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Chemical Reactor
Analysis and Design
3rd Edition
Gilbert F. Froment
Texas A&M University
Kenneth B. Bischoff†
University of Delaware
Juray De Wilde
Université Catholique de Louvain, Belgium
John Wiley & Sons, Inc.
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Library of Congress Cataloging-in-Publication Data
Froment, Gilbert F.
Chemical reactor analysis and design. -- 3rd ed. / Gilbert Froment, Juray DeWilde, and Kenneth
Bischoff.
p. cm.
Includes bibliographical references and index.
ISBN 978-0-470-56541-4 (cloth)
1. Chemical reactors. 2. Chemical reactions. 3. Chemical engineering. I. DeWilde, Juray. II. Bischoff,
Kenneth B. III. Title.
TP157.F76 2011
660'.2832--dc22
2010014481
Printed in the United States of America
10 9 8 7 6 5 4 3 2 1
From Gilbert to Mia.
From Juray, to my brother Tibor, to Junior and Mathieu.
Chemical Reactor Analysis and Design
Gilbert F. Froment, Texas A&M University; K.B. Bischoff†, University of
Delaware; Juray De Wilde, Université Catholique de Louvain.
This is the Third Edition of Chemical Reactor Analysis and Design. The first
was published by Wiley in 1979 and the second, after a substantial revision, in
1990. When we undertook the third edition in 2008, eighteen years had elapsed
since the second edition. This is a significant period of time during which
chemical reaction engineering has considerably evolved. The tremendous growth
of computer power and the easy access to it has significantly contributed to a
more comprehensive description of phenomena, operations and equipment, thus
enabling the development and application of more fundamental and presumably
more accurate models. Modern chemical reaction engineering courses should
reflect this evolution towards a more scientific approach. We have been
permanently aware of these trends during the elaboration of the present edition
and have largely rewritten the complete text. The more fundamental approach
has not distracted us, however, from the emphasis on the real world of chemical
reaction engineering, one of the main objectives and strengths of the first edition
already, widely recognized all over the world.
We have maintained the structure of the previous editions, dividing the
content into two parts. The first part deals with the kinetics of phenomena that
are important in reaction engineering: reaction kinetics, both “homogeneous” —
in a single phase — and “heterogeneous,” involving a gas- and a liquid- or solid
phase. The mechanism of the reactions has been accounted for in greater detail
than previously, in an effort to be more realistic, but also more reliable in their
kinetic modeling e.g., in thermal cracking, polymerization, hydrocarbon
processing and bio-processes. The field of reaction kinetics has substantially
progressed by the growing availability through commercial software of quantum
chemical methods. Students of chemical reaction engineering can no longer
ignore their potential and they should be taught how to apply them meaningfully
to real processes. Chapters 1, 2 and 3 attempt to do that. In the heterogeneous
reaction case, heat and mass transfer phenomena at the interface and inside the
reaction phase have to be considered. In modeling these the internal structure of
the catalyst has been given more emphasis, starting from insight provided from
well developed characterization tools and using advanced techniques like Monte
Carlo simulation, Percolation theory and Effective Medium Approximation. This
approach is further applied in Chapter 4 on gas-solid reactions and Chapter 5 on
catalyst deactivation. The insertion of more realistic kinetics into structure
models of the catalyst has also allowed accounting for the role of catalyst
deactivation by coke formation in important commercial hydrocarbon conversion
processes, like butene dehydrogenation, steam reforming of natural gas and the
catalytic cracking of vacuum gas oil. Chapter 6 on gas-liquid kinetics has
retained its previous structure.
Part II addresses the chemical reactor itself, inserting the kinetic aspects
of Part I into the modeling and simulation of the reactor operation. Chapter 7
introduces the fundamental mass-, energy- and momentum balances. The
Chapters 8, 9, 10 and 11, dealing with the basic types, like the batch, semi-batch,
continuous flow reactor with complete mixing and the tubular reactor, filled or
not with solid catalyst, have been maintained, of course, and also their strong ties
to industrial processes. Deviations of what was previously called “ideal “ models
and behavior are dealt with along entirely new lines, made possible by the
progress of CFD — computational fluid dynamics — also made available by
commercial software. This approach is introduced already in Chapter 11 on fixed
bed reactors and consistently applied in Chapter 12, leading to a unified and
structured approach of flow, residence time and conversion in the variety of
reactors encountered in industrial practice. This is another field that has not yet
received sufficient attention in chemical engineering curricula. Substantial
progress and a growing number of applications can be expected in the coming
years. It is illustrated also in Chapter 13 on fluidized- and transport bed reactors,
that enters into greater details than before on the catalytic cracking of heavy oil
fractions and reports on simulations based upon computational fluid dynamics.
A book like this has to show the path and prepare the future. We should not look
down, however, upon the correlations derived from experimentation and
collected by the profession over the years, be they limited in their range of
application. There is no way that these could be refined or completely replaced
yet by CFD application only. Unfortunately, the computational effort involved in
the use of CFD in combination with reaction and transport phenomena
throughout the entire reactor is overwhelming and its routine-like application to
real, practical cases not for the immediate future. Chapter 14 on multiphase
reactors is evidence for this and illustrates sound and proved engineering
practice.
Finally, we want to remember Ken Bischoff, who deceased in July 2007
and could not participate in this third edition.
Gilbert F. Froment
Texas A & M University
December 2009
Juray De Wilde
Université Catholique de Louvain
About the Authors
G.F. Froment
Gilbert F. Froment received his Ph.D. in Chemical Engineering from the
University of Gent, Belgium, in 1957. He did post-doctoral work at the
University of Darmstadt in Germany and the University of Wisconsin. In 1968 he
became a full professor of Chemical Engineering in Gent and launched the
“Laboratorium voor Petrochemische Techniek” that became world famous. His
scientific work centered on fixed bed reactor modeling, kinetic modeling,
catalyst deactivation and thermal cracking for olefins production. In 1998 he
joined the Chemical Engineering Department of Texas A & M University as a
Research Professor. He has directed the work of 68 Ph.D students and published
350 scientific papers in international journals. He presented more than 320
seminars in universities and at international symposia all over the world. The
book Chemical Reactor Analysis and Design (with K.B. Bischoff) is used
worldwide in graduate courses and industrial research groups and was translated
into Chinese. He has been on the editorial board of the major chemical
engineering journals. In his present position, at Texas A & M University, Dr.
Froment directs the research of a group of Ph.D students and post-docs on
Chemical Reaction Engineering aspects of Hydrocarbon Processing in the
Petroleum and Petrochemical Industry, more particularly on the kinetic modeling
of complex processes like hydrocracking and hydrotreatment, catalytic cracking,
catalytic reforming, methanol-to-olefins, solid acid alkylation, thermal cracking,
using single event kinetics, a concept that he launched in the eighties. He
received the prestigious R.H. Wilhelm Award for Chemical Reaction
Engineering from the A.I.Ch.E. in 1978, the first Villermaux-Medal from the
European Federation of Chemical Engineering in 1999 and the 3-yearly
Amundson Award of ISCRE in 2007.
G.F. Froment is a Doctor Honoris Causa of the Technion, Haifa, Israel
(1985), of the University of Nancy, France (2001) and an Honorary Professor of
the Universidad Nacional de Salta (Argentina). He is a member of the Belgian
Academy of Science (1984), the Belgian Academy of Overseas Science (1977), a
Foreign Associate of the United States National Academy of Engineering (1999)
and a member of the Texas Academy of Medicine, Science and Engineering
(2003). He was a member of the Scientific Council of the French Petroleum
Institute (1989-1997), of the Technological Council of Rhône-Poulenc (19881997) and has intensively consulted for the world’s major petroleum and
(petro)chemical companies.
K.B. Bischoff †
Kenneth B. Bischoff was the Unidel Professor of Biomedical and Chemical
Engineering and past Chairman, Department of Chemical Engineering at the
University of Delaware. Previously he was Acting Director for the Center for
Catalytic Science and Technology. He was the Walter R. Read Professor of
Engineering and Director of the School of Chemical Engineering at Cornell
University and had been on the faculties of the Universities of Maryland and
Texas (Austin), as well as a Postdoctoral Fellow at the University of Gent,
Belgium. He had served as a consultant for Exxon Research and Engineering
Company, General Foods Company, the National Institutes of Health, W. R.
Grace company, Koppers Company, E. I. du Pont de Nemours & Co., Inc.,
and Westvaco Co., and was a registered professional engineer in the State of
Texas. His research interests were in the areas of chemical reaction
engineering and applications to pharmacology and toxicology, resulting in
more than 100 journal articles and two textbooks: Process Analysis and
Simulation (with D.M. Himmelblau) (1968); and Chemical Reactor Analysis and
Design, (with G.F. Froment) (1979). He was elected to the National Academy
of Engineering in 1988, and he received the 1972 Ebert Prize of the
Academy of Pharmaceutical Sciences, the 1976 Professional Progress
Award, the 1982 Institute Lecture Award, the 1982 Food, Pharmaceutical
and Bioengineering Division Award, and the 1987 R. H. Wilhelm Award. In
1987 he was named a Fellow of the American Institute of Chemical
Engineers. He was a Fellow of AAAS since 1980. Editorial boards on which
he had served include J. Pharmacokinetics and Biopharmaceutics, from 1972
on; and ACS Advances in Chemistry Series, 1974 to 1981. In 1981 he became
an Associate Editor of Advances in Chemical Engineering,
Dr. Bischoff passed away in 2007.
J. De Wilde
Juray De Wilde received his Ph.D in Chemical Engineering from the Ghent
University, Belgium, in 2001. He did post-doctoral work at the Ghent University
and was post-doc research associate at the Chemical Engineering Department of
Princeton University, NJ. In 2005 he became professor of Chemical Engineering
at the Université catholique de Louvain, Belgium, where he received his tenure
in 2008. Dr. De Wilde published more than 30 papers in international journals
and served as a member of scientific committees and as a consultant for
numerous companies, including Total Petrochemicals, Tribute Creations, Dow
Corning, PVS Chemicals, The Catalyst Group, Nanotech-Nanopole, Certech,
etc.. His research interests and expertise include dynamic methods for catalytic
kinetics, the modeling and simulation of gas-solid flows, and process
intensification, in particular for fluidized bed processes. With A. de Broqueville,
he developed the rotating fluidized bed in a static geometry and the rotating
chimney technologies.
Contents — Chemical Reactor Analysis and Design,
Third edition
G.F. Froment, K.B. Bischoff, J. De Wilde
Chapter 1: Elements of Reaction Kinetics
1.1
1.2
1.3
1.4
1.5
1.6
1.7
Definitions of Chemical Rates
1.1.1 Rates of Disappearance of Reactants and of Formation
of Products
1.1.2 The Rate of a Reaction
Rate Equations
1.2.1 General Structure
1.2.2 Influence of Temperature
Example 1.2.2.A Determination of the Activation
Energy
1.2.3 Typical Rate Equations for Simple Reactions
1.2.3.1 Reversible First-Order Reactions
1.2.3.2 Second-Order Reversible Reactions
1.2.3.3 Autocatalytic Reactions
1.2.4 Kinetic Analysis
1.2.4.1 The Differential Method of Kinetic Analysis
1.2.4.2 The Integral Method of Kinetic Analysis
Coupled Reactions
1.3.1 Parallel Reactions
1.3.2 Consecutive Reactions
1.3.3 Mixed Parallel-Consecutive Reactions
Reducing the Size of Kinetic Models
1.4.1 Steady State Approximation
1.4.2 Rate Determining Step of a Sequence of Reactions
Bio-Kinetics
1.5.1 Enzymatic Kinetics
1.5.2 Microbial Kinetics
Complex Reactions
1.6.1 Radical Reactions for the Thermal Cracking
for Olefins Production
Example 1.6.1.A Activation Energy of a Complex
Reaction
1.6.2 Free Radical Polymerization Kinetics
Modeling the Rate Coefficient
2
2
3
5
5
7
8
9
9
10
11
13
13
14
17
17
19
21
21
21
22
23
23
26
30
30
32
38
43
1.7.1 Transition State Theory
1.7.2 Quantum Mechanics. The Schrödinger Equation
1.7.3 Density Functional Theory
43
48
49
Chapter 2: Kinetics of Heterogeneous Catalytic Reactions
2.1
2.2
2.3
2.4
2.5
2.6
2.7
Introduction
61
Adsorption on Solid Catalysts
67
Rate Equations
71
2.3.1 Single Reactions
72
Example 2.3.1.A Competitive Hydrogenation Reactions 76
2.3.2 Coupled Reactions
81
2.3.3 Some Further Thoughts on the Hougen-Watson Rate 86
Equations
Complex Catalytic Reactions
87
2.4.1 The Kinetic Modeling of Commercial Catalytic Processes 87
2.4.2 Generation of the Network of Elementary Steps
89
2.4.3 Modeling of the Rate Parameters
92
2.4.3.1 The Single Event Concept
92
2.4.3.2 The Evans-Polanyi Relationship for the
94
Activation Energy
2.4.4 Application to Hydrocracking
96
Experimental Reactors
99
Model Discrimination and Parameter Estimation
104
2.6.1 The Differential Method of Kinetic Analysis
104
2.6.2 The Integral Method of Kinetic Analysis
110
2.6.3 Parameter Estimation and Statistical Testing of Models 112
and Parameters in Single Reactions
2.6.3.1 Models That Are Linear in the Parameters
112
2.6.3.2 Models That Are Nonlinear in the Parameters 117
2.6.4 Parameter Estimation and Statistical Testing of Models 119
and Parameters in Multiple Reactions
Example 2.6.4.A Benzothiophene Hydrogenolysis
123
2.6.5 Physicochemical Tests on the Parameters
126
Sequential Design of Experiments
126
2.7.1 Sequential Design for Optimal Discrimination between 127
Rival Models
2.7.1.1 Single Response Case
127
Example 2.7.1.1.A Model Discrimination in the
130
2.8
Dehydrogenation of 1-Butene into
Butadiene
Example 2.7.1.1.B Ethanol Dehydrogenation:
133
Sequential Discrimination using
the Integral Method of Kinetic
Analysis
2.7.1.2 Multiresponse Case
137
2.7.2 Sequential Design for Optimal Parameter Estimation
138
2.7.2.1 Single Response Models
138
2.7.2.2 Multiresponse Models
139
Example 2.7.2.2.A Sequential Design for Optimal
139
Parameter Estimation in Benzothiophene Hydrogenolysis
Expert Systems in Kinetics Studies
142
Chapter 3: Transport Processes with Reactions Catalyzed
by Solids
PART ONE INTERFACIAL GRADIENT EFFECTS
3.1
3.2
3.3
Reaction of a Component of a Fluid at the Surface of a Solid 154
Mass and Heat Transfer Resistances
156
3.2.1 Mass Transfer Coefficients
156
3.2.2 Heat Transfer Coefficients
158
3.2.3 Multicomponent Diffusion in a Fluid
160
Example 3.2.3.A Use of a Mean Binary Diffusivity
162
Concentration or Partial Pressure and Temperature Differences 163
Between Bulk Fluid and Surface of a Catalyst Particle
Example 3.3.A Interfacial Gradients in Ethanol
165
Dehydrogenation Experiments
PART TWO INTRAPARTICLE GRADIENT EFFECTS
3.4
3.5
Molecular, Knudsen, and Surface Diffusion in Pores
Diffusion in a Catalyst Particle
3.5.1 A Pseudo-Continuum Model
3.5.1.1 Effective Diffusivities
3.5.1.2 Experimental Determination of Effective
Diffusivities of a Component and of the
Tortuosity
Example 3.5.1.2.A Experimental
Determination of the
172
176
176
176
177
178
Example 3.5.1.2.B
3.6
3.7
3.8
3.9
3.10
3.11
3.12
3.13
Effective Diffusivity of
a Component and of the
Catalyst Tortuosity by
Means of the Packed
Column Technique
Application of the Pellet
Technique
180
3.5.2 Structure Models
180
3.5.2.1 The Random Pore Model
181
3.5.2.2 The Parallel Cross-Linked Pore Model
182
3.5.3 Network Models
184
3.5.3.1 A Bethe Tree Model
184
3.5.3.2 Disordered Pore Media
188
Example 3.5.A Optimization of Catalyst Pore Structure
189
3.5.4 Diffusion in Zeolites. Configurational Diffusion
190
3.5.4.1 Molecular Dynamics Simulation
191
3.5.4.2 Dynamic Monte-Carlo Simulation
193
Diffusion and Reaction in a Catalyst Particle. A Continuum
193
Model
3.6.1 First-Order Reactions. The Concept of Effectiveness
193
Factor
3.6.2 More General Rate Equations. The Generalized Modulus 197
Example 3.6.2.A Application of Generalized Modulus 200
for Simple Rate Equations
3.6.3 Multiple Reactions
201
Falsification of Rate Coefficients and Activation Energies by 204
Diffusion Limitations
Example 3.7.A Effectiveness Factors for Sucrose Inversion 206
in Ion Exchange Resins
Influence of Diffusion Limitations on the Selectivities of
207
Coupled Reactions
Criteria for the Importance of Intraparticle Diffusion
213
Limitations
Example 3.9.A Application of the Extended Weisz-Prater
217
Criterion
Multiplicity of Steady States in Catalyst Particles
218
Combination of External and Internal Diffusion Limitations
219
Diagnostic Experimental Criteria for the Absence of Internal 221
and External Mass Transfer Limitations
Nonisothermal Particles
223
3.13.1 Thermal Gradients Inside Catalyst Particles
3.13.2 External and Internal Temperature Gradients
Example 3.13.2.A Temperature Gradients Inside the
Catalyst Particles in Benzene
Hydrogenation
223
225
228
Chapter 4: Noncatalytic Gas-Solid Reactions
4.1
4.2
4.3
4.4
4.5
A Qualitative Discussion of Gas-Solid Reactions
General Model with Interfacial and Intraparticle Gradients
Heterogeneous Model with Shrinking Unreacted Core
Example 4.3.A Combustion of Coke within Porous Catalyst
Particles
Models Accounting Explicitly for the Structure of the Solid
On the Use of More Complex Kinetic Equations
240
243
252
255
259
264
Chapter 5: Catalyst Deactivation
5.1
5.2
5.3
Types of Catalyst Deactivation
5.1.1 Solid-State Transformations
5.1.2 Poisoning
5.1.3 Coking
Kinetics of Catalyst Poisoning
5.2.1 Introduction
5.2.2 Kinetics of Uniform Poisoning
5.2.3 Shell-Progressive Poisoning
5.2.4 Effect of Shell-Progressive Poisoning on the
Selectivity of Simultaneous Reactions
Kinetics of Catalyst Deactivation by Coke Formation
5.3.1 Introduction
5.3.2 Kinetics of Coke Formation
5.3.2.1 Deactivation Functions
5.3.2.2 Catalyst Deactivation by Site Coverage Only
5.3.2.3 Catalyst Deactivation by Site Coverage and
Pore Blockage
5.3.2.4 Deactivation by Site Coverage and Pore
Blockage in the Presence of Diffusion
Limitations
5.3.2.5 Deactivation by Site Coverage, Growth of
Coke, and Blockage in Networks of Pores
270
270
271
271
271
271
273
275
280
285
285
288
288
288
294
296
298
5.3.3
5.3.4
Kinetic Analysis of Deactivation by Coke Formation 299
Example 5.3.3.A Application to Industrial Processes: 303
Coke Formation in the Dehydrogenation of 1-Butene into Butadiene
Example 5.3.3.B Application to Industrial Processes: 309
Rigorous Kinetic Equations for
Catalyst Deactivation by Coke
Deposition in the Dehydrogenation
of 1-Butene into Butadiene
Example 5.3.3.C Application to Industrial Processes: 312
Coke Formation and Catalyst
Deactivation in Steam Reforming
of Natural Gas
Example 5.3.3.D Application to Industrial Processes: 316
Coke Formation in the Catalytic
Cracking of Vacuum Gas Oil
Conclusions
318
Chapter 6: Gas-Liquid Reactions
6.1
6.2
6.3
6.4
6.5
Introduction
Models for Transfer at a Gas-Liquid Interface
Two-Film Theory
6.3.1 Single Irreversible Reaction with General Kinetics
6.3.2 First-Order and Pseudo-First-Order Irreversible
Reactions
6.3.3 Single, Instantaneous, and Irreversible Reactions
6.3.4 Some Remarks on Boundary Conditions and on
Utilization and Enhancement Factors
6.3.5 Extension to Reactions with Higher Orders
6.3.6 Coupled Reactions
Surface Renewal Theory
6.4.1 Single Instantaneous Reactions
6.4.2 Single Irreversible (Pseudo)-First-Order Reactions
6.4.3 Surface Renewal Models with Surface Elements of
Limited Thickness
Experimental Determination of the Kinetics of Gas-Liquid
Reactions
6.5.1 Introduction
6.5.2 Determination of kL and AV
322
323
326
326
328
332
337
340
342
346
347
351
355
356
356
357
6.5.3 Determination of kG and AV
6.5.4 Specific Equipment
358
359
Chapter 7: The Modeling of Chemical Reactors
7.1
7.2
7.3
Approach
Aspects of Mass, Heat and Momentum Balances
The Fundamental Model Equations
7.3.1 The Species Continuity Equations
7.3.1.1 A General Formulation
7.3.1.2 Specific Forms
7.3.2 The Energy Equation
7.3.2.1 A General Formulation
7.3.2.2 Specific Forms
7.3.3 The Momentum Equations
366
367
369
369
369
373
377
377
378
380
Chapter 8: The Batch and Semibatch Reactors
Introduction
384
8.1
The Isothermal Batch Reactor
385
Example 8.1.A Example of Derivation of a Kinetic Equation 388
from Batch Data
Example 8.1.B Styrene Polymerization in a Batch Reactor
390
Example 8.1.C Production of Gluconic Acid by Aerobic
394
Fermentation of Glucose
8.2
The Nonisothermal Batch Reactor
396
Example 8.2.A Decomposition of Acetylated Castor Oil Ester 399
8.3
Semibatch Reactor Modeling
402
Example 8.3.A Simulation of Semibatch Reactor Operation
403
(with L.H. Hosten†)
8.4
Optimal Operation Policies and Control Strategies
407
8.4.1 Optimal Batch Operation Time
407
Example 8.4.1.A Optimum Conversion and Maximum 410
Profit for a First-Order Reaction
8.4.2 Optimal Temperature Policies
411
Example 8.4.2.A Optimal Temperature Trajectories
412
for First-Order Reversible Reactions
Example 8.4.2.B Optimum Temperature Policies for
418
Consecutive and Parallel Reactions
Chapter 9: The Plug Flow Reactor
9.1
9.2
9.3
The Continuity, Energy, and Momentum Equations
Kinetic Studies Using a Tubular Reactor with Plug Flow
9.2.1 Kinetic Analysis of Isothermal Data
9.2.2 Kinetic Analysis of Nonisothermal Data
Design and Simulation of Tubular Reactors with Plug Flow
9.3.1 Adiabatic Reactor with Plug Flow
9.3.2 Design and Simulation of Non-Isothermal Cracking
Tubes for Olefins Production
427
432
432
435
438
439
441
Chapter 10: The Perfectly Mixed Flow Reactor
10.1
10.2
10.3
10.4
Introduction
453
Mass and Energy Balances
454
10.2.1 Basic Equations
454
10.2.2 Steady-State Reactor Design
455
Design for Optimum Selectivity in Simultaneous Reactions
461
10.3.1 General Considerations
461
10.3.2 Polymerization in Perfectly Mixed Flow Reactors
468
Stability of Operation and Transient Behavior
471
10.4.1 Stability of Operation
471
10.4.2 Transient Behavior
478
Example 10.4.2.A Temperature Oscillations in a Mixed
481
Reactor for the Vapor-Phase Chlorination
of Methyl Chloride
Chapter 11: Fixed Bed Catalytic Reactors
PART ONE INTRODUCTION
11.1 The Importance and Scale of Fixed Bed Catalytic Processes
11.2 Factors of Progress: Technological Innovations and Increased
Fundamental Insight
11.3 Factors Involved in the Preliminary Design of Fixed Bed
Reactors
11.4 Modeling of Fixed Bed Reactors
503
PART TWO PSEUDOHOMOGENEOUS MODELS
11.5 The Basic One-Dimensional Model
11.5.1 Model Equations
505
505
493
494
495
11.6
11.7
Example 11.5.1.A Calculation of Pressure Drop in
Packed Beds
11.5.2 Design of a Fixed Bed Reactor According to the OneDimensional Pseudohomogeneous Model
11.5.3 Runaway Criteria
Example 11.5.3.A Application of the First Runaway
Criterion of Van Welsenaere and
Froment
11.5.4 The Multibed Adiabatic Reactor
11.5.5 Fixed Bed Reactors with Heat Exchange Between the
Feed and Effluent or Between the Feed and Reacting
Gas. “Autothermal Operation”
11.5.6 Nonsteady-State Behavior of Fixed Bed Catalytic
Reactors Due to Catalyst Deactivation
One-Dimensional Model with Axial Mixing
Two-Dimensional Pseudohomogeneous Models
11.7.1 The Effective Transport Concept
11.7.2 Continuity and Energy Equations
11.7.3 Design or Simulation of a Fixed Bed Reactor for
Catalytic Hydrocarbon Oxidation
11.7.4 An Equivalent One-Dimensional Model
11.7.5 A Two-Dimensional Model Accounting for Radial
Variations in the Bed Structure
11.7.6 Two-Dimensional Cell Models
510
510
513
519
522
530
548
559
565
565
571
572
578
579
583
PART THREE HETEROGENEOUS MODELS
11.8 One-Dimensional Model Accounting for Interfacial Gradients 585
11.8.1 Model Equations
585
11.8.2 Simulation of the Transient Behavior of a Reactor
589
Example 11.8.2.A A Gas-Solid Reaction in a Fixed Bed 591
Reactor
11.9 One-Dimensional Model Accounting for Interfacial and
597
Intraparticle Gradients
11.9.1 Model Equations
597
Example 11.9.1.A Simulation of a Primary Steam
604
Reformer
Example 11.9.1.B Simulation of an Industrial Reactor 614
for 1-Butene Dehydrogenation into
Butadiene
Example 11.9.1.C Influence of Internal Diffusion
621
Limitations in Catalytic Reforming
11.10 Two-Dimensional Heterogeneous Models
623
Chapter 12: Complex Flow Patterns
12.1
12.2
12.3
12.4
12.5
12.6
Introduction
639
Macro- and Micro-Mixing in Reactors
640
Models Explicitly Accounting for Mixing
643
Micro-Probability Density Function Methods
649
12.4.1 Micro-PDF Transport Equations
649
12.4.2 Micro-PDF Methods for Turbulent Flow and Reactions 653
Micro-PDF Moment Methods: Computational Fluid Dynamics 658
12.5.1 Turbulent Momentum Transport. Modeling of the
662
Reynolds-Stresses
Annex 12.5.1.A Reynolds-Stress Transport Equations (web)
12.5.2 Turbulent Transport of Species and Heat. Modeling of 666
the Scalar Flux
Annex 12.5.2.A Scalar Flux Transport Equations
(web)
12.5.3 Macro-Scale Averaged Reaction Rates
667
Annex 12.5.3.A Moment Methods: Transport Equa- (web)
tions for the Species Concentration
Correlations
12.5.3.1 Models Based upon the Concept of Eddy
668
Dissipation
12.5.3.2 The Eddy Break-Up Model
669
Example 12.5.A Three Dimensional CFD Simulation of
670
Furnace and Reactor Tubes for the Thermal
Cracking of Hydrocarbons
Macro-PDF / Residence Time Distribution Methods
677
12.6.1 Reactor Scale Balance and Species Continuity
677
Equations
Example 12.6.1.A Population Balance Model for
678
Micro-Mixing in a Perfectly
Macro-Mixed Reactor: PDF
Moment Method
12.6.2 Age Distribution Functions
685
Example 12.6.2.A RTD of a Perfectly Mixed Vessel 688
Example 12.6.2.B Experimental Determination of
689
the RTD
12.6.3 Flow Patterns Derived from the RTD
691