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ATTAINABLE REGION THEORY an Introduction to Choosing An k ATTAINABLE REGION THEORY k k k k k k k k ATTAINABLE REGION THEORY An Introduction to Choosing an Optimal Reactor By DAVID MING University of the Witwatersrand, Johannesburg DAVID GLASSER and DIANE HILDEBRANDT Material and Process Synthesis research unit, University of South Africa BENJAMIN GLASSER Rutgers, The State University of New Jersey MATTHEW METZGER Merck & Co., Inc k k k k Copyright © 2016 by John Wiley & Sons, Inc. All rights reserved Published by John Wiley & Sons, Inc., Hoboken, New Jersey Published simultaneously in Canada No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http://www.wiley.com/go/permission. Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice andstrategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at (800) 762-2974, outside the United States at (317) 572-3993 or fax (317) 572-4002. k k Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic formats. For more information about Wiley products, visit our web site at www.wiley.com. Library of Congress Cataloging-in-Publication Data: Names: Ming, David, 1985- author. | Glasser, David, 1936- author. | Hildebrandt, Diane, 1961- author. | Glasser, Benjamin John, 1968- author. | Metzger, Matthew, 1983- author. Title: Attainable region theory : an introduction to choosing an optimal reactor / by David Ming, David Glasser, Diane Hildebrandt, Benjamin Glasser, Matthew Metzger. Description: Hoboken, New Jersey : John Wiley & Sons, 2016. | Includes index. Identifiers: LCCN 2016022700 (print) | LCCN 2016025203 (ebook) |ISBN 9781119157885 (cloth) | ISBN 9781119244714 (pdf) | ISBN 9781119244707 (epub) Subjects: LCSH: Chemical reactors–Design and construction. | Statistical tolerance regions. Classification: LCC TP157 .M528 2016 (print) | LCC TP157 (ebook) |DDC 660/.2832–dc23 LC record available at https://lccn.loc.gov/2016022700 Cover Image Credit: Courtesy of the Author Typeset in 10/12pt TimesLTStd-Roman by SPi Global, Chennai, India Printed in the United States of America 10987654321 k k CONTENTS Preface xi Acknowledgments xiii Prior Knowledge xiv How this book is Structured xv Software and Companion Website xvii k Nomenclature xix k SECTION I BASIC THEORY 1 1 Introduction 3 1.1 Introduction, 3 1.2 Motivation, 3 1.2.1 Toluene Production as a Case Study, 3 1.2.2 Part One: Initial Investigations, 4 1.2.3 Part Two: Iterative Improvement, 4 1.2.4 Part Three: Coffee, 5 1.2.5 Part Four: Additional Improvements, 6 1.2.6 What this Book is About, 7 1.3 Reactor Network Synthesis, 8 1.4 Solving the Reactor Network Synthesis Problem, 12 1.4.1 Reactor Superstructures, 12 1.4.2 AR Theory, 14 1.4.3 Attainability Problems Outside of Reactor Design, 15 1.5 Chapter Review, 16 References, 17 k k vi CONTENTS 2 Concentration and Mixing 19 2.1 Introduction, 19 2.1.1 Review, 19 2.1.2 Revisualizing Concentration Data, 19 2.2 Concentration Vectors and Dimension, 23 2.2.1 Moving on a Line: Table Salt and Water, 23 2.2.2 Moving Freely Through Space, 25 2.3 Mixing, 28 2.3.1 Introduction, 28 2.3.2 Additional Insights, 33 2.3.3 Different Ways of Synthesizing CC,35 2.3.4 Mixing and Attainability, 37 2.3.5 n-Dimensional Mixing and Convex Hulls, 41 2.4 Chapter Review, 47 References, 47 3 The Attainable Region 49 3.1 Introduction, 49 3.2 A Mixing and Reaction Game, 49 3.2.1 Introduction and Rules of the Game, 49 3.2.2 Filling in the Region, 49 3.2.3 Scenario 1: Selecting Points from Region A, 50 3.2.4 Scenario 2: Selecting Points from Region B1,51 3.2.5 Further Improvements, 53 3.3 The AR, 57 3.3.1 Ten Experiments, 57 k 3.3.2 The Limit of Infinitely Many Batches, 57 k 3.4 Elementary Properties of the AR, 58 3.5 Chapter Review, 61 References, 61 4 Reaction 63 4.1 Introduction, 63 4.2 Reaction Rates and Stoichiometry, 63 4.2.1 Benzene Reaction Rate, 63 4.2.2 Toluene Reaction Rate, 64 4.3 Reaction from a Geometric Viewpoint, 66 4.3.1 The Rate Vector, 66 4.3.2 Rate Fields, 69 4.4 Three Fundamental Continuous Reactor Types, 73 4.4.1 Motivation, 73 4.4.2 The Plug Flow Reactor, 73 4.4.3 The Continuous-Flow Stirred Tank Reactor, 82 4.4.4 The Differential Sidestream Reactor, 95 4.5 Summary, 102 4.6 Mixing Temperatures, 102 4.6.1 Motivation, 102 4.6.2 Adiabatic Energy Balance, 102 4.6.3 Non-adiabatic Energy Balance, 104 4.7 Additional Properties of the AR, 105 4.8 Chapter Review, 106 References, 107 k k CONTENTS vii 5 Two-Dimensional Constructions 109 5.1 Introduction, 109 5.2 A Framework for Tackling AR Problems, 109 5.3 Two-Dimensional Van De Vusse Kinetics, 110 5.3.1 Introduction, 110 5.3.2 Scenario 1: a1 = a2, 111 < 5.3.3 Scenario 2: a1 a2, 114 > 5.3.4 Scenario 3: a1 a2, 114 5.3.5 Review, 123 5.4 Multiple CSTR Steady States and ISOLAS, 125 5.4.1 Introduction, 125 5.4.2 Step 1: Define the Problem, 125 5.4.3 Step 2: AR Construction, 126 5.4.4 Steps 3–5: Interpretation and Optimization, 130 5.5 Constructions in Residence Time Space, 131 5.5.1 Significance of Residence Time Constructions, 131 5.5.2 Mixing in Residence Time Space, 132 5.5.3 Visualizing Residence Time Data, 132 5.5.4 Unbounded Regions, 133 5.5.5 Example: Optimal Reactor Structure for Minimum Residence Time, 134 5.6 Chapter Review, 141 References, 141 SECTION II EXTENDED TOPICS 143 k k 6 Higher Dimensional AR Theory 145 6.1 Introduction, 145 6.2 Dimension and Stoichiometry, 146 6.2.1 The Stoichiometric Subspace, 146 6.2.2 Concentrations Orthogonal to the Stoichiometric Subspace, 152 6.2.3 Number of Independent Reactor Structures, 158 6.3 The Three Fundamental Reactor Types Used in AR Theory, 159 6.3.1 Introduction, 159 6.3.2 Extreme Points and Reaction, 159 6.3.3 Two Important Theorems, 162 6.4 Critical DSRs and CSTRs, 166 6.4.1 Overview, 166 6.4.2 Controllability, 166 6.4.3 Computing Critical DSR Trajectories, 169 6.4.4 Computing Critical CSTR Points, 182 6.5 Chapter Review, 189 References, 190 7 Applications of AR Theory 191 7.1 Introduction, 191 7.2 Higher Dimensional Constructions, 191 7.2.1 Three-Dimensional Van de Vusse Kinetics, 191 7.2.2 BTX Kinetics, 198 k k viii CONTENTS 7.3 Nonisothermal Constructions and Reactor Type Constraints, 205 7.3.1 Adiabatic Reaction, 205 7.3.2 Constrained AR Construction Using Only PFRs, 208 7.3.3 Insights into Interstage and Cold-Shot Cooling Operation, 211 7.4 AR Theory for Batch Reactors, 222 7.4.1 Introduction, 222 7.4.2 Similarities Between Batch and Continuous Reactive Equipment, 223 7.4.3 Example: Three-Dimensional Van de Vusse Kinetics Revisited, 230 7.5 Chapter Review, 232 References, 233 8 AR Construction Algorithms 235 8.1 Introduction, 235 8.2 Preliminaries, 235 8.2.1 Hyperplanes, 235 8.2.2 Computing the Stoichiometric Subspace S, 237 8.3 Overview of AR Construction Methods, 246 8.3.1 Introduction, 246 8.3.2 Inside-Out versus Outside-In Methods, 247 8.4 Inside-out Construction Methods, 248 8.4.1 The Recursive Constant Control Policy Algorithm, 248 8.4.2 The Iso-State Method, 253 k 8.4.3 The Complement Method, 258 k 8.5 Outside-in Construction Methods, 262 8.5.1 Overview, 262 8.5.2 The Method of Bounding Hyperplanes, 262 8.5.3 The Shrink-Wrap Algorithm, 267 8.6 Superstructure Methods, 270 8.6.1 LP Formulations, 270 8.6.2 IDEAS Approach, 276 8.7 Chapter Review, 279 References, 279 9 Attainable Regions for Variable Density Systems 281 9.1 Introduction, 281 9.2 Common Conversions to Mass Fraction Space, 281 9.2.1 Preliminary Notation, 281 9.2.2 Conversions Involving Molar Quantities, 283 9.2.3 Average Density, 285 9.2.4 Mixing and Reaction, 285 9.2.5 Residence Time in Mass Fraction Space, 287 9.2.6 Fundamental Reactor Types, 288 9.2.7 Computing the Stoichiometric Subspace, 289 9.3 Examples, 293 9.3.1 Three-Dimensional Van de Vusse Kinetics, 293 9.3.2 Steam Reforming and Water–gas Shift Reaction, 295 9.4 Chapter Review, 298 References, 299 k k CONTENTS ix 10 Final Remarks, Further Reading, and Future Directions 301 10.1 Introduction, 301 10.2 Chapter Summaries and Final Remarks, 301 10.3 Further Reading, 304 10.3.1 AR-related Papers, 304 10.3.2 Non-reactor-Related Papers, 305 10.4 Future Directions, 305 10.4.1
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