Computational Methods for Process Simulation (eBook)

Cover 1
Contents 4
Preface 10
Acknowledgments 12
Introduction 14
Definition of the Problem 15
Mathematical Modeling of the Process 16
Equation Organization 16
Computation 16
Interpretation of Results 17
Limitations of Process Simulation 17
Usefulness of Process Simulation 17
Reference 18
Chapter 1. Development of Macroscopic Mass, Energy, and Momentum Balances 20
1.1 Conservation of Total Mass 21
1.2 Conservation of Component i 23
1.3 Method of Working Problems 23
1.4 Conservation of Total Energy 28
1.5 Method of Working Problems 32
1.6 Mechanical Energy Balance 36
1.7 Conservation of Momentum 41
Problems 47
References 52
Chapter 2. Steady-State Lumped Systems 54
2.1 Methods 55
2.2 Simultaneous Solution of Linear Equations 56
2.3 Solution of Nonlinear Equations 76
2.4 Structural Analysis and Solution of Systems of Algebraic Equations 96
Problems 120
References 131
Chapter 3. Unsteady-State Lumped Systems 134
3.1 Single Step Algorithms for Numerical Integration 134
3.2 Basic Stirred Tank Modeling 144
3.3 Multistep Methods 150
3.4 Stirred Tanks with Flow Rates a Function of Level 153
3.5 Enclosed Tank Vessel 161
3.6 Stirred Tank with Heating Jacket 165
3.7 Energy Balances with Variable Properties 167
3.8 Tanks with Multicomponent Feeds 169
3.9 Stiff Differential Equations 171
3.10 Catalytic Fluidized Beds 173
Problems 176
References 185
Chapter 4. Reaction-Kinetic Systems 186
4.1 Chlorination of Benzene 186
4.2 Autocatalytic Reactions 191
4.3 Temperature Effects in Stirred Tank Reactors 193
Problems 218
References 225
Chapter 5. Vapor–Liquid Equilibrium Operations 226
5.1 Boiling in an Open Vessel 226
5.2 Boiling in a Jacketed Vessel (Boiler) 227
5.3 Multicomponent Boiling„Vapor.Liquid Equilibrium 236
5.4 Batch Distillation 238
5.5 Binary Distillation Columns 240
5.6 Multicomponent Distillation Columns 244
Problems 264
References 265
Chapter 6. Microscopic Balances 266
6.1 Conservation of Total Mass (Equation of Continuity) 266
6.2 Conservation of Component i 268
6.3 Dispersion Description 269
6.4 Method of Working Problems 272
6.5 Stagnant Film Diffusion 272
6.6 Conservation of Momentum (Equation of Motion) 273
6.7 Dispersion Description 275
6.8 Pipe Flow of a Newtonian Fluid 275
6.9 Development of Microscopic Mechanical Energy Equation and Its Application 281
6.10 Pipeline Gas Flow 283
6.11 Development of Microscopic Thermal Energy Balance and Its Application 284
6.12 Heat Conduction Through Composite Cylindrical Walls 286
6.13 Heat Conduction with Chemical Heat Source 291
6.14 Mathematical Modeling for a Styrene Monomer Tubular Reactor 292
Problems 306
References 312
Chapter 7. Solution of Split Boundary–Value Problems 314
7.1 Digital Implementation of Shooting Techniques: Tubular Reactor with Dispersion 314
7.2 A Generalized Shooting Technique 320
7.3 Superposition Principle and Linear Boundary–Value Problems 325
7.4 Superposition Principle: Radial Temperature Gradients in an Annular Chemical Reactor 329
7.5 Quasilinearization 331
7.6 Nonlinear Tubular Reactor with Dispersion: Quasilinearization Solution 336
7.7 The Method of Adjoints 339
7.8 Modeling of Packed Bed Superheaters 343
Problem 358
References 360
Chapter 8. Solution of Partial Differential Equations 362
8.1 Techniques for Convection Problems 362
8.2 Unsteady–State Steam Heat Exchanger: Explicit Centered-Difference Problem 364
8.3 Unsteady–State Countercurrent Heat Exchanger: Implicit Centered–Difference Problem 368
8.4 Techniques for Diffusive Problems 379
8.5 Unsteady–State Heat Conduction in a Rod 381
8.6 Techniques for Problems with Both Convective and Diffusion Effects: The State–Variable Formulation 383
8.7 Modeling of Miscible Flow of Surfactant in Porous Media 387
8.8 Unsteady–State Response of a Nonlinear Tubular Reactor 391
8.9 Two–Phase Flow Through Porous Media 401
8.10 Two-Dimensional Flow Through Porous Media 409
8.11 Weighted Residuals 417
8.12 Orthogonal Collocation 423
Problems 432
References 439
Nomenclature 440
Appendix A. Analytical Solutions to Ordinary Differential Equations 444
A.1 First–Order Equations 444
A.2 Nth Order Linear Differential Equations with Constant Coefficients 449
Reference 453
Appendix B. MATLAB Reference Tables 454
Index 464