Amundson / Aris / Varma The Mathematical Understanding of Chemical Engineering Systems

1. Auflage 2014
ISBN: 978-1-4831-8886-7
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 840 Seiten, Web PDF

Mathematical Understanding of Chemical Engineering Systems is a collection of articles that covers the mathematical model involved in the practice of chemical engineering. The materials of the book are organized thematically into section. The text first covers the historical development of chemical engineering, and then proceeds to tackling a much more technical and specialized topics in the subsequent sections. The second section talks about the physical separation process, while the third section deals with stirred tank stability and control. Next, the book tackles polymerization and particle problems. Section 6 discusses empty tubular and fixed-bed catalytic reactors, while Section 7 details fluid-bed reactors and coal combustion. In the last two sections, the text presents mathematical and miscellaneous papers. The book will be most useful to researchers and practitioners of chemical engineering. Mathematicians and chemists will also benefit from the text.

Autoren/Hrsg.

Amundson, Neal R.

Aris, Rutherford

Varma, Arvind

Inhaltsverzeichnis

1;Front Cover;1
2;The Mathematical Understanding of Chemical Engineering Systems;6
3;Copyright Page
;7
4;Table of Contents
;8
5;Editors' Preface;10
6;Biographical Introduction;14
7;The Chief;17
8;Bibliography;20
9;Section 1:
HISTORICAL HIGHLIGHTS;32
9.1;CHAPTER 1. APPLICATION OF MATRICES AND FINITE DIFFERENCE
EQUATIONS TO BINARY DISTILLATION;34
9.1.1;LITERATURE CITED;41
9.2;CHAPTER 2.
Applications of Matrix Mathematics to Chemical Engineering Problems;42
9.3;CHAPTER 3.
Analog Computer Applied to Engineering Problems;43
9.4;CHAPTER 4. Multicomponent Distillation Calculations on a Large
Digital Computer;44
9.4.1;First Numerical Example;46
9.4.2;Multiple Feeds and Side Stream Drawoffs;48
9.4.3;Second Numerical Example;49
9.4.4;Further Comments on Method;50
9.4.5;Acknowledgment;50
9.4.6;Nomenclature;50
9.4.7;Literature Cited;50
9.5;CHAPTER 5. Multicomponent Distillation on a Large Digital Computer;51
9.5.1;DEVELOPMENT OF EQUATIONS—MAIN COLUMN;51
9.6;CHAPTER 6.
Chemical Reactor Stability and Sensitivity;52
9.6.1;A REACTOR WITH A RECYCLE STREAM;58
9.6.2;SUMMARY;60
9.6.3;ACKNOWLEDGMENT;60
9.6.4;NOTATION;60
9.6.5;LITERATURE CITED;60
9.7;CHAPTER 7.
Chemical Reactor Stability and Sensitivity;61
9.7.1;COMPUTER SOLUTIONS;62
9.7.2;ANALYTICAL TREATMENT OF PARAMETRIC
SENSITIVITY;62
9.7.3;STABILITY OF A TUBULAR REACTOR WITH A RECYCLE LOOP;68
9.7.4;SUMMARY;70
9.7.5;ACKNOWLEDGMENT;70
9.7.6;NOTATION;70
9.7.7;LITERATURE CITED;70
9.8;CHAPTER 8.
Optimum temperature gradients in tubular reactors—I;71
9.8.1;1. INTRODUCTION;71
9.8.2;2. SIMPLE REACTIONS;72
9.8.3;3.THEORY FOR TWO CONSECUTIVE REACTIONS;74
9.8.4;4. A MOKE COMPLICATED CASE;77
9.8.5;5. THE IMPLICIT METHOD;78
9.8.6;6. EQUIVALENCE OF TWO PROBLEMS;80
9.8.7;7. DISCUSSION
;81
9.8.8;NOTATION;82
9.8.9;REFERENCES;82
9.9;CHAPTER 9.
Optimum temperature gradients in tubular reactors—II;83
9.9.1;8. NUMERICAL STUDY OF TWO CONSECUTIVE REACTIONS;83
9.10;CHAPTER 10. Three Problems in Chemical Reactor Design;84
9.10.1;Summary;84
9.10.2;A. Stability of the Well-Agitated Reactor;84
9.11;CHAPTER 11. Some Remarks on Longitudinal Mixing or Diffusion in Fixed Beds;85
9.11.1;ACKNOWLEDGMENT;87
9.11.2;NOTATION;87
9.11.3;LITERATURE CITED;87
9.12;CHAPTER 12.
Intraparticle diffusion and conduction in porous catalysts—I;88
9.12.1;NUMERICAL EXAMPLES;94
9.12.2;NOTATION;98
9.12.3;REFERENCES;98
9.13;CHAPTER 13.
Intraparticle diffusion and conduction in porous catalysts—II;99
9.13.1;INTRODUCTION;99
9.14;CHAPTER 14.
The Digital Computer as a Process Controller;100
9.15;CHAPTER 15. STABILITY
of some chemical systems under control;101
9.16;CHAPTER 16.
Stability in Distributed Parameter Systems;102
9.16.1;MODEL 1
;103
9.16.2;PRINCIPLE OF THE ARGUMENT;106
9.16.3;MODEL 2;108
9.16.4;MODEL 3;109
9.16.5;NOTATION;113
9.16.6;LITERATURE CITED;113
9.17;CHAPTER 17.
Mathematical Models of Fixed Bed Reactors;114
9.17.1;Introduction;114
9.17.2;Elementary Model;114
9.17.3;Axial Dispersion and Intraparticle Transport;115
9.17.4;Radial Dispersion Model;118
9.17.5;Some Remarks on Moving Bed Reactors;119
9.17.6;Cell Models for Fixed Beds;119
9.17.7;Conclusions and Remarks;121
9.17.8;Nomenclature;121
9.17.9;References;121
9.18;CHAPTER 18.
NONLINEAR PROBLEMS IN CHEMICAL REACTOR THEORY;123
9.18.1;THE EMPTY TUBULAR REACTOR;123
9.18.2;References;33
10;Section 2:
PHYSICAL SEPARATION PROCESSES;124
10.1;Bibliography;125
10.2;CHAPTER 19. On the steady state fractionation of multicomponent and complex
mixtures in an ideal cascade;126
10.2.1;1. INTRODUCTION;126
10.2.2;2. THE IDEAL COLUMN. THE BASIC EQUATIONS FOR THE RECTIFICATION OF DISCRETE MIXTURES ;126
10.2.3;3. THE SOLUTION OF THE PROBLEM FOR
DISCRETE MIXTURES;128
10.2.4;4. THE SOLUTION OF THE PROBLEM FOR
COMPLEX MIXTURES;131
10.2.5;NOTATION
;135
10.2.6;REFERENCES;135
10.3;CHAPTER 20. On the steady state fractionation of multicomponent and complex
mixtures in an ideal cascade;136
10.3.1;5. INTRODUCTION;136
10.3.2;6. MINIMUM REFLUX FOR DISCRETE
MIXTURES;136
10.3.3;7. MINIMUM REFLUX FOR COMPLEX
MIXTURES;139
10.3.4;8. CONCLUSIONS;141
10.3.5;NOTATION;142
10.3.6;REFERENCES;142
10.4;CHAPTER 21. On the steady state fractionation of multicomponent and complex
mixtures in an ideal cascade;143
10.4.1;RESUME AND FURTHER DEVELOPMENT
OF NECESSARY FORMULAE;143
10.5;CHAPTER 22. On the steady state fractionation of multicomponent and complex mixtures in an ideal cascade;144
10.5.1;INTRODUCTION;144
10.5.2;THEOREM;144
10.6;CHAPTER 23. On the steady state fractionation of multicomponent and complex mixtures in an ideal cascade;145
10.6.1;MULTICOMPONENT SYSTEMS;145
10.7;CHAPTER 24. On the steady state fractionation of multicomponent and complex
mixtures in an ideal cascade;146
10.7.1;1. INTRODUCTION;146
10.8;CHAPTER 25.
A NOTE ON THE MATHEMATICS OF ADSORPTION IN BEDS;147
10.8.1;REFERENCES;151
10.9;CHAPTER 26.
MATHEMATICS OF ADSORPTION IN BEDS. II;152
10.9.1;SUMMARY;160
10.9.2;REFERENCES;160
10.10;CHAPTER 27.
MATHEMATICS OF ADSORPTION IN BEDS. Ill;161
10.10.1;FUNDAMENTAL DIFFERENTIAL EQUATION;161
10.10.2;SUMMARY;169
10.10.3;REFERENCES;169
10.11;CHAPTER 28. MATHEMATICS OF ADSORPTION. IV. EFFECT OF INTRAPARTICLE DIFFUSION IN AGITATED STATIC SYSTEMS;170
10.12;CHAPTER 29. MATHEMATICS OF ADSORPTION IN BEDS. V. EFFECT OF INTRAPARTICLE DIFFUSION IN FLOW SYSTEMS IN FIXED BEDS;171
10.12.1;Introduction;171
10.13;CHAPTER 30. MATHEMATICS OF ADSORPTION IN BEDS. VI. THE EFFECT OF LONGITUDINAL DIFFUSION IN ION EXCHANGE AND CHROMATOGRAPHIC COLUMNS;172
10.13.1;Appendix;175
10.14;CHAPTER 31.
THE RATE-DETERMINING STEPS IN RADIAL ADSORPTION ANALYSIS;177
10.14.1;Theoretica;177
10.15;CHAPTER 32.
On simple exchange waves in fixed beds;178
10.15.1;NTRODUCTION;178
10.15.2;ON THE THEORY OF MULTICOMPONENT
CHROMATOGRAPHY;179
10.15.3;INTRODUCTORY REMARKS AND NOTATION;180
10.15.4;Notation;181
10.15.5;1. FUNDAMENTAL DIFFERENTIAL EQUATION;183
10.15.6;2. LANGMUIR ADSORPTION ISOTHERM;185
10.15.7;3. RlEMANN INVARIANTS AND CHARACTERISTIC PARAMETERS;186
10.15.8;4. CHARACTERISTICS AND SIMPLE WAVES;189
10.15.9;5. SHOCK WAVES;190
10.15.10;6. ENTROPY CHANGE ACROSS A SHOCK;192
10.15.11;7. CONSTRUCTION OF SOLUTION;194
10.15.12;8. STEPWISE DATA AND PATTERNS OF INTERACTION;201
10.15.13;9. INTERACTION ANALYSIS;202
10.15.14;10. CHROMATOGRAPHIC CYCLE;209
10.15.15;REFERENCES;215
10.16;CHAPTER 33. MULTICOMPONENT ADSORPTION IN CONTINUOUS COUNTERCURRENT EXCHANGERS;216
10.16.1;INTRODUCTORY REMARKS;216
10.17;CHAPTER 34.
An Analysis of an Adiabatic Adsorption Column: Part 1. Theoretical Development;217
10.17.1;ABSTRACT;217
10.17.2;1. INTRODUCTION;217
10.17.3;2. CONSERVATION EQUATIONS;218
10.17.4;3. FUNDAMENTAL DIFFERENTIAL EQUATION AND CHARACTERISTICS;219
10.17.5;4. HODOGRAPH SPACE IMAGE G AND SIMPLE WAVE;220
10.17.6;5. CONSTRUCTION OF SOLUTION;221
10.17.7;6. DISCONTINUOUS SOLUTION;222
10.17.8;7. DISCONTINUITIES;223
10.17.9;8. FINITE COLUMN ANALYSIS;225
10.17.10;9. µ-SPECTRUM;226
10.17.11;NOMENCLATURE;229
10.17.12;REFERENCES;230
10.17.13;RESUME;230
10.17.14;ZUSAMMENFASSUNG;230
10.18;CHAPTER 35. An Analysis of an Adiabatic Adsorption Column: Part II. Adiabatic Adsorption of a Single Solute;231
10.18.1;ABSTRACT;231
10.18.2;1. INTRODUCTION;231
10.18.3;2. MATHEMATICAL FORMULATION;231
10.18.4;3. EXAMPLE;233
10.18.5;4. FIXED BED OPERATIONS;234
10.18.6;5. CONTINUOUS COUNTERCURRENT
OPERATIONS;238
10.18.7;NOMENCLATURE;241
10.18.8;REFERENCES;242
10.18.9;RESUME;242
10.18.10;ZUSAMMENFASSUNG;242
10.19;CHAPTER 36. An Analysis of an Adiabatic Adsorption Column Part III: Adiabatic Adsorption of Two Solutes;243
10.19.1;Abstract;243
10.19.2;1. INTRODUCTION;243
10.19.3;2. MATHEMATICAL FORMULATION;243
10.19.4;3. EXAMPLE;246
10.19.5;4. FIXED BED OPERATIONS;247
10.19.6;5. CONTINUOUS COUNTERCURRENT
OPERATIONS;252
10.19.7;NOMENCLATURE;254
10.19.8;REFERENCES;255
10.20;CHAPTER 37. An Analysis of an Adiabatic Adsorption Column Part IV: Adsorption in the High Temperature Range;256
10.20.1;Abstract;256
10.20.2;1. INTRODUCTION;256
10.20.3;2. THEORETICAL BASIS;256
10.20.4;3. ADSORPTION OF A SINGLE SOLUTE;261
10.20.5;4. ADSORPTION OF TWO SOLUTES;265
10.20.6;5. CONCLUSIONS;269
10.20.7;NOMENCLATURE;269
10.20.8;REFERENCES;270
10.21;CHAPTER 38.
A study of the shock layer in equilibrium exchange systems;271
10.21.1;1. INTRODUCTION;271
10.21.2;2. EXISTENCE AND UNIQUENESS;271
10.21.3;3. SHOCK LAYER THICKNESS;274
10.21.4;4. ASYMPTOTIC STABILITY;274
10.21.5;5. NUMERICAL SOLUTION OF TRANSIENT
EQUATION;275
10.21.6;6. ILLUSTRATIONS;277
10.21.7;NOTATION;279
10.21.8;REFERENCES;279
10.22;CHAPTER 39.
A study of the shock layer in nonequilibrium exchange systems;281
10.22.1;1. INTRODUCTION;281
10.22.2;2. BASIC FORMULATION;281
10.23;CHAPTER 40. Asymptotic solution to moving-bed exchange equations;282
10.23.1;1. INTRODUCTION;282
10.23.2;2. FORMULATION;282
10.24;CHAPTER 41. SHOCK LAYER IN TWO SOLUTE CHROMATOGRAPHY: EFFECT OF AXIAL DISPERSION
AND MASS TRANSFER;283
10.24.1;1. INTRODUCTION;283
10.24.2;2. BASIC EQUATIONS;283
10.24.3;3. PROPAGATION SPEED AND COMPATIBILITY CONDITION;284
10.24.4;4. EXISTENCE AND UNIQUENESS;285
10.24.5;5. NUMERICAL EXAMPLES;287
10.24.6;6. CASE OF EQUAL PECLET NUMBERS;288
10.24.7;7. CASE OF UNEQUAL PECLET NUMBERS;290
10.24.8;8. COMPARISON TO TRANSIENT SOLUTIONS;291
10.24.9;NOTATION;293
10.24.10;REFERENCES;293
10.24.11;APPENDIX;294
10.25;CHAPTER 42.
Stagewise Absorption and Extraction Equipment;295
10.26;CHAPTER 43. An Elementary Theory of Adsorption in Fluidized Beds;296
10.27;CHAPTER 44.
PROBABILITY CONSIDERATIONS IN THE BED;296
10.27.1;Solid-Fluid Heat Exchange in
Moving Beds;297
10.28;CHAPTER 45.
Adsorber Design Data;298
10.29;CHAPTER 46.
On optimum cross-current extraction;299
10.29.1;1. THE NOTION OF DYNAMIC PROGRAMMING;299
10.30;CHAPTER 47. Heat Transfer and Heat Release in Fluidized Beds;300
10.31;CHAPTER 48. Solid-Fluid Interactions in Fixed and Moving Beds;301
10.31.1;Axial conduction is neglected in studying fixed beds with small particles;301
10.31.2;Problems including axial conduction are somewhat more easily solved;305
10.31.3;Use of finite transforms has advantages over separation of variables;308
10.31.4;Choice of boundary conditions it dictated by experiment;309
10.31.5;Conclusion;309
10.31.6;Literatur cited;310
10.32;CHAPTER 49.
Fixed Beds with Large Particles;311
10.32.1;Conclusion;309
10.32.2;Nomenclature;309
10.32.3;Literatur cited;310
10.33;CHAPTER 50.
Fixed Beds with Large Particles;311
10.33.1;Axial mixing is neglected in considering
fixed beds with large particles;311
10.33.2;Inclusion of axial mixing
alters nature of problem;315
10.33.3;Calculation of roots of Equation 110 is involved in all these problems;318
10.33.4;Conclusion;319
10.33.5;Literature cited;319
10.33.6;Two Problems on Moving Beds;320
10.33.7;Treatment of nonadiabatic countercurrent reactor is considered;320
10.34;CHAPTER 51.
HEAT TRANSFER IN FLUIDISED AND MOVING BEDS;321
10.34.1;SUMMARY;321
10.34.2;Introduction;321
10.34.3;Regular Fluid Motion—Random Particle Motion;321
11;Section 3:
STIRRED TANK STABILITY AND CONTROL;322
11.1;CHAPTER 52.
An analysis of chemical reactor stability and control—I;324
11.1.1;1. INTRODUCTION;324
11.1.2;2. THE EQUATIONS;325
11.1.3;3. LOCAL LINEARIZATION;327
11.1.4;4. MODES OF PERFECT CONTROL;328
11.1.5;5. IMPERFECT CONTROL;330
11.1.6;6. A MEASURE OF LOCAL CONTROL;332
11.1.7;CONCLUSIONS;333
11.1.8;REFERENCES;334
11.2;CHAPTER 53. An analysis of chemical reactor stability and control—II;335
11.2.1;7. TUE HEAT TRANSFER FUNCTION;335
11.2.2;8. THE PHASE PLANE;336
11.2.3;9. THE PHASE PLANE WITH CONTROL;337
11.2.4;10. THE TRANSITION AT k = 9;341
11.2.5;11. DESCRIPTION OF RESULTS;345
11.2.6;CONCLUSIONS;349
11.2.7;LIST OF SYMBOLS;349
11.3;CHAPTER 54. An analysis of chemical reactor stability and control—III;351
11.3.1;12. THE PRINCIPLES OF PROGRAMMING THE CALCULATIONS;351
11.4;CHAPTER 55.
Statistical analysis of a reactor;352
11.4.1;INTRODUCTION;352
11.5;CHAPTER 56. An analysis of chemical reactor stability and control—IV;353
11.5.1;1. THE SYSTEM;353
11.6;CHAPTER 57. An analysis of chemical reactor stability and control—Va;354
11.6.1;INTRODUCTION;354
11.6.2;BASIC PHENOMENA AND MATHEMATICAL MODELS;356
11.6.3;ANALYSIS AND CALCULATIONS FOR SOME MODELS OF TWO-PHASE REACTING SYSTEMS;357
11.6.4;NOTATION;376
11.6.5;REFERENCES;377
11.7;CHAPTER 58. An analysis of chemical reactor stability and control†—Vb;379
11.8;CHAPTER 59. An analysis of chemical reactor stability and control†—VI;379
11.9;CHAPTER 60. An analysis of chemical reactor stability and control†—VII;379
11.10;CHAPTER 61.
SUMMARY AND CONCLUSIONS;380
11.11;CHAPTER 62.
An analysis of chemical reactor stability and control—VIII;382
11.11.1;1. INTRODUCTION;382
11.12;CHAPTER 63.
An analysis of chemical reactor stability and control—IX;383
11.12.1;5. LYAPUNOV FUNCTIONS FOR GENERAL TWO DIMENSIONAL SYSTEMS WITH APPLICATION TO A SECOND ORDER REACTION IN A STIRRED TANK REACTOR§;383
11.13;CHAPTER 64.
An analysis of chemical reactor stability and control—XIII;384
11.13.1;INTRODUCTION;384
11.14;CHAPTER 65. An analysis of chemical reactor stability and sensitivity – XIV;385
11.14.1;INTRODUCTION;385
11.14.2;MATHEMATICAL MODEL OF THE CONTINUOUS FLOW STIRRED TANK REACTOR;385
11.15;CHAPTER 66. An analysis of chemical reactor stability and control – XV;386
11.15.1;1. INTRODUCTION;386
11.15.2;Summary and Conclusions;323
11.15.3;References;323
12;Section 4: POLYMERIZATION;388
12.1;CHAPTER 67. ANALYSIS OF POLYMERIZATION KINETICS AND THE USE OF A DIGITAL COMPUTER;390
12.1.1;ABSTRACT;391
12.1.2;SUMMARY FOR PART A;392
12.1.3;B. COPOLYMERIZATION;392
12.1.4;SUMMARY FOR PART B;393
12.1.5;SUMMARY FOR PART C;394
12.1.6;REFERENCES;395
12.2;CHAPTER 68.
Polymerization Reactor Stability;396
12.3;CHAPTER 69.
Calculation of molecular weight distributions in polymerization;397
12.3.1;INTRODUCTION;397
12.3.2;MATHEMATICAL DEVELOPMENT;397
12.3.3;NON-ISOTHERMAL CASE;401
12.3.4;NOTATION;401
12.3.5;REFERENCES;402
12.4;CHAPTER 70. Stability and control of addition polymerization reactions†;403
12.4.1;INTRODUCTION;403
12.4.2;STEADY-STATE SOLUTION;404
12.4.3;CONTROL;405
12.4.4;OTHER TERMINATION STEPS;411
12.4.5;CONCLUSIONS;411
12.4.6;REFERENCES;412
12.5;CHAPTER 71.
Continuous Models for Polymerization;413
12.5.1;THE CONTINUOUS VARIABLE TECHNIQUE;413
12.5.2;MECHANISMS OF LINEAR ADDITION POLYMERIZATION;413
12.5.3;ADDITION POLYMERIZATION IN A STIRRED TANK REACTOR;414
12.5.4;ADDITION POLYMERIZATION IN A SERIES OF CONTINUOUS WELL-AGITATED REACTORS;415
12.5.5;LINEAR ADDITION POLYMERIZATION IN A BATCH REACTOR;416
12.5.6;NOTATION;418
12.5.7;LITERATURE CITED;418
12.6;CHAPTER 72.
Continuous polymerization models—I;419
12.6.1;1.1 INTRODUCTION;419
12.6.2;1.2 CHARACTERIZATION OF LINEAR POLYMERIC SYSTEMS;419
12.6.3;1.3 INTRODUCTORY EXAMPLES OF THE CONTINUOUS VARIABLE TECHNIQUE;421
12.6.4;1.4 TERMINATION STUDIES;423
12.6.5;1.5 EFFECT OF THE DEPENDENCE OF RATE CONSTANTS ON POLYMER CHAIN LENGTH;425
12.6.6;1.6 CATALYST INITIATED POLYMERIZATION SYSTEMS;427
12.6.7;1.7 EFFECT OF MULTIPLE PROPAGATION;428
12.6.8;1.8 POLYMERIZATION IN A SERIES OF CONTINUOUS STIRRED TANK REACTORS;430
12.6.9;1.8 POLYMERIZATION IN A SERIES OF CONTINUOUS STIRRED TANK REACTORS;430
12.6.10;1.9 CHARACTERIZATION OF COPOLYMERIZATION SYSTEMS;432
12.6.11;1.10 APPLICATION OF THE CONTINUOUS VARIABLE TECHNIQUE TO COPOLYMERIZATION SYSTEMS;433
12.6.12;1.11 DISTRIBUTION OF MONOMERIC SPECIES IN COPOLYMERIZATION SYSTEMS;435
12.6.13;1.12 A MODEL FOR BLOCK COPOLYMERIZATION;438
12.6.14;1.13 NONLINEAR POLYMERIZATION MODELS;443
12.6.15;REFERENCES;449
12.7;CHAPTER 73. Continuous polymerization models—part II;450
12.7.1;2.1 INTRODUCTION;450
12.8;CHAPTER 74.
An analysis of chemical reactor stability and control—Xa;451
12.8.1;INTRODUCTION;451
13;Section 5:
PARTICLE PROBLEMS;452
13.1;References;452
13.2;CHAPTER 75. Intraparticle Diffusion in Catalytic
Heterogeneous Systems;454
13.3;CHAPTER 76. Catalytic particle stability studies—I. Lumped resistance model†;455
13.3.1;INTRODUCTION;455
13.3.2;DEVELOPMENT OF EQUATIONS;455
13.4;CHAPTER 77. Catalytic particle stability studies—II*
Lumped thermal resistance model;456
13.4.1;INTRODUCTION;456
13.4.2;DEVELOPMENT OF EQUATIONS;456
13.5;CHAPTER 78. Catalytic particle stability studies—III*
Complex distributed resistances model;457
13.5.1;INTRODUCTION;457
13.5.2;DEVELOPMENT OF EQUATIONS AND STEADY STATE ANALYSIS;457
13.5.3;LlNEARIZED EQUATIONS AND STABILITY ANALYSIS OF A SIMPLE CASE;458
13.5.4;STABILITY ANALYSIS OF THE GENERAL CASE;460
13.5.5;A UNIQUENESS AND STABILITY CONDITION;462
13.5.6;NUMERICAL EXAMPLES;463
13.5.7;NOTATION;468
13.5.8;REFERENCES;469
13.6;CHAPTER 79. Uniqueness of the steady state solutions for chemical reaction occurring in a catalyst particle or in a tubular reactor with axial diffusion;470
13.6.1;INTRODUCTION;470
13.6.2;STEADY STATE EQUATIONS AND CONDITIONS
FOR UNIQUENESS (ONE REACTION);470
13.6.3;DETERMINATION OF A CRITICAL SIZE BELOW WHICH ONLY A UNIQUE STEADY STATE IS POSSIBLE;472
13.6.4;PARTICLES OF ARBITRARY CONFIGURATION;474
13.6.5;GENERALIZATION TO THE CASE OF n INDEPENDENT REACTIONS;474
13.6.6;TUBULAR REACTOR WITH AXIAL DIFFUSION;480
13.6.7;SUMMARY;481
13.6.8;REFERENCES;482
13.6.9;NOTE ADDED IN PROOF;483
13.6.10;REFERENCE;483
13.7;CHAPTER 80. On a Conjecture of Aris: Proof and Remarks;484
13.7.1;EXPLORATION OF EXTREMA FOR A SIMPLE CASE;485
13.7.2;SOME CONJECTURES ON PARTICLE SHAPE;487
13.7.3;NOTATION;487
13.7.4;LITERATURE CITED;487
13.7.5;APPENDIX;487
13.8;CHAPTER 81. UNIQUENESS OF THE STEADY STATE FOR AN ISOTHERMAL POROUS CATALYST;489
13.9;CHAPTER 82. Maximum Temperature Rise in Gas-Solid
Reactions;490
13.10;CHAPTER 83. Global asymptotic stability in distributed parameter systems:
comparison function approach;491
13.10.1;INTRODUCTION;491
13.11;CHAPTER 84. Maximal and minimal solutions, effectiveness factors for chemical reaction in porous catalysts†;492
13.11.1;1. INTRODUCTION;492
13.11.2;2. THE BASIC EQUATIONS;493
13.11.3;3. THE PHASE PLANE BEHAVIOR;495
13.11.4;4. MAXIMAL AND MINIMAL SOLUTIONS, EFFECTIVENESS FACTORS;496
13.11.5;5. NUMERICAL EXAMPLES;500
13.11.6;6. CONCLUSIONS AND DISCUSSION;502
13.11.7;NOTATION;504
13.11.8;REFERENCES;504
14;Section 6: EMPTY TUBULAR AND FIXED-BED CATALYTIC REACTORS;506
14.1;References;507
14.2;CHAPTER 85.
Tubular Reactor Sensitivity;508
14.2.1;MATHEMATICAL DEVELOPMENT;508
14.2.2;EXAMPLE I;510
14.2.3;EXAMPLE II;511
14.2.4;CONCLUSIONS;512
14.2.5;NOTATION;512
14.2.6;LITERATURE CITED;512
14.3;CHAPTER 86. Taylor Diffusion in Tubular Reactors;513
14.3.1;General Problem;513
14.3.2;Finite Cell Model;514
14.3.3;Conclusions;515
14.3.4;Nomenclature;515
14.3.5;References;515
14.4;CHAPTER 87.
A Vertical-Flow Reactor;516
14.5;CHAPTER 88.
A Tubular Reactor;517
14.6;CHAPTER 89. STABILITY OF ADIABATIC PACKED BED REACTORS. AN ELEMENTARY TREATMENT;518
14.6.1;Development of Equations;519
14.6.2;Steady States;519
14.6.3;Numerical Solution of Transient Equations;521
14.6.4;Discussion of Calculations;522
14.6.5;Conclusions;524
14.6.6;Nomenclature;526
14.6.7;Acknowledgment;526
14.6.8;Literature Cited;526
14.7;CHAPTER 90. STABILITY OF NONADIABATIC PACKED BED REACTORS;527
14.8;CHAPTER 91. STABILITY OF ADIABATIC PACKED-BED REACTORS;528
14.8.1;Summary of the Equations;528
14.9;CHAPTER 92.
REGENERATION OF ADIABATIC FIXED BEDS;529
14.9.1;Mathematical Model, Model C;529
14.9.2;Stationary-State Model;531
14.9.3;Numerical Procedure;531
14.9.4;Results;531
14.9.5;Comparison with Other Models;532
14.9.6;Conclusions;533
14.9.7;Nomenclature;533
14.9.8;Literature Cited;533
14.10;CHAPTER 93. Stability of Adiabatic Packed Bed Reactors;534
14.10.1;SIMPLE UNCOUPLED CELL MODEL;535
14.10.2;STEADY STATE DETERMINATION;535
14.10.3;STABILITY ANALYSIS;536
14.10.4;NUMERICAL SOLUTION OF TRANSIENT EQUATIONS;537
14.10.5;EFFECTS OF CHANGES IN THE GAS VELOCITY;538
14.10.6;COUPLED CELL MODELS;539
14.10.7;CONCLUSIONS;541
14.10.8;ACKNOWLEDGMENT;541
14.10.9;NOTATION;541
14.10.10;LITERATURE CITED;541
14.11;CHAPTER 94. Creeping reaction zone in a catalytic, fixed-bed reactor: a cell model approach;542
14.11.1;1. INTRODUCTION;542
14.11.2;2. COUPLED CELL MODEL;542
14.11.3;3. NUMERICAL SOLUTION;544
14.11.4;4. CREEP VELOCITY;546
14.11.5;5. EFFECT OF OPERATING CONDITIONS;547
14.11.6;6. CONCLUSION;549
14.11.7;NOTATION;549
14.11.8;REFERENCES;550
14.12;CHAPTER 95.
Equilibrium Theory of Creeping Profiles in Fixed-Bed Catalytic Reactors;551
14.12.1;Introduction;551
14.12.2;Basic Formulation;551
14.13;CHAPTER 96.
Creeping Profiles in Catalytic Fixed Bed Reactors. Continuous Models;552
14.13.1;Introduction;552
14.13.2;Two-Phase Continuous Model;552
14.13.3;Numerical Solution;553
14.13.4;Formulation of Creep Velocity;554
14.13.5;Parametric Studies on Creep Velocity;555
14.13.6;Conclusion;557
14.13.7;Acknowledgment;557
14.13.8;Nomenclatur;557
14.13.9;Literature Cited;558
14.14;CHAPTER 97. Some Observations on Tubular Reactor Stability;559
14.14.1;Steady State Analysis;560
14.14.2;Transient Analysis;561
14.14.3;Problem 1;561
14.14.4;Problem 2;562
14.14.5;Conclusions;563
14.14.6;Nomenclature;563
14.14.7;References;563
14.15;CHAPTER 98. Some Further Observations on Tubular Reactor Stability;564
14.15.1;The Set of Equations and the Steady State;564
14.15.2;The Unsteady State and its Linearization;565
14.15.3;Analysis of Equations (SI), (32) and (33);567
14.15.4;Suggested Numerical Procedure;569
14.15.5;Conclusions;570
14.15.6;Nomenclature;570
14.15.7;References;570
14.16;CHAPTER 99. Some General Observations on Tubular Reactor Stability;571
14.16.1;Global Stability;572
14.16.2;The Character of Steady State Solutions;573
14.16.3;Conclusions;576
14.16.4;Nomenclature;576
14.16.5;Subscripts;576
14.16.6;References;576
14.17;CHAPTER 100. Qualitative and Quantitative Observations on the Tubular Reactor;577
14.17.1;I. The Lumped Constant Model;578
14.17.2;Unsteady State;579
14.17.3;II. The Tubular Reactor with Axial Dispersion;579
14.17.4;Some General Theorems on Qualitative Behavior;581
14.17.5;Numerical Computations;583
14.17.6;Example 1;585
14.17.7;Example 2;585
14.17.8;Example 3;585
14.17.9;III. Some General Remarks on Tubular Reactors;585
14.17.10;Acknowledgment;586
14.17.11;Nomenclature;586
14.17.12;Reference;586
14.18;CHAPTER 101.
The Effect of Recycle on a Linear Reactor;587
14.18.1;PRELIMINARY ANALYSIS AND SOLUTION;588
14.18.2;CHARACTER OF THE EIGENVALUES;589
14.18.3;APPLICATION OF THE ARGUMENT PRINCIPLE;589
14.18.4;FURTHER INFORMATION FROM THE ARGUMENT PRINCIPLE;591
14.18.5;THE EIGENVALUE CURVE;592
14.18.6;LOCATION OF THE SMALLER EIGENVALUES;592
14.18.7;CALCULATIONS;593
14.18.8;CONCLUSIONS;596
14.18.9;ACKNOWLEDGMENT;596
14.18.10;NOTATION;596
14.18.11;LITERATURE CITED;596
14.19;CHAPTER 102.
Stability of Loop Reactors;597
14.20;CHAPTER 103. PERFORMANCE AND STABILITY OF COUNTERCURRENT TWO-PHASE EXTRACTIVE TUBULAR REACTORS;598
14.20.1;Development of Equations;598
14.21;CHAPTER 104. Some Problems Concerning the Non-Adiabatic Tubular Reactor;599
14.21.1;Development of equations;599
14.22;CHAPTER 105.
Local Stability of Tubular Reactors;600
14.23;CHAPTER 106. Some Observations on Uniqueness and Multiplicity of Steady States In Non-Adiabatic
Chemically Reacting Systems;601
14.23.1;1. Introduction;601
14.23.2;2. The system equations;601
14.23.3;3. The stirred tank reactor;603
14.23.4;4. The tubular reactor;606
14.23.5;5. Some conclusions and remarks;620
14.23.6;A cknowledgment;620
14.23.7;Nomenclature;620
14.23.8;References;621
14.24;CHAPTER 107. The Non-Adiabatic Tubular Reactor: Stability Considerations;622
14.24.1;Stability through direct numerical integrationof the transient equations;623
14.24.2;Stability through eigenvalue computations;628
14.24.3;Concluding remarks;629
14.24.4;Nomenclature;630
14.24.5;Greek letters;630
14.24.6;References;630
14.25;CHAPTER 108. Some General Considerations of Reversible Chemical Reactions in Batch and Tubular Reactors;631
14.25.1;Some preliminaries;631
14.25.2;The basic equations;632
14.25.3;Definition of system equilibrium;632
14.25.4;Adiabatic reactors;633
14.25.5;Non-adiabatic reactors;634
14.25.6;Conclusions and significance;637
14.25.7;APPENDIX 1;638
14.25.8;APPENDIX 2;638
14.25.9;APPENDIX 3;638
14.25.10;APPENDIX 4;639
14.25.11;Nomenclature;640
14.25.12;Greek letters;640
14.25.13;Subscripts;640
14.25.14;Superscripts;640
14.25.15;References;641
14.26;CHAPTER 109. STUDIES IN THE CONTROL OF TUBULAR REACTORS—I;642
14.26.1;1. INTRODUCTION;642
14.27;CHAPTER 110. STUDIES IN THE CONTROL OF TUBULAR
REACTORS—II;643
14.27.1;l. LINEAR DYNAMICAL MODEL;643
14.28;CHAPTER 111.
STUDIES IN THE CONTROL OF TUBULAR REACTORS—III;644
14.28.1;1. OBSERVABILITY;644
15;Section 7: FLUID-BED REACTORS AND COAL
COMBUSTION;646
15.1;References;646
15.2;CHAPTER 112.
Stability of Batch Catalytic Fluidized Beds;648
15.2.1;PART I: UNIFORM TEMPERATURE MODEL;648
15.3;CHAPTER 113. ANALYTICAL STUDY OF AN IDEALIZED CONTINUOUS FLUIDIZED-BED CHEMICAL REACTOR;649
15.3.1;PART I;649
15.3.2;THE MODEL;649
15.4;CHAPTER 114. ANALYSIS OF A MODEL FOR A NONISOTHERMAL CONTINUOUS FLUIDIZED BED CATALYTIC REACTOR;650
15.4.1;INTRODUCTION;650
15.4.2;THE MODEL;650
15.4.3;ANALYSIS OF THE CONSERVATION EQUATIONS FOR THE CASE OF PERFECT MIXING OF THE INTERSTITIAL GAS;655
15.4.4;ANALYSIS OF THE CONSERVATION EQUATIONS FOR A MODEL WITH PLUG FLOW OF THE INTERSTITIAL GAS;655
15.4.5;COMPARISON OF THE TWO MODELS;656
15.4.6;NUMERICAL SOLUTION FOR A SINGLE IRREVERSIBLE FIRST ORDER REACTION;659
15.4.7;NUMERICAL SOLUTION FOR A SINGLE FIRST ORDER IRREVERSIBLE REACTION WITH A DECAYING CATALYST;664
15.4.8;NUMERICAL SOLUTION FOR THE CASE OF TWO CONSECUTIVE FIRST ORDER REACTIONS;665
15.4.9;NOTATION;667
15.4.10;REFERENCES;669
15.5;CHAPTER 115. MODELLING OF FLUIDIZED BED REACTORS—II†;670
15.5.1;NTRODUCTION;670
15.5.2;THE MODEL;670
15.5.3;UNIQUENESS;672
15.5.4;NUMERICAL CALCULATION OF STEADY STATE;674
15.5.5;INFLUENCE OF THE MEAN PARTICLE RESIDENCE TIME;674
15.5.6;INFLUENCE OF INTERCHANGE COEFFICIENTS FOR INTERPHASE TRANSFER BETWEEN THE DILUTE PHASE AND THE INTERSTITIAL GAS PHASE;674
15.5.7;MODEL WITH NEGLIGIBLE HEAT AND MASS TRANSFER RESISTANCE BETWEEN THE INTERSTITIAL GAS AND THE PARTICLES;675
15.5.8;NUMERICAL METHOD;677
15.5.9;NUMERICAL RESULTS;678
15.5.10;NOTATION;680
15.5.11;REFERENCES;681
15.6;CHAPTER 116. MATHEMATICAL MODELLING OF FLUIDIZED BED REACTORS—III;682
15.6.1;INTRODUCTION;682
15.6.2;THE MODEL;682
15.6.3;NUMERICAL METHOD;685
15.6.4;CONCLUSIONS;689
15.6.5;NOTATION;690
15.6.6;REFERENCES;690
15.7;CHAPTER 117. MODELLING OF FLUIDIZED BED REACTORS—IV†;691
15.7.1;INTRODUCTION;691
15.7.2;THE MODEL;691
15.7.3;THE CONSERVATION EQUATIONS;694
15.7.4;UNIQUENESS;698
15.7.5;INFLUENCE OF BUBBLE SIZE;702
15.7.6;INFLUENCE OF INTERCHANGE COEFFICIENTS BETWEEN DILUTE PHASE AND INTERSTITIAL GAS PHASE;703
15.7.7;DILUTE PHASE PROFILES;704
15.7.8;CONCLUSIONS;704
15.7.9;NOTATION;705
15.7.10;REFERENCES;706
15.8;CHAPTER 118.
MODELLING OF FLUIDIZED BED REACTORS—V;707
15.8.1;INTRODUCTION;707
15.8.2;THE MODEL;707
15.9;CHAPTER 119. COMPARATIVE STUDY OF SOME MODELS FOR FLUIDIZED BED CATALYTIC REACTORS;708
15.9.1;INTRODUCTION;708
15.10;CHAPTER 120. Diffusion and Reaction in a Stagnant Boundary Layer about a Carbon Particle;709
15.10.1;Introduction;709
15.10.2;The Models;709
15.10.3;The Rates of Reactions;710
15.10.4;The Flat Carbon Surface;710
15.10.5;The Region of Feasible Solutions;712
15.10.6;The Solution of the Equations;713
15.10.7;The Spherical Particle;716
15.10.8;Summary and Conclusions;718
15.10.9;Acknowledgment;719
15.10.10;Nomenclature;719
15.10.11;Literature Cited;719
15.11;CHAPTER 121. An Analytical Study of Single Particle Char Gasification;720
15.11.1;SCOPE;720
15.11.2;CONCLUSIONS AND SIGNIFICANCE;720
15.11.3;ASSUMPTIONS FOR THE MODEL;721
15.11.4;KINETIC MECHANISM AND REACTION RATE EXPRESSIONS;723
15.11.5;MASS CONSERVATION EQUATIONS;725
15.11.6;CONSERVATION OF ENERGY EQUATION;726
15.11.7;NUMERICAL RESULTS;730
15.11.8;ACKNOWLEDGMENT;734
15.11.9;NOTATION;734
15.11.10;LITERATURE CITED;735
15.12;CHAPTER 122. Char Gasification in a Countercurrent Reactor;736
15.12.1;SCOPE;736
15.12.2;CONCLUSIONS AND SIGNIFICANCE;736
15.13;CHAPTER 123.
Diffusion and Reaction in a Stagnant Boundary Layer about a Carbon Particle. 2. An Extension;737
15.13.1;Introduction;737
16;Section 8: MATHEMATICAL PAPERS;738
16.1;CHAPTER 124.
Nonlinear Boundary-Value Problems Arising in Chemical Reactor Theory;740
16.1.1;1. DYNAMICS OF CERTAIN CHEMICAL REACTORS;740
16.1.2;2. QUALITATIVE THEORY OF A REACTOR WITH A SINGLE REACTION;743
16.1.3;3. NONLINEAR BOUNDARY-VALUE PROBLEMS;744
16.1.4;REFERENCES;751
16.2;CHAPTER 125.
WHY MATHEMATICS?;752
16.2.1;COURSES IN APPLIED MATHEMATICS;752
16.2.2;BIBLIOGRAPHY;756
16.3;CHAPTER 126. Self-adjoint operators from selected nonsymmetric matrices: application to kinetics and rectification;757
16.3.1;INTRODUCTION;757
16.3.2;FIRST ORDER REACTION SYSTEMS;758
16.3.3;MULTICOMPONENT RECTIFICATION;759
16.3.4;CONCLUSIONS;760
16.3.5;REFERENCES;761
16.4;CHAPTER 127. On Vibration Problems With Discretely Distributed Loads–A Rigorous Formalism;762
16.4.1;Introduction;762
16.5;CHAPTER 128. TRANSPORT IN COMPOSITE MATERIALS: REDUCTION TO A SELF ADJOINT FORMALISM;763
16.5.1;1. INTRODUCTION;763
16.5.2;2. THEORY;763
16.5.3;3. HEAT CONDUCTION IN A
COMPOSITE SLAB OF n LAYERS;764
16.5.4;4. AXIAL DISPERSION OF A SOLUTE IN A TUBE OF VARYING CROSS-SECTION;767
16.5.5;5·AN EXAMPLE IN DIFFUSION;768
16.5.6;6. CONCLUSIONS;769
16.5.7;NOTATION;770
16.5.8;REFERENCES;770
16.6;CHAPTER 129. STIRRED POTS, TUBULAR REACTORS, AND SELF-ADJOINT OPERATORS;771
16.6.1;INTRODUCTION;771
16.6.2;PROBLEM 1;771
16.6.3;PROBLEM 2;774
16.6.4;NOTATION;779
16.6.5;REFERENCES;779
16.7;CHAPTER 130.
COMPUTATIONAL METHODS FOR THE TUBULAR CHEMICAL REACTOR;780
16.7.1;1. Introduction;780
16.7.2;2. A simple example illustrating the difficulties;781
16.7.3;3. The steady state;784
16.7.4;4. Orthogonal collocation methods;787
16.7.5;5. Transient calculations;789
16.7.6;6. Concluding observations;790
16.7.7;References;791
17;Section 9:
MISCELLANEOUS PAPERS;792
17.1;Reference;792
17.2;CHAPTER 131. Transient Behavior of Single-phase Natural-circulation Loop Systems;794
17.2.1;PREVIOUS INVESTIGATIONS;794
17.3;CHAPTER 132. Oscillatory Behavior of a Two-phase Natural-circulation Loop;795
17.3.1;EXPERIMENTAL LOOP;795
17.3.2;THEORETICAL ANALYSIS;795
17.3.3;STABILITY ANALYSES;796
17.3.4;RESULTS;797
17.3.5;CONCLUSIONS;798
17.3.6;ACKNOWLEDGMENT;798
17.3.7;NOTATION;798
17.3.8;LITERATURE CITED;800
17.4;CHAPTER 133.
A Study of Iterative Optimization;801
17.4.1;THEORY;801
17.5;CHAPTER 134. ANALYSIS OF BREAKAGE IN DISPERSED PHASE SYSTEMS;802
17.5.1;General Considerations;803
17.5.2;Description of Breakage Process;804
17.5.3;Discrete Breakage Kernel;805
17.5.4;Continuous Breakage Kernel;805
17.5.5;Numerical Solution of Droplet Equation;806
17.5.6;Numerical Example for Full Breakage;806
17.5.7;Numerical Example for Limited Breakage;808
17.5.8;Summary of Results;809
17.5.9;Nomenclature;810
17.5.10;GREEK SYMBOLS;810
17.5.11;Literature Cited;810
17.6;CHAPTER 135. BREAKAGE AND COALESCENCE IN DISPERSED PHASE SYSTEMS;811
17.6.1;Coalescence Frequency;811
17.6.2;Droplet Size Equation;812
17.6.3;Collision Frequency;813
17.6.4;Temperature Dependence of Coalescence Efficiency;813
17.6.5;Stable Size for Coalescence;814
17.6.6;Transients in CSTR;814
17.6.7;Batch Reactor;817
17.6.8;Conclusions;819
17.6.9;Nomenclature;819
17.6.10;Literature Cited;820
17.7;CHAPTER 136. INFLUENCE OF DROPLET SIZE-AGE DISTRIBUTION ON RATE PROCESSES IN DISPERSED-PHASE SYSTEMS;821
17.7.1;Defining Equation for Size-Age Distribution of Dispersed Phase;821
17.7.2;A Model for Evaporation of a Multicomponent Droplet;822
17.7.3;SCOPE;822
17.7.4;CONCLUSIONS AND SIGNIFICANCE;822
17.7.5;PREVIOUS WORK;822
17.8;CHAPTER 137.
On a mechanism for autocatalysis;823
17.8.1;1. INTRODUCTION;823
17.8.2;2. THE EQUATIONS OF THE MECHANISM;824
17.8.3;3. ASYMPTOTIC SOLUTION;826
17.8.4;4. COMPARISON WITH NUMERICAL SOLUTIONS;829
17.8.5;5. SECOND-ORDER AUTOCATALYTIC MECHANISM;830
17.8.6;6. CONCLUSIONS;831
17.8.7;NOTATION;832
17.8.8;REFERENCES;832
18;NAME INDEX;834