Chemical
Reactor
Analysis
and
Design
Gilbert
F.
Froment
Rijksuniversiteit Gent,
Belgium
Kenneth
B.
Bischoff
University
of
Delaware
John Wiley
8
Sons
New York Chichester Brisbane Toronto
Copyrrght
@
1979
by John Wlley
&
Sons. Inc
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

1098765432
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 on 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 do 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," or local region first and then extend this to overall
reactor behavior.
Several special features include discussions of chain reactions
(e.g., hydrocarbon

of Houston in 1973, at the Centre de Perfectionnement des Industries
Chimiques
at Nancy, France, from 1973 onwards and at 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 at the Katholieke Universiteit Leuven,
Belgium, in 1976. Substantial parts were presented
by
both of us at
a
NATO-
sponsored Advanced Study Institute on "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

.I
Reaction Rate
1.2
Conversion and Extent of Reaction
1.3
Order
of
Reaction
E,uample 1.3-1 The Rare ofan Autocaralytic Reacrion,
13
1.4
Complex Reactions
Esumple
1.4-1
Comp1e.r Reaction Nertt~orks,
19
E.rattipk
I .J-2
Cu~al~tic 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

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
1.7
Thermodynamicaily Nonideal Conditions
60
E.uumple
1.7-1
Reaction of Dilure Strong Electro!vres,
63
E-~umple
1.7-2
Pressure Eficts in Gus-Phase Reactions,
64
2
Kinetics
of
Heterogeneous
Catalytic Reactions
2.1
Introduction
2.2
Rate Equations

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
33
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

Liquid-FiNed Pores,
175
3.6
Reaction with Pore Diffusion
178
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

Dehydrogenution.
2
17
3.9
Reaction with Diffusion in Complicated Pore Structures
22
1
3.9.a Particles
with
Micro- and Macropores
22
1
3.9.b Parallel Cross-Linked Pores 223
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
43

5.2.c Shell Progressive Poisoning
5.2.d Effect of Shell Progressive Poisoning on the Selectivity of Complex
Reactions
53
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

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
83
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

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
CONTENTS
xiii
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,

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 11.5.~-
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

.8.b-1
.4
Gus-Solid Reaction in
u
Fixed Bed Reactor,
551
11.9 One-Dimensional
%Idel 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,

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
Distribution,
653
13
Fluidized Bed Reactors
13.1
Introduction
13.2
Fluid
Catalytic Cracking
CONTENTS
xv
13.3
Some Features of the Design of Fluidized Bed Reactors
13.4

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 ofu Liquid-Phase o-Xj.lene Oxidurion Reactor.
A.
Stirred rank reacror.
B.
Bubble
reactor,

of
the engineering units. Finally, great attention has been given to 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
Am
logarithmic mean of
A,
and m2 m

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
volume
order of
reactlon with
respect to
A
order
of

A,
B
.
.
.
drag coefficient for spheres
mpl:mp3
mp2,'mp3
mPZ'kg
cat.
mP2;kg cat.
m,z!m,' mpZ
mp3
kmol/m3
kmolirn,'
kmol,kg
cat.
kmolikg cat.
xviii
-
NOTATION
S.I.
units
molar concentration of
reacting component
S
of
solid
coke content of catalyst
molar concentration of

reactanr molar
concentration at centerline
of particle (Chapter
3)
Laplace transform of
C,
molar concentration of
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

enhancement factor
molar feed rate of reactants
A
and
j
force exerted per unit
cross section
objective function
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

enthalpy of liquid on
plate
n
heat of format~on of species
j
height of stirrer above
bottom
molar enthalpy of species
j
heat of reaction
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

kp
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

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
propagation reaction in
addition polymerization
NOTATION
mf3"(kmol A)'-" mf3"(krnol
.A)'
-"
(kmol
S)-"
(krnol
s)-"
m:'"-
"
hr-
mP3(m-
"s"
kg cokeikg cat. hr
kg
coke!kg cat
atm or
hr-' s(N;m2) or
s-
'

k,
li.,
k,.
k2 .
k;
k
;
k
;
k
;
(k6c)b
(kdb
reaction rate coefficient
(Chapter
3)
rate coefficient for catalytic
reaction subject to
poisoning
rate coefficient for
first-order poisoning
reaction at core boundary
surface-based rate
coefficient for catalytic
reaction (Chapter
5)
rate coefficients for
termination reactions
volume-based rate
coefficient for catalytic

ml J,'m2 cat. hr m,'/mz cat. s
m13/m2 cat. hr m13/mZ cat. s
m131m2 cat. hr
mf3.!m2 cat. s
m3/kmol hr or hr-
'
mJ/kmol s or
s-'
mJ3/m3 cat. hr
m,31m3 cat. s
see
k,,
k,.
k,
depending on rate
dimensions
see
k,
kmol
A
m13/mb3 hr mJ3/m,' s
xxiv
NOTATIO~
Engineering
units
S.I.
units
(kce)b
mass transfer coeficient
from interchange zone to

.I,./P,c,,
D,
vacant active site
ratio of initial
concentrations
CewiC,,
molecular weight of
species
j
mean molecular weight
monomer
(Sec.
1.4-6)
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,
2ff/R,pc,k,
(Sec. 11.5.~)
'VA

A,
B,
j
.
.
.
in reactor
dimensionless group,
total number of kmoles in
reactor
minimum stirrer speed for
efficient dispersion
characteristic speed for
bubble aspiration and
dispers~on
order of reaction
reaction product
also power input (Chapter
14)
Prandtl number,
c,dl
profit over
N
adiabatic
fixed beds
active polymer
Peclet number based on
particle diameter,
uiddD,.
Peclet number based on

s
s/s
xxvi
NOTATIC
Eng~neering
units S.1. units
critical pressure
film pressure factor
total pressure
reaction component
heats of oxidation,
adsorption, absorption
stoichiometric coefficient;
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
per unit catalyst mass
rate of coke deposition
rate of poison deposition
rate of reaction of
S,
reactive component
of
solid, in gas-solid reactions
atrn
N(m2
atm N;mZ
atm N/mZ
kca1,'kmol kJ/'kmol
kcal/mZ hr
kJ/m2s or kWim2
kcal/kmol
K
or klikrnol
K
atm m3/kmol
K
m
kmol/kg
cat.
hr
kmol,&g.
cat.
s
kg

p/pD
internal surface area per
unit mass of catalyst
external surface area of
a
pellet
modified Sherwood number
for liquid film.
kuA,.D,,
modified Sherwood
number,
k,
L,
D,
(Chapter
3)
modified Sherwood number
for poisoning,
k,,R:D,,
stoichiometric coefficient
also parameter in
Danckwerts' age
distribution function
also
Laplace transform
variable
experimental error variance
of model
i
order of reaction with