Attainable Region Theory
An Introduction to Choosing an Optimal Reactor
Published on 12. September 2016
352 pages
978-1-119-24470-7 (ISBN)
Description
Learn how to effectively interpret, select and optimize reactors for complex reactive systems, using Attainable Region theory
* Teaches how to effectively interpret, select and optimize reactors for complex reactive systems, using Attainable Region (AR) theory
* Written by co-founders and experienced practitioners of the theory
* Covers both the fundamentals of AR theory for readers new to the field, as we all as advanced AR topics for more advanced practitioners for understanding and improving realistic reactor systems
* Includes over 200 illustrations and 70 worked examples explaining how AR theory can be applied to complex reactor networks, making it ideal for instructors and self-study
* Interactive software tools and examples written for the book help to demonstrate the concepts and encourage exploration of the ideas
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David Ming | David Glasser | Diane Hildebrandt
Attainable Region Theory
An Introduction to Choosing an Optimal Reactor
Book
11/2016
Wiley
€201.50
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Software
09/2016
Wiley
€178.99
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Persons
David Ming holds a B.Sc. and Ph.D. in chemical engineering from the University of the Witwatersrand, Johannesburg. His research interests involve using AR theory to optimize chemical reactors, including batch reactors, and AR numerical methods.
David Glasser is a Professor of Chemical Engineering and co-director of the Material and Process Synthesis (MaPS) research unit at the University of South Africa (UNISA). He was Head of Department of Chemical Engineering, and Dean of the Faculty of Engineering at University of the Witwatersrand, and is one of the co-founders of AR theory. He holds a B.Sc. in chemical engineering from University of Cape Town, and a Ph.D. in chemical engineering from Imperial College.
Diane Hildebrandt is a Professor of Chemical Engineering and co-Director of the MaPS research unit at UNISA. She was the first woman in South Africa to be appointed a full professor of Chemical Engineering when she was the Unilever Professor of Reaction Engineering at the University of the Witwatersrand, and is also a co-developer of AR theory. She holds a B.Sc., M.Sc. and Ph.D. in chemical engineering from University of the Witwatersrand. Her research area is the reduction of CO2 emissions through the design of energy efficient processes.
Benjamin Glasser is a Professor of Chemical and Biochemical Engineering at Rutgers University, New Jersey, USA. He holds a B.Sc. and M.Sc. in chemical engineering from University of the Witwatersrand, and a Ph.D. in chemical engineering from Princeton University. His research interests include heat and mass transfer, multiphase reactors and particle technology applied to chemical and pharmaceutical manufacturing.
Matthew Metzger is a Senior Scientist at Merck & Co., Inc. He has co-authored over 14 publications, holds a B.S. in chemical engineering from Lafayette University, and a Ph.D. in chemical engineering from Rutgers University.
Content
Preface xi
Acknowledgments xiii
Prior Knowledge xiv
How this book is Structured xv
Software and Companion Website xvii
Nomenclature xix
SECTION I BASIC THEORY 1
1 Introduction 3
1.1 Introduction 3
1.2 Motivation 3
1.3 Reactor Network Synthesis 8
1.4 Solving the Reactor Network Synthesis Problem 12
1.5 Chapter Review 16
References 17
2 Concentration and Mixing 19
2.1 Introduction 19
2.2 Concentration Vectors and Dimension 23
2.3 Mixing 28
2.4 Chapter Review 47
References 47
3 The Attainable Region 49
3.1 Introduction 49
3.2 A Mixing and Reaction Game 49
3.3 The AR 57
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
4.3 Reaction from a Geometric Viewpoint 66
4.4 Three Fundamental Continuous Reactor Types 73
4.5 Summary 102
4.6 Mixing Temperatures 102
4.7 Additional Properties of the AR 105
4.8 Chapter Review 106
References 107
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
5.4 Multiple CSTR Steady States and ISOLAS 125
5.5 Constructions in Residence Time Space 131
5.6 Chapter Review 141
References 141
SECTION II EXTENDED TOPICS 143
6 Higher Dimensional AR Theory 145
6.1 Introduction 145
6.2 Dimension and Stoichiometry 146
6.3 The Three Fundamental Reactor Types Used in AR Theory 159
6.4 Critical DSRs and CSTRs 166
6.5 Chapter Review 189
References 190
7 Applications of AR Theory 191
7.1 Introduction 191
7.2 Higher Dimensional Constructions 191
7.3 Nonisothermal Constructions and Reactor Type Constraints 205
7.4 AR Theory for Batch Reactors 222
7.5 Chapter Review 232
References 233
8 AR Construction Algorithms 235
8.1 Introduction 235
8.2 Preliminaries 235
8.3 Overview of AR Construction Methods 246
8.4 Inside-out Construction Methods 248
8.5 Outside-in Construction Methods 262
8.6 Superstructure Methods 270
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
9.3 Examples 293
9.4 Chapter Review 298
References 299
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
10.4 Future Directions 305
References 307
Appendix A Fundamental Reactor Types 309
A.1 The Plug Flow Reactor 309
A.2 The Continuous-Flow Stirred Tank Reactor 309
A.3 The Differential Sidestream Reactor 310
Appendix B Mathematical Topics 311
B.1 Set Notation 311
B.2 Aspects of Linear Algebra 311
B.3 The Complement Principle 313
References 315
Appendix C Companion Software and Website 317
C.1 Introduction 317
C.2 Obtaining Python and Jupyter 318
Index 321
A Stoichiometric coefficient matrix for a system of reactions C Molar concentration vector C = [cA, cB, ., cn]T C0 DSR sidestream mixing concentration C0 A point residing on a hyperplane H(n, b) b = nTC0 C* Concentration vector from a mixture C* = ?C1 + (1 - ?)C2 C# Equilibrium concentration achieved in a reactor E DSR controllability matrix E = [K, N]T F Set of feed concentrations F = {Cf1, Cf2, ., CfN} G Mass flow rate vector for variable density systems G = [g1, g2, ., gn]T I The identity matrix J(C) Jacobian matrix of r(C). Sometimes also given as dr(C) L Set of points belonging to a lineation K Controllability matrix for a critical DSR excluding null space N N Null space of the stoichiometric coefficient matrix A N = null(AT) n Hyperplane normal vector ni Molar flow rate vector ni = [cAi, cBi, ., cni]T z Mass fraction vector z = [zA, zB, ., zn]T r(C) Rate vector of a function of C S Set of points representing the stoichiometric subspace S\X The complement region of X to S. t(C) CSTR tangent vector v(C) Mixing vector v(C) = C2 - C1 W Molecular weight matrix X Set of points representing a current set of achievable states z[k] The kth iterated Lie bracket ? Extent of reaction vector 0 The zero vector 0 = [0, 0, ., 0]T
d Number of independent reactions ci Molar concentration of component i F(t) Fed-batch feeding rate as a function of reaction time G Total mass flow rate through a reactor or reactor network gi Mass flow rate of stream i in a network H(n, b) Hyperplane defined by normal vector n and scalar b ki Rate constant i in a rate expression M Total mass mi Mass of component i n Number of components participating in a reaction P Reactor pressure Pk Polytope representing the AR at iteration k Q Volumetric flow rate through a reactor or reactor network ri(C) Rate expression for component i as a function of C T Reactor temperature t Batch reaction time V Reactor volume or total volume of a reactor network V(t) Fed-batch volume as a function of reaction time Wi Molecular weight of component i Wavg Average molecular weight of a mixture Yi Yield of component i Z The compressibility constant for real gases zi Mass fraction of component i R The set of all real numbers Rn The set of all vectors (n-tuples) with n real numbers (n-dimensional space)
a DSR sidestream mixing parameter for constant density systems ß DSR sidestream mixing parameter for variable density systems ?i Extent of reaction for reaction i in a system of reactions. ? Angle between two vectors ?(C) Critical CSTR determinant surface ? Mixing fraction ?i Stoichiometric coefficient of a component i in a reaction ?avg Average density of a mixture (by mass) s Reactor residence time in mass fraction space Sij Instantaneous selectivity of component i to j t Reactor residence time (constant density) ?i Instantaneous yield of component i ?(C) vDelR critical DSR condition for a system in R3 (d = 3)
Del operator (nabla) ?x? The norm of a vector x Lfh(C) Lie derivative of a scalar function h(C) with respect to a vector function f(C). [f, g](C) Lie bracket of vector functions f(C) and g(C) [f, g](C) = dg(C)f(C) - df(C)g(C) Det(A) Determinant of a matrix A conv(X) Convex hull of a set of points X cl (X) The closure of a set of points X rank(A) Rank of matrix A null(A) Null space of matrix A
f Refers to feed streams Cf = [cAf, cBf, ., cnf]T i, j, k, n General reference to elements in a list, or index counter
T Matrix transpose # Relating to an equilibrium state C# is an equilibrium concentration * Relating to a mixture C* is a concentration obtained from a mixture
AR Attainable region BTX Benzene-toluene-xylene...
Nomenclature
Commonly used symbols and notation adopted in this book are listed in the following table. Symbols that are only used once for a particular description and that are defined at the point of use may not be listed. Also note that some symbols may be used in different chapters for different situations, and thus more than one definition may apply.
Vector, matrices, and sets
A Stoichiometric coefficient matrix for a system of reactions C Molar concentration vector C = [cA, cB, ., cn]T C0 DSR sidestream mixing concentration C0 A point residing on a hyperplane H(n, b) b = nTC0 C* Concentration vector from a mixture C* = ?C1 + (1 - ?)C2 C# Equilibrium concentration achieved in a reactor E DSR controllability matrix E = [K, N]T F Set of feed concentrations F = {Cf1, Cf2, ., CfN} G Mass flow rate vector for variable density systems G = [g1, g2, ., gn]T I The identity matrix J(C) Jacobian matrix of r(C). Sometimes also given as dr(C) L Set of points belonging to a lineation K Controllability matrix for a critical DSR excluding null space N N Null space of the stoichiometric coefficient matrix A N = null(AT) n Hyperplane normal vector ni Molar flow rate vector ni = [cAi, cBi, ., cni]T z Mass fraction vector z = [zA, zB, ., zn]T r(C) Rate vector of a function of C S Set of points representing the stoichiometric subspace S\X The complement region of X to S. t(C) CSTR tangent vector v(C) Mixing vector v(C) = C2 - C1 W Molecular weight matrix X Set of points representing a current set of achievable states z[k] The kth iterated Lie bracket ? Extent of reaction vector 0 The zero vector 0 = [0, 0, ., 0]T
Letters
d Number of independent reactions ci Molar concentration of component i F(t) Fed-batch feeding rate as a function of reaction time G Total mass flow rate through a reactor or reactor network gi Mass flow rate of stream i in a network H(n, b) Hyperplane defined by normal vector n and scalar b ki Rate constant i in a rate expression M Total mass mi Mass of component i n Number of components participating in a reaction P Reactor pressure Pk Polytope representing the AR at iteration k Q Volumetric flow rate through a reactor or reactor network ri(C) Rate expression for component i as a function of C T Reactor temperature t Batch reaction time V Reactor volume or total volume of a reactor network V(t) Fed-batch volume as a function of reaction time Wi Molecular weight of component i Wavg Average molecular weight of a mixture Yi Yield of component i Z The compressibility constant for real gases zi Mass fraction of component i R The set of all real numbers Rn The set of all vectors (n-tuples) with n real numbers (n-dimensional space)
Greek symbols
a DSR sidestream mixing parameter for constant density systems ß DSR sidestream mixing parameter for variable density systems ?i Extent of reaction for reaction i in a system of reactions. ? Angle between two vectors ?(C) Critical CSTR determinant surface ? Mixing fraction ?i Stoichiometric coefficient of a component i in a reaction ?avg Average density of a mixture (by mass) s Reactor residence time in mass fraction space Sij Instantaneous selectivity of component i to j t Reactor residence time (constant density) ?i Instantaneous yield of component i ?(C) vDelR critical DSR condition for a system in R3 (d = 3)
Mathematical operations and abbreviations
Del operator (nabla) ?x? The norm of a vector x Lfh(C) Lie derivative of a scalar function h(C) with respect to a vector function f(C). [f, g](C) Lie bracket of vector functions f(C) and g(C) [f, g](C) = dg(C)f(C) - df(C)g(C) Det(A) Determinant of a matrix A conv(X) Convex hull of a set of points X cl (X) The closure of a set of points X rank(A) Rank of matrix A null(A) Null space of matrix A
Subscripts
f Refers to feed streams Cf = [cAf, cBf, ., cnf]T i, j, k, n General reference to elements in a list, or index counter
Superscripts
T Matrix transpose # Relating to an equilibrium state C# is an equilibrium concentration * Relating to a mixture C* is a concentration obtained from a mixture
Abbreviations
AR Attainable region BTX Benzene-toluene-xylene...
