chemical reactor analysis and design by gilbert f. froment

129 3 Transport Processes with Fluid-Solid Heterogeneous Reactions Part I Interfacial Gradient Effects 3.1 Surface Reaction Between a Solid and a Fluid 3.2 Mass and Heat Tramfer Res

Chemical Reactor Analysis and Design

Gilbert F Froment Rijksuniversiteit Gent, Belgium

Kenneth B Bischoff University of Delaware

J o h n Wiley 8 Sons New York Chichester Brisbane Toronto

All rights reserved Published simultaneousiy tn Cdna Reproduction or translatron of any pan of thrs work beyond that permrtted by Sections

107 and 108 of the 1976 United States Copyright Act without the permrssion of the copyrrght owner is unlawful Requests for permtssron

or further tnformation should be addressed to the Permrsstons Department John Wiley & Sons Library of Congress Cataloging in Publication Data Frornent Gilbert F

Chemical reactor analysis and design

Includes index

1 Chemical reactors 2 Chemical reacttons

3 Chemical engineering I Bischoti Kenneth B joint author 11 Title

Printed in the United States of America

1 0 9 8 7 6 5 4 3 2

To our wives: Mia and Joyce

Preface

This book provides a comprehensive study of chemical reaction engineering, be- ginning with the basic definitions and fundamental principles and continuing a11 the way to practical application It emphasizes the real-world aspects of chemi- cal reaction engineering encountered in industrial practice A rational and rigorous

approach, based o n mathematical expressions for the physical and chemical phenomena occurring in reactors, is maintained as far as possible toward useful solutions However, the notions of calculus, differential equations, and statistics required for understanding the material presented in this book d o not extend beyond the usual abilities of present-day chemical engineers In addition to the practical aspects, some of the more fundamental, often more abstract, topics are also discussed to permit the reader to understand the current literature The book is organized into two main parts: applied or engineering kinetics and reactor analysis and design This allows the reader to study the detailed kinetics in a given "point," o r local region first and then extend this to overall reactor behavior

Several special features include discussions of chain reactions (e.g., hydrocarbon pyrolysis), modem methods of statistical parameter estimation and model dis- crimination techniques, pore diffusion in complex media, genera1 models for fluid-solid reactions, catalyst deactivation mechanisms and kinetics, analysis methods for chemical processing aspects of fluid-fluid reactions design calcula- tions for plug flow reactors in realistic typical situations (e.g., thermal cracking), fixed bed reactors, fluidized be'd reactor design, and multiphase reactor design Several of these topics are not usually covered in chemical reaction engineering texts, but are of high current interest in applications

Comprehensive and detailed examples are presented, most of which utilize real kinetic data from processes of industrial importance and are based on the authors' combined research and consulting experience

We firmly believe, based on our experience, that this book can be taught to both undergraduate and graduate classes If a distinction must be made between undergraduate and graduate material it should be in the extension and the depth

of coverage of the chapters But we emphasize that t o prepare the student to solve the problems encountered in industry, a s well as in advanced research, the approach must be the same for both levels: there is no point in ignoring the more complicated areas that d o not fit into idealized schemes of analysis Several chapters of the book have been taught for more than 10 years at the

vii

Rijksuniversiteit Gent, at the University of Maryland, Cornell University, and the University of Delaware Some chapters were taught by G.F.F at the University

of Houston in 1973, at the Centre de Perfectionnement des Industries Chimiques

at Nancy, France, from 1973 onwards and a t the Dow Chemical Company, Terneuzen, The Netherlands in 1978 K.B.B used the text in courses taught at Exxon and Union Carbide and also a t the Katholieke Universiteit Leuven, Belgium, in 1976 Substantial parts were presented by both of us a t a NATO- sponsored Advanced Study Institute o n "Analysis of Fluid-Solidcatalytic Systems" held at the Laboratorium voor Petrochemische Techniek, Rijksuniversiteit, Gent,

in August 1974

We thank the following persons for helpful discussions, ideas, and critiques: among these are dr ir L Hosten, dr ir F Dumez, dr ir J Lerou, ir J De Geyter and ir J Beeckman, all from the Laboratorium voor Petrochemische Techniek

of Rijksuniversiteit Gent; Prof Dan Luss of the University of Houston and Professor W D Smith of the University of Rochester

Gilbert F Froment Kenneth B Biihoff

vlll

1 Elements of Reaction Kinetics

Esumple 1.4-1 Comp1e.r Reaction Nertt~orks, 19

E.rattipk I J-2 C u ~ a l ~ t i c Cracking of Gusoil, 24

E.uumple 1.4-3 Rate Determinin,g Step und S~eudv-Sture Appro.uimution, 27

E.uample 1.4-4 Classicul Unimoleculur Rure Theory 30

E.rample 1.4-5 Thermal Cracking of Efhune, 35

Example 1.4-6 Free Radical Addition Polymeri~ation Kinetics, 38

E-\ample 1.5-1 Determination of the Actiration Enery?: 43

E.uample 1.5-2 Acticurion Energy for Comp1e.u Reuctions 44

E.rump1e 1.6.2-1 Rure Constunr Deiermination by file Himmelblau-Jones-

Bischoj'method 50

Example 1.6.2-2 Olejin Codimerization Kinetics, 53

E.rample 1.6.2-3 Thermal Cracking of Propane, 57

E.uumple 1.7-1 Reaction of Dilure Strong Electro!vres, 63

E-~umple 1.7-2 Pressure E f i c t s in Gus-Phase Reactions, 64

2 Kinetics of Heterogeneous Catalytic Reactions

2.1 Introduction

2.2 Rate Equations

Exumple 2.2-1 Cnmpetitir-e Hydrogenation Reocrions 94

E.xumple 2.2-2 Kinetics of Erhyiene O.ridur~on on a Supporred Silver

Carafvsr, 101

2.3 Model Discrimination and Parameter Estimation

2.3.a Experimental Reactors

2.3.b The Differental Method for Kinetic Analysis

2.3.c The Integral Method of Kinetic Analysis

2.3.d Sequential Methods for Optimal Design of Experiments

2.3.d-1 Optimal Sequential Discrimination

Exurnpie 2.3.d.l-i Model Discrimination in rhe Dehydrogeno~ion of

f-Burene inro Buradiene, 121

E.rumple 2.3.d.l-I Ethanol Deh.vdrogenarion Seqrientiul Discnminarion

Using rhe Inregra! Method of'Kineric Anall~is, 125

2.3.d-2 Sequential Design Procedure for Optimal Parameter Estimation

E.xumple 2.3.d.2-I Sequentiuf Descqn of Experimenrs /or Optimuf Puramerer Esrimution in n-Penfane Isomeriiur!on Integral 'Method oJ'Kinrrlc Analysis 129

3 Transport Processes with Fluid-Solid Heterogeneous

Reactions

Part I Interfacial Gradient Effects

3.1 Surface Reaction Between a Solid and a Fluid

3.2 Mass and Heat Tramfer Resistances

3.2.a Mass Transfer Coefficients

3.2.b Heat Transfer Coefficients

3.2.~ Multicomponent Diffusion in a Fluid

E.~umple 3.2.c-1 Use of Mean Efectice Binarv Drffusic~ry, 149

3 3 Concentration or Partial Pressure and Temperature Differences Between

Bulk Fluid and Surface of a Catalyst Particle

E.rampfe 3.3-1 Interfaciui Gradienrs rn Erhunol Dehydrogenarion

Expertments, 15 1

Part 11 Intraparticle Gradient Effects

3.4 Catalyst Internal Structure

3 5 Pore Diusion

3.5.a Definitions and Experimental Observations

E.rcunpIe 3.5.0-1 Effect of Pore D~jiusion in the Cracking ofdlkanes on

Zeolites, 164

3.5.b General Quantitative Description of Pore Diffusion

3.5.c The Random Pore Model I 70 3.5.d The Pdrallrl Cross-Linked Pore Model 172

3.5.5 Pore Diifuslon with Adsorption: Surface Diffuslon: Configurational

E.rumpie 3.S.e-1 Surface Diff~ision m Liquid-FiNed Pores, 175

3.6.a Concept of Effectiveness Factor 178 3.6.b Generalized Effectiveness Factor 182

E.xumple 3.6.6-1 Generuiized Modrclus for First-Order Reversible

Reaction, 185

E.wmpfe 3.6.b-2 Effecrit,eness Facrorsfor Sucrose Inrersion in Ion

E.xchunge Resms 187

E.wmple 3.6.b-3 Methanol Synthesis, 189

3.6.c Criteria for Importance of Diffusional Limitations

E.xumple 3.6.c-I Minimum Distance Ber~veen BiJw1crionuI Cutulr.st

Sites for Absence of Diffusionaf Limtrurions, 192

E.rample 3.6.c-2 Use of Extended Weisz-Prurer Criterion 196

3.6.d Combinat~on of External and Internal Diffusion Resistance 197

E.rumple 3.6.d-1 E.rperimenrul Drferenriution Berbi~een E.~rernul und

Internu[ Diffirsion Control, 199

3.7.a Thermal Gradients Inside Catalyst Pellets 200 3.7.b External and Internal Temperature Gradients 108

E,~umple 3.7.u-I Temperur~tre Gradients nilh Catalytic Reactions, 2 10

3.8 Complex Reactions with Pore Diffusion 214

E.rample 3.8.1 Effect oJCutalyst Purricle Size on Selecrlriiy in Burenr

Dehydrogenution 2 17

3.9 Reaction with Diffusion in Complicated Pore Structures 22 1 3.9.a Particles with Micro- and Macropores 22 1

3.9s Reaction with Configuritional Diffusion 224

Example 3.91-1 Cutalyiic Demerallizution (and Desu~urrzarion) o/ Heu0.v

Residium Petroleum Feedsrocks, 225

4 Noncatalytic Gas-Solid Reactions

4.1 A Qualitative Discunion of Gas-Solid Reactions

4.2 A General Model with Interfacial and Intraparticle Gradients

4 3 A Heterogeneow iModel with Shrinking Unreacted Core

Example 4.3-1 Combustion of Coke wirhin Porous Catalyst Particles, 252

4.4 Grain model Accounting Explicitly for the Structure of the Solid

4 5 Pore Model Acmmting Explicitly for the Structure of the Solid

4.6 Reaction Inside Nonisothermal Particles

4.7 A Concluding Remark

5 Catalyst Deactivation

5.1 Types of Catalyst Deactivation

5.2 Kinetics of Catalyst Poisoning

5.2.a Introduction

5.2.b Kinetics of Uniform Poisoning

5.2.c Shell Progressive Poisoning

5.2.d Effect of Shell Progressive Poisoning on the Selectivity of Complex

Reactions

5 3 Kinetics of Catalyst Deactivation by Coking

5.3.a Introduction

5.3.b Kinetics of Coking

5.3.c Influence of Coking on the Selectivity

5.3.d Coking Inside a Catalyst Particle

Example 5.3.d-I Coking in the Dehvdrogenution of I-Butene into Butadiene

on a Chromia-Alumina Cutafvst, 294

5.3.e Determination of the Kinetics of Processes Subject to Coking

Example 5.3.e-I Deh.vdrogenution of I-Burene into Butudiene, 297

6 Gas-Liquid Reactions

6.1 Introduction

6.2 Models for Transfer at a Gas-Liquid Interface

6.3 Two-Film Theory

6.3.a Single Irreversible Reaction with General Kinetics

6.3.b First-Order and Pseudo-First-Order Irreversible Reactions

6.3.c Single Instantaneous, and Irreversible Reaction

6.3.d Some Remarks on Boundary Conditions and on Utilization and

Enhancement Factors

6.3.e Extension to Reactions with Higher Orders

6.3.f Complex Reactions

6.4 Surface Renewal Theory

6.4.a Single Instantaneous Reaction

6.4.b Single Irreversible (Pseudo) First-Order Reaction

6.4.c Surface Renewal Models with Surface Elements of Limited Thickness

6.5 Experimental Determination of the Kinetics of Gas-Liquid Reactions

Part Two-Analysis and Design of Chemical Reactors

7 The Fundamental Mass, Energy, and Momentum

Balance Equations

7.1 Introduction

7 l a The Continuity Equations

7.1.b The Energy Equation

7 l .c The Momentum Equation

7.2 The Fundamental Equations

7.2.a The Continuity Equations

7.2.b Simplified Forms of the "General" Continuity Equation

7.2.c The Energy Equation

7.2.d Simplified Forms of the "General" Energy Equation

8 The Batch Reactor

8.1 The Isothermal Batch Reactor

Exmple 8.1-1 Example of Derivurion of a Kinetic Equation by Means oj

Butch Data, 364

8.2 The Nonisothermal Batch Reactor

Example 8.2-1 Hydrolysis of Acetyluted Cusror Oil Ester, 370

8 3 Optimal Operation Policies and Control Strategies

8.3.a Optimal Batch Operation Time

Example 8.3.0-1 Optimum Conversion und iWu.~irnum Profit for u

Firs!-Order Reuction, 376

8.3.b Optimal Temperature Policies

E.rumple 8.3.6-1 Optimal Temperarure Trujec!orres for Firsi-Order

Rerrrsible Reucrions, 378

E.uumple 8.3.b-2 Oprimum Temperature Policiestor Conseczrtice und

Purullel Reuct~ons, 383

9 The Plug Flow Reactor

9.1 The Continuity, Energy, and Momentum Equations

E.xump1e 9.1-1 Dericurion of u Kineric Equution from E.t-prrimenrs in un

Isoihermul Tubulur Reuctor wiih Plug Flotr, Thermul Cracking of

Propune 397

9.2 Kinetic Analysis of Nonisothermal Data

Esumple 9.2-1 Dericarion o f u Rare Equurionfor rhe Thermul Crucking

of Acerone from Nonisorhermul Dora, 402

9 3 Design of Tubular Reactors with Plug Flow

E.uumple 9.3-1 An Adiubur~c Reuctor with Plug Flow Conditions, 408

E.rumple 9.3-2 Design of u Nonisothermai Reucror for Tl~ermoi Cracking

of Ethane, 410

10 The Perfectly Mixed Flow Reactor

10.1 Introduction

10.2 Mass and Energy Balances

10.2.a Basic Equations

10.2.b Steady-State Reactor Design

E.xumple IO.2.b-I Single Irrecersible Reaction in u Srirred Flow Reoctor, 424

10.3 Design for Optimum Selectivity in Complex Reactions

10.3.a General Considerations

10.3.b Polymerization Reactions

10.4 Stability of Operation and Transient Behavior

10.4.a Stability of Operation

E.rample 10.4.0-I Mulripiicity and Sfabiiity in un Adiabatic Stirred Tunk Reactor, 446

1 1.1 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

Part 11 Pseudo-Homogeneous Models

11.5 The Basic OneDimensional models

11.5.a Model Equations

E.rumple 1 1 5 ~ - I Culcu/anon of Pressure Drop m Packed Beds, 48 1

1 1.S.b Design of a Fixed Bed Reactor According to the One-Dimensional pseudo-Homogeneous Model

1 1 5 ~ Runaway Criteria

E.rump1e 11.5.~- 1 Application ofthe Firsr Runaway Criterion of

Van Wel~rnaere and Fromenr, 490

11.5.d The Multibed Adiabatic Reactor

11.5.e Fixed Bed Reactors with Heat Evchange between the Feed and Effluent or between the Feed and Reacting Gases "Autothemic Operation"

I 1.5.f Non-Steady-State Behavior of Fixed Bed Catalytic Reactors Due to Catalyst Deactivation

11.6 One-Dimensional Model with Axial Mixing

11.7 Two-Dimensional Pseudo-Homogeneous Models

1 1.7.a The Effective Transport Concept

11.7.b Continu~ty and Energy Equations

I I 7.c Design of a Fixed Bed Reactor for Catalytic Hydrocarbon

Oxidation

Part 111 Heterogeneous Models

11.8 One-Dimensional Model Accounting for Interfacial Gradients

1 f 8.a Model Equations

11.8.b Simulation of the Transient Behavior of a Reactor 549

E.~umple 1 I .8.b-1 .4 Gus-Solid Reaction in u Fixed Bed Reactor, 551

11.9 One-Dimensional % I d e l Accounting for Interfacial and Intraparticle

Gradients

11.9.a Model Equations

Exumple 11.9.~-1 Stmulur ion of u Fuuser-!Monrecaf~ni Reactor for

High-Pressure Methunoi Synthesis 562

E.~ample 11.9.~-2 Simulurion of an Industrial Reactor for I-Bu~ene

Dehydrogenation into Butudiene, 571

11.10 Two-Dimensional Heterogeneous &lodeis

12 Nonideal Flow Patterns and Population Balance Models 592

12.1 Introduction

12.2 Age-Distribution Functions

Example 12.2-1 RTD of a Perfect/y ibfixed Vessel 595

Example 12.2-2 Determination of RTDfrom Experimenrol Tracer Cur~ve 596

E,~ampie 12.2-3 Calculutron of Age-Disrriburion Funcrionsfrom

E.rperimento/ Dufa, 598

' 12.3 Interpretation of Flow Patterns from Age-Distribution Fulctions

12.3.a Measures of the Spectrum of Fluid Residence Times

E.rurnple 12.3-1 Aye-Distriburion Func~iom for a Series ofn-Stirred Tanks, 603

Exumple 12.3-2 RTDfor Combinations oj~Noninteracting Regions, 605

12.3.b Detection of Regions of Fluid Stagnancy from Characteristics of

Age Distributions

12.4 Application of Age-Distribution Functions

Example 12.4-1 Mean Vulue of'Rute Constant in a Well-Mixed Reactor, 609 E.rumple 12.4-2 Second-Order Reaction in a Stirred Tank 61 1

Exumple 12.4-3 Reactions in Series Plug Flow and Perfecfly Mired

Reucrors 61 2

12.5 Flow Models

12.5.a Basic Models

Example 12.5.~-I Axial Dispersion ~Lfodelfor kiminar Flow in Round

Tubes, 620

12.5.b Combined Models

Example 12.5.b-I Transient Mass Tramfer in a Packed Column, 631

Example 12.5.b-2 Recycle Model for Large-Scale S4ixing Egects, 634

12.5.c Flow Model Parameter Estimation

12.6 Population Balance Models

Example 12.6-1 Population Balonce Modei for Micromixing, 646

Example 12.6-2 Surfae Reaction-Induced Changes m Pore-Size

13.3 Some Features of the Design of Fluidized Bed Reactors

13.4 Modeling of Fluidized Bed Reactors

E.~umple 13.4-1 iuodeling of un Acrylonitrile Reactor, 685

14 Multiphase Flow Reactors

14.1 Types of ~Multiphase Flow Reactors

14.2 Design iModels for Multiphase Flow Reactors

14.2.a Gas and Liquid Phase Completely Mixed

14.2.b Gas and Liquid Phase in Plug Flow

14.2.c Gas Phase in Plug Flow Liquid Phase Completely M~xed

14.2.d An Effective Diffusion Model

14.2.e A Two-Zone Model

14.2.f An Alternate Approach

14.3 Specific Design Aspects

14.3.a Packed Absorbers

E.vumple 14.3.0-1 Design of u Pucked Column for Curbon Dio.ridr

Absorption, 704

E.rumpk 14.3.~-2 Design 4spects of u Pucked Column /or rhc

Absorprion of 4mmoniu in Suljuric Acid, 708

14.3 b Two-phase Fixed Bed Catalytic Reactors with Cocurrent

Downflow Trickle Bed Reactors and Packed Downflow Bubble Reactors

14.3.c Two-Phase Fixed Bed Catalytic Reactors with Cocurrent L'pflow

"Upflow Packed Bubble Reactors"

14.3.d Plate Columns

E.\-ample 14.3.d-1 Gus Absorption wirh Reuction in u Plate Coluner, 722

14.3.e Spray Towers

14.3.f Bubble Reactors

14.3.g Stirred Vessel Reactors

E.rump/e 14.3.g-I Design o f u Liquid-Phase o-Xj.lene Oxidurion Reactor

A Stirred rank reacror B Bubble reactor, 732

Acknowledgments

Author Index

Subject Index

Notation

Two consistent sets of &its are listed in the following pages: one that is currently the most common in engineering calculations (including, for example, m, hr, atm, kcal) and the S.I units, which are only slowly penetrating into everyday use

In some formulas other units had t o be used: the chemical engineering literature

contains many correlations that are not based o n dimensionless groups and they require the quantities to be expressed in certain given units only This has been carefully indicated in the text, however

All the numerical calculations in the text are in the above mentioned engineer- ing units, but the intermediate and final results are also given in S.I units We feel that this reffects-and even simplifies-the practical reality that is going to last for many more years, and we have preferred tfiis pragmatic approach to preserve the feeling for orders of magnitude gained from years of manipulation

of the engineering units Finally, great attention has been given t o the detailed definition of the units of the different quantities: for example, when a dimension

of length is used, it is always clarified as to whether this length concerns the catalyst

or the reactor We have found that this greatly promotes insight into the mathe- matical modeling of a phenomenon

Engineering units S.I units

A reaction component

A b heat exchange surface, m2 m2

packed bed side

A , reacting species in a

reaction system

A, heat exchange surface in a mZ m2

batch reactor, on the side of

the reaction mixture

A, or of Ab and A ,

A, heat exchange surface for a mz m 2

batch reactor on the side of

the heat transfer medium

'4, total heat exchange surface m2 m 2

xvii

Engineer~ng units S.I unlts

c, c,, c,

C.4br C8b

heat exchange surface for a

packed bed on the side of

the heat transfer medium

gas-liquid interfacial area

per unit liquid volume

interfacial area per unit tray

surface

frequency factor

absorption factor, L'!mF

gas-liquid interfac~al area

per unlt gas + liquid volume

stoichiometric coefficient

parameters (Sec 8.3.b)

surface to volume ratio of a

particle

external particle surface

area per unit catalyst mass

external particle surface

area per unit reactor

gas-liquid interfacial area

per unit packed volume

liquid-solid interfacial area

per unit packed volume

sorbed poison inside

catalyst, with respect to

fluid reactant in front of

the solid surface

molar concentration of A

inside completely

reacted zone of solid

specific heat of fluid

specific heat of solid

Damkahler number for

poisoning, k,, RID.,

molecular diffusivities of A,

B in liquid film

molecular diffusivity for A in

a binary mixture of A and B

xix NOTATION

Eo,

stirrer diameter

internal tube diameter also

tower diameter (Chapter 14)

activation energy

Murphree tray efficiency

corrected for entrainment

exponential integral

Murphree tray efficiency

overall tray efficiency

point tray efficiency along

volumetr~c gas flow rate

volumetr~c gas feed rate

volumetric gas flow rate

(Chapter 14)

friction factor in Fanning

equation

fraction of total fluidized

bed volume occupied by

bubble gas

fraction of total fluidized

bed volume occupied by

emulsion gas

superficial mass flow

velocity

matrix of partial derivatives

of model with respect to the

parameters

transpose of G

Engineering units S.I units

Engineering units S.I units

acceleration of gravity

external force on species j in

the 1 direction per unit

mass of j

partial derivative of

reaction rate with respect to

the parameter K, at the uth

set of experimental

conditions

Henry's law coefficient

enthalpy of gas on plate n

heat transfer coefficient for

film surrounding a particle

initiator; also intermediate

species: inert;

unit matrix

molar flux of species j in 1

direction, with respect to

mass average velocity

pressure drop in straight

tubes

j-factor for mass transfer,

j-factor for heat transfer,

equilibrium constants

matrix of rate coefficients

kinetic energy per unit mass

flow averaged kinetic

energy per unit mass

reaction rate coefficient

xxii

kcalikmol kcal/kmol kcal/m: hr "C

Nmikmol kJ;kmol

m kJ/kmoi

kJ/kmol

m

kJ;kmol

kJ, kmol kJ,'mPz s K

kmol/m2 hr kmol/m2 s

kgf;mZ or atm N!m2

see k: k,, k p

NOTATION

Engineering units S.1 units

k rate coefficient with respect

to unit solid mass for a

reaction with order n with

respect to fluid reactant A

and order m with respect to

solid component S

coking rate coefficient

gas phase mass transfer

coefficient referred to unit

interfacial area

liquid phase mass transfer

coefficient referred to unit

inierfacial area

mass transfer coefficient

(including interfacial area)

between flowing and

stagnant liquid in a

multiphase reactor

ki-I, k 7 2 mass transfer coefficient

(including interfacial area)

beween regions I and 2 of

flow model (Chapter 12)

kc rate coefficient based on

concentrations

k g gas phase mass transfer

coefficient; when based on

concentrations; when based

on mole fractions ; when

based on partial pressures;

in a fluidized bed

interfacial mass transfer

coeficient for catalyst

poison

mass transfer coefficient

between liquid and catalyst

surface, referred to unit

interfacial area

kp reaction rate coefficient

based on partial pressures

kw rate coefficient for

m,3/mp' hr; mfJ, rn; S;

kmol/mp2 hr: kmol!mP2 s; kmol/mpz hr atm kmollmpL s (Nim'); mf3;m,%r m /','m," s

xxiii

Engineering units S.I units

coefficient for catalytic

reaction during poisoning,

resp in absence of poison

rate coefficient based on

mole fractions

slutriation rate coefficient

(Chapter 13)

reaction rate coefficients

rate coefficient of catalytic

reaction in absence of coke

mass transfer coefficient in

case of equirnolar

counterdiKusion, k,yJl

mass transfer coefficient

between stagnant liquid

and catalyst surface in a

multiphase reactor

surface based reaction rate

coefficient for gas-solid

reaction

mass transfer-coefficient

from bubble to interchange

zone referred to unit

bubble volume

overall mass transfer

coefficient from bubble to

emulsion, referred to unit

kmol A

m13/mb3 hr mJ3/m,' s

Engineering units S.I units

(kce)b mass transfer coeficient

from interchange zone to

emulsion, referred to unit

bubble volume

( k t A mass transfer coefficient

from bubble + interchange

zone to emulsion, referred

to unit bubble +

interchange zone volume

L volumetric liquid flow rate

also distance from center to

surface of catalyst pellet

(Chapter 3)

also distance between pores

in a solid particle (Sec 4.5)

and thickness of a slab

(Sec 4.6)

total height of fluidized bed

height of a fluidized bed at

minimum fluidization

molar liquid flow rate

modified Lewis number

Henry's coefficient based on

mole fractions also order

of reaction

mt total mass

m total mass flow rate

mi mass flow rate of

component j

N stirrer revolution speed;

also runaway number,

2 f f / R , p c , k , (Sec 11.5.~)

'VA molar rate of absorption

per unit gas-liquid

interfacial area

kgi kmol

kg/kmoi

Engineering units S.I units

N,,, N B , N ,

P A ~ P s - P ~

Par

also molar flux of A with

respect to fixed coordinates

instantaneous molar

absorption rate in element

of age t per unit gas-liquid

characteristic speed for

bubble aspiration and

Peclet number based on

particle diameter, uiddD,

Peclet number based on

reactor length, uiL/D,

number averaged degree of

Eng~neering units S.1 units

also heat flux

order of reaction wirh

respect to Q

order of reaction with

respect to Aj

gas constant

also radius of a spherical

panicle (Chapters 4 and 5)

also reaction component

Reynolds number, d , G / p

or d, G / p

total rate of change of the

amount of component j

pore radius in pore model

of Szekely and Evans

also pore radius (Chapter 3)

also radial position in

or per unit catalyst mass

rate of coke deposition

rate of poison deposition

kmol/kg cat hr kmol,&g cat s

kg cokekg cat hr kg cokehg cat s kmol/kg cat hr kmol/kg cat s

kmolkg solid hr kmolhg solid s

Engineering units S.I units

internal surface area per

unit mass of catalyst

external surface area of a

pellet

modified Sherwood number

for liquid film kuA,.D,,

temperature instde solid,

resp at solid surface

m2cat.,'kg cat m'cat., kg cat

bubble rising velocity, with

respect to emulsion phase

emulsion gas velocity,

superficial gas velocity

terminal velocity of particle

reactor volume or volume

of considered "point "

volume of a particle

equivalent reactor volume

that is, reactor volume

volume of interchange zone

product molar volume

bubble volume corrected

for the wake

corrected volume of bubble

+ interchange zone

Engineering units S.I units

Engineering units S.I units

volume of interchange zone, m3 m 3

corrected for wake

total catalyst mass kg cat kg cat

mass of amount of catalyst kg kg

cost of reactor idle time,

reactor charging time Sihr % is

reactor discharging time

and of reaction time

radius of grain in grain m

model of Sohn and Szekely

(Chapter 4)

kmol

kmol/m3

calculated value of

dependent variable (Sec

1.6-2)

also experimental value of

dependent variable (Sec

1.6-2)

coordinate perpendicular to

gas-liquid interface

also radial position inside a

grain in grain model of

Sohn and Szekely (Chapter

4)

also position of reaction

front inside the solid in

pore model of Szekely and

Evans (Chapter 4)

mole reaction of species '4,

5.j

gas film thickness

liquid film th~ckness for

vector of mole fractions

compressibility factor also

total reactor or column

Greek Symbols

Engineering units S.I units

convective heat transfer

coefficient

also profit resulting from

the conversion of 1 kmole

of .4 into desired product

(Sec 11.S.d)

also weighung factor in

objective function (Sec

2.3.~-2)

vector of flow model

parameters (Chapter 12)

deactivation constants

convective heat transfer

coefficient, packed bed side

stoichiometric coeficient of

component j in a single

with respect to the ith,

reaction

convective heat transfer

coefficient on the side of the

reaction mixture

convective heat transfer

coefficient on the side of the

heat rransfer medium

convective heat transfer

coefficient for a packed bed

on the side of the heat

transfer medium

convective heat transfer

coefficient in the vicinity of

the wall

wall heat transfer coefficient

for solid phase

wall heat transfer coefficient

for fluid

kg cat ;kg coke

or h r - ' kcal:m2 hr 'C

kg cat kg coke

or s - '

kJ,m's K

xxxiii

Engineering

radical involved in a

bimolecular propagation

step; also weighting factor

in objective function (Sec

locus of the points in x - T

diagram where the rate is

maximum

locus of maximum rate

along adiabatic reaction

also weighting factor in

objective function (Section

E void fraction of packing m13/mr3 mj3/m,'

&A expansion factor, yA,6,

VG

'lb

llquid holdup in flowing

fluid zone in packed bed

void fraction of cloud, that

is, bubble + interchange

zone

pore volume of macropores

void fraction at minimum

factor used in pressure drop

equation for the bends; also

correction factor in (Sec

global utilization factor

effectiveness factor for

particle + film

fractional coverage of

catalyst surface; also

dimensionless time D,I/L'

(Chapter 3), ak'C,r

(Chapter 4); residence time

reactor chang~ng time

reactor idle time

angle described by bend of

xi.*- I

xxxvi

Engineering units S.I units

thermal conductivity: also

slope of the change of

conductivity for the fluid

phase with respect to a

solid phase in a packed bed

dynamic viscosity: also

radical in a unimolecular

propagation step

viscosity at the temperature

of the heating coil surface

v~scosity at the temperature

extent of ith reaction

radial coordinate inside

particle

extent of ith reaction per

unit mass of reaction

Engineering

units S.I units

with the ith model used in

the design of the nth

variance of response values

predicted by the ith model

surface tension of liquid

critical surface tensron of

liquid

sorption distribution

coefficient Chap 5

tortuosity factor (Chapter

3); also mean residence

age distribution function

cross section of reactor o r

column

xxxvii

bulk ; also bubble phase

bubble + interchange zone; also critical value: based on concentration

desorption

emulsion phase; also effective or exit stream from reactor

at chemical equilibrium

fluid; also film; aiso at final conversion

average; also grain or pas

interface; aiso ith reaction

with respect to jth component

liquid: also in 1 direct~on

maximum; also measurement point (Chapter I?)

tray number

pellet, particle; also based on partial pressures

reactor dimension; also surroundings also in radial direct~on

inside solid; also surface based or superficial velocity

surface reaction

total: also tube

volume based

at the wall

based on mole fractions

initial or inlet condition; also overall value

Superscripts

T transpose

d stagnant fraction of Ruid

f flowing fraction of fluid

s condition at external surface

0 in absence of poison or coke

radical

calculated or estimated value

xxxix

Part One

CHEMICAL

ENGINEERING

KI N €TI CS

ELEMENTS

OF

REACTION KINETICS

We begin the study of chemical reactor behavior by considering only "local" regions By this we mean a "point" in the reactor in much the same way as is customary in physical transport phenomena, that is, a representative volume element After we develop quantitative relations for the local rate of change of the amount of the various species involved in the reaction, they can be "added together" (mathematically integrated) to described an entire reactor

In actual experiments, such local phenomena cannot always be unambiguously observed, but in principle they can be discussed The real-life complications will then be added later in the book

1.1 Reaction Rate

The rate of a homogeneous reaction is determined by the composition of the reaction mixture, the temperature, and the pressure The pressure can be deter- mined from an equation of state together with the temperature and composition; thus we focus on the influence of the latter factors

Consider the reaction

It can be stated that A and B react at rates

and Q and S are formed a t rates