Attainable Region Theory (eBook)

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.

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