Attainable Region Theory

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