledge of the material in this section is not required for preliminary vessel design, but the equations derived here will be referenced and applied in subsequent sections. A full discussion of the topics covered can be found in any text on the “Strength of Materials” (Mechanics of Solids).

14.3.1 Principal Stresses The state of stress at a point in a structural member under a complex system of loading is described by the magnitude and direction of the principal stresses. The principal stresses are the maximum values of the normal stresses at the point, which act on planes on which the shear stress is zero. In a two-dimensional stress system, Figure 14.2, the principal stresses at any point are related to the

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CHAPTER 14 Design of Pressure Vessels

σy

τxy σx

σx τxy

σy

FIGURE 14.2 Two-dimensional stress system.

normal stresses in the x and y directions σx and σy and the shear stress τxy at the point by the following equation: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (14.1) Principal stresses, σ 1 , σ 2 = 1 ðσ y + σ x Þ ± 1 ½ðσ y − σ x Þ2 + 4τ2xy 2

The maximum shear stress at the point is equal to half the algebraic difference between the principal stresses: Maximum shear stress = 1ðσ 1 − σ 2 Þ 2

(14.2)

Compressive stresses are conventionally taken as negative; tensile as positive.

14.3.2 Theories of Failure The failure of a simple structural element under unidirectional stress (tensile or compressive) is easy to relate to the tensile strength of the material, as determined in a standard tensile test, but for components subjected to combined stresses (normal and shear stress) the position is not so simple, and several theories of failure have been proposed. The three theories most commonly used are described below: Maximum principal stress theory: postulates that a member will fail when one of the principal stresses reaches the failure value in simple tension, σe. The failure point in a simple tension is taken as the yield-point stress, or the tensile strength of the material, divided by a suitable factor of safety. Maximum shear stress theory: postulates that failure will occur in a complex stress system when the maximum shear stress reaches the value of the shear stress at failure in simple tension. For a system of combined stresses there are three shear stress maxima: τ1 =

σ1 − σ2 2

(14.3a)

14.3 Fundamentals of Strength of Materials

569

τ2 =

σ2 − σ3 2

(14.3b)

τ3 =

σ3 − σ1 2

(14.3c)

σe 2

(14.4)

In the tensile test, τe =

The maximum shear stress will depend on the sign of the principal stresses as well as their magnitude, and in a two-dimensional stress system, such as that in the wall of a thin-walled pressure vessel, the maximum value of the shear stress may be that given by putting σ3 = 0 in Equations 14.3b and c. The maximum shear stress theory is often called Tresca’s, or Guest’s, theory. Maximum strain energy theory: postulates that failure will occur in a complex stress system when the total strain energy per unit volume reaches the value at which failure occurs in simple tension. The maximum-shear-stress theory has been found to be suitable for predicting the failure of ductile materials under complex loading and is the criterion normally used in pressure-vessel design.

14.3.3 Elastic Stability Under certain loading conditions failure of a structure can occur not through gross yielding or plastic failure, but by buckling, or wrinkling. Buckling leads to a gross and sudden change of shape of the structure, unlike failure by plastic yielding, where the structure retains the same basic shape. This mode of failure will occur when the structure is not elastically stable, when it lacks sufficient stiffness, or rigidity, to withstand the load. The stiffness of a structural member is dependent not on the basic strength of the material but on its elastic properties (EY and v) and the cross-sectional shape of the member. The classic example of failure due to elastic instability is the buckling of tall thin columns (struts), which is described in any elementary text on the “Strength of Materials.” For a structure that is likely to fail by buckling there will be a certain critical value of load below which the structure is stable; if this value is exceeded catastrophic failure through buckling can occur. The walls of pressure vessels are usually relatively thin compared with the other dimensions and can fail by buckling under compressive loads. This is particularly important for tall wide vessels such as distillation columns that can experience compressive loads from wind loads. Elastic buckling is the decisive criterion in the design of thin-walled vessels under external pressure.

14.3.4 Secondary Stresses In the stress analysis of pressure vessels and pressure vessel components, stresses are classified as primary or secondary. Primary stresses can be defined as those stresses that are necessary to satisfy the conditions of static equilibrium. The membrane stresses induced by the applied pressure and the bending stresses due to wind loads are examples of primary stresses. Primary stresses are not selflimiting; if they exceed the yield point of the material, gross distortion, and in the extreme situation, failure of the vessel will occur.

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Secondary stresses are those stresses that arise from the constraint of adjacent parts of the vessel. Secondary stresses are self-limiting; local yielding or slight distortion will satisfy the conditions causing the stress, and failure would not be expected to occur in one application of the loading. The “thermal stress” set up by the differential expansion of parts of the vessel, due to different temperatures or the use of different materials, is an example of a secondary stress. The discontinuity that occurs between the head and the cylindrical section of a vessel is a major source of secondary stress. If free, the dilation of the head would be different from that of the cylindrical section; they are constrained to the same dilation by the welded joint between the two parts. The induced bending moment and shear force due to the constraint give rise to secondary bending and shear stresses at the junction. The magnitude of these discontinuity stresses can be estimated by analogy with the behavior of beams on elastic foundations; see Hetenyi (1958) and Harvey (1974). The estimation of the stresses arising from discontinuities is covered in the books by Bednar (1990) and Farr and Jawad (2006). Other sources of secondary stresses are the constraints arising at flanges, supports, and the change of section due to reinforcement at a nozzle or opening (see Section 14.6). Though secondary stresses do not affect the “bursting strength” of the vessel, they are an important consideration when the vessel is subject to repeated pressure loading. If local yielding has occurred, residual stress will remain when the pressure load is removed, and repeated pressure cycling can lead to fatigue failure.

14.4 GENERAL DESIGN CONSIDERATIONS FOR PRESSURE VESSELS This section describes general pressure vessel design specifications, most of which would normally be specified by a process engineer.

14.4.1 Design Pressure A vessel must be designed to withstand the maximum pressure to which it is likely to be subjected in operation. For vessels under internal pressure, the design pressure (sometimes called maximum allowable working pressure or MAWP) is taken as the pressure at which the relief device is set. This will normally be 5% to 10% above the normal working pressure, to avoid spurious operation during minor process upsets. For example, the API RP 520 recommended practice sets a 10% margin between the normal operating pressure and the design pressure. When deciding the design pressure, the hydrostatic pressure in the base of the column should be added to the operating pressure, if significant. Vessels subject to external pressure should be designed to resist the maximum differential pressure that is likely to occur in service. Vessels likely to be subjected to vacuum should be designed for a full negative pressure of 1 bar, unless fitted with an effective, and reliable, vacuum breaker.

14.4.2 Design Temperature The strength of metals decreases with increasing temperature (see Chapter 6) so the maximum allowable stress will depend on the material temperature. The maximum design temperature at

14.4 General Design Considerations for Pressure Vessels

571

which the maximum allowable stress is evaluated should be taken as the maximum working temperature of the material, with due allowance for any uncertainty involved in predicting vessel wall temperatures. Additional rules apply for welded vessels, as described in ASME BPV Code Sec. VIII D.1 part UW. The minimum design metal temperature (MDMT) should be taken as the lowest temperature expected in service. The designer should consider the lowest operating temperature, ambient temperature, auto-refrigeration, process upsets, and other sources of cooling in determining the minimum.

14.4.3 Materials Pressure vessels are constructed from plain carbon steels, low and high alloy steels, other alloys, clad plate, and reinforced plastics. Selection of a suitable material must take into account the suitability of the material for fabrication (particularly welding) as well as the compatibility of the material with the process environment; see Chapter 6. The pressure vessel design codes and standards include lists of acceptable materials, in accordance with the appropriate material standards. The ASME BPV Code Sec. II Part D gives maximum allowable stresses as a function of temperature and maximum temperatures permitted under Sections I, III, VIII, and XII of the BPV code for ferrous and nonferrous metals. The design of pressure vessels using reinforced plastics is described in ASME BPV Code Sec. X.

14.4.4 Maximum Allowable Stress (Nominal Design Strength) For design purposes it is necessary to decide a value for the maximum allowable stress (nominal design strength) that can be accepted in the material of construction. This is determined by applying a suitable safety factor to the maximum stress that the material could be expected to withstand without failure under standard test conditions. The safety factor allows for any uncertainty in the design methods, the loading, the quality of the materials, and the workmanship. The basis for establishing the maximum allowable stress values in the ASME BPV Code is given in ASME BPV Code Sec. II Part D, Mandatory Appendix 1. At temperatures where creep and stress rupture strength do not govern the selection of stresses, the maximum allowable stress is the lowest of: 1. 2. 3. 4.

The The The The

specified minimum tensile strength at room temperature divided by 3.5 tensile strength at temperature divided by 3.5 specified minimum yield strength at room temperature divided by 1.5 yield strength at temperature divided by 1.5

At temperatures where creep and stress rupture strength govern, the maximum allowable stress is the lowest of: 1. The average stress to produce a creep rate of 0.01%/1000 hr 2. F times the average stress to cause rupture at the end of 100,000 hr, where F = 0.67 for temperatures below 1500 ºF (815 ºC)—see the code for higher temperatures 3. 0.8 times the minimum stress to cause rupture after 100,000 hr

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CHAPTER 14 Design of Pressure Vessels

In some cases where short-time tensile properties govern and slightly greater deformation is acceptable, higher stress values are allowed under ASME BPV Code Sec. VIII D.1. These exceed 67% but do not exceed 90% of the yield strength at temperature. These cases are indicated with a note (G5) in the BPV Code tables. Use of these higher values can result in deformation and changes in the vessel dimensions. They are not recommended for flanges or other applications where changes in dimensions could lead to leaks or vessel malfunction. The maximum allowable stress values for ASME BPV Code Sec. VIII D.1 are given in ASME BPV Code Sec II Part D Table 1A for ferrous metals and Table 1B for nonferrous metals. Maximum allowable stress values for Sec. VIII D.2 are given in Sec. II Part D Table 2A for ferrous metals and Table 2B for nonferrous metals. Different values are given for plate, tubes, castings, forgings, bar, pipe, and small sections as well as for different grades of each metal. Typical maximum allowable stress values for some common materials are shown in Table 14.2. These may be used for preliminary designs. The ASME BPV Code should be consulted for the values to be used for detailed vessel design.

14.4.5 Welded Joint Efficiency, and Construction Categories The strength of a welded joint will depend on the type of joint and the quality of the welding. The ASME BPV Code Sec. VIII D.1 defines four categories of weld (Part UW-3): A. Longitudinal or spiral welds in the main shell, necks, or nozzles, or circumferential welds connecting hemispherical heads to the main shell, necks, or nozzles B. Circumferential welds in the main shell, necks, or nozzles or connecting a formed head other than hemispherical C. Welds connecting flanges, tubesheets, or flat heads to the main shell, a formed head, neck, or nozzle D. Welds connecting communicating chambers or nozzles to the main shell, to heads, or to necks Details of the different types of welds used in pressure vessel construction are given in Section 14.11. The soundness of welds is checked by visual inspection and by nondestructive testing (radiography). The possible lower strength of a welded joint compared with the virgin plate is usually allowed for in design by multiplying the allowable design stress for the material by a joint efficiency E. The value of the joint efficiency used in design will depend on the type of joint and amount of radiography required by the design code. Typical values are shown in Table 14.3. A joint efficiency of 1.0 is only permitted for butt joints formed by double welding and subjected to full radiographic examination. Taking the factor as 1.0 implies that the joint is equally as strong as the virgin plate; this is achieved by radiographing the complete weld length, and cutting out and remaking any defects. The use of lower joint efficiencies in design, though saving costs on radiography, will result in a thicker, heavier vessel, and the designer must balance any cost savings on inspection and fabrication against the increased cost of materials. The ASME BPV Code Sec. VIII D.1 Part UW describes the requirements for pressure vessels fabricated by welding. Limiting plate thicknesses are specified for each type of weld with the exception of double-welded butt joints. Requirements for radiographic examination of welds are also specified. Section UW-13 of the code specifies the types of welds that can be used to attach heads and tubesheets to shells. Section UW-16 gives rules for attachment of nozzles to vessels.

Table 14.2 Typical Maximum Allowable Stresses for Plate under ASME BPV Code Sec. VIII D.1 (The Appropriate Material Standards Should Be Consulted for Particular Grades and Plate Thicknesses) Min Yield Strength (ksi)

900

12.9

11.5

5.9

1000

17.1

14.3

5.9

1200

17.1

16.6

13.6

65 75

30 30

1200 1500

18.6 20.0

17.8 15.0

17.2 12.9

16.2 11.7

12.3 10.8

347

1500

20.0

17.1

15.0

13.8

13.4

321

1500

20.0

16.5

14.3

13.0

12.3

316

1500

20.0

15.6

13.3

12.1

11.5

Grade

Carbon steel

A285 Gr A A515 Gr 60 A387 Gr 22 410 304

Low alloy steel 1¼ Cr, ½ Mo, Si Stainless steel 13 Cr Stainless steel 18 Cr, 8 Ni Stainless steel 18 Cr, 10 Ni, Cb Stainless steel 18 Cr, 10 Ni, Ti Stainless steel 16 Cr, 12 Ni, 2 Mo

Maximum Allowable Stress at Temperature °F (ksi = 1000 psi)

Min Tensile Strength (ksi)

Material

Killed carbon Steel

Maximum Temperature (ºF)

100

Note: 1. The stress values for type 304 stainless steel are not the same as those given for stainless steel 304L in Table 7.8. 2. 1 ksi = 1000 psi = 6.8948 N/mm2

300

500

700

900

573

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CHAPTER 14 Design of Pressure Vessels

Table 14.3 Maximum Allowable Joint Efficiency Degree of Radiographic Examination Joint Description

Joint Category

Full

Spot

Double-welded butt joint or equivalent Single-welded butt joint with backing strip Single-welded butt joint without backing strip Double full fillet lap joint Single full fillet lap joint with plug welds Single full fillet lap joint without plug welds

A, B, A, B, A, B, A, B, B, C A, B

1.0 0.9 NA NA NA NA

0.85 0.8 NA NA NA NA

C, D C, D C C

None 0.70 0.65 0.60 0.55 0.50 0.45

The BPV Code should be consulted to determine the allowed joint types for a particular vessel. Any pressure vessel containing lethal substances will require full radiographic testing of all butt welds.

14.4.6 Corrosion Allowance The “corrosion allowance” is the additional thickness of metal added to allow for material lost by corrosion and erosion, or scaling (see Chapter 6). The ASME BPV Code Sec. VIII D.1 states that the vessel user shall specify corrosion allowances (Part UG-25). Minimum wall thicknesses calculated using the rules given in the code are in the fully corroded condition (Part UG-16). Corrosion is a complex phenomenon, and it is not possible to give specific rules for the estimation of the corrosion allowance required for all circumstances. The allowance should be based on experience with the material of construction under similar service conditions to those for the proposed design. For carbon and low-alloy steels, where severe corrosion is not expected, a minimum allowance of 2.0 mm should be used; where more severe conditions are anticipated this should be increased to 4.0 mm. Most design codes and standards specify a minimum allowance of 1.0 mm, but under the ASME BPV Code Sec. VIII no corrosion allowance is needed when past experience indicates that corrosion is only superficial or does not occur.

14.4.7 Design Loads A structure must be designed to resist gross plastic deformation and collapse under all the conditions of loading. The loads to which a process vessel will be subject in service are listed below. They can be classified as major loads that must always be considered in vessel design, and subsidiary loads. Formal stress analysis to determine the effect of the subsidiary loads is only required in the codes and standards where it is not possible to demonstrate the adequacy of the proposed design by other means, such as by comparison with the known behavior of existing vessels.

Major Loads 1. Design pressure: including any significant static head of liquid 2. Maximum weight of the vessel and contents under operating conditions 3. Maximum weight of the vessel and contents under the hydraulic test conditions

14.5 The Design of Thin-Walled Vessels Under Internal Pressure

575

4. Wind loads 5. Earthquake (seismic) loads 6. Loads supported by, or reacting on, the vessel

Subsidiary Loads 1. Local stresses caused by supports, internal structures, and connecting pipes. 2. Shock loads caused by water hammer, or by surging of the vessel contents. 3. Bending moments caused by eccentricity of the center of the working pressure relative to the neutral axis of the vessel. 4. Stresses due to temperature differences and differences in the coefficient of expansion of materials. 5. Loads caused by fluctuations in temperature and pressure. A vessel will not be subject to all these loads simultaneously. The designer must determine what combination of possible loads gives the worst situation (the “governing case”), and design for that loading condition.

14.4.8 Minimum Practical Wall Thickness There will be a minimum wall thickness required to ensure that any vessel is sufficiently rigid to withstand its own weight, and any incidental loads. The ASME BPV Code Sec. VIII D.1 specifies a minimum wall thickness of 1/16 inch (1.5 mm) not including corrosion allowance, and regardless of vessel dimensions and material of construction. As a general guide the wall thickness of any vessel should not be less than the values given below; the values include a corrosion allowance of 2 mm: Vessel Diameter (m) 1 1 to 2 2 to 2.5 2.5 to 3.0 3.0 to 3.5

Minimum Thickness (mm) 5 7 9 10 12

14.5 THE DESIGN OF THIN-WALLED VESSELS UNDER INTERNAL PRESSURE 14.5.1 Cylinders and Spherical Shells

The walls of thin vessels can be considered to be “membranes,” supporting loads without significant bending or shear stresses, similar to the walls of a balloon. The analysis of the membrane stresses induced in the wall by internal pressure gives a basis for determining the minimum wall thickness required for vessel shells. The actual thickness required will also depend on the stresses arising from the other loads to which the vessel is subjected.

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CHAPTER 14 Design of Pressure Vessels

For a cylindrical shell, the stresses in the walls can be determined from simple force balances, as the wall stresses must balance the forces due to pressure. If we consider a horizontal section through the vessel (Figure 14.3(a)), then the force due to pressure on the cross section is FL =

Pi π D2 4

(14.5)

where Pi = internal pressure D = mean diameter FL = force in longitudinal direction This force must be balanced by the longitudinal stress in the wall of the cylinder, which acts only on the sectioned area of the wall: FL = σ L π D t

(14.6)

where σL = longitudinal stress t = wall thickness Equating Equations 14.5 and 14.6: σL =

Pi D 4t

(14.7)

Similarly, if we consider a vertical section in an infinite cylinder (Figure 14.3(b)), the force due to pressure on a vertical section of length L is Fv = Pi D L

(14.8)

where Fv = force in horizontal direction L = length This force is balanced by the circumferential or hoop stress in the wall of the cylinder, which acts only on the sectioned area of the cylinder: Fv = σ h ð2 L tÞ

(14.9)

where σh = hoop stress Equating Equations 14.8 and 14.9: σh =

Pi D 2t

(14.10)

The minimum wall thickness that is required to contain the internal pressure can be determined using Equations 14.7 and 14.10. If Di is internal diameter and t the minimum thickness required, the mean diameter will be (Di + t); substituting this for D in Equation 14.10 gives t=

Pi ðDi + tÞ 2S

where S is the maximum allowable stress and Pi the internal pressure. Rearranging gives t=

Pi Di 2S − Pi

(14.11)

14.5 The Design of Thin-Walled Vessels Under Internal Pressure

577

If we allow for the welded joint efficiency, E, this becomes t=

Pi Di 2SE − Pi

(14.12)

The equation specified by the ASME BPV Code (Sec. VIII D.1 Part UG-27) is t=

Pi Di 2SE − 1:2 Pi

(14.13)

This differs slightly from Equation 14.12 as it is derived from the formula for thick-walled vessels. Similarly, for longitudinal stress the code specifies t=

Pi Di 4SE + 0:8Pi

(14.14)

The ASME BPV Code specifies that the minimum thickness shall be the greater value determined from Equations 14.13 and 14.14. If these equations are rearranged and used to calculate the maximum allowable working pressure (MAWP) for a vessel of a given thickness, then the maximum allowable working pressure is the lower value predicted by the two equations. For a spherical shell the code specifies t=

Pi Di 4SE − 0:4Pi

(14.15)

Any consistent set of units can be used for Equations 14.13 to 14.15.

Pressure Pi acts on area DL Pressure Pi acts on area πD2/4

Hoop stress σh acts on area 2Lt

Longitudinal stress σL acts on area πDt L

(a) Horizontal section

(b) Vertical section

FIGURE 14.3 Stresses in the walls of cylindrical vessels due to internal pressure.

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CHAPTER 14 Design of Pressure Vessels

14.5.2 Heads and Closures The ends of a cylindrical vessel are closed by heads of various shapes. The principal types used are: 1. 2. 3. 4.

Flat plates and formed flat heads; Figure 14.4 Hemispherical heads; Figure 14.5(a) Ellipsoidal heads; Figure 14.5(b) Torispherical heads; Figure 14.5(c)

Hemispherical, ellipsoidal, and torispherical heads are collectively referred to as domed heads. They are formed by pressing or spinning; large diameters are fabricated from formed sections. Torispherical heads are often referred to as dished ends. The preferred proportions of domed heads are given in the standards and codes. Vessel heads can be made in any size, but standard sizes (which come in six-inch increments) will usually be cheaper.

Choice of Closure Flat plates are used as covers for manways and as the channel covers of heat exchangers. Formed flat ends, known as “flange-only” ends, are manufactured by turning over a flange with a small radius on a flat plate, Figure 14.4(a). The corner radius reduces the abrupt change of shape at the junction with the cylindrical section, which reduces the local stresses to some extent. “Flange-only”

45°

De De

(a)

(b) De

45° ts

ts De (c)

(d)

(e)

FIGURE 14.4 Flat-end closures: (a) flanged plate; (b) welded plate; (c) welded plate; (d) bolted cover; (e) bolted cover.

14.5 The Design of Thin-Walled Vessels Under Internal Pressure

579

(a)

Flange

(b)

Flange (c)

FIGURE 14.5 Domed heads: (a) hemispherical; (b) ellipsoidal; (c) torispherical.

heads are the cheapest type of formed head to manufacture, but their use is limited to low-pressure and small-diameter vessels. Standard torispherical heads (dished ends) are the most commonly used end closure for vessels up to operating pressures of 15 bar. They can be used for higher pressures, but above 10 bar their cost should be compared with that of an equivalent ellipsoidal head. Above 15 bar an ellipsoidal head will usually prove to be the most economical closure to use. A hemispherical head is the strongest shape, capable of resisting about twice the pressure of a torispherical head of the same thickness. The cost of forming a hemispherical head will, however, be higher than that for a shallow torispherical head. Hemispherical heads are used for high pressures.

14.5.3 Design of Flat Ends Though the fabrication cost is low, flat ends are not a structurally efficient form, and very thick plates would be required for high pressures or large diameters. The design equations used to determine the thickness of flat ends are based on the analysis of stresses in flat plates. The thickness required will depend on the degree of constraint at the plate periphery.

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CHAPTER 14 Design of Pressure Vessels

The ASME BPV Code specifies the minimum thickness as rffiffiffiffiffiffiffiffiffi C Pi t = De SE

(14.16)

where C = a design constant, dependent on the edge constraint De = nominal plate diameter S = maximum allowable stress E = joint efficiency Any consistent set of units can be used. Values for the design constant C and the nominal plate diameter De are given in the ASME BPV Code for various arrangements of flat end closures (Sec. VIII D.1 Part UG-34). Some typical values of the design constant and nominal diameter for the designs shown in Figure 14.4 are given below. For detailed design the ASME BPV Code should be consulted. (a) Flanged-only end, C = 0.17 if corner radius is not more than 3t, otherwise C = 0.1; De is equal to Di. (b, c) Plates welded to the end of the shell with a fillet weld, angle of fillet 45° and weld depth 70% of the thickness of the shell, C = 0.33 t/ts, where ts is the shell thickness. De = Di. (d) Bolted cover with a full face gasket (see Section 14.10), C = 0.25 and De is the bolt circle diameter (the diameter of a circle connecting the centers of the bolt holes). (e) Bolted end cover with a narrow-face gasket, C = 0.3 and De should be taken as the mean diameter of the gasket.

14.5.4 Design of Domed Ends Design equations and charts for the various types of domed heads are given in the ASME BPV Code and should be used for detailed design. The code covers both unpierced and pierced heads. Pierced heads are those with openings or connections. The head thickness must be increased to compensate for the weakening effect of the holes where the opening or branch is not locally reinforced (see Section 14.6). For convenience, simplified design equations are given in this section. These are suitable for the preliminary sizing of unpierced heads and for heads with fully compensated openings or branches.

Hemispherical Heads For equal stress in the cylindrical section and hemispherical head of a vessel the thickness of the head need only be half that of the cylinder; however, as the dilation of the two parts would then be different, discontinuity stresses would be set up at the head and cylinder junction. For no difference in dilation between the two parts (equal diametrical strain) it can be shown that for steels (Poisson’s ratio = 0.3) the ratio of the hemispherical head thickness to cylinder thickness should be 7/17. However, the stress in the head would then be greater than that in the cylindrical section, and the optimum thickness ratio is normally taken as 0.6; see Brownell and Young (1959). In the ASME BPV Code Sec. VIII D.1, the equation specified is the same as for a spherical shell: t=

Pi Di 4SE − 0:4Pi

(14.17)

14.5 The Design of Thin-Walled Vessels Under Internal Pressure

581

Ellipsoidal Heads Most standard ellipsoidal heads are manufactured with a major and minor axis ratio of 2:1. For this ratio, the following equation can be used to calculate the minimum thickness required (ASME BPV Code Sec. VIII D.1 Part UG-32): t=

Pi Di 2SE − 0:2Pi

(14.18)

Torispherical Heads A torispherical shape is formed from part of a torus and part of a sphere (Figure 14.6). The shape is close to that of an ellipse but is easier and cheaper to fabricate. In Figure 14.6 Rk is the knuckle radius (the radius of the torus) and Rc the crown radius (the radius of the sphere). The stress will be higher in the torus section than the spherical section. There are two junctions in a torispherical end closure: that between the cylindrical section and the head, and that at the junction of the crown and the knuckle radii. The bending and shear stresses caused by the differential dilation that will occur at these points must be taken into account in the design of the heads. The ASME BPV Code gives the design equation (Sec. VIII D.1 Part UG-32): t=

0:885 Pi Rc SE − 0:1Pi

(14.19)

The ratio of the knuckle to crown radii should not be less than 0.06, to avoid buckling, and the crown radius should not be greater than the diameter of the cylindrical section. Any consistent set of units can be used with Equations 14.17 to 14.19. For formed heads (no welds or joints in the head) the joint efficiency E is taken as 1.0.

FIGURE 14.6 Torisphere.

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CHAPTER 14 Design of Pressure Vessels

Flanges (Skirts) on Domed Heads Formed domed heads are made with a short straight cylindrical section, called a flange or skirt; see Figure 14.5. This ensures that the weld line is away from the point of discontinuity between the head and the cylindrical section of the vessel.

14.5.5 Conical Sections and End Closures Conical sections (reducers) are used to make a gradual reduction in diameter from one cylindrical section to another of smaller diameter. Conical ends are used to facilitate the smooth flow and removal of solids from process equipment, such as hoppers, spray-dryers, and crystallizers. The thickness required at any point on a cone is related to the diameter by the following expression: t=

Pi Dc . 1 2SE − Pi cos α

(14.20)

where Dc = is the diameter of the cone at the point α = half the cone apex angle The equation given in the ASME BPV Code is t=

Pi Di 2 cos α ðSE − 0:6Pi Þ

(14.21)

This equation will only apply at points away from the cone to cylinder junction. Bending and shear stresses will be caused by the different dilation of the conical and cylindrical sections. A formed section would normally be used for the transition between a cylindrical section and conical section, except for vessels operating at low pressures, or under hydrostatic pressure only. The transition section would be made thicker than the conical or cylindrical section and formed with a knuckle radius to reduce the stress concentration at the transition (Figure 14.7). The thickness for the conical section away from the transition can be calculated from Equation 14.21. The code should be consulted for details of how to size the knuckle zone. Example 14.1 Estimate the thickness required for the component parts of the vessel shown in the diagram. The vessel is to operate at a pressure of 14 bar (absolute) and temperature of 260 °C. The material of construction will be plain carbon steel. Welds will be fully radiographed. A corrosion allowance of 2 mm should be used.

Solution

Design pressure, take as 10% above operating gauge pressure = ð14 − 1Þ × 1:1 = 14:3 bar = 1:43 N/mm2 Design temperature 260 °C (500 ºF).

14.5 The Design of Thin-Walled Vessels Under Internal Pressure

583

14° max

ek Knuckle radius

Dc ec

FIGURE 14.7 Conical transition section.

From Table 14.2, maximum allowable stress = 12.9 × 103 psi = 88.9 N/mm2. Cylindrical Section

1:43 × 1:5 × 103 = 12:2 mm ð2 × 89 × 1Þ − ð1:2 × 1:43Þ add corrosion allowance 12:2 + 2 = 14:2 mm say 15 mm plate or 9=16 inch plate

(14.13)

Domed Head

Try a standard dished head (torisphere): crown radius Rc = Di = 1.5 m knuckle radius = 6% Rc = 0.09 m A head of this size would be formed by pressing: no joints, so E = 1. 3 t = 0:885 × 1:43 × 1:5 × 10 = 21:4 mm ð89 × 1Þ − ð0:1 × 1:43Þ

(14.19)

ii. Try a “standard” ellipsoidal head, ratio major: minor axes = 2:1: t=

1:43 × 1:5 × 103 = 12:1 mm ð2 × 89 × 1Þ − ð0:2 × 1:43Þ

(14.18)

So an ellipsoidal head would probably be the most economical. Take the thickness as being the same as the thickness of the wall, 15 mm or 9/16 inch.

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CHAPTER 14 Design of Pressure Vessels

Flat Head

Use a full face gasket C = 0.25. De = bolt circle diameter, take as approximately 1.7 m. rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi t = 1:7 × 103 0:25 × 1:43 = 107:7 mm 89 × 1

(14.16)

Add corrosion allowance and round-off to 111 mm (43/8 inch). This shows the inefficiency of a flat cover. It would be better to use a flanged domed head.

14.6 COMPENSATION FOR OPENINGS AND BRANCHES All process vessels will have openings for connections, manways, and instrument fittings. The presence of an opening weakens the shell and gives rise to stress concentrations. The stress at the edge of a hole will be considerably higher than the average stress in the surrounding plate. To compensate for the effect of an opening, the wall thickness is increased in the region adjacent to the opening. Sufficient reinforcement must be provided to compensate for the weakening effect of the opening without significantly altering the general dilation pattern of the vessel at the opening. Over-reinforcement will reduce the flexibility of the wall, causing a “hard spot,” and giving rise to secondary stresses; typical arrangements are shown in Figure 14.8. The simplest method of providing compensation is to weld a pad or collar around the opening (Figure 14.8(a)). The outer diameter of the pad is usually between 1½ to 2 times the diameter of the hole or branch. This method, however, does not give the best disposition of the reinforcing material about the opening, and in some circumstances high thermal stress can arise due to the poor thermal conductivity of the pad to shell junction. At a branch, the reinforcement required can be provided, with or without a pad, by allowing the branch to protrude into the vessel (Figure 14.8(b)). This arrangement should be used with caution for process vessels, as the protrusion will act as a trap for crud, and crevices are created in which localized corrosion can occur. Forged reinforcing rings (Figure 14.8(c)) provide the most effective method of compensation, but are expensive. They would be used for any large openings and branches in vessels operating under severe conditions. The rules for calculating the minimum amount of reinforcement required are complex. For design purposes, consult the ASME BPV Code Sec. VIII D.1 Part UG-37.

14.7 DESIGN OF VESSELS SUBJECT TO EXTERNAL PRESSURE Two types of process vessel are likely to be subjected to external pressure: those operated under vacuum, where the maximum pressure will be 1 bar (1 atm); and jacketed vessels, where the inner vessel will be under the jacket pressure. For jacketed vessels, the maximum pressure difference should be taken as the full jacket pressure, as a situation may arise in which the pressure in the inner vessel is lost. Thin-walled vessels subject to external pressure are vulnerable to failure through elastic instability (buckling) and it is this mode of failure that determines the wall thickness required.

14.8 Design of Vessels Subject to Combined Loading

585

(a)

(b)

(c)

FIGURE 14.8 Types of compensation for openings: (a) welded pad; (b) inset nozzle; (c) forged ring.

The method recommended by the BPV Code for vessels subject to compressive stresses is substantially more complex than the method used for tensile stresses and takes into account the fact that the maximum allowable stress in compression is different from that in tension. The ASME BPV Code Sec. VIII D.1 Part UG-28 should be consulted for the approved method for detailed design of cylindrical vessels subject to external pressure. For detailed design of hemispherical vessel heads subject to external pressure the method given in ASME BPV Code Sec. VIII D.1 Part UG-33 must be followed. Design methods for different shaped heads under external pressure are also given in the standards and codes. Vessels that ares subject to external pressure are often reinforced with internal stiffening rings. Methods for sizing the stiffening rings and determining their spacing are given in the BPV Code.

14.8 DESIGN OF VESSELS SUBJECT TO COMBINED LOADING Pressure vessels are subjected to other loads in addition to pressure (see Section 14.4.7) and must be designed to withstand the worst combination of loading without failure. It is not practical to give an explicit relationship for the vessel thickness to resist combined loads. A trial thickness must be

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CHAPTER 14 Design of Pressure Vessels

assumed (based on that calculated for pressure alone) and the resultant stress from all loads determined to ensure that the maximum allowable stress intensity is not exceeded at any point. When combined loads are analyzed, the maximum compressive stress must be considered as well as the maximum tensile stress. The maximum allowable stress in compression is different from the maximum allowable stress in tension, and is determined using the method given in ASME BPV Code Sec. VIII D.1 Part UG-23. The main sources of load to consider are: 1. 2. 3. 4. 5.

Pressure Dead weight of vessel and contents Wind Earthquake (seismic) External loads imposed by piping and attached equipment

The primary stresses arising from these loads are considered in the following paragraphs, for cylindrical vessels (Figure 14.9).

Primary Stresses 1. The longitudinal and circumferential stresses due to pressure (internal or external), given by σL =

PDi 4t

(14.7)

σh =

PDi 2t

(14.10)

2. The direct stress σw due to the weight of the vessel, its contents, and any attachments. The stress will be tensile (positive) for points below the plane of the vessel supports, and compressive (negative) for points above the supports (Figure 14.10). The dead-weight stress will normally only be significant, compared to the magnitude of the other stresses, in tall vessels. σw =

Wz πðDi + tÞt

(14.22)

where Wz is the total weight which is supported by the vessel wall at the plane considered; see Section 14.8.1. 3. Bending stresses resulting from the bending moments to which the vessel is subjected. Bending moments will be caused by the following loading conditions: a. The wind loads on tall self-supported vessels (Section 14.8.2). b. Seismic (earthquake) loads on tall vessels (Section 14.8.3). c. The dead weight and wind loads on piping and equipment that is attached to the vessel, but offset from the vessel center line (Section 14.8.4). d. For horizontal vessels with saddle supports, from the disposition of dead-weight load (see Section 14.9.1). The bending stresses will be compressive or tensile, depending on location, and are given by M Di +t (14.23) σb ¼ ± Iv 2

14.8 Design of Vessels Subject to Combined Loading

587

W M σz

σh

t Di

σz

FIGURE 14.9 Stresses in a cylindrical shell under combined loading.

where M is the total bending moment at the plane being considered and Iv the second moment of area of the vessel about the plane of bending: π (14.24) ðD4 − D4i Þ Iv = 64 o 4. Torsional shear stresses τ resulting from torque caused by loads offset from the vessel axis. These loads will normally be small, and need not be considered in preliminary vessel designs. The torsional shear stress is given by T Di +t (14.25) τ= Ip 2

588

CHAPTER 14 Design of Pressure Vessels

–ve σw

+ve σw

FIGURE 14.10 Stresses due to dead-weight loads.

where T = the applied torque Ip = polar second moment of area Iv = ðπ/32Þ ðD4o − D4i Þ.

Principal Stresses The principal stresses will be given by qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 σ 1 = σ h + σ z + ðσ h − σ z Þ2 + 4τ2

(14.26)

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi σ 2 = 1 σ h + σ z − ðσ h − σ z Þ2 + 4τ2

(14.27)

where σz = total longitudinal stress = σ L + σ w ± σb σw should be counted as positive if tension and negative if compressive. τ is not usually significant. The third principal stress, that in the radial direction σ3, will usually be negligible for thin-walled vessels (see Section 14.1.1). As an approximation it can be taken as equal to one-half the pressure loading: σ 3 = 0:5 P

(14.28)

σ3 will be compressive (negative).

Allowable Stress Intensity The maximum intensity of stress allowed will depend on the particular theory of failure adopted in the design method (see Section 14.3.2). The maximum shear stress theory is normally used for pressure vessel design.

14.8 Design of Vessels Subject to Combined Loading

589

Using this criterion the maximum stress intensity at any point is taken for design purposes as the numerically greatest value of the following: ðσ 1 − σ 2 Þ ðσ 1 − σ 3 Þ ðσ 2 − σ 3 Þ The vessel wall thickness must be sufficient to ensure the maximum stress intensity does not exceed the maximum allowable stress (nominal design strength) for the material of construction, at any point. The ASME BPV Code Sec. II Part D should be consulted for the maximum allowable stress values in tension or in compression.

Compressive Stresses and Elastic Stability Under conditions where the resultant axial stress σz due to the combined loading is compressive, the vessel may fail by elastic instability (buckling) (see Section 14.3.3). Failure can occur in a thinwalled process column under an axial compressive load by buckling of the complete vessel, as with a strut (Euler buckling); or by local buckling, or wrinkling, of the shell plates. Local buckling will normally occur at a stress lower than that required to buckle the complete vessel. A column design must be checked to ensure that the maximum value of the resultant axial stress does not exceed the critical value at which buckling will occur. For a curved plate subjected to an axial compressive load the critical buckling stress σc is given by (see Timoshenko, 1936) EY t (14.29) σ c = pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 R p 3ð1 − ν Þ where Rp is the radius of curvature. Taking Poisson’s ratio as 0.3 gives σ c = 0:60 EY

t Rp

(14.30)

By applying a suitable factor of safety, Equation 14.30 can be used to predict the maximum allowable compressive stress to avoid failure by buckling. A large factor of safety is required, as experimental work has shown that cylindrical vessels will buckle at values well below that given by Equation 14.29. For steels at ambient temperature EY = 200,000 N/mm2, and Equation 14.30 with a factor of safety of 12 gives t N=mm2 (14.31) σ c = 2 × 104 Do The maximum compressive stress in a vessel wall should not exceed that given by Equation 14.31, or the maximum allowable design stress for the material, whichever is the least. For detailed design, the ASME BPV Code Sec. VIII should be consulted and the recommended procedure in the code should be followed.

590

CHAPTER 14 Design of Pressure Vessels

Stiffening As with vessels under external pressure, the resistance to failure by buckling can be increased significantly by the use of stiffening rings, or longitudinal strips. Methods for estimating the critical buckling stress for stiffened vessels are given in the standards and codes.

Loading The loads to which a vessel may be subjected will not all occur at the same time. For example, it is the usual practice to assume that the maximum wind load will not occur simultaneously with a major earthquake. The vessel must be designed to withstand the worst combination of the loads likely to occur in the following situations: 1. 2. 3. 4.

During erection (or dismantling) of the vessel With the vessel erected but not operating During testing (the hydraulic pressure test) During normal operation

14.8.1 Weight Loads The major sources of dead-weight loads are: 1. 2. 3. 4. 5. 6. 7.

The vessel shell The vessel fittings: manways, nozzles Internal fittings: plates (plus the fluid on the plates); heating and cooling coils External fittings: ladders, platforms, piping Auxiliary equipment that is not self-supported; condensers, agitators Insulation The weight of liquid to fill the vessel. The vessel will be filled with water for the hydraulic pressure test, and may fill with process liquid due to misoperation.

Note: For vessels on a skirt support (see Section 14.9.2), the weight of the liquid to fill the vessel will be transferred directly to the skirt. The weight of the vessel and fittings can be calculated from the preliminary design sketches. The weights of standard vessel components (heads, shell plates, manways, branches, and nozzles) are given in various handbooks; Megyesy (2008) and Brownell and Young (1959). For preliminary calculations the approximate weight of a cylindrical vessel with domed ends, and uniform wall thickness, can be estimated from the following equation: Wv = Cw π ρm Dm gðHv + 0:8 Dm Þ t × 10−3

(14.32)

where Wv = total weight of the shell, excluding internal fittings, such as plates, N Cw = a factor to account for the weight of nozzles, manways, internal supports, etc; which can be taken as = 1.08 for vessels with only a few internal fittings = 1.15 for distillation columns, or similar vessels, with several manways, and with plate support rings, or equivalent fittings

14.8 Design of Vessels Subject to Combined Loading

591

Hv = height, or length, between tangent lines (the length of the cylindrical section), m g = gravitational acceleration, 9.81 m/s2 t = wall thickness, mm ρm = density of vessel material, kg/m3 (see Table 6.2) Dm = mean diameter of vessel = (Di + t × 10−3), m For a steel vessel, Equation 14.32 reduces to: Wv = 240 Cw Dm ðHv + 0:8 Dm Þt

(14.33)

The following values can be used as a rough guide to the weight of fittings; see Nelson (1963): Caged ladders, steel, 360 N/m length Plain ladders, steel, 150 N/m length Platforms, steel, for vertical columns, 1.7 kN/m2 area Contacting plates, steel, including typical liquid loading, 1.2 kN/m2 plate area Typical values for the density of insulating materials are (all kg/m3): Foam glass Mineral wool Fiberglass Calcium silicate

150 130 100 200

These densities should be doubled to allow for attachment fittings, sealing, and moisture absorption.

14.8.2 Wind Loads (Tall Vessels) Wind loading will only be important on tall columns installed in the open. Columns and chimneystacks are usually free standing, mounted on skirt supports, and not attached to structural steel work. Under these conditions the vessel under wind loading acts as a cantilever beam, see Figure 14.11. For a uniformly loaded cantilever the bending moment at any plane is given by Mx =

W x2 2

(14.34)

where x is the distance measured from the free end and W the load per unit length (Newtons per meter run). So the bending moment, and hence the bending stress, will vary parabolically from zero at the top of the column to a maximum value at the base. For tall columns the bending stress due to wind loading will often be greater than direct stress due to pressure, and will determine the plate thickness required. The most economical design will be one in which the plate thickness is progressively increased from the top to the base of the column, with the thickness at the top being sufficient for the pressure load, and that at the base sufficient for the pressure plus the maximum bending moment. Any local increase in the column area presented to the wind will give rise to a local, concentrated load, see Figure 14.12. The bending moment at the column base caused by a concentrated load is given by Mp = Fp Hp

(14.35)

Bending moment diagram

CHAPTER 14 Design of Pressure Vessels

Wind load, W N/m

592

FIGURE 14.11 Wind loading on a tall column.

FIGURE 14.12 Local wind loading.

14.8 Design of Vessels Subject to Combined Loading

593

where Fp = local, concentrated load Hp = the height of the concentrated load above the column base.

Dynamic Wind Pressure The load imposed on any structure by the action of the wind will depend on the shape of the structure and the wind velocity: Pw = 1Cd ρa u2w 2

(14.36)

where Pw = wind pressure (load per unit area) Cd = drag coefficient (shape factor) ρa = density of air uw = wind velocity The drag coefficient is a function of the shape of the structure and the wind velocity (Reynolds number). For a smooth cylindrical column or stack the following semi-empirical equation can be used to estimate the wind pressure: Pw = 0:05 u2w

(14.37)

where Pw = wind pressure, N/m2 uw = wind speed, km/h If the column outline is broken up by attachments, such as ladders or pipework, the factor of 0.05 in Equation 14.37 should be increased to 0.07, to allow for the increased drag. A column must be designed to withstand the highest wind speed that is likely to be encountered at the site during the life of the plant. The probability of a given wind speed occurring can be predicted by studying meteorological records for the site location. Data and design methods for wind loading are given in the Engineering Sciences Data Unit (ESDU) Wind Engineering Series (www .esdu.com). Design loadings for locations in the United States are given by Moss (2003), Megyesy (2008), and Escoe (1994). A wind speed of 160 km/h (100 mph) can be used for preliminary design studies, equivalent to a wind pressure of 1280 N/m2 (25 lb/ft2). At any site, the wind velocity near the ground will be lower than that higher up (due to the boundary layer), and in some design methods a lower wind pressure is used at heights below about 20 m, typically taken as one-half of the pressure above this height. The loading per unit length of the column can be obtained from the wind pressure by multiplying by the effective column diameter: the outside diameter plus an allowance for the thermal insulation and attachments, such as pipes and ladders. W = Pw Deff

(14.38)

An allowance of 0.4 m should be added for a caged ladder. The calculation of the wind load on a tall column, and the induced bending stresses, is illustrated in Example 14.2. Further examples of the design of tall columns are given by Brownell (1963), Henry (1973), Bednar (1990), Escoe (1994), and Farr and Jawad (2006).

594

CHAPTER 14 Design of Pressure Vessels

Deflection of Tall Columns Tall columns sway in the wind. The allowable deflection will normally be specified as less than 150 mm per 30 meters of height (6 in. per 100 ft). For a column with a uniform cross-section, the deflection can be calculated using the formula for the deflection of a uniformly loaded cantilever. A method for calculating the deflection of a column where the wall thickness is not constant is given by Tang (1968).

Wind-induced Vibrations Vortex shedding from tall thin columns and stacks can induce vibrations which, if the frequency of shedding of eddies matches the natural frequency of the column, can be severe enough to cause premature failure of the vessel by fatigue. The effect of vortex shedding should be investigated for free standing columns with height to diameter ratios greater than 10. Methods for estimating the natural frequency of columns are given by Freese (1959) and DeGhetto and Long (1966). Helical strakes (strips) are fitted to the tops of tall smooth chimneys to change the pattern of vortex shedding and so prevent resonant oscillation. The same effect will be achieved on a tall column by distributing any attachments (ladders, pipes, and platforms) around the column.

14.8.3 Earthquake Loading The movement of the earth’s surface during an earthquake produces horizontal shear forces on tall self-supported vessels, the magnitude of which increases from the base upward. The total shear force on the vessel will be given by Wv (14.39) F s = ae g where ae = the acceleration of the vessel due to the earthquake g = the acceleration due to gravity Wv = total weight of the vessel and contents The term (ae/g) is called the seismic constant Ce, and is a function of the natural period of vibration of the vessel and the severity of the earthquake. Values of the seismic constant have been determined empirically from studies of the damage caused by earthquakes, and are available for those geographical locations that are subject to earthquake activity. Values for sites in the United States and procedures for determining the stresses induced in tall columns are given by Megyesy (2008), Escoe (1994), and Moss (2003).

14.8.4 Eccentric Loads (Tall Vessels) Ancillary equipment attached to a tall vessel will subject the vessel to a bending moment if the center of gravity of the equipment does not coincide with the center line of the vessel (Figure 14.13). The moment produced by small fittings, such as ladders, pipes, and manways, will be small and can be neglected. That produced by heavy equipment, such as reflux condensers and side platforms, can be significant and should be considered. The moment is given by Me = We Lo

(14.40)

where We = dead weight of the equipment Lo = distance between the center of gravity of the equipment and the column center line

14.8 Design of Vessels Subject to Combined Loading

595

FIGURE 14.13 Bending moment due to offset equipment.

To avoid putting undue stress on the column walls, equipment such as reflux condensers and overhead receiving drums is usually not attached to the top of a column, but is instead located adjacent to the column in the plant structure. Condensers and receiving vessels are often placed above grade level to provide net positive suction head for reflux and overhead pumps sited at grade.

14.8.5 Torque Any horizontal force imposed on the vessel by ancillary equipment, the line of thrust of which does not pass through the center line of the vessel, will produce a torque on the vessel. Such loads can arise through wind pressure on piping and other attachments; however, the torque will normally be small and usually can be disregarded. The pipework and the connections for any ancillary equipment will be designed so as not to impose a significant load on the vessel. Example 14.2 Make a preliminary estimate of the plate thickness required for the distillation column specified below:

Height, between tangent lines Diameter Hemispherical head Skirt support, height 100 sieve plates, equally spaced Insulation, mineral wool Material of construction, stainless steel, maximum allowable stress

50 m 2m 3m 75 mm thick 135 N/mm2 at design temperature 20 °C

(Continued )

596

CHAPTER 14 Design of Pressure Vessels

Operating pressure 10 bar (absolute) Vessel to be fully radiographed (joint efficiency 1) Process service

Gasoline debutanizer

Solution

Design pressure, take as 10% above operating pressure = ð10 − 1Þ × 1:1 = 9:9 bar, say 10 bar = 1:0 N/mm2 Minimum thickness required for pressure loading: t=

1 × 2 × 103 = 7:4 mm ð2 × 135 × 1Þ − ð1:2 × 1Þ

(14.13)

A much thicker wall will be needed at the column base to withstand the wind and dead-weight loads. As a first trial, divide the column into five sections (courses), with the thickness increasing by 2 mm per section. Try 10, 12, 14, 16, 18 mm. Dead Weight of Vessel

Though Equation 14.33 only applies strictly to vessels with uniform thickness, it can be used to get a rough estimate of the weight of this vessel by using the average thickness in the equation, 14 mm. Take

Cw = 1:15, vessel with plates Dm = 2 + 14 × 10−3 = 2:014 m Hv = 50 m t = 14 mm Wv = 240 × 1:15 × 2:014 ð50 + 0:8 × 2:014Þ14 = 401643 N = 402 kN

Weight of plates: plate area = π/4 × 22 = 3.14 m2 weight of a plate including liquid on it (see Section 14.8.1) ≈ 1.2 × 3.14 = 3.8 kN 100 plates = 100 × 3.8 = 380 kN Weight of insulation: mineral wool density = 130 kg/m3 approximate volume of insulation = π × 2 × 50 × 75 × 10−3 = 23.6 m3 weight = 23.6 × 130 × 9.81 = 30,049 N double this to allow for fittings, etc. = 60 kN Total weight: shell plates & contents insulation

402 380 60 842 kN

(14.33)

14.8 Design of Vessels Subject to Combined Loading

597

Note that the weight of the contents of the column would be substantially greater if the column was flooded or entirely filled with liquid. This is the case during hydraulic testing, which should be examined as a different loading scenario. Wind Loading

Take dynamic wind pressure as 1280 N/m2, corresponding to 160 kph (100 mph). Mean diameter, including insulation = 2 + 2ð14 + 75Þ × 10−3 = 2:18 m Loading ðper linear meterÞW = 1280 × 2:18 = 2790 N/m

(14.38)

Bending moment at bottom tangent line: Mx =

2790 × 502 = 3,487,500 Nm 2

(14.34)

Analysis of Stresses

At bottom tangent line: Pressure stresses: 3 σ L = 1:0 × 2 × 10 = 27:8 N=mm2 4 × 18 3 σ h = 1 × 2 × 10 = 55:6 N=mm2 2 × 18

(14.7) (14.10)

Dead weight stress: σw =

3 Wv = 842 × 10 πðDi + tÞt πð200 + 18Þ18

= 7:4 N=mm2 ðcompressiveÞ

(14.22)

Bending stresses: Do = 2000 + 2 × 18 = 2036 mm Iv = π ð20364 − 20004 Þ = 5:81 × 1010 mm4 64 σb = ±

3,487,500 × 103 2000 + 18 2 5:81 × 1010

= ± 61:11 N=mm2 The resultant longitudinal stress is σz = σL + σw ± σb σw is compressive and therefore negative. σz (upwind) = 27.8 − 7.4 + 61.1 = +81.5 N/mm2. σz (downwind) = 27.8 − 7.4 − 61.1 = −40.7 N/mm2.

(14.24)

(14.23)

598

CHAPTER 14 Design of Pressure Vessels

As there is no torsional shear stress, the principal stresses will be σz and σh. The radial stress is negligible, (Pi/2) = 0.5 N/mm2. The greatest difference between the principal stresses will be on the downwind side: ð55:6 − ð−40:7ÞÞ = 96:5 N/mm2 well below the maximum allowable design stress. Note that the bending stress due to wind loading is much larger than the dead weight stress. The hydraulic testing case will have a greater dead weight when the vessel is filled with water, but a simple calculation shows that the maximum weight of water in the vessel (neglecting volume of vessel internals) is π/12 × ρ × g (3Di2L + 2Di3) = 1582 kN. If this is added to the total weight calculated above then the dead weight stress will increase by about a factor 3. This is still a lot less than the bending stress due to wind load, so the wind load case is the governing case. The hydraulic test will obviously not be scheduled for a day on which 100 mph winds may occur. Check Elastic Stability (Buckling)

Critical buckling stress: σ c = 2 × 104

18 = 176:8 N=mm2 2036

(14.31)

The maximum compressive stress will occur when the vessel is not under pressure = 7.4 + 61.1 = 68.5, well below the critical buckling stress. So the design is satisfactory. The designer could reduce the plate thickness and recalculate.

14.9 VESSEL SUPPORTS The method used to support a vessel will depend on the size, shape, and weight of the vessel; the design temperature and pressure; the vessel location and arrangement; and the internal and external fittings and attachments. Horizontal vessels are usually mounted on two saddle supports (Figure 14.14). Skirt supports are used for tall, vertical columns (Figure 14.15). Brackets, or lugs, are used for all types of vessel (Figure 14.16). The supports must be designed to carry the weight of the vessel and contents, and any superimposed loads, such as wind loads. Supports will impose localized loads on the vessel wall, and the design must be checked to ensure that the resulting stress concentrations are below the maximum allowable design stress. Supports should be designed to allow easy access to the vessel and fittings for inspection and maintenance.

14.9.1 Saddle Supports Though saddles are the most commonly used support for horizontal cylindrical vessels, legs can be used for small vessels. A horizontal vessel will normally be supported at two cross-sections; if more than two saddles are used the distribution of the loading is uncertain. A vessel supported on two saddles can be considered as a simply supported beam, with an essentially uniform load, and the distribution of longitudinal axial bending moment will be as

14.9 Vessel Supports

Saddles

Horn of saddle

ML1

ML2

ML2 Bending moment diagram

FIGURE 14.14 Horizontal cylindrical vessel on saddle supports.

Shell Strap Skirt

Bearing plate

Foundation

(b)

(a)

FIGURE 14.15 Typical skirt-support designs: (a) straight skirt; (b) conical skirt.

599

600

CHAPTER 14 Design of Pressure Vessels

(b)

(a)

FIGURE 14.16 Bracket supports: (a) supported on legs; (b) supported from steel-work.

shown in Figure 14.14. Maxima occur at the supports and at mid-span. The theoretical optimum position of the supports to give the least maximum bending moment will be the position at which the maxima at the supports and at mid-span are equal in magnitude. For a uniformly loaded beam the position will be at 21% of the span, in from each end. The saddle supports for a vessel will usually be located nearer the ends than this value, to make use of the stiffening effect of the ends. In addition to the longitudinal bending stress, a vessel supported on saddles will be subjected to tangential shear stresses, which transfer the load from the unsupported sections of the vessel to the supports, and to circumferential bending stresses. All these stresses need to be considered in the design of large, thin-walled, vessels, to ensure that the resultant stress does not exceed the maximum allowable design stress or the critical buckling stress for the material. A detailed stress analysis is beyond the scope of this book. A complete analysis of the stress induced in the shell by the supports is given by Zick (1951). Zick’s method forms the basis of the design methods given in the national codes and standards. The method is also given by Brownell and Young (1959), Escoe (1994), and Megyesy (2008).

Design of Saddles The saddles must be designed to withstand the load imposed by the weight of the vessel and contents. They are constructed of bricks or concrete, or are fabricated from steel plate. The contact angle should not be less than 120°, and will not normally be greater than 150°. Wear plates are often welded to the shell wall to reinforce the wall over the area of contact with the saddle. The dimensions of typical “standard” saddle designs are given in Figure 14.17. To take up any thermal expansion of the vessel, such as that in heat exchangers, the anchor bolt holes in one saddle can be slotted. Procedures for the design of saddle supports are given by Brownell and Young (1959), Megyesy (2008), Escoe (1994), and Moss (2003).

14.9 Vessel Supports

601

14.9.2 Skirt Supports A skirt support consists of a cylindrical or conical shell welded to the base of the vessel. A flange at the bottom of the skirt transmits the load to the foundations. Typical designs are shown in Figure 14.15. Openings must be provided in the skirt for access and for any connecting pipes; the openings are normally reinforced. The skirt may be welded to the bottom head of the vessel (Figure 14.18(a)), welded flush with the shell (Figure 14.18(b)), or welded to the outside of the vessel shell (Figure 14.18(c)). The arrangement shown in Figure 14.18(b) is usually preferred. Skirt supports are recommended for vertical vessels as they do not impose concentrated loads on the vessel shell; they are particularly suitable for use with tall columns subject to wind loading as the support is equally strong in all directions.

Skirt Thickness The skirt thickness must be sufficient to withstand the dead-weight loads and bending moments imposed on it by the vessel; it will not be under the vessel pressure. The resultant stresses in the skirt will be σ s ðtensileÞ = σ bs − σ ws

(14.41)

120° t1 V

t1 t1 J E

J E

G Y

Vessel Diam. (m)

Dimensions (m) Maximum Weight (kN)

mm G

Bolt Diam.

Bolt Holes

0.6

0.48

0.15

0.55

0.24

0.190

0.095

0.8

0.58

0.15

0.70

0.29

0.225

0.095

0.9

0.63

0.15

0.81

0.34

0.275

0.095

1.0

0.68

0.15

0.91

0.39

0.310

0.095

1.2

180

0.78

0.20

1.09

0.45

0.360

0.140

All contacting edges fillet welded.

(a)

FIGURE 14.17(a) Standard steel saddles (adapted from Bhattacharyya, 1976): (a) for vessels up to 1.2 m. (b) for vessels greater than 1.2 m.

602

CHAPTER 14 Design of Pressure Vessels

120° t1 V

t1 t1 J E

J E

G Y

Vessel Diam. (m)

Dimensions (m) Maximum Weight (kN)

mm G

Bolt Diam.

Bolt Holes

1.4

230

0.88

0.20

1.24

0.53

0.305

0.140

1.6

330

0.98

0.20

1.41

0.62

0.350

0.140

1.8

380

1.08

0.20

1.59

0.71

0.405

0.140

2.0

460

1.18

0.20

1.77

0.80

0.450

0.140

2.2

750

1.28

0.225

1.95

0.89

0.520

0.150

2.4

900

1.38

0.225

2.13

0.98

0.565

0.150

2.6

1000

1.48

0.225

2.30

1.03

0.590

0.150

2.8

1350

1.58

0.25

2.50

1.10

0.625

0.150

3.0

1750

1.68

0.25

2.64

1.18

0.665

0.150

3.2

2000

1.78

0.25

2.82

1.26

0.730

0.150

3.6

2500

1.98

0.25

3.20

1.40

0.815

0.150

All contacting edges fillet welded.

(b)

FIGURE 14.17(b) (Continued)

and σ s ðcompressiveÞ = σ bs + σ ws

(14.42)

where σbs = bending stress in the skirt =

4 Ms πðDs + tsk Þ tsk Ds

(14.43)

Wv πðDs + tsk Þ tsk

(14.44)

σws = the dead weight stress in the skirt =

14.9 Vessel Supports

(b)

603

(c)

(a)

FIGURE 14.18 Skirt-support welds.

where Ms = maximum bending moment, evaluated at the base of the skirt (due to wind, seismic and eccentric loads, see Section 14.8) Wv = total weight of the vessel and contents (see Section 14.8) Ds = inside diameter of the skirt, at the base tsk = skirt thickness The skirt thickness should be such that under the worst combination of wind and dead-weight loading the following design criteria are not exceeded: σ s ðtensileÞ < Ss E sinθs t σ s ðcompressiveÞ < 0:125 EY sk sin θs Ds

(14.45) (14.46)

where S s = maximum allowable design stress for the skirt material, normally taken at ambient temperature, 20 °C E = weld joint efficiency, if applicable θs = base angle of a conical skirt, normally 80° to 90° The minimum thickness should be not less than 6 mm. Where the vessel wall will be at a significantly higher temperature than the skirt, discontinuity stresses will be set up due to differences in thermal expansion. Methods for calculating the thermal stresses in skirt supports are given by Weil and Murphy (1960) and Bergman (1963).

Base Ring and Anchor Bolt Design The loads carried by the skirt are transmitted to the foundation slab by the skirt base ring (bearing plate). The moment produced by wind and other lateral loads will tend to overturn the vessel; this will be opposed by the couple set up by the weight of the vessel and the tensile load in the anchor bolts. Various base ring designs are used with skirt supports. The simplest types, suitable for small vessels, are the rolled angle and plain flange rings shown in Figure 14.19(a) and (b). For larger columns a double ring stiffened by gussets, Figure 14.19(c), or chair supports are used. Design

604

CHAPTER 14 Design of Pressure Vessels

Gusset

(a)

(b)

(c)

FIGURE 14.19 Flange ring designs: (a) rolled-angle; (b) single plate with gusset; (c) double plate with gusset.

methods for base rings, and methods for sizing the anchor bolts, are given by Brownell and Young (1959). For preliminary design, the shortcut method and nomographs given by Scheiman (1963) can be used. Scheiman’s method is based on a more detailed procedure for the design of base rings and foundations for columns and stacks given by Marshall (1958). Example 14.3 Design a skirt support for the column specified in Example 14.2.

Solution

Try a straight cylindrical skirt (θs = 90°) of plain carbon steel, maximum allowable stress 89 N/mm2 and Young’s modulus 200,000 N/mm2 at ambient temperature. The maximum dead weight load on the skirt will occur when the vessel is full of water. Approximate weight = π × 22 × 50 1000 × 9:81 4 = 1,540,951 N = 1541 kN Weight of vessel, from Example 14:2 = 842 kN Total weight = 1541 + 842 = 2383 kN Wind loading, from Example 14:2 = 2:79 kN/m 2 Bending moment at base of skirt = 2:79 × 53 2 = 3919 kNm

(14.34)

As a first trial, take the skirt thickness as the same as that of the bottom section of the vessel, 18 mm. σ bs =

4 × 3919 × 103 × 103 πð2000 + 18Þ 2000 × 18 2

= 68:7 N=mm

(14.43)

14.9 Vessel Supports

σ ws ðtestÞ =

2383 × 103 = 20:9 N=mm2 πð2000 + 18Þ 18

σ ws ðoperatingÞ =

842 × 103 = 7:4 N=mm2 πð2000 + 18Þ 18

605

(14.43) (14.44)

Note: The “test” condition is with the vessel full of water for the hydraulic test. In estimating total weight, the weight of liquid on the plates has been counted twice. The weight has not been adjusted to allow for this as the error is small, and on the “safe side.” Maximum σ^s ðcompressiveÞ = 68:7 + 20:9 = 89:6 N=mm2

(14.42)

Maximum σ^s ðtensileÞ = 68:7 − 7:4 = 61:3 N=mm2

(14.41)

Take the joint efficiency E as 0.85. Criteria for design: σ^s ðtensileÞ < Ss E sinθ

(14.45)

61:3 < 0:85 × 89 sin 90 61:3 < 75:6 t σ^s ðcompressiveÞ < 0:125 EY sk sinθ Ds 89:6 < 0:125 × 200,000 18 sin90 2000 89:6 < 225

(14.46)

Both criteria are satisfied; adding 2 mm for corrosion gives a design thickness of 20 mm.

14.9.3 Bracket Supports Brackets, or lugs, can be used to support vertical vessels. The bracket may rest on the building structural steel work, or the vessel may be supported on legs (Figure 14.16). The main load carried by the brackets will be the weight of the vessel and contents; in addition the bracket must be designed to resist the load due to any bending moment due to wind, or other loads. If the bending moment is likely to be significant, skirt supports should be considered in preference to bracket supports. As the reaction on the bracket is eccentric (Figure 14.20), the bracket will impose a bending moment on the vessel wall. The point of support, at which the reaction acts, should be made as close to the vessel wall as possible, allowing for the thickness of any insulation. Methods for estimating the magnitude of the stresses induced in the vessel wall by bracket supports are given by Brownell and Young (1959) and by Wolosewick (1951). Backing plates or collars are often used to carry the bending loads. The brackets, and supporting steel work, can be designed using the usual methods for structural steelwork. Suitable methods are given by Bednar (1986) and Moss (2003). A quick method for sizing vessel reinforcing rings (backing plates) for bracket supports is given by Mahajan (1977).

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CHAPTER 14 Design of Pressure Vessels

Bending moment

Backing plate

Reaction

FIGURE 14.20 Loads on a bracket support.

Typical bracket designs are shown in Figures 14.21(a) and (b). The loads that steel brackets with these proportions will support are given by the following formula: Single-gusset plate design, Figure 14.21(a): Fbs = 60 Ld tc

(14.47)

Double-gusset plate design, Figure 14.21(b): Fbs = 120 Ld tc

(14.48)

where Fbs = maximum design load per bracket, N Ld = the characteristic dimension of bracket (depth), mm tc = thickness of plate, mm

14.10 BOLTED FLANGED JOINTS Flanged joints are used for connecting pipes and instruments to vessels, for manhole covers, and for removable vessel heads when ease of access is required. Flanges may also be used on the vessel body, when it is necessary to divide the vessel into sections for transport or maintenance. Flanged joints are also used to connect pipes to other equipment, such as pumps and valves. Screwed joints are often used for small-diameter pipe connections, below 2 in. (50 mm). Flanged joints are also used for connecting pipe sections where ease of assembly and dismantling is required for maintenance, but pipework will normally be welded to reduce costs. Flanges range in size from a few millimeters diameter for small pipes, to several meters diameter for those used as body or head flanges on vessels.

14.10 Bolted Flanged Joints

607

1.5 Lc

Fillet welds all round Throat = 0.7 tc Leg = tc

1.5 Ld

1.5 Lc

(a)

2 Ld

(b)

FIGURE 14.21 Bracket designs: (a) single gusset plate; (b) double gusset plate.

14.10.1 Types of Flange, and Selection Several different types of flange are used for various applications. The principal types used in the process industries are: 1. 2. 3. 4. 5.

Welding-neck flanges Slip-on flanges, hub and plate types Lap-joint flanges Screwed flanges Blank, or blind, flanges

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CHAPTER 14 Design of Pressure Vessels

(a)

(b)

(c)

(d)

FIGURE 14.22 Flange types: (a) welding-neck; (b) slip-on; (c) lap-joint; (d) screwed.

Welding-neck flanges, Figure 14.22(a), have a long tapered hub between the flange ring and the welded joint. This gradual transition of the section reduces the discontinuity stresses between the flange and branch, and increases the strength of the flange assembly. Welding-neck flanges are suitable for extreme service conditions, where the flange is likely to be subjected to temperature, shear, and vibration loads. They will normally be specified for the connections and nozzles on process vessels and process equipment. Slip-on flanges, Figure 14.22(b), slip over the pipe or nozzle and are welded externally, and usually also internally. The end of the pipe is set back from 0 to 2.0 mm. The strength of a slip-on flange is from one-third to two-thirds that of the corresponding standard welding-neck flange. Slipon flanges are cheaper than welding-neck flanges and are easier to align, but have poor resistance to shock and vibration loads. Slip-on flanges are generally used for pipework. Figure 14.22(b) shows a forged flange with a hub; for light duties slip-on flanges can be cut from plate. Lap-joint flanges, Figure 14.22(c), are used for pipework. They are economical when used with expensive alloy pipe, such as stainless steel, as the flange can be made from inexpensive carbon steel. Usually a short lapped nozzle is welded to the pipe, but with some schedules of pipe the lap can be formed on the pipe itself, and this will give a cheap method of pipe assembly. Lap-joint flanges are sometimes known as “Van-stone flanges.” Screwed flanges, Figure 14.22(d), are used to connect screwed fittings to flanges. They are also sometimes used for alloy pipe that is difficult to weld satisfactorily. Blind flanges (blank flanges) are flat plates, used to blank off flange connections, and as covers for manholes and inspection ports.

14.10.2 Gaskets Gaskets are used to make a leak-tight joint between two surfaces. It is impractical to machine flanges to the degree of surface finish that would be required to make a satisfactory seal under pressure without a gasket. Gaskets are made from “semi-plastic” materials that will deform and flow under load to fill the surface irregularities between the flange faces, yet retain sufficient elasticity to take up the changes in the flange alignment that occur under load.

14.10 Bolted Flanged Joints

609

A great variety of proprietary gasket materials is used, and reference should be made to the manufacturers’ catalogs and technical manuals when selecting gaskets for a particular application. Design data for some of the more commonly used gasket materials are given in Table 14.4. Further data can be found in the ASME BPV Code Sec. VIII D.1 Mandatory Appendix 2, ASME B16.20 and in Green and Perry (2007). The minimum seating stress y is the force per unit area (pressure) on the gasket that is required to cause the material to flow and fill the surface irregularities in the gasket face. The gasket factor m is the ratio of the gasket stress (pressure) under the operating conditions to the internal pressure in the vessel or pipe. The internal pressure will force the flanges’ faces apart, so the pressure on the gasket under operating conditions will be lower than the initial tightening-up pressure. The gasket factor gives the minimum pressure that must be maintained on the gasket to ensure a satisfactory seal. The following factors must be considered when selecting a gasket material: 1. The process conditions: pressure, temperature, corrosive nature of the process fluid 2. Whether repeated assembly and disassembly of the joint are required 3. The type of flange and flange face (see Section 14.10.3) Up to pressures of 20 bar, the operating temperature and corrosiveness of the process fluid will be the controlling factor in gasket selection. Vegetable fiber and synthetic rubber gaskets can be used at temperatures of up to 100 °C. Solid polyfluorocarbon (Teflon) and compressed asbestos gaskets can be used to a maximum temperature of about 260 °C. Metal-reinforced gaskets can be used up to around 450 °C. Plain soft metal gaskets are normally used for higher temperatures.

14.10.3 Flange Faces Flanges are also classified according to the type of flange face used. There are two basic types: 1. Full-faced flanges, Figure 14.23(a), where the face contact area extends outside the circle of bolts, over the full face of the flange 2. Narrow-faced flanges, Figures 14.23(b), (c), (d), where the face contact area is located within the circle of bolts Full-face, wide-faced flanges are simple and inexpensive, but are only suitable for low pressures. The gasket area is large, and an excessively high bolt tension would be needed to achieve sufficient gasket pressure to maintain a good seal at high operating pressures. The raised-face, narrow-faced flange shown in Figure 14.23(b) is probably the most commonly used type of flange for process equipment. Where the flange has a plain face, as in Figure 14.23(b), the gasket is held in place by friction between the gasket and flange surface. In the spigot and socket, and tongue and grooved faces, Figure 14.23(c), the gasket is confined in a groove, which prevents failure by “blowout.” Matched pairs of flanges are required, which increases the cost, but this type is suitable for high-pressure and high-vacuum service. Ring joint flanges, Figure 14.23(d), are used for high temperatures and highpressure services.

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CHAPTER 14 Design of Pressure Vessels

Table 14.4 Gasket Materials (Based on Table 2-5.1 in ASME BPV Code Sec. VIII D.1 Mandatory Appendix 2, and a similar table in BS 5500–2003)

Gasket Factor m

Min. Design Seating Stress y(N/mm2)

0.50 1.00

0 14

2.00 2.75 3.50

11.0 25.5 44.8

1.25

2.8

83-ply
2.0

Side-entering Agitators Side-entering agitators are used for blending low viscosity liquids in large tanks, where it is impractical to use conventional agitators supported from the top of the tank; see Oldshue, Hirshland, and Gretton (1956).

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CHAPTER 15 Design of Reactors and Mixers

Where they are used with flammable liquids, particular care must be taken in the design and maintenance of the shaft seals, as any leakage may cause a fire. For blending flammable liquids, the use of liquid jets should be considered as an “intrinsically” safer option; see Fossett and Prosser (1949).

15.5.3 Gas-liquid Mixing Gases can be mixed into liquids using either inline mixing, stirred vessels, or the vapor-liquid contacting devices described in Chapter 17. When a small amount of gas is fed or the gas dissolves completely, inline mixing can be used. The most common arrangement is an injection mixer (Figure 15.9(b)) followed by a static mixer. In some cases, a long injection tube with multiple holes drilled in it is used. This is known as a sparger (Figure 15.17). If a gas is injected into a stirred tank, the location of the gas injection must be chosen based on the mixing pattern obtained with the impeller that has been selected. The gas injection device is usually an annular ring with multiple small openings, and the openings are oriented to promote the desired circulation of gas bubbles. Methods such as computational fluid dynamics (CFD) are used to analyze the gas bubble flow pattern and ensure that the gas hold-up and interfacial area are adequate; see Section 15.11.3. The rate of mass transfer from gas to liquid can be predicted using Equations 15.13 to 15.15. It should always be assumed that any excess vapor leaving a stirred tank will be saturated with all the components of the liquid, and it is reasonable to assume at least 1 to 2 volume percent entrainment of liquid in the vapor if the rate of agitation is high. The extent of agitation caused by injecting a gas into a liquid can be seen from Table 15.6, which is based on information from Green and Perry (2007). A small flow of liquid can be dispersed into a gas stream using a spray nozzle (Figure 15.18). Many different proprietary spray nozzles are available and the nozzle is usually selected in consultation with a vendor. When large flow rates of vapor and liquid are to be contacted to carry out reaction, mass transfer, or direct heat transfer, plate or packed columns are usually used; these are discussed in detail in Chapter 17.

Liquid

Gas

FIGURE 15.17 Gas sparger.

15.6 Heating and Cooling of Reacting Systems

669

Table 15.6 Air Rate (ft3/ft2.min) Required to Cause Agitation of Water at 1 atm (Green & Perry, 2007) Degree of Agitation

Liquid Depth 9ft

Moderate Complete Violent

0.65 1.3 3.1

Liquid Depth 3ft 1.3 2.6 6.2

Gas

Liquid

FIGURE 15.18 Liquid injection into gas.

15.5.4 Solid-liquid Mixing Solids are mixed into liquids to dissolve solid feeds and to form slurries for transport and reaction of insoluble solids. Solids are usually added to a liquid in a stirred tank, although liquids are sometimes introduced into screw conveyors, which then act as mixing troughs. The design of stirred tanks is covered in Section 15.5.2. Liquids and solids are usually mixed at atmospheric pressure, to make handling and flow of the solid easier. The resulting mixture or slurry can then be pumped to the process pressure. Mixing of liquids and solids is often carried out as a batch operation to allow more accurate control of dissolved solid concentration. A modest inventory of solution or slurry can then be used to maintain a constant feed to continuous downstream operations. If an inventory of slurry is maintained, it must be continuously agitated to prevent settling. The formation of slurry feeds for hydraulic conveying is discussed in Section 18.3.5. Many of the same considerations apply when feeding a solid to a liquid-phase reactor.

15.6 HEATING AND COOLING OF REACTING SYSTEMS Heat addition and removal are important for maintaining temperature control of exothermic and endothermic reactions. For endothermic reactions, the rate of heat input can sometimes be the ratelimiting step.

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CHAPTER 15 Design of Reactors and Mixers

15.6.1 Heating and Cooling Reactors: Basic Principles Adding heating or cooling to a reactor design always increases the reactor cost. The designer should first consider the following: 1. Can the reaction be carried out adiabatically? If the heat of reaction is small, a small change in temperature across the reactor may be acceptable and heating or cooling can be avoided. If a diluent is added to the system, the thermal mass of the reagents will increase and the temperature change across the reactor will be reduced, so adding a diluent can enable adiabatic operation. 2. Can the feeds provide the required heating or cooling? Staged addition of hot feed to a reactor can provide additional heat to an endothermic reaction. Similarly, staged addition of cold feed can provide quench to an exothermic reaction. A commercial example of this is the use of hydrogen quenches to control the temperature increase during hydrocracking reactions; see Figure 15.19. In a stirred tank or other reactor that approximates well-mixed reactor behavior, the heat of reaction can sometimes be balanced by a sensible heat change between a hot or cold feed temperature and the reactor temperature. 3. Would it be more cost effective to carry out the heat exchange outside the reactor? If the required heat transfer surface is large, it may be difficult to fit into a simple reactor design, in which case the designer should consider using an external heat exchange system. Examples are given in the following sections. 4. Would it be more effective to carry out the reaction inside a heat transfer device? If the required residence time is small, or if the volume of catalyst is small, the reaction can sometimes be carried out inside the tubes of a heat exchanger or fired heater. The use of heat-exchange devices as reactors is discussed in Section 15.6.4. 5. Does the proposed design allow the process to be started up and shut down smoothly? The heating or cooling system must be flexible to respond to nonsteady operating conditions of the plant as well as steady-state operation. 6. Are there safety concerns with heating or cooling the reactor? For exothermic reactions, the designer should consider what would happen if there was a failure of the cooling system. How quickly can the control system respond and shut the reaction down before the exothermic reaction runs away? Exothermic reactors should not require a heater, and feedback between feed heaters, feed-effluent heat exchangers, and the reactor must be considered. Are there concerns about the heat transfer medium leaking into the reactor or reactor contents leaking into the heat transfer medium? The heating or cooling duty of the reactor is usually most easily estimated using commercial process simulation software. The designer must take care to ensure that the enthalpy of reaction and the heat capacities used by the simulator are sufficiently accurate for design purposes; see Section 15.3.1. Novice designers often make the mistake of forgetting to preheat (or precool) the reactor feeds, leading to unreasonably large reactor heating or cooling duties. The reactor feed should be at the desired reaction temperature unless hot or cold feed is being used as a temperature control strategy.

15.6 Heating and Cooling of Reacting Systems

671

Feed

Cold hydrogen quench gas

Catalyst bed

Collection, mixing and redistribution grids

Product

FIGURE 15.19 Use of hydrogen quench in hydrocracking reactor.

15.6.2 Heating and Cooling Stirred Tank Reactors A stirred-tank reactor can be operated in batch or continuous mode. In either case, the objective in heating or cooling the contents is to achieve a uniform temperature throughout the vessel and eliminate hot or cold spots that could cause fouling and nonselective reaction, or lead to hazards such as reaction runaway. The heating or cooling should be accomplished without disrupting the mixing in the vessel and creating undermixed zones or dead spots.

Indirect Heat Transfer Heat transfer to stirred vessels is described in detail in Section 19.18 and correlations for heat-transfer coefficients are given in Section 19.18.3. Figure 15.20 shows the most common approaches to providing heating or cooling to stirred vessels. Low heating duties can be accommodated with a jacketed vessel (Figure 15.20(a)). The mechanical and thermal design of jacketed vessels are discussed in Section 19.18.1. Different utility flow patterns can be accommodated in a jacketed vessel. For example, when steam is used for

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CHAPTER 15 Design of Reactors and Mixers

Feed

Feed Hot or cold utility in

Feed

Hot or cold utility out

Hot or cold utility in

Hot or cold utility out

Product (a) Jacketed vessel

Product (b) Internal coil

Product

FIGURE 15.20 Heating or cooling stirred-tank reactors.

heating a reactor the steam usually flows in at the top of the jacket and condensate is drained near the bottom, whereas cooling water is usually fed from the bottom up. If the area of a jacket is insufficient, an internal coil can be used (Figure 15.20(b)). Heat transfer to internal coils and coil pressure drop are covered in Section 19.18.2. Although coils can provide much more area, the volume of the reactor must be increased to accommodate the coil and coils can be difficult to clean and sterilize. For high rates of heat addition or removal, an external pumped circuit should be considered, as shown in Figure 15.20(c). The use of an external heat exchanger removes any volume limit on accommodating the heat transfer surface and allows the heat exchange to be optimized independently of reactor design considerations. The residence time of the fluid in the pump, piping, and heat exchanger should be subtracted from the required residence time of the reactor. If a shell and tube heat exchanger is used, the reacting fluid will usually (but not always) be placed on the tube side, to minimize the likelihood of forming dead spots or undermixed zones. Plate heat exchangers are often used in reactor pump-around circuits because of their low inventory of fluid, short residence time, and ease of cleaning. In any reactor that uses indirect heat transfer, the designer must check carefully to ensure that local hot spots or cold spots on the heat transfer surface will not lead to fouling, excessive corrosion, or poor reaction selectivity. A calculation of the hottest and coldest metal surface temperatures should be made. These will normally be in regions close to where the utility enters and exits. The calculation can be based on a sophisticated model of reactor hydrodynamics, as described in Section 15.11.3, or can be as simple as an estimate based on internal and external heat-transfer coefficients with suitably conservative assumptions. If there is a concern that either the hottest or coldest surface temperature could have a serious impact on reactor performance, the designer should reconsider the choice of hot or cold utility to attempt to reduce the temperature difference between the utility and reactor contents. This will generally lead to an increase in required area and may cause the selection of a different reactor design.

Direct Heat Transfer: Heating Using Live Steam If the reacting mixture is compatible with addition of water and the temperature and pressure are suitable, direct heat transfer to a vessel can be accomplished by injecting live steam into a reactor; see Figure 15.21. Steam is usually injected through a distribution ring or sparger, but if the vessel is well agitated a simple dip tube may suffice.

15.6 Heating and Cooling of Reacting Systems

673

The use of live steam eliminates the need for heat transfer surface and saves capital cost in the reactor. The trade-off is that the steam is lost to the process fluid and condensate cannot be recovered, so the cost of live steam must include the cost of replacing the boiler feed water. Process wastewater costs are also increased. When live steam is used it is unlikely that all the steam will condense, so provision must be made for a net vapor flow from the reactor. Any vapor leaving the reactor will be saturated with all the components of the reacting mixture, so the off-gas will normally be cooled and condensed to recover material that was vaporized. The cost impact of adding a vapor recovery system must also be considered when evaluating use of live steam if such a system was not already in place.

Direct Heat Transfer: Evaporative Cooling If the process feed, solvent, or product can be made to evaporate at the reaction temperature, evaporative cooling can be used to cool the reactor. In an evaporative cooling system the vapor from the reactor is usually cooled externally and condensed to recover process fluids. In some cases two stages of cooling are used, with an air or water cooler followed by a refrigerated chiller. The condensed fluid is usually refluxed to the reactor to provide additional cooling; see Figure 15.22. If the overhead system has adequate capacity, evaporative cooling can provide very sensitive temperature control. A small decrease in pressure will quickly cause more evaporation and remove heat from the reactor, so the reactor temperature control can be cascaded onto the pressure control. Steam To vapor recovery section

Feed

Product

FIGURE 15.21 Live steam injection. PIC

Cooler

Feed

Knockout drum

Product

FIGURE 15.22 Evaporative cooling.

To vent gas recovery

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CHAPTER 15 Design of Reactors and Mixers

15.6.3 Heating and Cooling Catalytic Reactors Slurry Reactors If a solid catalyst is mixed into a reacting liquid to form a slurry, heat transfer can be accomplished using the methods described in Section 15.6.2. Since slurries can cause erosion, the use of internal coils is not preferred. If an external pumped circuit is used, the pump design must be suitable for slurry service and the fluid should be placed on the tube side of the exchanger to prevent settling or filtering out of catalyst particles in dead spots. Plate heat exchangers can be used for slurries, but the designer should consult with a plate exchanger vendor to ensure that the gap spacing is adequate to prevent plugging.

Fixed-bed Reactors It is usually difficult to heat or cool a fixed-bed reactor by indirect heat transfer, as it is hard to maintain a uniform temperature profile across a radial section of the bed. Radial variation in temperature can cause faster deactivation of catalyst in the hotter zones and shorten the time between plant shutdowns for catalyst change out. The most common approach for heating or cooling a fixed-bed reactor is to divide the reactor into a series of smaller adiabatic beds and use interstage heating or cooling, as shown in Figure 15.23. Each bed is sized to have an acceptable adiabatic change in temperature. In the case of an endothermic

Feed

Utility

Catalyst Utility

Product

FIGURE 15.23 Fixed-bed reactor with interstage heating or cooling.

15.6 Heating and Cooling of Reacting Systems

675

reaction, the inlet temperature must not be so hot that selectivity is compromised, while the outlet temperature must be hot enough to maintain reasonable catalyst activity. For an exothermic reaction, the situation is reversed, and care must be taken to ensure that the reaction will not run away at the outlet temperature. The bed sizes are not necessarily equal, as the reaction rate may vary from bed to bed. In scaling up nonisothermal packed-bed reactors, the designer must ensure that the temperature change across each bed remains about the same as the capacity is increased. Since the temperature across any given bed is not uniform, both the bed inlet temperature and the average bed temperature should be kept the same during scale-up. Occasionally, it will be possible to pack the catalyst into tubes of a heat exchanger or fired heater. The use of heat-exchange devices as reactors is discussed in Section 15.6.4.

Fluidized-bed Reactors Fluidized beds have high heat-transfer coefficients; see Zenz and Othmer (1960). Indirect heat transfer to fluidized-bed reactors using coils or stab-in heat exchange bundles is therefore often effective. The heat capacity of the solids in a fluidized bed allows the solid particles themselves to be used as a heat transfer medium. In processes such as fluidized catalytic cracking, the catalyst is heated to a temperature above the reaction temperature in a regeneration reactor. Hot catalyst is then circulated back to the reactor where it provides the heat of reaction and heat needed to vaporize the feed. Deactivated catalyst is returned to the regeneration reactor. This process is discussed in more detail in Section 15.8.4 and illustrated in Figure 15.42.

15.6.4 Heat-exchange Devices as Reactors When it is necessary to operate a reactor isothermally and there is a large heat of reaction, the heat transfer requirements dominate the design and the reactor must be designed as a heat transfer device. Some common situations where this occurs include: • •

High-temperature endothermic reactions that quickly quench without continuous heat input. Low-temperature exothermic reactions that must be kept at constant temperature to maintain selectivity or for safety reasons. Many selective oxidation reactions fall into this category.

Reactions can be carried out inside any heat transfer device, but the most commonly used arrangements are shell and tube heat exchangers or fired heaters. Plate heat-exchanger reactors have been the subject of much research, but are not yet in widespread commercial use.

Homogeneous Reaction If the reaction mixture is a single phase and there is no need for a catalyst then the mechanical design and layout of a heat-exchanger reactor is the same as a conventional heat transfer device. The thermal design of a heat-exchanger reactor is, however, much more complex than a conventional heat exchanger. The heat-exchanger design equations that are normally used for heat transfer will not apply to the design of a heat-exchanger reactor, due to the nonlinear behavior of the reaction rate with temperature and hence the variation in heat release (or uptake) along the exchanger tubes. For example,

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CHAPTER 15 Design of Reactors and Mixers

Rate of reaction

Temperature Distance along tube

FIGURE 15.24 Schematic profiles of temperature and reaction rate for an exothermic reaction in a heat exchange tube.

in the case of an exothermic reaction, the rate of reaction might be expected to be highest at the inlet, where the concentrations of feeds are highest, but as the reaction proceeds and temperature increases the rate of reaction will increase, so the hot spot in the tube may actually be at some distance in from the inlet, as illustrated schematically in Figure 15.24. The location of the hot spot can be further complicated by the flow pattern on the shell side of the heat exchanger; hence determination of the effective temperature difference for the exchanger is not trivial. Many shell and tube heat-exchanger reactors are operated using a constant temperature utility such as boiling water or a boiling refrigerant as coolant to simplify the thermal design and ensure good control of utility-side temperature. It is usually not wise to make a conservative assumption of the temperature difference and proceed with a standard heat exchanger design. A design with excessive area will not achieve the desired reaction temperature and, if placed in operation, may require changes in utility temperature that could compromise process safety margins. Although such an approach can be useful as a means of generating an approximate capital cost for the reactor in the early stages of design, great care must be taken to ensure that the design is revised before detailed design begins. The approach that is typically followed in industrial practice is to construct a detailed model of the reaction kinetics and hydraulics, as described in Section 15.11.3. The model can then be fitted to experimental data to give confidence in its validity for scale-up of the design.

Heterogeneous Reaction When a catalyst is used inside a heat-exchange device, the designer faces the same issues as for homogeneous reactions, with the added complication of modifying the exchanger mechanical design to contain the catalyst. Catalyst can be loaded into the tubes of a shell and tube heat exchanger if the exchanger is mounted vertically and a suitable retaining screen is used at the end of each tube or immediately below the bottom tubesheet. This arrangement is used in the oxidation of orthoxylene to phthallic anhydride, where the reaction is cooled using a circulating molten salt, as illustrated in Figure 15.25. Heat from the molten salt is used to raise steam. For high-temperature endothermic reactions, heat input from steam or molten salt is not practical and the reactor must be designed for heat input from a fired heater. The rate of heat input in

15.6 Heating and Cooling of Reacting Systems

677

Feed

Molten salt coolant

Steam Boiler feed water Catalyst

Product

FIGURE 15.25 Phthallic anhydride reactor.

the convective section of a heater is usually too low to be useful, because of the low heat-transfer coefficient of the flue gas, so the reactor tubes must normally be placed in the radiant section of the furnace. It is difficult to maintain a uniform loading of catalyst in a horizontal tube, so the reactor tubes are typically hung vertically. The design must allow for thermal expansion of the tubes, which makes the use of U-tubes difficult, as the cold spot may be in one side of the U, causing the tube to bend. Several ingenious proprietary designs have been developed to overcome this problem. For example, ICI developed a tube-in-tube design for use in the steam reforming of methane to hydrogen, which is illustrated in Figure 15.26. The chemistry of methane steam reforming is discussed in more detail in Example 4.5. In the ICI design the feed is preheated in the convection section of the furnace, passed through a pre-reforming reactor and reheated in the convection section before entering the reforming tubes. The reforming tubes have a tube-in-tube arrangement, with catalyst loaded in the annular space. The process gas passes down through the catalyst and then exits through the inner tube. It can be seen that if the inner and outer tubes experience different thermal expansion there will be no loss of containment of the catalyst or bending of the tubes. Heat transfer to packed beds of catalyst can be modeled using the equations developed by Leva (1949); see Section 15.3.4. The same cautions apply as for design of homogeneous heatexchanger reactors and detailed models of the kinetics and hydrodynamics must be used to scale up a design.

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CHAPTER 15 Design of Reactors and Mixers

Product

Feed

Catalyst Pre-reforming reactor

Reformer tube

Fuel

FIGURE 15.26 ICI tube-in-tube steam reforming reactor (from US 4,985,231).

15.7 MULTIPHASE REACTORS In multiphase reactors, the design is complicated by the need to promote mass transfer between the phases, which is usually accomplished by providing a high interfacial area. If more than one phase is flowing the design may also need to allow for phase separation.

15.7.1 Vapor-liquid Reactors Vapor-liquid reactions are important in many chemical processes. Many oxygenation and hydrogenation reactions of organic compounds are carried out with the organic component in the liquid phase. Vapor-liquid contacting columns are preferred for vapor-liquid reactors if the residence time requirements are short enough, because of the high area for mass transfer. Packed columns are usually used; see Section 17.14. When long residence time is needed for the liquid phase, stirred tanks or tubular reactors are used. Methods of mixing a gas into a liquid are described in Section 15.5.3, and

15.7 Multiphase Reactors

679

the mass-transfer rates obtained when gas is sparged into a stirred tank can be predicted using Equations 15.13 to 15.15; see Section 15.3.4. The kinetics of gas-liquid reactions depends on the relative rates of mass transfer and chemical reaction. Consider the case where a gas species A reacts with a liquid species B. If the reaction is second order, the rate of reaction per unit volume can be written as (15.17)

ℜ = k2 CA CB where CA = concentration of A in the liquid phase CB = concentration of B in the liquid phase k2 = second order rate constant

If component B is present in excess in the liquid, we can assume that its composition is constant, in which case we can rewrite Equation 15.17 as (15.18)

ℜ ≈ k1 CA where k1 = k2 CB

Now consider mass transfer of component A through the boundary layer at the vapor-liquid interface, shown schematically in Figure 15.27. The rate of mass transfer per unit volume of liquid can be written as Rate of mass transfer = kL a ðCA,i − CA,bulk Þ

(15.19)

where kL = mass transfer coefficient for component A in the liquid phase a = interfacial area per unit volume of liquid CA,i = concentration of A in the liquid at the interface (as predicted by phase equilibrium) CA,bulk = concentration of A in the bulk liquid Vapor-liquid interface δ CB CA,i

CA,bulk

FIGURE 15.27 Mass transfer from vapor to liquid.

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CHAPTER 15 Design of Reactors and Mixers

If most of the reaction occurs in the bulk liquid then the rate of reaction in the liquid must be equal to the rate of mass transfer through the film and we can equate Equations 15.18 and 15.19: k1 CA,bulk = kL a ðCA,i − CA,bulk Þ

(15.20)

hence CA,bulk =

kL a CA,i ðk1 + kL aÞ

(15.21)

and we can rewrite the rate of reaction as ℜ = k1 CA,bulk = kL a CA,i

k1 ðk1 + kL aÞ

(15.22)

Two cases are apparent from Equation 15.22. If kLa >> k1 ℜ ≈ k1 CA,i

(15.23)

This is known as the slow kinetics-controlled regime, and the reaction occurs at the rate that would be predicted with the liquid-phase concentration predicted by phase equilibrium. In this regime the rate is not sensitive to the interfacial area and increasing the agitation rate or packing area per unit volume will not affect the conversion. Alternatively, if k1 >> kLa ℜ ≈ kL a CA,i

(15.24)

This is known as the slow mass-transfer-controlled regime, in which the reaction rate is equal to the rate of mass transfer that would be obtained if the concentration of A in the bulk were zero. The rate of reaction is directly proportional to the interfacial area. If the thickness of the boundary layer is δ, and the condition for either of these regimes is that the reaction rate in the bulk is greater than the reaction rate in the film, we can write the condition as aδ k1 CA,i 1:0 ∑

zi > 1:0 K

17.3 Continuous Distillation: Basic Principles

815

Check the feed condition: Ki C2 C3 iC4 nC5

Ki zi

3.8 1.3 0.43 0.16

0.95 0.33 0.11 0.04 Σ 1.43

zi /Ki 0.07 0.19 0.58 1.56 Σ 2.40

Therefore, the feed is a two-phase mixture. Flash calculation: Try L/V = 1.5 Ki C2 C3 iC4 nC5

Ai = L/VKi

3.8 1.3 0.43 0.16

Try L/V = 3.0

Vi = Fzi /(1 + Ai)

0.395 1.154 3.488 9.375

14.34 9.29 4.46 1.93 Vcalc = 30.02 80 − 30:02 = 1:67 L /V = 30:02

0.789 11.17 2.308 6.04 6.977 2.51 18.750 1.01 Vcalc = 20.73 L /V = 2:80

Hengstebeck’s method is used to find the third trial value for L/V. The calculated values are plotted against the assumed values and the intercept with a line at 45° (calculated = assumed) gives the new trial value, 2.4. Try L /V = 2.4 Ai C2 C3 iC4 nC5

0.632 12.26 1.846 7.03 5.581 3.04 15.00 1.25 Vcalc = 23.58

yi = Vi /V

xi = (Fzi − Vi)/L

0.52 0.30 0.13 0.05 1.00

0.14 0.23 0.30 0.33 1.00

L = 80 − 23.58 = 56.42 kmol/h L/V calculated = 56.42/23.58 = 2.39 close enough to the assumed value of 2.4.

Adiabatic Flash In many flash processes the feed stream is at a higher pressure than the flash pressure and the heat for vaporization is provided by the enthalpy of the feed. In this situation the flash temperature will not be known and must be found by iteration. A temperature must be found at which both the material and energy balances are satisfied. This is easily solved using process simulation software, by specifying the flash outlet pressure and specifying zero heat input. The program then calculates the temperature and stream flow rates that satisfy the MESH equations.

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CHAPTER 17 Separation Columns (Distillation, Absorption, and Extraction)

17.4 DESIGN VARIABLES IN DISTILLATION

It was shown in Chapter 1 that to carry out a design calculation the designer must specify values for a certain number of independent variables to define the problem completely, and that the ease of calculation will often depend on the judicious choice of these design variables. The choice of design variables is particularly important in distillation, as the problem must be sufficiently well defined to find a feasible solution when simulated using a computer. The total number of variables and equations required to describe a multicomponent distillation can be very large, since the MESH equations must be solved for every stage, including the reboiler and condenser. It becomes difficult for the designer to keep track of all the variables and equations, and mistakes are likely to be made, as the number of degrees of freedom will be the difference between two large numbers. Instead, a simpler procedure known as the “description rule” given by Hanson, Duffin, and Somerville (1962) can be used. The description rule states that to determine a separation process completely, the number of independent variables that must be set (by the designer) will equal the number that are set in the construction of the column or that can be controlled by external means in its operation. The method is best illustrated by considering the operation of the simplest type of column, with one feed, no side streams, a total condenser, and a reboiler. The construction will fix the number of stages above and below the feed point (two variables). The feed rate, column pressure, and condenser and reboiler duties (cooling water and steam flows) will be controlled (four variables). There are therefore six variables in total. To design the column this number of variables must be specified, but the same variables need not be selected. Typically, in a design situation the feed rate will be fixed by the upstream design. The column pressure will also usually be fixed early in the design. Distillation processes are usually operated at low pressure, where relative volatility is high, but the pressure is usually constrained to be high enough for the condenser to operate using cooling water rather than refrigeration. If the feed rate and pressure are specified then four degrees of freedom remain. Rigorous column models in process simulation programs require the designer to specify the number of stages above and below the feed, leaving the designer with two degrees of freedom. If two additional independent parameters are specified, then the problem is completely defined and has a single solution. For example, if the designer specifies a reflux ratio and a boil-up ratio or a reflux ratio and a distillate rate, then there will be a corresponding unique set of distillate and bottoms compositions for a given feed composition. If the designer chooses to specify the compositions of two key components in either the distillate or the bottoms then there will be a required reflux rate, boil-up rate, distillate flow rate, etc. Similarly, specifying the purity and recovery of a single component in one of the products will completely specify the problem. When replacing variables identified by the application of the description rule it is important to ensure that those selected are truly independent, and that the values assigned to them lie within the range of possible, practical, values. For example, if the distillate mass flow rate is specified then the bottoms flow rate is fixed by overall material balance and cannot be specified independently. Proper attention to the specification of variables is particularly important when using purity or composition specifications in multicomponent distillation. It would clearly not be possible to obtain 99% purity of the light key component in the distillate if the feed contained 2% of components that boiled at lower temperatures than the light key component. The selection of key components and product specifications for multicomponent distillation are discussed in more detail in Section 17.6.

17.5 Design Methods for Binary Systems

817

The number of independent variables that have to be specified to define a problem will depend on the type of separation process being considered. Some examples of the application of the description rule to more complex columns are given by Hanson et al. (1962).

17.5 DESIGN METHODS FOR BINARY SYSTEMS The distillation of binary mixtures is a relatively simple problem. With a binary mixture, fixing the composition of one component fixes the composition of the other. The stage and reflux requirements can be determined using simple graphical methods developed in the 1920s, and iterative calculations are not required. It must, however, be emphasized that the graphical methods for binary distillation are no longer used in any practical context. Very few industrial distillation problems involve true binary mixtures. There will usually be other components present even if the two main components constitute more than 99.9 mol% of the mixture. The design engineer will usually need to know how these other components distribute between the distillate and bottoms to ensure that product specifications can be met and to determine the contaminant loads on downstream operations. Furthermore, the distillation design problem is rarely solved in isolation from the overall process design and the widespread use of process simulation programs has made the graphical methods obsolete. The initialization of a rigorous simulation of a binary distillation uses the same methods used for a multicomponent distillation (as described in Section 4.5.2). The graphical methods give no insight into the solution procedures used for multicomponent distillation. Despite the above considerations, many educators find the graphical methods for binary distillation to be useful as a means of explaining some of the phenomena that can occur in multistage separations, and these methods are part of the required chemical engineering curriculum in most countries. The graphical methods can be used to illustrate some problems that are common to binary and multicomponent distillation. Graphical methods are still useful in understanding and initializing other staged separation processes such as absorption, stripping, and extraction. The discussion of binary distillation methods in this chapter has been limited to a brief overview with emphasis on the insights that can be obtained from the graphs. For more details of the classical binary distillation methods see Richardson et al. (2002) and earlier editions of this book.

17.5.1 Basic Equations Sorel (1899) first derived and applied the basic stage equations to the analysis of binary systems. Figure 17.4(a) shows the flows and compositions in the top part of a column. Taking the system boundary to include the stage n and the condenser, gives the following equations: Material balance, total flows: Vn+1 = Ln + D

(17.11)

where D is the distillate flow rate, and for either component Vn+1 yn+1 = Ln xn + Dxd

(17.12)

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CHAPTER 17 Separation Columns (Distillation, Absorption, and Extraction)

yn, V′n

L′n + 1, xn+1

hn+1

D, xd, hd

yn+1, Vn+1 Ln, xn Hn+1 hn

B, xb, hb

(a)

(b)

FIGURE 17.4 Column flows and compositions: (a) above feed; (b) below feed.

Energy balance, total stream enthalpies: Vn+1 Hn+1 = Ln hn + Dhd + qc

(17.13)

where qc is the heat removed in the condenser. Combining Equations 17.11 and 17.12 gives yn+1 =

Ln D xn + xd Ln + D Ln + D

(17.14)

Combining Equations 17.11 and 17.13 gives Vn+1 Hn+1 = ðLn + DÞHn+1 = Ln hn + Dhd + qc

(17.15)

Analogous equations can be written for the stripping section, Figure 17.4(b): xn+1 =

V′n B yn + xb V′n + B V′n + B

(17.16)

and L′n+1 hn+1 = ðV′n + BÞhn+1 = V′n Hn + Bhb − qb where B is the bottoms flow rate.

(17.17)

17.5 Design Methods for Binary Systems

819

At constant pressure, the stage temperatures will be functions of the vapor and liquid compositions only (dew and bubble points) and the specific enthalpies will therefore also be functions of composition: H = f ðyÞ

(17.18a)

h = f ðxÞ

(17.18b)

Lewis-Sorel Method (Equimolar Overflow) For most distillation problems a simplifying assumption, first proposed by Lewis (1909), can be made that eliminates the need to solve the stage energy-balance equations. The molar liquid and vapor flow rates are taken as constant in the stripping and rectifying sections. This condition is referred to as equimolar overflow: the molar vapor and liquid flows from each stage are constant. This will only be true where the component molar latent heats of vaporization are the same and, together with the specific heats, are constant over the range of temperature in the column; there is no significant heat of mixing; and the heat losses are negligible. These conditions are substantially true for practical systems when the components form near-ideal liquid mixtures. Even when the latent heats are substantially different, the error introduced by assuming equimolar overflow to calculate the number of stages is often small compared to the error in the stage efficiency, and is acceptable. With equimolar overflow, Equations 17.14 and 17.16 can be written without the subscripts to denote the stage number: yn+1 = xn+1 =

L x D x n+ d L+D L+D

(17.19)

V′ B yn + xb V′ + B V′ + B

(17.20)

where L = the constant liquid flow in the rectifying section = the reflux flow, L0, and V′ is the constant vapor flow in the stripping section. Equations 17.19 and 17.20 can be written in an alternative form: L D xn + x d V V

(17.21)

L′ B xn+1 − xb V′ V′

(17.22)

yn+1 = yn =

where V is the constant vapor flow in the rectifying section = (L + D), and L′ is the constant liquid flow in the stripping section = V′ + B. These equations are linear, with slopes L/V and L′/V′. They are referred to as operating lines, and give the relationship between the liquid and vapor compositions between stages. For an equilibrium stage, the compositions of the liquid and vapor streams leaving the stage are given by the equilibrium relationship.

820

CHAPTER 17 Separation Columns (Distillation, Absorption, and Extraction)

17.5.2 McCabe-Thiele Method Equations 17.21 and 17.22 and the equilibrium relationship are conveniently solved by the graphical method developed by McCabe and Thiele (1925). A simple procedure for the construction of the diagram is given below and illustrated in Example 17.2.

Procedure Refer to Figure 17.5, all compositions are those of the more volatile component. 1. Plot the vapor-liquid equilibrium curve from data available at the column operating pressure. In terms of relative volatility: y=

αx ð1 + ðα − 1ÞxÞ

(17.23)

where α is the geometric average relative volatility of the lighter (more volatile) component with respect to the heavier component (less volatile). It is usually more convenient, and less confusing, to use equal scales for the x and y axes. 2. Make a material balance over the column to determine the top and bottom compositions, xd and xb, from the data given. 3. The upper and lower operating lines intersect the diagonal at xd and xb respectively; mark these points on the diagram.

Top operating line

q y

q line Bottom operating line

(q − 1) φ xb

xd x

FIGURE 17.5 McCabe-Thiele diagram.

17.5 Design Methods for Binary Systems

821

4. The point of intersection of the two operating lines is dependent on the phase condition of the feed. The line on which the intersection occurs is called the q line. The q line is found as follows: i. Calculate the value of the ratio q given by heat to vaporise 1 mol of feed q= molar latent heat of feed ii. Plot the q line, slope = q/(q − 1), intersecting the diagonal at zf (the feed composition). 5. Select the reflux ratio and determine the point where the upper operating line extended cuts the y axis: x (17.24) ϕ= d 1+R 6. Draw in the upper operating line (UOL), from xd on the diagonal to ϕ. 7. Draw in the lower operating line (LOL), from xb on the diagonal to the point of intersection of the top operating line and the q line. 8. Starting at xd or xb, step off the number of stages. Note: The feed point should be located on the stage closest to the intersection of the operating lines. The reboiler, and a partial condenser if used, act as equilibrium stages; however, when designing a column there is little point in reducing the estimated number of stages to account for this. Not counting the reboiler as a stage can be considered an additional design margin. It can be seen from Equation 17.24 and Figure 17.5 that as R increases, ϕ decreases, until the limit is reached where ϕ = 0 and the upper and lower operating lines both lie along the diagonal, as in Figure 17.6. This is the total reflux condition, in which the minimum number of stages is needed for the separation. Similarly, as R is reduced, the intersection between the upper and lower operating lines moves away from the diagonal until it reaches the equilibrium line, as illustrated in Figure 17.7. This is

FIGURE 17.6

FIGURE 17.7

Total reflux.

Minimum reflux.

822

CHAPTER 17 Separation Columns (Distillation, Absorption, and Extraction)

Equilibrium curve

A Operating line

C Stage efficiency =

Actual enrichment BC = AC Theoretical enrichment

FIGURE 17.8 Stage efficiency.

the minimum reflux condition. If the reflux ratio were to be reduced further, then there would be no feasible intersection of the operating lines. It can also be seen that at minimum reflux the space between the operating and equilibrium lines becomes very small at the intersection point, which is known as a “pinched” condition. An infinite number of trays is required at minimum reflux because of these pinch points, as can be seen in Figure 17.7. Pinch points also often occur when the relative volatility of the mixture is not constant, particularly when azeotropes or near azeotropes form, as illustrated in Figure 17.9. Pinch points also occur at the top or bottom of the column if very stringent purity specifications must be met. Pinch points are also found in multicomponent distillation and are easily visualized as regions where the composition profiles appear to be varying only very slightly from stage to stage. When a pinch point occurs, the solution is usually to increase the reflux or else change column pressure to obtain a more favorable equilibrium. The efficiency of real contacting stages can be accounted for by reducing the height of the steps on the McCabe-Thiele diagram, see the diagram in Figure 17.8. Stage efficiencies are discussed in Section 17.10. The McCabe-Thiele method can be used for the design of columns with side streams and multiple feeds. The liquid and vapor flows in the sections between the feed and takeoff points are calculated and operating lines drawn for each section.

Example 17.2 Acetone is to be recovered from an aqueous waste stream by continuous distillation. The feed contains 10 mol% acetone. Acetone of at least 95 mol% purity is wanted, and the aqueous effluent must not contain more than 1 mol% acetone. The feed will be a saturated liquid. Estimate the number of ideal stages required.

17.5 Design Methods for Binary Systems

823

Solution

There is no point in operating this column at other than atmospheric pressure. The equilibrium data of Kojima, Tochigi, Seki, and Watase (1968) will be used. Mol fraction x, liquid Acetone y, vapor bubble point °C

0.00 0.00 100.0

0.05 0.6381 74.80

0.10 0.7301 68.53

0.15 0.7716 65.26

0.20 0.7916 63.59

0.25 0.8034 62.60

0.30 0.8124 61.87 0.65 0.8615 58.71

x y °C

0.35 0.8201 61.26

0.40 0.8269 60.75

0.45 0.8376 60.35

0.50 0.8387 59.95

0.55 0.8455 59.54

0.60 0.8532 59.12

x y °C

0.70 0.8712 58.29

0.75 0.8817 57.90

0.80 0.8950 57.49

0.85 0.9118 57.08

0.90 0.9335 56.68

0.95 0.9627 56.30

The equilibrium curve can be drawn with sufficient accuracy to determine the stages above the feed by plotting the concentrations at increments of 0.1. Following the procedure given above, we can mark the product compositions. Since the feed is a saturated liquid, q = 1, and the slope of the q line is 1/(1 − 1) = ∞, the q line is thus plotted as a vertical line through the feed composition. For this problem the condition of minimum reflux occurs where the top operating line just touches the equilibrium curve at the point where the q line cuts the curve. From Figure 17.9, ϕ for the operating line at minimum reflux = 0:59 From Equation 17.24, Rmin = 0.95/0.59 − 1 = 0.62. Take R = Rmin × 2 = 1.24. As the flows above the feed point will be small, a high reflux ratio is justified; the condenser duty will be small: ϕ=

0:95 = 0:42 1 + 1:24

We can then plot the upper operating line (UOL) and lower operating line (LOL). Stepping off from the bottom, we require two stages in the stripping section and an additional eight stages in the rectifying section. The feed should be on the third stage from the bottom. Note that the number of stages below the feed is small, and since the reboiler counts as an equilibrium stage, if we feed onto the third plate from the bottom we would actually be feeding onto the stage marked 4 in Figure 17.9. This feed would be badly mismatched with the vapor and liquid compositions in the column, so it would be advisable to allow for possible feeds to the second and third plates from the bottom so that the feed point can be moved. Note also that the column is close to pinched at the top of the rectifying section. It would be prudent to add extra trays in this section.

824

CHAPTER 17 Separation Columns (Distillation, Absorption, and Extraction)

1 8 6 7 5

0.9 Equilibrium line

9 10 xD

0.8 UOL 3

y, mol fraction acetone

0.7

UOL, Rmin 0.6

0.5 2

0.4

q-line 0.3

0.2 LOL

0.1

0 0

0.2

0.4 0.6 x, mol fraction acetone

0.8

FIGURE 17.9 McCabe-Thiele plot, Example 17.2.

17.6 MULTICOMPONENT DISTILLATION: GENERAL CONSIDERATIONS The problem of determining the stage and reflux requirements for multicomponent distillations is much more complex than for binary mixtures. With a multicomponent mixture, fixing one component composition does not uniquely determine the other component compositions and the stage temperature. Also when the feed contains more than two components it is not possible to specify the complete composition of the top and bottom products independently. The separation between the top and bottom products is usually specified by setting limits on two “key” components, between which it is desired to make the separation. The complexity of multicomponent distillation calculations can be appreciated by considering a typical problem. The normal procedure is to solve the MESH equations (Section 17.3.1) stage by stage, from the top or bottom of the column. For such a calculation to converge to a solution, the

17.6 Multicomponent Distillation: General Considerations

825

compositions obtained from either the bottom-up and top-down calculations must match the composition at the other end of the column predicted from an overall material balance. But the calculated compositions will depend on the compositions assumed for the top or bottom products at the start of the calculations. Though it is possible to match the key components, the other components will not match unless the designer was particularly fortunate in choosing the trial top and bottom compositions. For a completely rigorous solution, the compositions must be adjusted and the calculations repeated until satisfactory convergence is obtained. Clearly, the greater the number of components considered, the more difficult the problem. As was shown in Section 17.3.2, iterative calculations will be needed to determine the stage temperatures. For other than ideal mixtures, the calculations will be further complicated by the fact that the component volatilities will be functions of the unknown stage compositions and temperatures. The relationship between volatility, composition, and temperature may be highly nonlinear, as discussed in Chapter 4. If more than a few stages are required, stage-by-stage calculations are complex and tedious and even with sophisticated process simulation programs convergence cannot be guaranteed. Before the widespread availability of digital computers, various “shortcut” methods were developed to simplify the task of designing multicomponent columns. A comprehensive summary of the methods used for hydrocarbon systems is given by Edmister (1947 to 1949) in a series of articles in the journal The Petroleum Engineer. Though computer programs will normally be available for the rigorous solution of the MESH equations, shortcut methods are still useful in preliminary design work, and as an aid in initializing problems for computer solution.

17.6.1 Key Components Before starting the column design, the designer must select the two key components between which it is desired to make the separation. The light key will be the component that the designer desires to keep out of the bottom product, and the heavy key the component to be kept out of the top product. The keys are known as adjacent keys if they are “adjacent” in a listing of the components in order of volatility, and split keys or nonadjacent keys if some other component lies between them in the volatility order. A separation between adjacent keys is known as a sharp split, while a separation with nonadjacent keys is known as a sloppy split. The choice of key components will normally be clear, but sometimes, particularly if close boiling isomers are present, judgment must be used in their selection. If any uncertainty exists, trial calculations should be made using different components as the keys to determine the pair that requires the largest number of stages for separation (the worst case). The Fenske equation can be used for these calculations; see Section 17.7.1. The nonkey components that appear in both top and bottom products are known as distributed components; and those that are not present, to any significant extent, in one or other product, are known as nondistributed components.

17.6.2 Product Specifications Specifications for the column will normally be set in terms of the purity or recovery of the key components. A purity specification sets the mole (or mass) fraction of a component in one of the product streams. Purity specifications are easily understood and are easy to relate to the required product

826

CHAPTER 17 Separation Columns (Distillation, Absorption, and Extraction)

specifications. For example, if the standard specification for the desired grade of product is 99.5% pure then the designer could specify 99.5% purity of the product in the distillate of a finishing column. Similarly, if the purity of the heavy key component in the distillate must be less than 50 ppm then this can be used as the specification. Although purity specifications are intuitively obvious, their use often leads to infeasible column specifications. The designer must check carefully to ensure that the amounts of lighter-than-lightkey (or heavier-than-heavy-key) components are not large enough to render the purity specification infeasible. Consider, for example, a feed that contains 0.5 mol% A, 49.5 mol% B, and 50 mol% C, where A is most volatile and C is least volatile. The highest purity of B that can be obtained in the distillate is 99%, and that would require complete recovery of B and complete rejection of C from the distillate, with a very high reflux ratio. If only 99% of the C is recovered in the bottoms product and only 99% of the B is recovered overhead, then the maximum feasible purity of B is 0.99(49.5)/ [0.5 + 0.99(49.5) + 0.5] = 98%. When a purity specification must be met in a column that forms part of a multicomponent sequence of columns then it is essential to set the specifications of the other columns so that the desired purity specification is feasible. Instead of specifying purity, the designer can specify the recovery of one or more of the key components in either the distillate or bottoms. The recovery of a component in a product stream is defined as the fraction of the feed molar flow rate of the component that is recovered in that product stream. The relationship between purity and recovery is often not simple, particularly when many components are present or the key components are nonadjacent. Recovery specifications are easily related to economic trade-offs, since the value of recovering an additional 0.1% or 0.01% of the desired product is easily assessed and can be traded off against the additional capital and operating costs of the column. Recovery of the desired product is usually set at 99% or greater. Recovery specifications for a distillation column are less likely to be infeasible than purity specifications; however, their use does not guarantee that the product will meet the specifications required for sale. In general, it is better to use purity specifications for the final column that produces product (usually termed the finishing column) and recovery specifications elsewhere in the distillation sequence. A combination of purity and recovery specifications can also be used for a single column. For example, in a finishing column in which the desired product is taken as distillate, the designer could specify the purity and recovery of the desired (light key) component in the distillate. No specifications on the heavy key or other components are needed, but the same feasibility checks must be made for the purity specification. In mixtures that form azeotropes the volatility order changes with composition. This creates additional problems when setting product specifications. The design of azeotropic distillation sequences is discussed in Section 17.6.5. Most process simulation programs allow the designer to select two specifications for a distillation column corresponding to the two remaining degrees of freedom once the feed rate, pressure, number of stages, and feed stage have been selected. If the column is to be designed to achieve a given purity or recovery then it obviously makes sense to use this as a specification if the simulation program allows it, but the designer may need to provide an initial estimate of other parameters such as reflux ratio or distillate rate to ensure good convergence. Estimates of these parameters can be made using shortcut calculations or shortcut column models, as described in Section 17.7.

17.6 Multicomponent Distillation: General Considerations

827

The use of shortcut models to initialize a rigorous simulation model was discussed in Section 4.5.2 and illustrated in Example 4.3. Example 4.4 showe

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