Understanding Distillation Using Column Profile Maps E-Book

Daniel Beneke

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 609

Veröffentlichungsjahr: 2012

Beschreibung

Researchers share their pioneering graphical method for designing almost any distillation structure Developed by the authors in collaboration with other researchers at the Centre of Material and Process Synthesis, column profile maps (CPMs) enable chemical engineers to design almost any distillation structure using novel graphical techniques. The CPM method offers tremendous advantages over other design methods because it is generalized and not constrained to a particular piece of equipment. Understanding Distillation Using Column Profile Maps enables readers to understand, analyze, and design distillation structures to solve common distillation problems, including distillation by simple columns, side rectifiers and strippers, multiple feed columns, and fully thermally coupled columns. In addition, the book presents advanced topics such as reactive distillation, membrane permeation, and validation of thermodynamic models. For all these processes, the authors set forth easy-to-follow design techniques, solution strategies, and insights gained using CPMs. This book offers everything needed to fully understand and use CPMs as a design tool: * Figures help readers understand how to use CPMs as design and optimization tools * Examples clearly illustrate how to solve specific problems using CPMs * Tutorials allow readers to explore key concepts through experimentation * Design and Optimization of Distillation Systems software package, developed for this book, enables readers to reproduce the examples in the book, follow the tutorials, and begin designing their own distillation systems With its many examples and step-by-step tutorials, Understanding Distillation Using Column Profile Maps is recommended for students in chemical engineering in advanced undergraduate and graduate courses. The book also provides new practical techniques that can be immediately applied by chemical engineering professionals in industry.

Leseprobe

Contents

Cover

Title Page

Copyright

Preface

Background

Target Audience

Expected Outcomes

Examples and Tutorials

Software

Acknowledgments

Nomenclature and Abbreviations

About the Authors

Chapter 1: Introduction

1.1 Context and Significance

1.2 Important Distillation Concepts

1.3 Summary

References

Chapter 2: Fundamentals of Residue Curve Maps

2.1 Introduction

2.2 Batch Boiling

2.3 The Mass Balance Triangle (MBT)

2.4 The Residue Curve Equation

2.5 Residue Curve Maps

2.6 Properties of Residue Curve Maps

2.7 Applicability of RCMs to Continuous Processes

2.8 Limitations of RCMs

2.9 Residue Curve Maps: The Bigger Picture

2.10 Summary

References

Chapter 3: Derivation and Properties of Column Profile Maps

3.1 Introduction

3.2 The Column Section (CS)

3.3 The Difference Point Equation (DPE)

3.4 Column Profile Maps

3.5 The Effect of CPM Parameters

3.6 Properties of Column Profile Maps

3.7 Pinch Point Loci

3.8 Some Mathematical Aspects of CPMs

3.9 Some Insights and Applications of CPMs

3.10 Summary

References

Chapter 4: Experimental Measurement of Column Profiles

4.1 Introduction

4.2 The Rectifying Column Section

4.3 The Stripping Column Section

4.4 Validation of Thermodynamic Models

4.5 Continuous Column Sections

4.6 Summary

References

Chapter 5: Design of Simple Columns Using Column Profile Maps

5.1 Introduction

5.2 Absorbers and Strippers

5.3 Simple Column Design

5.4 Azeotropic Systems

5.5 Constant Relative Volatility Systems

5.6 Summary

References

Chapter 6: Design of Complex Columns Using Column Profile Maps

6.1 Introduction

6.2 Distributed Feed Addition

6.3 Sidestream Withdrawal

6.4 Thermally Coupled Columns: Side Rectifiers and Strippers

6.5 Summary

References

Chapter 7: Design of Fully Thermally Coupled Complex Columns Using Column Profile Maps

7.1 Introduction

7.2 A Simplified Infinite Reflux Case

7.3 General Petlyuk Design

7.4 Sharp Split Petlyuk Design Using TTs

7.5 Insights into Kaibel Column Design

7.6 Summary

References

Chapter 8: Reactive Distillation Design Using Column Profile Maps

8.1 Introduction

8.2 Simple Reactive Distillation

8.3 Reactive Column Sections

8.4 Summary

References

Chapter 9: Application of Column Profile Maps to Alternative Separation Processes: Membrane Permeation

9.1 Introduction

9.2 Membrane Permeation

9.3 Generalized Membrane Column Sections

9.4 Theory

9.5 MCS Profiles: Total Reflux

9.6 Column Section Profiles: Finite Reflux

9.7 Conclusions

9.8 Example: Design of Hybrid Systems Using Distillation-Membrane Processes

References

Chapter 10: Concluding Remarks

10.1 Overall Conclusions

10.2 Limitations

10.3 Extensions and the Way Forward

References

Appendix A: DODS Software Package

A.1 Background to the DODS Package

A.2 System Requirements

A.3 Installation

A.4 DODS-ProPlot

A.5 DODS-SiCo

A.6 DODS-DiFe

A.7 DODS-SiSt and DODS-SiRe

Appendix B: NRTL Parameters and Antoine Coefficients

Index

Copyright © 2013 by John Wiley & Sons, Inc. All rights reserved.

Published by John Wiley & Sons, Inc., Hoboken, New Jersey.

Published simultaneously in Canada.

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Library of Congress Cataloging-in-Publication Data:

Beneke, Daniel, 1985-

Understanding distillation using column profile maps / Daniel Beneke, Mark Peters, David Glasser, Diane Hildebrandt, Centre of Material and Process Synthesis (COMPS), University of the Witwatersrand, Johannesburg.

pages cm

Includes bibliographical references and index.

ISBN 978-1-118-14540-1 (cloth)

1. Distillation–Simulation methods. 2. Distillation apparatus–Design and construction. I. Title.

TP156.D5B46 2013

660′.28425–dc23

2012023640

Preface

Background

The Centre of Materials and Process Synthesis (COMPS) was founded in 1998 by Professors Hildebrandt, Glasser, and Moys as a research group within the University of the Witwatersrand that would provide a platform for interaction between university expertise and industry. With the initiative being to reduce financial dependence of research on grant-awarding foundations, COMPS was set up as a channel to enhance scientific expertise through consulting, corporate training, and process development with industry. This endeavor has proven to be extremely beneficial to the research output of the group, at one time supporting as many as 40 graduate students, mostly supervised by Professors Hildebrandt and Glasser. The group has been at the forefront of several key areas of the field of process engineering, including reaction engineering and the attainable region, comminution, biosystems, Fischer–Tropsch synthesis, process synthesis, and of course separation synthesis.

This book is a culmination of approximately 15 years of research in the field of separation synthesis from the COMPS team. Many graduate students have passed through COMPS' doors during these times that have made valuable contributions to the work presented in this book. In particular, Simon Holland and Michaela Vrey developed much of the early work and fundamentals of what is now known as column profile maps (CPMs), which forms the heart of this book. These maps are thought to be a new take on distillation, allowing a designer the freedom to design virtually any distillation structure. The refined form of the work that is presented in this book is the result of countless research meetings, arguments, debates, and scribbling. Through all of this, however, all that have been involved with the work have found it to be stimulating, exciting, and thought provoking, and the authors hope that this has been transferred to the reader.

The origin of our research into column profile maps began (inadvertently) due to a project initiated by John Marriot from Sasol. The project was to look at the design and optimization of divided wall columns. We originally started trying to simulate these columns on Aspen Plus® and found that we could not get converged designs easily (or even at all!). We went back to the drawing board and developed code to model a section of the column. Simon Holland worked on this as a graduate student for his M.Sc. Every week his supervisors, Professors David Glasser and Diane Hildebrandt, would meet with the separations research group and Simon would show his plots where his liquid composition profiles predicted negative mole fractions! David and Diane disbelieved his results and sent him back week after week to check his code—it was obviously wrong! After some months, seeing Simon's predicting negative mole fractions in the liquid composition (again) and after him claiming (again) that there was no fault in his code, Diane sat down one evening to prove to Simon why his code had to be wrong, and indeed found that there was no mathematical reason why mole fractions had to stay positive. After drawing many triangles and mixing and separation vectors, it eventually dawned on us that there was a beautiful geometry sitting behind the column profiles, and further more that Simon's code was, in fact, correct.

We eventually were able to answer the question that was posed to us initially, namely, the design and optimization of divided wall columns, and indeed were able to answer many other interesting and important questions in the field of separations. We are very grateful to John Marriot and Sasol for inadvertently setting us on this exciting and important area of research.

Target Audience

This book has been written from the point of view that the student/reader is familiar with basic distillation and vapor–liquid equilibrium concepts. The material is suitable for use in chemical engineering curriculums as an advanced undergraduate, or a graduate level course. COMPS has used and adapted some of this material for these purposes as well as for industrial short courses, and the feedback has been largely positive. We have found that engineers with a more industrial background also find the concepts and ideas expressed in the book enlightening. There are many instructive examples and tutorials on problem solving, and many of them include use of the DODS software package. This too is a useful learning tool.

Expected Outcomes

The authors hope that with this book the reader is comfortable with the design of a variety of distillation columns. We have attempted to include and present solutions for many of the most prevalent problems encountered in academic and industrial literature. This includes distillation by simple columns, side rectifiers/strippers, multiple feed columns, and fully thermally coupled columns. Moreover, advanced topics such as reactive distillation, membrane permeation, and validation of thermodynamic models are also dealt with. For each of the aforementioned processes we present design techniques, solution strategies and insights that may be gained when using the CPM technique.

It should be mentioned that the majority of the work presented here is graphically based simply because it is easier to grasp column interactions and behavior when approached from this point of view. However, this need not be a limitation for the methods. The authors would also like to stress that it is not necessarily the specific material and problems presented in the book that are important, but more the tools that the reader should be equipped with. The concepts we present simply put tools into the designer's hand for him/her to create a unique column or separation structure that may solve his/her particular separation problem. For instance, both distributed feed and reactive distillation columns are discussed independently, although it is of course entirely possible to conceive of a reactive distributed feed system, which is not discussed. The tools in this book will thus first allow the reader understand, analyze, and design well-known and frequently encountered distillation problems. Second, the tools can be used to synthesize and develop new systems that perhaps have not even been thought of yet. This principle applies to virtually all the work in this book and the reader is urged to explore such concepts.

Examples and Tutorials

The primary purpose of this book is to teach the column profile map method to students and engineers alike. As such, the text includes numerous examples (with solutions) that elucidate clearly how a particular problem should be solved using the column profile map method. In many, but not all, of these examples it is possible for the user to reproduce or follow the principles of the example at hand using the appropriate software package (as discussed in Section “Software”).

Tutorials are indicated with the www symbol to the left, and all additional text will be available at booksupport.wiley.com by entering ISBN 9781118145401. The main purpose of each tutorial is for the user to become familiarize with the ideas discussed in this book through experimentation with the appropriate DODS software package (as discussed in Section “Software”). When coming across the tutorial symbol in the book, the user should then try and reproduce the applicable figure using one of the DODS packages. This will simultaneously assist the user in becoming comfortable with the ideas in text body as well as the accompanying software.

Software

Most of the examples and tutorials found in this book have been written to be used in conjunction with the Design and Optimization of Distillation Systems (DODS) software package. This package has been developed specifically for this book and should assist the reader in understanding sometimes complex behavior quicker. In all, there are five subcomponents of the package:

1. DODS-ProPlot (A Profile Plotting tool that allows one to construct CPMs and find pinch points)

2. DODS-SiCo (A tool for designing Simple Columns)

3. DODS-DiFe (A tool for designing Distributed Feed columns)

4. DODS-SiSt (A tool for designing Side Strippers)

5. DODS-SiRe (A tool for designing Side Rectifiers).

The DODS package is fairly intuitive and easy to use once the fundamental concepts of each package are grasped. In Appendix A, a manual is provided that gives the user instructions on how the DODS package should be installed and operated.

Acknowledgments

This book comprises of the work and ideas of many talented researchers who have worked at COMPS, without whom this manuscript would not have been possible. Specifically we, the authors, would like to mention, chapter by chapter, the following persons who were involved with the original development of the work:

Chapter 3: Simon Holland, Michaela VreyChapter 4: Tsepho Modise, Jean Mulopo, Cameron WilsonChapter 6: Simon Holland, Chan Yee MaChapter 7: Simon Holland, Ronald AbbasChapter 8: Jean Mulopo

Furthermore, the authors would like to thank the following graduate and postdoctoral students for their patience, suggestions, and discussions, all of which have contributed to writing a clear manuscript: Emmanuel Kasese, Naadhira Seedat, Edmund Bono, Celestin Sempuga, Chan Yee Ma, and Neil Stacey. A very special thanks to Dr. Brendon Hausberger for his valuable contributions in making certain that the message we are trying to convey is unambiguous and concise. We would also like to thank Darryn Peters for his contributions in the preparation of the cover artwork, as well as the editing of every figure within the book.

Several organizations have supported this work financially, both directly and indirectly, and we are grateful to them. These include the University of the Witwatersrand, Johannesburg, South Africa, The National Research Foundation (NRF) of South Africa, Sasol Technology, the South African Research Chair Initiative (SARChI) for Sustainable Process Engineering, and the Technology and Human Resources for Industry Programme (THRIP).

Daniel BenekeMark PetersDavid GlasserDiane Hildebrandt

Johannesburg, South Africa

Nomenclature and Abbreviations

Scalars are given in italics.

Vectors are given in bold.

SymbolsaActivity–ADimensionless membrane area–BBottoms flowratemol/sProduct (bottoms) removal ratemol/sCPSpecific heat capacity at constant pressurekJ/mol KDDistillate flowratemol/sDistillate (feed) addition ratemol/seEigenvector–FFeed flowratemol/sFeed addition ratemol/sHLiquid hold-upmolΔHRXNMolar heat of reaction at 298 KkJ/molΔHVAPMolar latent heat of vaporization at normal pressurekJ/molIIdentity matrix–JFlux through a membranemol/s m2JJacobian matrix–kfReaction rate constants-1KSeparation equilibrium constant–KeqReaction equilibrium constant–LLiquid flowratemol/sMMixing vector–NNumber of stages, or position–NTotal number of CSs in a Distributed Feed Column–PPressurePaP(A)(Chapter 9) Permeate flowrate, as a function of positionmol/sPermeability of component imol m/s m2 PaPVAPVapor pressurePaPSTotal number of product streams–QLiquid fraction of the feed–QHeat load or dutykWQ(t)Heat input ratekWR(Chapter 4) Reflux ratio [batch processes]–R(Chapter 8) Reaction rates-1RDimensionless reaction rate–rΔ(Chapter 9) Reflux ratio, as a function of position–R(A)Retentate flowrate, as a function of positionmol/sRReaction vector–RΔReflux ratio–SReboil ratio–SSidestream flowratemol/sSSeparation vector–TTimesTTemperatureKVStoichiometric coefficient–V(vector of) Stoichiometric coefficients–VVapor flowratemol/sVapor removal ratemol/sXLiquid phase molar fraction (individual species)–X(vector of) Liquid phase molar fractions–xpPinch points (or stationary points, or nodes) in liquid phase–XΔDifference point–yVapor phase molar fraction (individual species)–y(vector of) Vapor phase molar fractions–ypVapor composition in equilibrium with xp–ΔzHeight of packing, or positionmz'Dimensionless position–Greek LettersαRelative volatility–αVector of relative volatilities–αMRelative permeability–αMVector of relative permeabilities–βMixing coefficient–δEffective membrane thicknessmδDifference vector–ΔNet flow in a CSmol/sεReaction extentmol/sΦLLiquid split ratio–ΦVVapor split ratio–γLiquid phase activity coefficient–κDimensionless reaction coefficient–λEigen value–π(Chapter 9) PressurePaθReaction coefficientsθZero matrix–τRatio of enthalpies (ΔHVAP/ΔHRXN)–ξWarped, or dimensionless, time–ω(Chapter 4) Warped, or dimensionless, time–SubscriptsSymbolDesignatesBBottomDDistillateFFinalFFeedIComponent iJComponent jKColumn sectionKStreamMaxMaximumMINMinimumNStage, or position, nncNumber of componentsPPermeateRReference componentRRectifying sectionRRetentate (Chapter 9)SStripping sectionSSidestreamSRSide-rectifierSSSide-stripperTTotal (Chapter 6)TTopRXNReactionSuperscriptsSymbolDesignatesBBottomOInitial conditionTTopAbbreviationsSymbolDesignatesBPBoiling pointBVMBoundary value methodCMOConstant molar overflowCPMColumn profile mapCSColumn sectionDODSDesign and optimization of distillation systemsDPEDifference point equationFPFlow patternHETPHeight equivalent theoretical plateLLELiquid–liquid equilibriumMBTMass balance triangleMCSMembrane column sectionMRFMinimum reflux at feedMTBEMethyl tertiary-butyl etherNRTLNonrandom two liquidRCMResidue curve mapRCSReactive column sectionRCPMReactive column profile mapRDPEReactive difference point equationR-RCM-MReactive residue curve map with mixingR-RCMReactive residue curve mapTTTransformed triangleTT4Transformed tetrahedronVLEVapor–liquid equilibrium

About the Authors

Daniel Beneke obtained an undergraduate degree in Chemical Engineering from the North West University, Potchefstroom (NWU-PUK), South Africa in 2007, and a h.D. in Chemical Engineering from the University of the Witwatersrand, Johannesburg, South Africa, in 2011, focusing on distillation synthesis using column profile maps. He has authored or coauthored seven papers and has also presented papers at numerous international conferences on this topic, and spent two semesters at the University of Illinois at Chicago (UIC), Chicago, IL, USA, as a visiting research scholar focusing on computational methods for column profile map design. In 2011, he received a Graduate Student Award from the Separations Division of the AIChE for his work in the field of distillation. Currently, Daniel is a Process Engineering Consultant at the Centre of Material and Process Synthesis (COMPS), based at the University of the Witwatersrand, where he is involved with process design for liquid fuel processes and separations research.

Mark Peters has authored a book in the field of industrial separations, entitled Membrane Process Design Using Residue Curve Maps (Wiley, 2011). He obtained his undergraduate degree in Chemical Engineering cum laude in 2003 and his Ph.D. in 2008 from the University of the Witwatersrand, Johannesburg, South Africa. Mark has spent time at the University of Illinois at Chicago (UIC), Chicago, IL, USA, as a research scholar. He has authored two scientific articles in the field of membrane separation, and has presented work at numerous internationally recognized conferences. He previously worked as a research process engineer at Sasol Technology, focusing on low-temperature Fischer–Tropsch (LTFT) gas-to-liquids (GTL) conversion. He is currently a Separations Consultant and Research engineer at the Centre of Material and Process Synthesis (COMPS), based at the University of the Witwatersrand, where he is actively involved in separation research as well as innovative waste-to-energy processes.

David Glasser is a Professor of Chemical Engineering and director of the Centre of Material and Process Synthesis (COMPS) at the University of the Witwatersrand, Johannesburg, South Africa. He obtained his B.Sc. (Chemical Engineering) from the University of Cape Town and his Ph.D. from Imperial College in London. Along with Diane Hildebrandt, he pioneered the work in the attainable region (AR) approach for process synthesis and optimization. He has been awarded an A1 rating as a scientist in South Africa by the National Research Foundation (NRF) of South Africa. He coauthored the book Membrane Process Design Using Residue Curve Maps (Wiley, 2011). He has authored or coauthored more than 100 scientific papers and was editor-in-chief of the new book series on Chemical Engineering and Technology, published by Kluwer Academic Publishers of the Netherlands. He has authored a chapter published in Handbook of Heat and Mass Transfer, Vol. 4, Advances in reactor design and combustion science. He has worked in a very wide range of research areas, including optimization, chemical reactors, distillation, and process synthesis.

Diane Hildebrandt is the codirector for the Centre of Material and Process Synthesis (COMPS) at the University of the Witwatersrand, Johannesburg, South Africa. She obtained her B.Sc., M.Sc., and Ph.D. from the University of the Witwatersrand. She coauthored the book Membrane Process Design Using Residue Curve Maps (Wiley, 2011), and has authored or coauthored over 90 scientific papers and has supervised 60 postgraduate students. She has been both a plenary speaker and invited speaker at numerous local and international conferences. In 2005, she was recognized as a world leader in her area of research when she was awarded A rating by the National Research Foundation (NRF) of South Africa. She has been the recipient of numerous awards, including the Bill Neale-May Gold Medal from the South African Institute of Chemical Engineers (SAIChE) in 2000, and Distinguished Women Scientist Award presented by the Department of Science and Technology (DST), South Africa in 2009, and she was the first winner of the African Union Scientific Continental award Basic Science, Technology and Innovation category in the same year. In 2010, she was awarded the ASSAf “Science-for Society” Gold Medal Award. She has worked at Chamber of Mines, Sasol and the University of Potchefstroom and has spent a sabbatical at Princeton.

Chapter 1

Introduction

1.1 Context and Significance

In virtually any chemical process, whether it is in the food, pharmaceutical, biological or fuel industries, one or more chemical reactions take place to manufacture a wide range of products. Unfortunately, as nature would have it, these reactions invariably produce by-products which severely affect the quality and therefore the final market value of the final product. This generally means that some sort of separation scheme has to be devised to remove unwanted impurities and to upgrade the purity of the wanted component(s). Over the course of the past few decades, many technologies have become available and have been sufficiently developed to accomplish this task, including distillation, membrane separation, crystallization, and solvent extraction, among others. However, of all these methods of separations, distillation remains by far the most common, mainly because it is (relatively) well understood, and its economic properties on a large scale are at the present moment the most favorable. In short, distillation is a method of purifying binary and multicomponent mixtures into purer products by exploiting the difference in boiling points between the respective components.

In order to exploit the difference in boiling point temperatures (or vapor pressures), a distillation column generally requires heating. On a large scale this heating is not insignificant. In fact, Soave and Feliu have reported that in 1995 there were approximately 40,000 distillation columns in the United States [1], accounting for 90% of all industrial separations and consuming around ( TJ), which is equivalent to 54 million tons of crude oil or a continuous power consumption of 91 GW [2]. In another study, it has been estimated that energy inputs into distillation columns in the United States accounts for approximately 3% of the entire country's energy consumption [3]. It is evident that by saving or recovering only 1% of the energy used by distillation columns, the impact would be significant. Apart from the obvious opportunities in reducing the energy requirements of a distillation train, it is also important to consider the capital investments associated to a particular separation, that is, the cost to physically construct the column, which is a strong function of the steel price at the time of construction. Capital and energy costs are generally opposing objectives, namely an energy-intensive column usually requires a smaller capital investment, and vice versa. A typical simple, one-feed-two-product continuous distillation column is shown in Figure 1.1.

Figure 1.1 A typical continuous distillation column.

The column shown in Figure 1.1 generally accepts an impure or mixed feed, and purifies it into two product streams, namely the distillate and bottoms streams. The distillate stream has a higher purity in low-boiling components while the bottoms stream is richer in high-boiling components.

Due to the tremendous costs associated to distillation, it is essential that a design engineer fully knows and understands the phenomena and processes at work. As such, graphical methods for designing distillation schemes have been especially popular. In 1925, McCabe and Thiele published a landmark paper on a graphical design method for binary distillation [4], still used today as a quick means of understanding the relationship between energy and capital costs for simple distillation. Multicomponent distillation columns have been traditionally designed through the Underwood set of equations [5]. These equations assume constant relative volatility between all components, constant molar overflow, and a sharp separation between product streams, that is, one or more of the components are completely depleted in at least one of the products (sharp splits) [6]. These assumptions are very good approximations for a large number of industrial applications and these equations have been applied by numerous authors to a plethora of distillation structures [7–16].

Residue curve maps and distillation line maps have also been a useful graphical technique for screening ternary separation feasibility, especially for simple columns [17]. These maps are basically a range of trajectories that track the liquid compositions of the chemical species over time in a simple batch distillation operation and conveniently present the relationship between liquid and vapor phases, allowing one to quickly analyze potential splits, even for highly nonideal systems. Although these maps can tell much about the feasibility of separation, they have limitations in that they only give information at rather impractical conditions for the design engineer: infinite energy requirements when in continuous operation. This will become apparent especially in Chapters 2 and 3.

Numerous other design techniques have evolved over the years with varying degrees of complexity. One of these is the shortest stripping line method proposed by Lucia et al. [18], which states that the shortest stripping line will generally lead to the structure with lowest heat duty. Another technique, proposed in the 1980s by Doherty and coworkers, modeled sections above and below the feed stage of a simple column with a set of ordinary differential equations [19–23]. This approach, named the boundary value method, is relatively simple to employ (with modern day computers and mathematical software) and accepts virtually any phase equilibrium behavior and product distributions.

Other, so-called nonequilibrium models or rate-based models [24–28] have also received considerable attention. In short, these models do not assume perfect equilibrium on each stage in the distillation column, but rather use mass and heat transfer coefficients to compute the degree of fractionation. Although the nonequilibrium model is unquestionably more rigorous and precise, it may not allow the same insight and understanding afforded by its simpler, equilibrium counterpart. For the vast majority of distillation problems, the equilibrium model is quite sufficient, especially when the designer is still in the conceptual or “idea-generation” stage of the design.

Even advanced simulation packages such as Aspen Plus® or Hysys, although having undoubted modeling capabilities, have not provided much insight into the design of complex distillation systems. This is largely due to the fact that these packages require precise initialization values to ensure convergence to the specified product purities. Furthermore, because of the “black box” nature of these packages, the user often does not have any insight into the final solution and how one might go about improving it. Without the necessary experience or advanced knowledge of the problem at hand, rigorously determining a column's feasibility or optimal point(s) of operation is a time-consuming, if not impossible, task.

Recently, in a series of papers by the Centre of Material and Process Synthesis (COMPS) at the University of the Witwatersrand, Johannesburg, a new distillation design technique was proposed, Column Profile Maps (CPMs) [29, 30]. CPMs were derived from an adaptation of ordinary differential equations for simple columns first proposed by Doherty and coworkers [19–23]. The graphical, generalized CPM method has been shown to be extremely useful for designing and analyzing distillation systems, especially complex distillation systems [31, 32]. As with the boundary value method, the CPM method is an equilibrium model, and does not require any simplifying assumptions regarding the phase equilibrium behavior, that is, the ideality of the liquid–vapor phase or the product distribution. Furthermore, highly insightful design parameters, such as the feed and product placements, are a product of the design and do not require the designer to specify them blindly beforehand. However, it is thought that the CPM method is perhaps most useful in devising new, previously unthought-of structures, since it is completely generalized and not limited to any particular piece of equipment.

The CPM method is furthermore not only confined to classical distillation schemes like those mentioned above but also the distillation research group at COMPS have used the original CPM ideas to design and analyze reactive distillation systems (Chapter 8) [33], hybrid membrane-distillation systems (Chapter 9) [34, 35], experimental validation of thermodynamic models and column behavior (Chapter 4) [36–38], and fundamental work in the behavior of columns [39, 40]. This book aims to summarize some of the key ideas the group have developed over the past few years, with the hope that other researchers, students, and engineers may come up with new and interesting configurations, or at the very least, understand the underlying workings of a particular distillation column.

Although this book primarily advocates distillation synthesis using the CPM method and can be read on its own, the reader should be aware that it is by no means an all encompassing text on distillation. Among the books that are considered by the authors to be a useful addition to this book are Distillation Design [41] and Distillation Operation by Henry Kister [42], Conceptual Design of Distillation Systems by Doherty and Malone [43], Separation Process Principles by Seader and Henley [44], and Distillation Theory and its Application to Optimal Design of Separation Units by Petlyuk [45]. All these works present different perspectives on the separation synthesis problem. Specifically, the book by Doherty and Malone shows the fundamental roots of the CPM method, that is modeling distillation columns with differential equations.

1.2 Important Distillation Concepts

This book has been compiled for the student, engineer, or researcher that understands the fundamental concepts of distillation, or has at least attended an introductory course on the subject. The reader should be familiar with key vapor–liquid equilibrium concepts, how industrial distillation is performed and basic design techniques such as the McCabe–Thiele method. For the sake of completeness and clarity however, we give a brief overview here of core concepts that the reader should be aware of and that are often used in this book.

1.2.1 A Typical Column

As evident from Figure 1.1, heat is added to the column through a reboiler, which vaporizes material and causes a vapor stream to travel upward in the column. Moving upward in the column, this vapor stream becomes richer in low-boiling component(s). For an efficient separation to occur, the vapor stream at the top of the column is condensed, at the condenser, and a portion of the condensed liquid is sent back down the column. This recycling of material is a key design parameter in distillation and is known as reflux, or the reflux ratio, and is directly proportional to the energy requirement of the column, that is, the higher the reflux ratio of the column, the higher the heating and cooling loads of the column are. Therefore, from a purely energetic perspective, one would like to operate as close to the minimum column reflux as possible.

A column can be either packed or trayed, as shown in Figure 1.2a and b, respectively. Separation occurs continuously throughout the length of a packed column, and occurs in a more step-by-step fashion in trayed columns. In general, this book deals with packed columns but the behavior of these two types of columns are fundamentally similar and the results can be interpreted interchangeably. We will refer to the spatial coordinate representing the position down the length of the column as stage number, represented by the variable n. The total number of stages required to affect the separation is thus related to the height of the column, which is indicative of the capital costs. It should be noted that the entry point of the feed stream occurs at the feed stage. Determining the feed stage is also an important design factor as it has a significant impact on the final product distribution of the column.

Figure 1.2 (a) Packed column and (b) trayed column.

1.2.2 Complex Columns

Complex columns are in a broad sense all columns that are not simple columns, like the column shown in Figure 1.1. Complex columns may have multiple feeds, side product streams, stream transfers between two column units (thermally coupled columns), simultaneous chemical reaction(s) within the column body, hybrid membrane-distillation columns, and so on. Each of these columns present unique opportunities for cost saving. Typical complex columns are shown in Figure 1.3a–d.

Figure 1.3 Examples of complex columns (a) distributed feed, (b) side-draw columns, (c) thermally coupled side stripper, (d) reactive distillation column with reaction zone (R).

Due to the tremendous costs associated to distillative separations, many alternate schemes to the simple column shown above have been proposed over the past several years both to improve on some of its inherent costs. Traditionally, when purifying a multicomponent mixture, an entire series of distillation columns are used in series, and the way in which these columns are sequenced may make a tremendous difference in the eventual process costs. However, due to the large energy requirements of even the most optimal sequence, more complex column arrangements have been proposed and subsequently utilized. These arrangements include thermally coupled columns such as side rectifiers and strippers, the fully thermally coupled columns (often referred to as the Petlyuk and Kaibel columns), prefractionating columns, and multieffect arrangements [9, 10]. Up to 50% savings in energy expenditures have been reported with these thermally coupled arrangements [10, 11, 46–48].

Side stripping columns have found widespread use in the petrochemical industry to produce various cuts of petroleum products [49]. On the other hand, side rectifying columns have found application in air separation [45] as well as replacing entrainer regeneration columns in extractive distillation operations [50]. Even more complex columns such as the Petlyuk column or dividing wall column for separating a given feed into three products in a single distillation unit, requires only a single heat addition and removal, thereby reducing the energy costs of the separation. Despite the apparent advantages that these complex configurations offer, simple distillation columns are overwhelmingly more utilized in industry. One factor contributing to the underutilization of the complex arrangements is, possibly, a lack of understanding of these columns. Simple columns, on the other hand, are extremely well understood. Current research in distillation has therefore largely been directed toward complex column design.

1.2.3 Vapor–Liquid Equilibrium

The fundamental driving force for a separation to occur via distillation is that a mixture of components has different vapor and liquid compositions due to differences in vapor pressures. In other words, low-boiling components tend toward the vapor phase quicker than high-boiling components. Obviously, this difference in composition across coexisting vapor and liquid phases is dependent on the mixture being dealt with. From a modeling and design point of view, the relationship between the vapor composition of component i (yi) and its liquid compositions (xi) are centrally important, as it is ultimately this relationship which determines the design and operation of a distillation structure. In general, the relationship between vapor and liquid compositions can be expressed as

(1.1)

Depending on the system at hand, the equilibrium ratio Ki may be either constant (as in Henry's law), or a function of temperature, pressure, and/or composition. In this book, the following phase equilibrium models are primarily models dealt with (1) constant relative volatilities, (2) ideal solutions using Raoult's law, and (3) nonideal solutions using a modified Raoult's law and the NRTL activity coefficient model, although other activity coefficient models are also applicable. Each of these three models is briefly discussed here.

1.Constant Relative Volatilities. The constant relative volatility model is the simplest model for relating vapor and liquid compositions with each other. Essentially, this model assumes that the volatility of components with respect to each other remain constant, and are independent of temperature or composition. The relative volatility (αi) of a component i is defined simply as

(1.2)

where r is a reference component in the system and αi is a constant. The reference component is usually taken as the highest boiling component and its relative volatility will be unity, subsequently all other relative volatilities in the system will be greater than one. This is the convention used in this book, but any component can of course be taken as the reference component. Using the unity summation properties of both vapor and liquid compositions, elucidated in Equation 1.3, the relationship in Equation 1.4 can be derived

(1.3)

(1.4)

where nc is the total number of components in the system. Equation 1.4 shows that the vapor composition in equilibrium with its liquid composition is only a function of the liquid composition and the relative volatilities that have been assumed. Obviously, the higher the value for α is for a particular component, the greater its tendency is to escape to the vapor phase. The assumption of constant relative volatility is generally, but not always, acceptable when the species being dealt with are all from the same functional group. For example, benzene and toluene have constant volatilities of approximately 5.28 and 2.24 with respect to the higher boiling p-xylene, respectively. Figure 1.4 shows the effect of the relative volatility on vapor and liquid compositions for binary systems. Here, component 1 is the low-boiling component, that is, most volatile, and component 2 is the highest boiling component, that is, least volatile with volatility of 1.

Figure 1.4 clearly indicates that higher the volatility is between two components, the greater the difference is between vapor and liquid compositions at equilibrium. Since it is exactly this difference between liquid and vapor compositions, that is, the driving force for distillative separation, higher volatility mixtures are consequently “easier” to separate than low volatility mixtures.

2.Ideal Solutions. The constant relative volatility assumption is often very good for a large number of systems. However, in many systems the equilibrium ratio is not constant but a function of temperature and pressure. Such a system may be modeled with Raoult's law, assuming that the vapor phase is an ideal gas and the liquid is an ideal solution (typically when liquid phase molecules are of the same size and chemically similar). In such instances, the equilibrium ratio is given by

(1.5)

where P is the total system pressure, and is the vapor pressure of species i and a function of temperature using the familiar Antoine equation, which has the general form shown in Equation 1.6

(1.6)

Coefficients Ai, Bi, and Ci are constants unique to specie i, and T is the boiling (or bubble) temperature of the mixture. The temperature at which a liquid with a particular composition is in equilibrium with its vapor may be calculated by combining Equations 1.1, 1.3, 1.5 and 1.6, ultimately yielding Equation 1.7

(1.7)

If the system pressure (P), the liquid composition and the Antoine coefficients are known for all components, temperature is the only remaining variable in Equation 1.7. Solving for the temperature in Equation 1.7 requires an iterative numerical technique. Once the temperature (and therefore the equilibrium ratio) is known, the vapor in equilibrium with its liquid may be obtained quite simply through Equation 1.1. Examples of selected binary systems are shown in the x – y diagram in Figure 1.5

3.Nonideal Solutions. The final level of complexity for modeling the relationship between vapor and liquid compositions accounts for nonideal interactions in the liquid phase. The equilibrium ratio is still used for such systems, but in this instance it is defined as

(1.8)

where γi is known as the activity coefficient of component i, and takes into account deviations from ideal, Raoult's law behavior. It is evident that Raoult's law in Equation 1.5 is a special case of Equation 1.8 where the activity coefficients are assumed to be one. Thus, Equation 1.8 is known as the modified Raoult's law. The activity coefficient is a function of both temperature and composition and calculating it can be quite intricate. There are many models used to calculate activity coefficients (Wilson, Margules, UNIQAUC, NRTL, and so on), and certain models may be better suited to a certain system than others. In this book, however, we primarily focus on the NRTL (non-random-two-liquid) model because it is quite widely applicable to a large number of systems. The NRTL activity coefficient may be modeled through Equations 1.9 and 1.10

(1.9)

(1.10)

The coefficients aij, bij, and cij are binary interaction parameters specific to components i and j. A list of binary interaction parameters and Antoine coefficients for systems prominently featured systems in the book are given in Appendix B. Evidently, modeling nonideal systems can be rather laborious and computationally intensive, but the solution strategy is exactly the same to the one outlined for ideal solutions in Equation 1.7, and simply incorporating the activity coefficients. Activity coefficient models can account for azeotropes, that is, where vapor and liquid compositions are equal, while neither Raoult's law nor the constant volatility model is able to. Examples of binary nonideal systems modeled with the NRTL equation are shown in Figure 1.6.

Figure 1.6 shows a very different curvature when compared to the “well-behaved” mixtures in Figures 1.4 and 1.5. Specifically, the acetone/chloroform and ethyl acetate/water systems form azeotropes where the vapor and liquid compositions become equal and the equilibrium curve intersects the line. Systems with azeotropes present challenging design problems because it is no longer possible to obtain two high purity products in a single distillation unit. There are of course ways to overcome this problem, notably through adjusting the pressure for so-called pressure swing distillation (notice from Equation 1.8 that the y – x relationship is system pressure dependent), or through creative material recycling [43]. The acetone/water system, on the other hand, does not have azeotropic behavior, but it is still quite nonideal, as evident from the asymmetric nature of its y – x curve. None of the systems in Figure 1.6 are, therefore, good candidates for modeling with either constant volatility or ideal solution models.

Figure 1.4 The effect of the relative volatility (α) on vapor and liquid compositions in a binary system.

Figure 1.5 Behavior of selected binary systems' vapor and liquid compositions using Raoult's law at 1 atm.

Figure 1.6 Behavior of selected binary systems' vapor and liquid compositions using a modified Raoult's law at 1 atm.

1.3 Summary

It is hoped that from this chapter the reader understands the context and importance of industrial distillation, and realizes why efficient and insightful design techniques are so important. Although it is a comparatively old separation technique, there is still much room for improvement, especially in the area of complex distillation. The CPM technique that is presented in this book will aid in understating simple and complex distillation systems more clearly. Although the premise of the CPM technique is reasonably easy to follow and comprehend, it is a rather advanced technique, not recommended as a reader's first introduction to the field of distillation.

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Chapter 2

Fundamentals of Residue Curve Maps

2.1 Introduction

Residue curve maps (RCMs) have been long used as a tool for analyzing a given ternary system's phase equilibrium behavior. These maps, originally pioneered by Schreinemakers in 1902 [1], enable design engineers to quickly scan possible separation trains or sequences, and also to identify areas of difficult separation due to azeotropes.

In this chapter, the derivation of RCMs from simple batch boiling, as well as the fundamental properties behind RCMs, are discussed. Thereafter, the application of RCMs to continuous processes is explored. However, as will be shown, this application has limitations and these will also be addressed.

A reader familiar with distillation research will find much of the material in this chapter to be familiar. However, RCMs do form the fundamental backbone of column profile maps (CPMs), and thus the need for this chapter is important. Readers that are experienced with distillation may find Section 2.9, particularly interesting and useful when some not-so-common ways of looking at RCMs are discussed.

It should be noted that only the information needed for the development of the material in the book is included in this chapter. Hence, some parts of the RCM theory are omitted since it is out of the scope of context for this particular text, but interested readers can consult the reference list for more detailed information [2–7].

2.2 Batch Boiling

The idea of the RCM arises from a simple batch experiment, whereby a beaker is filled with a mixture of components in the liquid phase. The liquid mixture is brought to its boiling point, producing a vapor in equilibrium with the liquid mixture, as shown in Figure 2.1.

Figure 2.1 A simple batch boiling experiment.

In this batch experiment,

H represents the liquid holdup within the beaker (mol),

is the removal rate of vapor leaving the beaker (mol/s), and

x and y are the liquid and vapor molar fractions, respectively, in vector form.

One may assume that y is in equilibrium with x, but this will be discussed in Section 2.4.

The molar fractions are defined using the following vector notation (as indicated in bold):

(2.1)

where xi is the mole fraction of component i in the liquid phase, yi is the mole fraction of component i in the vapor phase, and nc is the total number of components in the system.

Furthermore, since the entries in these compositional vectors are mole fractions, it is then a necessary requirement that

(2.2)

With this condition, only (nc − 1) entries in a compositional vector are needed to fully define it. Thus, for example, a 3-component system only requires mole fractions of two components for it to be fully specified. The remaining component is inferred by unity summation property in Equation 2.2.

When the initial charge of liquid, of composition xo, is brought to its boiling (bubble) point, vapor will be produced in equilibrium with xo. By removing this vapor from the still as soon as it is formed, continual vaporization will occur. As separation proceeds, the more volatile components will vaporize quicker than the lower volatile components. The remaining liquid, or residue, will thus become progressively more concentrated in the less volatile species, thereby increasing the boiling point of the residue. Thus, in order for boiling to continue, the temperature of the system needs to be raised. If this increase in temperature occurs very slowly, and the liquid is well mixed, one can assume that near-perfect vapor–liquid equilibrium (VLE) is attained. It should be noted that the experiment, as shown in Figure 2.1, is conducted under isobaric conditions. A similar experiment can be set up for an isothermal process whereby the pressure is reduced to bring about vaporization. The reader is referred to Chapter 4 for more details regarding the various forms of boiling experiments.

Suppose the still is charged with a ternary mixture comprising of arbitrary components such that

Component 1 is a low-boiling (or most volatile) component,

Component 2 is a high-boiling (or least volatile) component, and

Component 3 is an intermediate-boiling component.

If one continuously analyzes the composition of the residual liquid in the still with time, until the last trace of liquid vaporizes, one is able to plot the change in both liquid and vapor composition over time. Figure 2.2 shows this plot for the least volatile component—plots for the other species are not shown but can easily be generated. In this instance, vapor and liquid compositions have been plotted against so-called reduced time defined as the instantaneous time of the experiment (t) divided by some final time (tf) when the experiment has reached completion.

Figure 2.2 Schematic showing the compositional change with time of the least volatile component in both vapor and liquid phases during a simple boiling experiment.

As boiling progresses, the liquid becomes richer in the least volatile component, namely component 2. A result of this is that the vapor (in equilibrium with this liquid) also gradually becomes richer in this component too, but tends to trail behind the liquid compositional change. After sufficient experimental time, the liquid phase tends to contain only the pure low-volatility component, that is, the lower boiling components have been boiled off. However, the amount of this remaining liquid has been greatly reduced since the commencement of boiling. Although the remaining liquid in the beaker has a higher purity of component 2 as the experiment progresses, the total amount of liquid is also gradually diminished.

2.3 The Mass Balance Triangle (MBT)

Another related, but more important plot is that of the change of each species' composition with each other, where each point along the profile is measured as time proceeds during the experimental run. For a ternary mixture, such a plot is shown in Figure 2.3. The label xo represents the initial composition in the still, that is, the composition at t = 0, as can be confirmed in Figure 2.2.

Figure 2.3 Schematic showing the compositional change of the residual liquid during batch experimentation. The axes are collectively known as the mass balance triangle.

Such a set of axes (or triangle) is known as a mass balance triangle (MBT), or sometimes referred to as a Gibbs Triangle, and is typically used for ternary systems. The region enclosed by the triangle represents all the physically attainable compositions in a ternary system, that is, 0 ≤ xi ≤ 1 for i = 1, 2, and 3. Also, Equation 2.2 applies. The boundaries of the triangle are graduated for molar compositions (fractions) for each component (some plots may use mass fractions, but only mole fraction plots will be used in this book). As an example, the point labeled as xo has the following composition (as read from Figure 2.3) of xo = [0.7, 0.1, 0.2]. However, as explained in Section 2, the last component can be inferred by material balance, and writing the composition vector as xo = [0.7, 0.1] is sufficient to fully define a ternary composition. Note that composition vectors presented here, and throughout the book, are arranged in accordance with their volatilities in the form [x1, x2] = [low boiling, high boiling].

The vertices of the triangle indicate the location of individual pure components, as labeled in Figure 2.3