scott fogler - elements of chemical reaction engineering [3rd ed.]

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CHEMICAL
ENGINEERING
Elements
of
Chemical
Reaction
Engineering
H.
Scott Fogler Third Edition
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Thorough coverage of the fundamentals of cfiemlcal reaction engineering forms the backbone of this trusted
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classical elements are covered. Elements of Ctiemical Reaction Engineering, Third Edition, builds a strong
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reactions in a variety of applications.
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•
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H.
Scott
Fogler
Elements
of
Chemical
Reaction
Engineering
Third
Edition
Prentice
Hall international Series
in
the Physical and Chemical
Engineering
Sciences

PRENTICE HALL INTERNATIONAL SERIES
IN THE PHYSICAL AND CHEMICAL ENGINEERING SCIENCES
NEAL
R.
AMUNDSGN, SERIES EDITOR,

University of Houston
ADVISORY EDITORS
ANDREAS
AcRrvos, Stanford University
JOHN DAHLER,
University of Minnesota
H. ScOTT FoGLER, University of Michigan
THOMAS
J.
HANRATTY,
University of Illinois
JOHN
M.
PRAUSNITZ,
University
of
California
L.
E.
SCRIVEN, University
of
Minnesota
BALZHISER, SAMUELS,
AND
ELIASSEN
Chemical Engineering Thermodynamics
BEQUETTE
Process
Dynamics
BlEGLER,

GROSSMAN, AND WESTERBERG
Systematic Methods
of
Chemical Process
Design
CROWL AND LOUVAR
Chemical Process
Safely
CUTLiP
AND
SHACHAM
Problem
Solving in
Chemical Engineering
with
Numerical
Metlwds
DENN
Process
Fluid Mechanics
ELLIOT AND LIRA
Introductory
Chemical
Engineering
Tliermodynamics
FOOLER
Elements
of
Chemical
Reaction

Engineering,
3rd Edition
HANNA AND SANDALL
Computational Methods
in
Chemical Engineering
HIMMELELAU
Basic Principles and
Calculations
in
Chemical
Engineering,
6th edition
HiNES
ANDMADDOX
Mass Transfer
KYLE
Chemical
and
Process
Thermodynamics,
3rd
edition
NEWMAN
Electrochemical
Systems,
2nd edition
PRAUSNITZ, LECHTENTHALER, AND DE AZEVEDO
Molecular Thermodynamics
of Fluid-Phase

Equilibria,
3rd edition
PRENTICE
Electrochemical
Engineering Principles
SHULER
AND
KARGI
Bioprocess Engineering
STEPHANOPOULOS
Chemical Process Control
TESTER AND MODELL
Thermodynamics
and
Its
Applications,
3rd edition
TURTON,
BAILIE, WHITING, AND SHAEIWITZ
Analysis,
Synthesis
and Design of
Chemical
Processes
WILKES
Fluid Mechanics
for
Chemical Engineering
Elements
of Chemical

Reaction
Engineering
Third Edition
H. SCOTT FOGLER
Ame
and
Catherine Vennema Professor
of Chemical Engineering
The University
of
Michigan, Ann Arbor
Prentice-Hall International, Inc.

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ISBN 0-13-'^737aS-S
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Dedicated to the memory of
Professors
Giuseppe Parravano
Joseph J. Martin
Donald L. Katz
of the University of Michigan
whose standards aiid lifelong achievements
serve to inspire us
Contents
PREFACE XV
1 MOLE BALANCES 1
1.1 Definition of the Rate of Reaction, -
v/^
2
1.2 The General Mole Balance Equation • 6
1.3 Batch Reactors 8
1.4 Continaous-Flow Reactors 10
L4.I Continuous-Stirred Tank
Reactoi-
10

L4.2 Tubular Reactor 11
1.4.3 Packed-Bed Reactor 14
1.5 Industrial Reactors 16
Summary 25
Questions and Problems 25
CD-ROM Material 31
Supplementary Reading 31
2 CONVERSION AND REACTOR SIZING 33
2.1 Definition of Conversion 33
2.2 Design Equations 34
2.2./
Batch Systems 34
2,2,2 Flow Systems 37
2.3 Applications of the Design Equations for Continuous-Flow
Reactors 40
2.4 Reactors in Series 48
2.5 Some Further Definitions 56
Summary 59
mr
VIII
Questions and Probiems 62
CD-ROM Material 66
Supplementary Reading 67
3 RATE LA WS AND STOICHIOMETRY
Contents
6S
3.1 Basic Definitions 68
3.1.1 The Reaction Rate Constant 69
3
J.2

The Reaction Order and the Rate Law
3.1.3 Elementary Rate Laws and Molecularity
3.1.4 Reversible Reactions 77
3.1.5 Nonelementary Rate Laws and Reactions
3.2 PresentStatusof Our Approach to Reactor Sizing
and Design 83
3.3 SloicMometric Table S4
3.3.1 Batch Systems 84
3.3.2 Constant-Volume Reaction Systems 87
3.3.3 Flow Systems 90
3.3.4 Volume Change with Reaction 92
3.4 Expressing Concentrations in Terms Other Than
Conversion 105
3.5 Reactions with Phase Change 107
Summary 111
Questions and Problems 114
CD-ROM Material 123
Supplementary Reading 123
220
73
75
81
4 ISOTHERMAL REACTOR DESIGN 125
4.1 Design Structure for Isothermal Reactors 125
4.2 Scaie-Up of Uquid-Phase Batch Reactor Data to the Design
ofaCSTR 129
4.2.1 Batch Operation 129
4.2.2 Design ofCSTRs 137
4.3 Tubular Reactors 147
4.4 Pressure Drop in Reactors 153

4.4.1 Pressure Drop and the Rate Law 153
4.4.2 Flaw Tlirough a Packed Bed 154
4.4.3 Spherical Packed-Bed Reactors 168
4.4.4 Pressure Drop in Pipes 173
4.5 Synthesizing a Chemical Plant 174
4.6 Using
Cfi^
(liquid) and F^ (gas) in the Mole Balances
and Rate Laws 176
4.6.1 CSTRs, PFRs, PBRs, mdBatch Reactors 111
4.6.2 Membrane Reactors 182
4.7 Unsteady-State Operation of Reactors 187
Contents
4.7.1 Startup of a CSTR 189
4.7.2 Semibatch Reactors 190
4.7.3 Reactive Distillation 197
4,8 Recycle Reactors 200
Summary 202
ODE Solver Algorithm 204
Questions and Probiems 205
Journal Critique Problems 219
Some Thoughts on Critiquing What You Read
CD-ROM Material 220
Supplementary Reading 222
5 COLLECTION AND ANALYSIS OF RATE DATA
5.1 Batch Reactor Data 224
5.1.1 Differential Method of Rate Analysis 224
5.1.2 Integral Method . 235
5.2 Melliod of Initial Rates 239
5.3 Method of Half-Lives 242

5.4 Differential Reactors 243
5.5 Least-Square Analysis 2S0
5.5.1 Linearization of the Rate Law 250
5.5.2 Nonlinear Least-Squares Analysis 252
5.5.3 Weighted Least-Squares Analysis 261
5.6 Experimental Planning (CD-ROM) 262
5.7 Evaluation of Laboratory Reactors (CD-ROM) 263
5.7.1 Integral (Fixed-Bed) Reactor 264
5.7.2 Stirred Batch Reactor 264
5.7.3 Stirred Contained Reactor (SCSR) 265
5.7.4 Continuous-Stirred Tank Reactor (CSTR) 265
5.7.5 Straight-Through Transport Reactor 266
5.7.6 Recirculating Transport Reactor 266
5.7.7 Summary of Reactor Ratings 267
Summary 26S
Questions and Problems 269
Journal Critique Problems 279
CD-ROM Material 280
Supplementary Reading 280
223
6 MULTIPLE REACTIONS
282
6.1 Maximizing the Desired Product in Parallel Reactions
6.1.1 Maximizing the Rate Selectivity Parameter S
for One Reactant 285
6.1.2 Maximizing the Rate Selectivity Parameter S
for Two Reactants 288
284
Contents
Contents

6.2 Maximizing the Desired Product in Series Reactions 291
6.3 Algorithm for Solution to Complex Reactions 295
6.3.1 Mole Balances 295
6.3.2 Net Rates of Reaction 296
6.3.3 Rate Laws 297
6.3.4 Stoichiometry: Relative Rates of Reaction 297
6.3.5 Stoichiometry: Concentrations 300
6.3.6 Combining Step 301
6.3.7 Multiple Reactions in a CSTR 307
6.4 Sorting It All Out 314
6.5 The Fun Part 315
6.6 The Attainable Region CD-ROM 316
Summary 318
Questions and Problems 320
Journal Critique Problems 335
CD-ROM Material 335
Supplementary Reading 336
7
NONELEMENTARY REACTION KINETICS
7.5.8 Oxygen-Limited Gennentation
7.5.9 Scale-up 407
Summary 408
Questions and Problems 410
CD-ROM Material 423
Journal Critique Problems 424
Supplemental^ Reading 424
S
STEADY-STATE NONISOTHERMAL REACTOR DESIGN
407
426

339
7.1
7.2
7.3
7.4
7.5
Fundamentals 340
7.I.! Active Intermediates 340
7.1.2 Pseudo-Steady-State Hypothesis (PSSH) 342
Searching for a Mechanism 344
7.2.1 General Considerations 344
7.2.2 Reaction Pathways 352
Polymerization 354
7.3.1 Step Polymerization 356
Chain Polymerizations Reactions 360
Modeling a Batch Polymerization Reactor 368
Molecular
Weight
Distribution 370
Anionic Polymerization 375
Enzymatic Reaction Fundamentals 383
7.4.1 Definitions and Mechanisms 383
Michaelis-Menten Equation 386
Batch Reactor Calculations 389
Inhibition of Enzyme Reactions 391
Multiple Enzyme and Substrate Systems 392
Bioreactors 393
7.5.1 Cell Growth 394
7.5.2 Rate Laws 396
7.5.3 Stoichiometry 398

7.5.4 Mass Balances 400
7.5.5 Chemostats 404
7.5.6 Design Equations 404
7.5.7 Wash-out 406
7.3.2
7.3.3
7.3.4
7.3.5
7.4.2
7.4.3
7.4.4
7.4.5
8.1 Rationale 426
8.2 The Energy Balance
427
8.2.1 First Law Thennodynamics 427
5.2.2 Evaluating the Work Term 429
8.2.3 Dissecting the Steady-State Molar Flow Rates
to Obtain the Heal of Reaction 430
8.2.4 Dissecting the Enthalpies 432
8.2.5
Relating
SHR^CF),
m°^, and hCp 434
8.2.6 Constant of Mean Heat Capacities 435
B.2.7 Variable Heat Capacities 436
8.2.8 Heat Added to the Reactor Q 438
8.3 Nonisothermal Continuous-Fiow Reactors 440
8.3.1 Application to the CSTR 441
8.3.2 Adiabatic Tubular Reactor 451

8.3.3 Steady-State Tubular Reactor
with Heat Exchange 458
8.4 Equilibrium Conversion 468
8.4.1 Adiabatic Temperature and Equilibrium
Conversion 468
8.4.2 Optimum Feed Temperature 476
8.5 Nonadiabatic Reactor Operation: Oxidation of Sulfur
Dioxide Example 478
8.5.1 Manufacture of Sulfuric Acid 478
8.5.2 Catalyst Quantities 481
8.5.3 Reactor Configuration 482
8.5.4 Operating Conditions 482
8.6 Multiple Steady States 490
8.6.1 Heat-Removed
Term.
R(T) 491
8.6.2 Heat of Generation, G{T) 492
8.6.3 Ignition-Extinction Curve 493
8.6.4 Runaway Reactions 497
8.6.5 Steady-State Bifurcation Analysis 498
5.7 Nonisothermal Multiple Chemical Reactions 500
8.7.1 Plug-Flow Reactors 500
8.7.2 CSTR 504
Summary 507
Contents
Questions and Probiems 511
Journal Cdtique Problems 530
CD-ROM Material 530
Supplementary Reading 532
9

UNSTEADY-STATE NONISOTHERMAL REACTOR DESIGN
534
9.1
9.2
9.3
9.4
9.5
9.6
The General Equation 534
Unsteady Operation of CSTRs and Semibatch Reactors 535
9.2.1 Batch Reactors 537
9.2.2 Adiabatic Operation of a Batch Reactor 537
9.2.3 Transient CSTR, Batch, and Semibatch Reactors
with Heat Exchanger—Ambient Temperature Not
Spatially Uniform 548
Approach to the Steady State 553
Control of Chemical Reactors 558
9.4.1 Falling Off the Steady State 558
9.4.2 Adding a Controller to a CSTR
Nonisothermal Multiple Reactions 566
Unsteady Operation of Plug-Flow Reactors
Summary 571
Questions and Problems 572
CD-ROM Material 579
Supplementary Reading 579
561
570
10
CATALYSIS
AND

CATALYTIC REACTORS
10.1 Catalysts 581
10.1.1 Definitions 582
10.1.2 Catalyst Properties 583
10.2 Steps in a Catalytic Reaction 591
10.2.1 Adsorption Isotherms 594
10.2.2 Surface Reaction 599
10.2.3 Desorption 601
10.2.4 The Rate-Limiting Step 601
10.3 Synthesizing a Rate Law, Mechanism,
and Rate-Limiting Step 603
10.3.1 Is the Adsorption of Cumene Rate-Limiting? 606
10.3.2 Is the Surface Reaction Rate-Limiting? 609
10.3.3 Is the Desorption of Benzene Rate-Limiting? 610
10.3.4 Summary of the Cumene Decomposition 612
10.3.5 Rate Laws Derived from the Pseudo-Steady-State
Hypothesis 616
10.4 Design of Reactors for Gas-SoUd Reactions 619
10.4.1 Basic Guidelines 619
10.4.2 The Design Equations 619
581
Contents
xm
10.5 Heterogeneous Data Analysis for Reactor Design 620
10.5.1 Deducing a Rate Law
from the Experimental Data 622
10.5.2 Finding a
Mechanism.
Consistent
with Experimental Observations 623

10.5.3 Evaluation of the Rate Law Parameters 624
10.5.4 Reactor Design 627
10.6 Chemical Vapor Deposition 631
10.7 Catalyst Deactivation 634
10.7.1 Types of Catalyst Deactivation 636
10.7.2 Temperature-Time Trajectories 647
10.7.3 Moving-Bed Reactors 649
10.7.4 Straight-Through Transport Reactors 655
10.7.5 Determining the Order of Deactivation 660
10.8 Reaction Engineering in Microelectronic
Device Fabrication 662
I0.8.I Etching 664
Summary 665
Questions and Problems 668
Journal Critique Problems 682
CD-ROM Material 683
Supplementary Reading 684
11
EXTERNAL DIFFUSION EFFECTS
ON
HETEROGENEOUS REACTIONS
686
11.1 Mass Transfer Fundamentals 687
11.1.1 Definitions 687
11.1.2 MolarFlux 687
11.1.3 Pick's First Law 688
11.2 Binary Diffusion 689
11.2.1 Evaluating the Molar Flux 689
11.2.2 Boundary Conditions 692
11.2.3 Modeling Diffusion Without Reaction 692

11.2.4 Temperature and Pressure Dependence
ofD^^ 691
11.2.5 Modeling Diffusion with Chemical Reaction
11.3 External Resistance to Mass Transfer 699
11.3.1 Mass Transfer Coefficient 699
11.3.2 Mass Transfer to a Single Particle 702
11.3.3 Mass Transfer-Limited Reactions
in Packed Beds 706
11.3.4 Mass Transfer-Limited Reaction
on Metallic Surfaces 714
11.4 What If ? (Parameter Sensitivity) 715
11.5 The Shrinking Core Model 719
698
Contents
n.5.1 Catalyst Regeneration 720
11.5.2 Dissolution of Monodispersed Solid Particles
11.5.3 Flow and Dissolution in Porous Media 726
Summary 728
Questions and Problems 729
Journal Article Problem 735
Journal Critique Problems 735
CD-ROM Materia! 735
Supplementary Reading 736
724
12
DIFFUSION AND REACTION
IN
POROUS CATALYSTS
738
12.1 Diffusion and Reaction in Spherical Catalyst Pellets 739

12.1.1 Effective Diffusivity 739
12.1.2 Derivation of
the
Differential Equation Describing
Diffusion and Reaction 741
12.1.3 Writing the Equation in Dimensionless Form 743
12.1.4 Solution to the Differential Equation
for a First-Order Reaction 746
12.2 Internal Effectiveness Factor 747
12.3 Falsified Kinetics 753
12.4 Overall Effectiveness Factor 755
12.5 Estimation of Diffusion- and Reaction-Limited
Regimes 758
12.5.1 Weisz-Prater Criterion for Internal Diffusion 758
12.6 Mass Transfer and Reaction in a Packed Bed 761
12.7 Determination of Limiting Situations
from Reaction Data 767
12.8 Multiphase Reactors 768
12.8.1 Slurry Reactors 769
12.8.2 Trickle Bed Reactors 783
12.9 FIuidized-Bed ReactorSoj.KOM
786
12.10 The Overall View 787
12.11 Chemical Vapor Deposition Reactors 789
Summary 793
795
804
805
Questions and Problems
Journal Article Problems

Journal Critique Problems
CD-ROM Material 805
Supplementary Reading 806
13 DISTRIBUTIONS OF RESIDENCE TIMES
FOR
CHEMICAL REACTORS
809
13.1 Genera! Characteristics 809
13.LI Residence-Time Distribution Function 811
•r
Contents
XV
13.2 Measurement of the RTD 812
13.2.1 Pulse Input 813
13.2.2 Step Tracer Experiment 818
13.3 Characteristics of theRTD 819
13.3.1 Integral Relationships 819
13.3.2 Mean Residence Time 821
13.3.3 Other Moments of the RTD 823
13.3.4 Normalized RTD Function, Ex 825
13.3.5 Internal-Age Distribution la 826
13.4 RTD in Ideal Reactors 829
13.4.1 RTDs in Batch and Plug-Flaw Reactors
13.4.2 Single-CSTR RTD 829
13.4.3 Laminar Flow Reactor 831
13.4.4 PFR/CSTR Series RTD 833
13.5 Reactor Modeling with the RTD 836
13.6 Zero-Parameter Models 838
13.6.1 Segregation Model 838
13.6.2 Maximum Mixedness 844

13.6.3 Heat Effects 851
13.7 Using Software Packages 8S1
13.8 RTD and Multiple Reactions 854
13.8.1 Segregation Model 854
13.8.2 Maximum Mixedness 855
Summary 860
Questions and Problems 861
CD-ROM Material 868
Supplementary Reading 869
829
14
MODELS
FOR
NONIDEAL REACTORS
871
14.1
14.2
14.3
Some Guidelines 871
One-Parameter Models 872
14.2.1 Tmks-in-Series Model 873
14.2.2 Dispersion Model 877
Two-Parameter Models—Modeling Real Reactors with Combi-
nations of Ideal Reactors 893
14.3.1 Real CSTR Modeled Using Bypassing
and Dead Space 893
Solving the Model System for
Cj^
and X 894
Using a Tracer to Determine the Model Parameters

in CSTR-with-Dead-Space-and'Bypass
Model 895
Real CSTR Modeled with an Exchange
Volume 899
Solving the Model System for C^ and X 900
14.3.1 A
14.3.1B
14.3.2
14.3.2A
XV!
14.4
14.5
!4.6
Contents
14.3.2B Using a Tracer to Determine the Model Parameters
in a CSTR with an Exchange Volume 900
Use of Software Packages to Determine the Model
Parameters 901
Other Models of Nonideal Reactors Using CSTRs
and FFRs 904
Using the RTD Versus Needing a Model 904
Summaiy 907
Questions and Problems 9Q9
CD-ROM Material 916
Supplementary Reading 917
Appendix A NUMERICAL TECHNIQUES
A. 1 Useful Integrals in Reactor Design 921
A.2 Equal-Area Graphical Differentiation 922
A.3 Solutions to Differential Equations 924
A.4 Numerical Evaluation of Integrals 924

A.5 Software Packages 926
Appendix B IDEAL GAS
CONSTANT
AND
CONVERSION FACTORS
Appendix C
THERMODYNAMIC RELATIONSHIPS INVOLVING
THE
EQUILIBRIUM CONSTANT
Appendix D
MEASUREMENT
OF
SLOPES
ON
SEMILOG PAPER
Appendix E
SOFTWARE PACKAGES
Appendix F NOMENCLATURE
Appendix G
MOLECULAR DYNAMICS
OF
CHEMICAL REACTIONS
G. 1 CoUision Theory 941
G.2 Transition State Theory 944
G-3 Moleculai- Dynamics 948
Appendix H
OPEN-ENDED PROBLEMS
H.
1
Design of Reaction Engineering Experiment

H.2 Effective Lubricant Design 953
H:3 Peach Bottom Nuclear Reactor 953
953
921
927
929
935
936
938
941
953
Appendix I
Appendix J
Contenfs
H.4 Underground Wet Oxidation 954
H.5 Hydrosuifurization Reactor Design 954
H.6 Continuous Bioprocessing 954
H.7 Methanol Synthesis 954
H.8 Cajun Seafood Gumbo 954
HOW TO USE THE CD-ROM
USE OF COMPUTATIONAL CHEMISTRY SOFTWARE
PACKAGES
XV([
INDEX
ABOUT THE CD
956
958
961
976
Preface

"The man who has ceased to learn ought not to be
allowed to wander around loose in these danger-
ous days."
M. M. Coady
(ca. 1870)
A. The Audience
This book is intended for use as both an undergraduate- and graduate-level text in
chemical reaction engineering. The level of difficulty will ctepend on the choice
of chapters to be covered and the type and degree of difhcully of problems
assigned. Most problems requiring significant numerical computations can be
solved with a personal computer using either POLYMATH or MATLAB.
B. The Goals
B.1,
To Develop a Fundamental Understanding
of Reaction Engineering
The first goal of this book is to enable the reader to develop a clear
understanding of the fundamentals of chemical reaction engineering. This goal
will be achieved by presenting a structure that allows the reader to solve reac-
tion engineering problems through reasoning rather than through memorization
and recall of numerous equations and the restrictions and conditions under
which each equation applies. To accomplish this, we use (1) conventional
problems that reinforce the student's understanding of the basic concepts and
principles (included at the end of each chapter); (2) problems whose solution
requires reading the literature, handbooks, or odier textbooks on chemical
engineering kinetics; and (3) problems that give swdents practice in problem
•T
XX
Preface
definition and alternative pathways to solutions. The algorithms presented in
die text for reactor design provide a framework through which one can develop

confidence through reasoning rather than memorization.
To give a reference point as to the level of understanding required in the
profession, a number of reaction engineering problems from the California
Board of Registration for Civil and Professional Engineers—Chemical Engi-
neering Examinations (PECEE) are included. Typically, each problem should
require approximately one-half hour to solve, Hints on how to work the Califor-
nia exam problems can be found in the Summary Notes and in the Tlioughts on
Problem Solving on the CD-ROM.
The second and third goals of
this
book are to increase the student's critical
thinking skills and creative thinking skills by presenting heuristics and problems
that encourage the student to practice these skills,
B.2. To Develop Critical Thinking Skills
Due to the rapid addition of new information and the advancement of sci-
ence and technology that occur almost daily, an engineer must constantly expand
his or her horizons beyond simply gathering infomaation and relying on the basic
engineering principles,
A number of homework problems have been included that are designed to
enhance critical thinking skills. Socratic questioning is at die heart of critical
thinking and a number of homework problems draw from R. W. Paul's six types
of Socratic questions:'
(1) Questions for clarification: Why do you say that? How does this
relate to our discussion?
(2) Questions that probe assumptions: What could we assume instead?
How can you verify or disprove that assumption?
(3) Questions that probe reasons and evidence: What would be an
example?
(4) Questions about viewpoints and perspectives: What would be an
alternative?

(5) Questions that probe implications and consequences: What generali-
zations can you make? What are the consequences of that assumption?
(6) Questions about the question: What was the point of this question?
Why do you think I asked this question?
Practice in critical thinking can be achieved by assigning additional parts to the
problems at the end of each chapter tiiat utilize R, W. Paul's approach. Most of
these problems have more than one part to them. The instructor may wish to
assign all or some of the parts. In addition, the instructor could add the following
parts to any of the problems:
• Describe how you went about solving this problem,
• How reasonable is each assumption you made in solving this problem?
' Paul, R. W., Critical Thinking (Published fay the Foundation for Critical Thinking,
Santa Rosa, CA, 1992).
Preface
XXI
• Ask another question or suggest another calculation that can be made
for this problem.
• Write a few sentences about what you learned from working this
homework problem and what you think the point of the problem is.
Anotiier important exercise in this text that fosters critical diinking is the
critiquing of journal articles. For the last 20 years, students in the graduate reac-
tion engineering class at the University of Michigan have been required to carry
out an in-depth critique of a journal article on chemical engineering kinetics.
Although the students were told that choosing an article with erroneous data or
reasoning was not necessary for a successful critique, finding an error made the
whole assignment much more fun and interesting. Consequently, a select number
of problems at the end of chapters involve the critique of journal articles on reac-
tion engineering which may or may not have major or minor inconsistencies, In
some cases, a small hint is given to guide the student in his or her analysis.
B.3. To Develop Creative Thinking Skills

To help develop creative Uiinking skills, a number of problems are
open-ended to various degrees. Beginning with Chapter 4, die first problem in
each chapter provides students the opportunity to practice their creative skills by
making up and solving an original problem. Problem 4-1 gives some guidehnes
for developing original problems. A number of techniques that can aid the stu-
dents in practicing their creativity (e.g., lateral thinking and brainstorming) can
be found in Fogler and LeBlanc.^
"What if " problems can serve to develop both critical and creative dunk-
ing skills. The second problem of each chapter (e.g., 4-2) contains "What if "
questions that encourage the student to think beyond a single answer or operating
condition. These problems can be used in conjunction with the living example
problems on die CD to explore die problem. Here, questioning can be carried out
by varying the parameters in die problems.
One of the major goals at the undergraduate level is to bring the students to
the point where they can solve complex reaction systems, such as multiple reac-
tions with heat effects, and then ask 'TVhat
if "
questions and look for opti-
mum operating conditions. One problem whose solution exemplifies this goal is
die Manufacture of Styrene, Problem 8-30-
(1) Ethyibenzene -> Styrene + Hydrogen: Endothermic
(2) Ethyibenzene -^ Benzene -i- Ediylene; Endothennic
(3) Ethyibenzene + Hydrogen -> Toltiene -i- Methane: Exothermic
In this problem, the students can find a number of operating conditions which
maximize the yield and selectivity.
The parameters can also be easily varied in the example problems by load-
ing die POLYMATH or MATLAB programs from the CD onto a computer to
explore and answer "What if " questions.
' Fogier, H, S. and S. E. LeBlanc, Strategies far
Creative Problem Solving

(Upper Sad-
dle River, NJ: Prentice Hall, 1995).
XXM
Preface Preface
XXI li
Margin Notes
C. The
Structure
The strategy behind the presentation of material is to continually build on a
few basic ideas in chemical reaction engineering to solve a wide variety of
problems. These ideas are referred to as the Pillars of Chemical Reaction
Engineering, on which different applications rest. The pillars holding up the
application of chemical reaction engineering ai'e shown in Figure P-1.
IMULTIPLEREACTJONSI
JMflSS TRanSFER OPERATiONS I
[NONISOT>ffiRMfll. OPERATION, WJLTIPLE BTEADY STATES |
IMOOEUNG REAL REACTORS, RTD. DISTCRSION. SESRECATION]
fettJAt-YSlB OF RATE DATA, LABORATORY REACTORS. LEAST-SQUARES ANALYSISl
jDESION OF CHEMICAL REACTORS, PFR. CSTR. BATCH. SEMIBATCH, PACKED BEDsl
^ ^ (TO
C=vP
^ ^S
ss.
Z=2.
rH
Figure P-1 Pillars of Chemical Reaction Engineering.
The architecture and construction of the structure shown in Figure P-1 had
many participants, most notably Professors Amundsen, Aris, Smith, Levenspiel,
and Denbigh. The contents of this book may be studied in virtually any order
after the fet four chapters, with few restrictions. A flow diagram showing possi-

ble paths is shown in Figure P-2.
In a three-hour undergraduate course at the University of Michigan, approx-
imately eight chapters are covered in the following order: Chapters 1, 2, 3, 4, and
6, Sections 5.1-5.3, and Chapters 8,10, and parts of either
7
or
13.
Complete sam-
ple syllabi for a 3-credit-hour course and a 4-credit-hour course can be found on
the CD-ROM.
The reader will observe that although metric units are used primarily in this
text (e.g., kmol/m^, J/mol), a variety of other units are also employed (e.g.,
Ib/ft^).
This is intentional. It is our feeling that whereas most papers published in
the future will use the metric system, today's engineers as well as those graduat-
ing over the next ten years will be caught in the transition between EngUsh, SI,
and metric units, As a resuit, engineers will be faced with extracting information
and reaction rate data from older Uterature which uses English units as well as the
current literature using metric units, and they should be equally at ease with both.
The notes in the margins are meant to serve two purposes. First, they act as
guides or as commentary as one reads through the material. Second, they identify
key equations and relationships that are used to solve chemical reaction engi-
neering problems.
Finally, in addition to developing the intellecmai skills discussed above,
this is a book for the professional
bookshelf.
It is a "how to" book with numerous
CH,1-MOLE BALANCES
i
CH.

3-CONVERSION
AND
REACTOR SIZING
i
CH.
3-RATE
LAWS AND
STOICHIOMETHV
i
CH.
4-ISOTHERMAL
REACTOR DESIGN
i
i
i
i
;
i I
CH,5
COLLECTION
AND
ANALYSIS OF
DATA
*->
CH.S
MULTIPLE
REACTIONS
«-+
CH,7
NONEt£MENTARY

HCM)GENEOUS
IHEACTimS
<->
CH,8
STEADY
STATE HEAT
EFFECTS
4~>
CH.tO
CATALYSIS
mo
CATALYTIC
REACTORS
<-*•
CH.t3
FIESIDENCE
TIME
DISTRIBUTION
i i i
CH.9
UNSTEADY
STATE HEAT
EFFECTS
CH.11
EXTERNAL
DIFFUSION
EFFECTS
CH.H
NONiDEAL
REACTORS

CH.9
UNSTEADY
STATE HEAT
EFFECTS
CH.11
EXTERNAL
DIFFUSION
EFFECTS
CH.H
NONiDEAL
REACTORS
"
i
SECTIONS
8.78 9,5
MULTIPLE
REACTIONS
WITH HEAT
cH.ia
DIFFUSION
!N POROUS
CATALYSTS
Figure P-2 Sequences for Studying the Text.
examples and clear explanations, rather than an outline of the principles and the
philosophy of chemical reaction engineering. There are many other applications
described in the text.
D. The Applications
Important applications of chemical reaction engineering (ORE) of all kinds can
be found both inside and outside the chemical process industries (CPI). In this
text, examples from the chemical process industries include the manufacture of

ethylene oxide, phthalic anhydride, ethylene glycol, metaxylene, styrene, sul-
fur trioxide, propylene glycol, ketene, and t-butane just to aame a few. Also,
plant safety in the CPI is addressed in both example problems and homework
problems. These are real industrial reactions with actual data and reaction rate
law parameters.
Because of the wide versatility of the principles of CRE, a number of
examples outside the CPI are included, such as the use of wetlands to degrade
toxic chemicals, smog formation, longevity of motor oils, oil recovery, and phar-
macokinetics (cobra bites, SADD-MADD, drug delivery). A samphng of the
applications is shown graphically in the following figures.
XXIV
Preface
I^^RVfJlMll
fPOuntT'ld
SmogCCh, l.Ch. 7)
Wetlands (Cti. 4)
i'liarmi'ctdiliictfcsyrCulim Bilis
[Body) Heatttte
CvoHiErmlc Rfdctlun^Thiii
Oil Recovery Cobra Bites (Ch. 6) Lubricant Design
PliinC
Sufety
(Ch.5) (Ch.7) (Ch,8&9)
Manufacture of Phttialic Anhydride {Ch. 3)
Chemical Piaat for Ethylene Glycol using Examples from Ch, 4
Preface
XXV
E. The Components of the CD-ROM
The primary purpose of the CD-ROM is to serve as an enrichment resource. Its
objectives are fourfold: (I)

To
provide the option/opportunity for further study or
clarification on a particular concept or topic through Summary Notes, additional
examples, interactive computing modules and web modules, (2) To provide the
opportunity to practice critical thinking skills, creative thinking skills, and prob-
lem solving skills through the use of "What
if "
questions and "living example
problems," (3) To provide additional technical material for the professional refer-
ence
shelf,
(4) To provide other tutorial information, such as additional home-
work problems, thoughts on problem solving, how to use computational software
in chemical reaction engineering, and representative course structures. The fol-
lowing components are listed atjhe end of most chapters and can be accessed, by
chapter, on the CD.
Learning Resources
These resources give an overview of the material in each chapter and
provide extra explanations, examples, and applications to reinforce
the basic concepts of chemical reaction engineering. The learning
resources on the CD-ROM include:
1.
Summary Nates
These are Summary Notes that will give an overview of each
chapter, and are taken from lecmre notes from an undergraduate
class at Michigan.
2.
Web Modules
These modules which apply key concepts to both standard and non-
standard reaction engineering problems (e.g., the use of wetlands

to degrade toxic chemicals, cobra bites) can be loaded directly from
the CD-ROM. Additional Web Modules are expected to be added
over the next several years, (
3.
Interactive Computer Modules
Students can use the corresponding Interactive Computer Modules
to review the important chapter concepts and then apply them to
real problems in
a
unique and entertaining fashion. The Murder
Mys-
tery module has long been a favorite with students across the nation,
4.
Solved Problems
A number of solved problems are presented along with prob-
lem-solving heuristics. Problem-solving strategies and additional
worked example problems are available in the Thoughts on
Problem Solving section of the CD-ROM.
Living Example Problems
A copy of POLYMATH is provided on the CD-ROM for the students
to use to solve the homework problems. The example problems that
use an ODE solver (e.g., POLYMATH) are referred to as "living exam-
ple problems" because the students can load the POLYMATH program
directly onto their own computer in order to study the problem. Stu-
xxvi
Preface
dents are encouraged to change pai-ameler values and to "play with"
the key variables and assumptions. Using the living example problems
to explore the problem and asking "What
if "

questions provides the
opportunity to practice critical and creative thinking skills.
Professional Reference Shelf
This section of the CD-ROM contains:
1.
material that is important to the practicing engineer, although it is
typically not included in the majority of chemical reaction engi-
neering courses.
2.
material that gives a iTiore detailed explanation of derivations that
were abbreviated in the text. The intermediate steps to these der-
ivations are given on the CD-ROM.
' Additional Homework Problems
New problems were developed for this edition that provide a greater
opportunity to use today's computing power to solve realistic problems.
• Other CD-ROM Material
In addition to the components listed at the end of each chapter the
following components are included on the CD-ROM:
1.
Software ToolBox
Instructions on how to use the different software packages (POLY-
MATH, MATLAB, and ASPEN PLUS) to solve examples.
2.
Representative Syllabi for a 3- and a 4-Credit Course
The syllabi give a sample pace at v/hich the course could be
taught as well as suggested homework problems.
3.
FAQ
These are Frequently Asked Questions (FAQ's) from undergradu-
ate stadeuts taking reation engineering,

• Virtual Reality Module (WWW)
This module provides an opportunity to move inside a catalyst pellet
to observe surface reactions and coking. It can be found at

Preface xxvii
F. The Integration of the Text and the CD-ROM
There are a number of ways one can use the CD in conjunction with the text. The
CD provides enrichment resouives for the reader in the form of interactive tutori-
a!s. Pathways on how to use the materials to learn chemical reaction engineering
are shown in Figure P-3 and
P-4.
The keys to the CRE learning flowsheets are
Primary resources
( CD 1 = Enrichment resources
F.I. For the University Student
In developing a fundamental understanding of the material, the student
may wish to use only the primary resources wiUiout using the CD-ROM, (i.e
using only the boxes shown in Figure P-3) or the smdent may use a few or ail
of the interacdve tutorials in the CD-ROM (i.e., the circles shown in Figure
P-3).
However, to practice die skills that enhance cridcal and creative diinking,
the students are strongly encouraged to use the Living Example Problems and
vary tlie model parameters to ask and answer "What
if "
questions.
Start
Figure P-3 A Student Patliway to Iniegraie ihe Class Text and CD.
•r
Pfaface
Start

•
Homework
Problems
figure P-4 A Problem-Solving Pathway to IniegraCe the text and the CD,
One notes that while the author recommends studying the living examples before
working home problems, they may be bypassed, as is the case with all the enrich-
ment resources if time is not available. However, class tesdng of the enrichment
resources reveals that they not only greatly aid in learning the material but they
may also serve to motivate students through the novel use of CRE principles.
F.2, For the Practicing Engineer
Practicing engineers may want to first review the CD summary notes or
the summaries at the end of each chapter to refresh their memories as to what
they have previously studied. They can then focus on the topics that they want
to study in the text using the web modules, solved problems, and interactive
computer modules as tutorials. They can also learn more about specialty topics
by using the CD reference
sheif.
The flow diagram is shown in Figure P-4.
G, The Web
The Web site (ch,edu/ cre) will be used to update the text
and the CD-ROM. It will identify typographical and otiier errors in the 3st and
2nd piintings of the 3rd edition of the text. In the neai" future, additiofia! mate-
rial will be added to include more solved problems as well as additional Web
Modules.
Preface
H. What's New
XXIX
The main thrust of the new edition is to enable the student to solve Digital
Age'^ reacdon engineering problems, Consequendy the content, example prob-
lems,

and homework problems focus on achieving this goal. These problems
provide the students an opportunity to pracdce their critical and creative think-
ing skills by "playing with" the problems through parameter variations. Conse-
quently, some of the text material, e.g., control of chemical reactors and safety,
was added because it provides opportunities to formulate and solve problems.
For example, in the Case Study on safety, the shident can use the CD-ROM to
cany out a post-mortem on the nitroanaline explosion in Example 9-2 to find
out what would have happened if the cooling h^ failed for 5 minutes instead
of 10 minutes. Significant effort has been devoted to developing example and
homework problems that foster critical and creative thinking.
The use of mole balances in terms of concentrations and flow rates rather
than conversions is introduced early in the text so diey can be easily applied to
membrane reactors and multiple reactions. The 3rd edition contains more
industrial chemistry with real reactors and real reactions and extends the wide
range of applications to which chemical reaction engineering principles can he
applied (i.e„ cobra bites, drug medication, ecological engineering). New mate-
rial includes spherical reactors, recycle reactors, trickle bed reactors, fluidized
bed reactors, regression of rate data, etching of semiconductors, multiple reac-
tions in RTD models, the application of process control to CSTRs, safety, col-
lision theory, transition state theory, and an- example using computational
chemistry to calculate an activation energy. The material that has been greatly
expanded includes polymerization, heat effects in batch reactors and in multi-
ple reactions, catalysts and catalytic reactions, experimental design, and reactor
staging. The living example problems on the CD-ROM are in both POLY-
MATH and MATLAB.
A large number of enrichment resources are provided on the CD-ROM
that can help the student over difficult spots. However, if there is a time con-
straint, or the reader's computer breaks down, the reader need only read the
text and proceed along the patiiway of the boxes shown in Figures P-3 and P-4,
I. Acknowledgments

Many of tlie problems at the end of the various chapters were selected from the
California Board of Registration for Civil and Professional Engineers—Chem-
ical Engineering Examinations (PECEE) in past years. The permission for use
of these problems, which, incidentally, may be obtained from the Documents
Section, California Board of Registration for Civil and Professional Engineers—
Chemical Engineering, 1004 6th Street, Sacramento, CA 95S14, is gratefully
acknowledged. (Note: These problems have been copyrighted by the California
Board of Registration and may not be reproduced without their permission.)
^
Fogler, H. S.,
"Teaching Critical
Tliiniiing,
Creative
Tliiiiking.
and
Problem Solving
in
the
Digital
Age"
(Phillips Lecture, Oklahoma State University Press, April 25, 1997),
XXX
Preface
However, all intensive laws tend often to have exceptions. Very interesting con-
cepts take orderly, responsible statements. Virtually ali laws intrinsically are nat-
ural thoughts. General observations become laws under experimentation.
There are so many colleagues and students who contributed to this book
that it would require another chapter to thank them all in an appropriate manner.
I would like to again acknowledge all my friends and colleagues for their
contributions to the 1st and 2nd editions (See Introduction, CD-ROM), For the

3rd edition, I would like to give special recognition to the students who con-
tributed so much to the CD-ROM: In particular". Dieter Schweiss, Anuj Hasija,
Jim Piana, and Susan Fugett, with thanks also to Anurag Murial, Gavin Sy,
Scott Conaway, Mayur Valanju, Matt Robinson, Tim Mashue, Lisa Ingalls, Sean
Conners, Gustavo Boiaiios, and EUyne Buckingham. Further, Tim Hubbard,
Jessica Hamman, David Johnson, Kylas Subramanian, Sumate Charoenchaidet,
Lisa Ingalls, Probjot Singh, Abe Sendijarevic, and Nicholas R. Abu-Absi
worked on the solution manual. Jason Ferns, Rob Drewitt, and Probjot Singh
contributed to the problems, while Professor Andy Hrymak, Probjot Singh,
Marty Johnson, Sumate Charoenchaidet, N. Vijay, and K. Subramanxan helped
with proofreading the galleys. Thanks to my graduate students Venkat Ram-
achandran, Chris Fredd, Dong Kim, Barry
Wolf,
Probjot Singh, Vaibhav Nal-
waya, and Ann Wattana for their patience and understanding. Barbara Zieder
(copy-editing), Lisa Garboski (production), andYvette Raven (CD-ROM) did
an excellent job in bringing the project to a successful completion. Bernard
Goodwin of Prentice Hall was extremely helpful and supportive throughout.
The stimulating discussions with Professors John Falconer, D. B. Battacharia,
Richard Braatz, Kristi Anseth, and Al Weimer are greatly appreciated. I also
appreciate the friendship and insights provided by Dr. Lee Brown, who contrib-
uted to chapters 8, 12, 13, and 14. Professor Mike Cutlip gave not only sug-
gestions and a critical reading of many sections, but most important provided
continuous support and encouragement throughout the course of this project.
Laura Bracken is so much a part of this manuscript through her excellent deci-
phering of equations and scribbles, and typing, her organization, and always
present wonderful disposition. Thanks Radar]! Finally, to my wife Janet, love
and thanks. Without her enormous help and support the project would not have
been possible.
HSF

Ann Arbor
Elements
of Chemical
Reaction
Engineering
Third
Edition
For updates on the CD and typographical errors for this printing see the web site;

Mole Balances ^
The first step to knowledge
is to know that we are ignorant.
Socrates (470-399 B,c.)
Chemical kinetics and reactor design are at the heart of producing almost all
industrial chemicals. It is prhnariiy a knowledge of chemical kinetics and reac-
tor design that distinguishes the chemical engineer from other engineers. The
selection of a reaction system that operates in the safest and most efficient
manner can be the key to the economic success or failure of a chemical plant.
For example, if a reaction system produced a large amount of undesirable
product, subsequent purification and separation of the desired product could
make the entire process economically unfeasible. The chemical kinetic princi-
ples learned here, in addition to the production of chemicals, can be applied in
areas such as living systems, waste treatment, and air and water pollution.
Some of the examples and problems used to illustrate the principles of chemi-
cal reaction engineering are: the use of wetlands to remove toxic chemicals
from rivers, increasing the octane number of gasoline, the production of anti-
freeze starting from ethane, the manufacture of computer chips, and the appli-
cation of enzyme kinetics to improve an artificial kidney.
This book focuses on a variety of chemical reaction engineering topics.
It is concerned with the rate at which chemical reactions take place, together

with the mechanism and rate-Umiting steps that control the reaction process.
The sizing of chemical reactors to achieve production goals is an important
segment. How materials behave within reactors, both chemically and physi-
cally, is significant to the designer of a chemical process, as is how the data
from chemical reactors should be recorded, processed, and interpreted.
Before entering into discussions of the conditions that affect chemical
reaction rates and reactor design, it is necessary to account for the various
chemical species entering and leaving a reaction system. This accounting pro-
cess is achieved through overall mole balances on individual species m the

Mote Balances Chap. 1
Sec.
1.1 Definition of the Rale of Reaction, -r^
nicotine
reacting system. In this chapter we develop a general mole balance that can be
applied to any species (usually a chemical compound) entering, leaving, and/or
remaining within the reaction system volume, After defining the rate of reac-
tion, -r^, iuid discussing the earlier difficulties of properly defining the chem-
ical reaction rate, in this chapter we show how the general balance equation
may be used to develop a preliminary form of the design equations of the most
common industrial reactors: batch, continuous-stirred tank (CSTR), and tubu-
lar. In developing these equations, the assumptions pertaining to the modeling
of each type of reactor are deUneated. Finally, a brief summary and series of
short review questions are given at the end of the chapter.
1.1 Definition of the Rate of Reaction, -0\
We begin our study by performing mole balances on each chemical species in
the system. Here, the tenn chemical species refers to any chemical compound
or element with a given identity. The identity of a chemical species is deter-
mined by the
kind,

number, and configuration of that species' atoms. For
example, the species nicotine (a bad tobacco alkaloid) is made up of a fixed
number of specific elements in a definite molecular arrangement or configura-
tion. The strucmre shown illustrates the kind, number, and configuration of the
species nicotine (responsible for "nicotine fits") on a molecular level.
Even though two chenaical compounds have exactly the same number of
atoms of each element, they could still be different species because of different
configurations. For example, 2-butene has four carbon atoms and eight hydro-
gen atoms; however, the atoms in this compound can form two different
arrangements.
When has a
chemical reaction
taken place?
H H
>=<
CH3 CH3
cw~2-buiene
and
H CH3
CHs H
trans-2-hatsne
As a consequence of the different configurations, tliese two isomers display
different chemical and physical properties. Therefore, we consider them as two
different species even though each has the same number of atoms of each
element.
We say that a chemical
reaction
has taken place when a detectable num-
ber of molecules of one or more species have lost their identity and assumed a
new form by a change in the kind or number of atoms in the compound and/or

by a change in structure or configuration of diese atoms. In this classical
approach to chemical change, it is assumed that the total mass is neither cre-
ated nor destroyed when a chemical reaction occurs. The mass refeixed to is
the total collective mass of all the different species in the system. However,
when considering the individual species involved in a particular reaction, we
do speak of the rate of disappearance of mass of a particular species. The rate
of disappearance of a species, say species A, is the number of A molecules that
A species can lose
its identity by
decomposition,
combination,
or isomerizacion
What is
-TA?
r.'?
lose their chemical identity per unit time per unit volume through the breaking
and subsequent re-forming of chemical bonds during the course of the reac-
tion. In order for a particular species to "appear" in the system, some pre-
scribed fraction of anodier species must lose its chemical identity.
There are three basic ways a species may lose its chemical identity. One
way is by decomposition, in which a molecule is broken down into smaller
molecules, atoms, or atom fragments. For example, if benzene and propylene
are formed from a cumene molecule,
CH(CH3)2
+ C3H,
cvimene benzene propylene
the cumene molecule has lost its identity (i.e., disappeared) by breaking its
bonds to form these molecules. A second way that a molecule may lose its spe-
cies identity is through combination with another molecule or atom. In the
example above, the propylene molecule would lose its species identity if the

reaction were carried out in the reverse direction so that it combined with ben-
zene to form cumene.
The thkd way a species may lose its identity is through isomerization,
such as the reaction
CH.
CH2=;C—CH2CH3
CH,
CH,C=CHCH,
Here, although the molecule neither adds other molecules to itself nor breaks
into smaller molecules, it still loses its identity through a change in configura-
tion.
To summarize this point, we say that a given number of molecules (e.g.,
mole) of a particular chemical species have reacted or disappeared when the
molecules have lost their chemical identity.
The rate at which a given chemical reaction proceeds can be expressed in
several ways. It can be expressed either as the rate of disappearance of reac-
tants or the rate of formation of products. For example, the insecticide DDT
(dichlorodiphenylttichloroethane) is produced from chlorobenzene and chloral
in the presence of filming sulfuric acid.
2C6H5CI + CCI3CHO
-> (QH4Cl)2CHCCl3 + HjO
Letting the symbol A represent the chemical chloral, the numerical value of the
rate of reaction, —r^, is defined
2&
the number of moles of
chloral
reacting
(disappearing)
per unit time per unit volume (mol/dm^
•

s).
In the next chapter
we delineate the prescribed relationship between the rate of formation of one
4 Mole Balances Chap. 1
species, r,- (e.g., DDT), and the rate of disappearance of another species, -r,
(e.g., chiorobenzene), in a chemical reaction.
In heterogeneous reaction systems, the rate of reacEion is usually
expressed in measures other than volume, such as reaction surface area or cat-
alyst weight. Thus for a gas~solid catalytic reaction, the dimensions of tliis
rate,

r!^,
are the number of moles of A reacted per unit time per unit mass of
catalyst (mol/s-g catalyst). Most of die introductory discussions on chemicai
reaction engineering in this book focus on homogeneous systems.
The mathematical definition of a chemical reaction rate has been a source
of confusion in chemical and chemical engineering literature for many years.
The origin of this confusion stems from laboratory bench-scale experiments
that were carried out to obtain chemical reaction rate data. These eaiiy experi-
ments were batch-type, in which the reaction vessel was closed and rigid; con-
sequently, the ensuing reaction took place at constant volume. The reactants
were mixed together at time t = 0 and the concentration of one of the reac-
tants,
C^, was measured at various times t. The rate of reaction was deter-
mined from the slope of a plot of C^ as a function of time. Letting r^ be the
rate of formation of A per unit volume (e.g., g mol/s-dm^), the investigators
then defined and reported the chemical reaction rate as
Sec.
1,1
dt

(i'i)
However, this definition was for a constant-volume batch reactor.
As a resuU of the limitations and restrictions given, Equation (1-1) is a
rather limited and confusing definition of die chemical reaction rate. For
amplification of this point, consider the following steady-flow system in which
the saponification of ethyl acetate is carried out.
Example 1-1 Is Sodium Hydroxide Reacting?
Sodium hydroxide and ethyl acetate are continuously fed to a rapidly stirred tank in
which they react to form sodium acetate and ethanol:
KaOH + CH^COOCH, -^ CH.COONa + CH.OH
(Figure El-1,1). The product stream, containing sodium acetate and etiianol,
together with the unreacted sodium hydroxide and ethyl acetate, is continuously
withdrawn from the tank at a rate equal to the total feed rate. The contents of the
tank in which this reaction is taking place may be considered to be perfectly mixed.
Because the system is operated at steady state, if we were to withdraw liquid sam-
ples at some location in the tank at various times and analyze them chemically, we
would find that the concentrations of the individual species in the different samples
were identical That is, the concentration of the sample taken at 1
P.M.
is the same
as that of the sample taken at 3
P.M.
Because the species concentrations are constant
and therefore do not change with time,
dC.
Definition of
r
What is -r^
a function of?
Definition of the Rate of Reaction, -r^

NoOH
-CHaCOOCjHg
CeHgOH.
CHjCOONa, ond
cto I ^-lunreacted
No OH ond
CHsCOOCgHa
Figure El-I.l Well mi-Ked reaction vessel.
where A ^ NaOH. Substitution of Equation (El-i.l) into Equation (i-I) leads to
'"A
= 0 (B1-L2)
which is incorrect because C^HjOH and CHaCOONa are being fomied from NaOH
and CHjCOOCjHj at a finite rate. Consequendy, the rate of reaction as defined by
Equation (M) cannot apply to a flow system and is incorrect if it is defined in this
manner.
By now you should be convinced that Equation (M) is not the definition
of the chemical reaction rate. We shall simply say that rj is the rate of forma-
tion of species j per unit volume. It is the number of moles of species j gener-
ated per unit volume per unit time. The rate equation for rj is solely a function
of the properties of the reacting materials [e.g., species concentration (i.e.
activities), temperature, pressure, or type of catalyst, if any] at a point in the
system and is independent of the type of system (i.e., batch or continuous
fiow) m which the reaction is carried out. However, since the properties of the
reacting materials can vary widi position in a chemical reactor, rj can in turn
be a function of position and can vary from point to point in the system.
The chemical reaction rate is an intensive quantity and depends on tem-
perature and concentration. The reaction rate equation (i.e., fiie rate law) is
essentially an algebraic equation involving concentration, not a differential
equation.' For example, the algebraic form of the rate law -r^ for the reaction
A > products

may be a Hnear function of concentration,
-r^ - kC^
or it may be some other algebraic fiinction of concentration, such as
0
(Ei-Li:
' For further elaboration on this point, see Chem. Eng. Set, 25, 337 (1970); B. L.
Crynes and H. S. Fogler, eds., AICliE Modular Instruction Series E: Kinetics. Vol 1
(New York: AIChE, 198!), p. i; and R. L. Kabel, "Rates," Chem. Eng. Commun., 9,
15 (1981). ^
The rate
law is an
algebraic equation
-r.
=
kCi
k,C,
Mole Balances Chap,
1
(1-2)
l+k^C.
For
a
given reaction.,
the
particular concentration dependence that
the
rate
law
follov/s (i.e., — r^
==

/cC^
or -r^^ =
iC^or
)
must be determined from exper-
imental observation. Equation (1-2) states that
the
rate
of
disappearance
of
A
is
equal
to
a rate constant
k
Umes
the square
of
the concentration
of
A.
By
conven-
tion,
t\ is
the rate
of
formation of A; consequently,

-TA
is the rate
of
disappear-
ance of A. Throughout this book the phrase rale of
generation
means exactly
the
same as the phrase
rate
offormation, and these phrases
are
used interchangeably.
1.2 The
General Mole Balance Equation
To perform
a
mole balance
on
any system,
the
system boundaries must first
be
specified.
The
volume 'enclosed
by
these boundaries will
be
referred

to as the
system
volume.
We shall perform
a
mole balance
on
species
j in a
system vol-
ume,
where species
j
represents
the
particular chemicai species
of
interest,
such
as
water
or
NaOH (Figure
1-1).
Mole balance
Figure
1-1
Balance
on
system volume.

A mole balance
on
species;
at
any instant
in
time,
i,
yields the following
equation:
rate
of
flow
of
j
into
the system
[(moles/time)
F,.
rate
of
generation
of
j by
chemical
reaction within
the system
(moles/time)
generation
G;

rate
of
flow
of j
out of
the system
(moles/dme)
out
rate of
accumulation
of
;•
within
the system
(moles/time)
accumulation
~df
(1-3)
where Nj represents
the
number
of
moles
of
species
j in the
system
at
time
/.

If all
the
system variables (e.g., temperature, catalytic activity, concentration
of
Sec,
1.2 The
Genera/ Mole Balance Equation
7
the chemical species)
are
spatially uniform diroughout
the
system volume,
the
rate
of
generation
of
species;',
G,-, is
just
the
product
of the
reaction volume,
V,
and the
rate
of
formation

of
species
j,
rj.
Gj
rrV
moles
time
moles
time
-
volume
volume
Suppose now that the rate
of
formation
of
species 7
for
the reaction varies
with the position
in the
system volume. That is,
it
has
a
value
rji at
location
1,

which
is
stuTounded
by a
small volume,
AVj,
within which
the
rate
is
uni-
form: similarly, the reaction rate has
a
value rj2
at
location
2
and an associated
volume, AV2 (Figure
1-2), The
rate
of
generation, AG^,,
in
terms
of ry, and
subvolume
AVi is
Figure
1-2

Dividing
up the
system volume
V.
AGj,
= rj, ^V,
Similar expressions
can be
written
for
AGj2
and the
other system subvolumes
AV;. The total rate
of
generation within
the
system volume
is the
sum
of all
the rates
of
generation
in
each
of
the subvolumes.
If
the total system volume

is
divided into
M
subvolumes,
die
total rate
of
generation
is
M
M
G;=X AGj,= 2 0/^^/'
1=1
i=i
By taking
the
appropriate limits (i.e.,
let
M -*
°=
and
A
V
^
0) and making
use
of
the
definition
of an

integral,
we can
rewrite
the
foregoing equation
in the
form
G,
rjdV
1
This is a basic
equation for
chemical reaction
engineering
-dNa
= -rAV
L
8 Mo:;
D-i.^ <:es
Chap, 1
From this equation we see that rj will be an indirect function of position, since
the properties of the reacting materials (e.g., concentration, temperature) can
have different values at different locations in the reactor
We now replace Gj in Equation (1-3),
Sec. 1.3 Batch Reactors
^jo
by its integral form to yield a form of the general mole balance equation for
any chemical species ; that is entering, leaving, reacting, and/or accumulating
within any system volume V
(1-4)

From this general mole balance equation we can develop the design equations
for the various types of industrial reactors: batch, semibatch, and continu-
ous-flow. Upon evaluation of these equations we can determine the time (batch)
or reactor volume (continuous-flow) necessary to convert a specified amount of
the reaclants to products.
1.3 Batch Reactors
A batch reactor has neither inflow nor outflow of reactaats or products while
the reaction is being carried out;
FJQ
ance on species / is
Fj = 0. The resulting general mole bal-
dNj
If
r:dV
dN:
=
rV
dt
If the reaction mixture is perfectiy mixed so tiiat there is no variation in the
rate of reaction throughout the reactor volume, we can take rj out of the inte-
gral and write the mole balance in the form
(1-5)
Figure 1-3 shows two different types of batch reactors used for gas-phase
reactions. Reactor A is a constant-volume (variable-pressure) reactor and Reac-
tor B is a constant-pressure (variable-volume) reactor. At time r = 0, the reac-
tants are injected mto the reactor and the reaction is initiated. To see clearly
the different forms the mole balance will take for each type of reactor, consider
the following examples, in which the gas-phase decomposition of dimethyl
ether is taking place to form methane, hydrogen, and carbon monoxide:
(CH3)20 -> CH4 -h H2 + CO

Figure 1-3 Batch reactors for
gas-phase
reactions.
Example
1-2
Constant Volume
or
Constant
Pressure:
Does
It
Make
a
Difference?
Write the moie balance for dimethyl ether in terms of the reactor volume, concen-
tration, and rate of formation of dimethyl ether for both a constant-pressure and a
constant-volume batch reactor.
Solution
To reduce the number of
subscripts,
we write the reaction symbolically as
A
>
M-HH
+ C
where A
is diraethyi ether,
M
is methane, H is hydrogen, and C is carbon monoxide.
For both batch reactors, the mole balance on A is

V dt
(1-5)
In writing the mole balance for dimethyl ether for
a
batch reactor, the only assump-
tion made is that there are no spatial variations m r^.
Constant-volume batch reactor. The reactor is perfectly mixed so that the
concentration of the reacting species is spatially uniform. Because the volume is
constant we can take
V inside
the differential and write the mole balance in terms of
the concenu-ation of
A:
ldNj^_d{N^/V) ^dC^
V dt dt
dt
(Ei-2.1)
Constant-pressure batch reactor. To write the mole balance for this reactor
in terms of concenuration, we again^use the fact that
^A^C.V
\dN^_\
d{C^V) dCj^^ Cf^dV
V dt
V
dt
dC^
r,=~
+
dt
dt

C/,d\nV
dt
(El-2.2)
(E3-2.3)
10
Mole Baiances Chap. 1 Sec. 1,4 Continuous-Flow Reactors
11
I The difference between equations (El-2.1) and (El-2.3) for the two different types
I of reactors is apparent.
1.4 Continuous-Flow Reactors
1.4.1 Continuous-Stirred Tank Reactor
A type of reactor used very commonly in iudustrial processing is a stin-ed
tank operated continuously (Figure 1-4). It
is
referred
to
as the
continuous-stirred
tank reactor (CSTR) or backmix
reactor.
The CSTR is normally run at steady
state and is usually operated so as to be quite well mixed. As
a
result of die latter
quality, the CSTR
is
generally modeled as having no spatial variations in concen-
tration, temperature, or reaction rate throughout
the
vessel. Since the temperature

and concentration are identical everywhere within the reaction vessel, they are
the same at the exit point as they are elsewhere in the tank, Thus the temperature
and concentration in the exit stream are modeled as being the same as those
inside the reactor. In systems where mixing is highly nonideal, the well-mixed
model is inadequate and we must resort to other modeling techniques, such as
residence-time distributions, to obtain meaningful
results.
This topic is discussed
in Chapters 13 and 14.
Reactants
Products
Figure 1-4 ConEinuous-stirred
tank
reactor.
When the general mole balance equation
dN-,
Fjo'Fj+l n^y-^
(1-4)
is applied to a CSTR operated at steady state (i.e., conditions do not change
with time),
dt
in which there are no spatial variations in the rate of reaction.
it takes the familiar form known as the design equation for a CSTR;
(1-6)
The CSTR design equation gives the reactor volume necessary to reduce
the entering flow rate of species,;,
FJQ,
to the exit flow rate
Fj.
We note that the

CSTR is modeled such that the conditions in the exit stream (e.g., concentra-
tion, temperature) are identical to those in the tank. The molar flow rate Fj is
just theproductof the concentration of species J and the volumetric flow rate u:
(1-7)
1.4.2 Tubular Reactor
In addition to the CSTR and batch reactors, another type of reactor com-
monly used in industry is the tubular
reactor.
It consists of a cylindrical pipe
and is normally operated at steady state, as is the CSTR. For the purposes of iiie
material presented here, we consider systems in which the flow is highly turbu-
lent and the flow field may be modeled by that of plug flow. That is, there is no
radial variation in concentration and the reactor is referred to as a plug-flow
reactor (PFR). (The laminar flow reactor is discussed in Chapter 13.)
In the tubular reactor, the reactants are continually consumed as they
flow down the length of the reactor. In modeling the mbular reactor, we
assume that the concentration varies continuously in the axial direction
through the reactor. Consequently, the reaction rate, which is a fimction of con-
centration for ail but zero-order reactions, will also vary axially. The general
mole balance equation is given by Equation (1-4):
i^;,
,.l>=^
(1-4)
To develop the PFR design equation we shall divide (conceptually) die reactor
into a number of subvolumes so that within each subvolume AV, the reaction
rate may be considered spatially uniform (Figure 1-5). We now focus our
attention on the subvolume that is located a distance y
firom
the entrance of the
reactor. We let Fj(y) represent the molar flow rate of species

;"
into volume AV
at y and Fj{y + Ay) the molar flow of species ; out of the volume at the loca-
tion (y -I- Ay). In a spatially uniform subvolume AV,
rj dV = Vrj
rjdV=rj^V
12
Mole Balances Char ••
PiFR
-H iy f—
i
-*-
Fi.
cxn
y+Ay
Fj{y)-
AV
F|(y+Ay)
Figare 1-5 Tubular reactor.
For a tubular reactor operated at steady state.
dNj
It"
0
Equation (1-4) becomes
F.(y) FJiy^^y)-^r:^V^O
(1-8)
In this expression
ry
is an indirect fimction ofy. That is, rj is a function of
reac-

tant concentration, which is a function of the position y down the reactor. The
volume A V is the product of the cross-sectional area A of the reactor and the
reactor length Aj.
i^V
=
A^y
We now substitute in Equation (1-8) for AV and then divide by Aj to obtain
>/y
+
Ay)-Fy(yy
= -Ar:
The term in brackets resembles the definition of the derivative
lim
fix
+
Ax)-fix)
AJC
dx
Taking the limit as Ay approaches zero, we obtain
or dividing by
—1,
we have
S = -Ar
dy "^'l
(1-9)
Sec. 1.4 Continuous-Flow Reactors
13
It is usually most convenient to have the reactor volume V rather than the
reactor length y as the independent variable. Accordingly, we shall change
variables using the relation dV ~ A dy to obtain one forai of the design equa-

tion for a tubular reactor:
djj
dV
(1-10)
We also note that for a reactor in which the cross-sectional area A varies along
the length of the reactor, the design equation remains unchanged. This equa-
tion can be generalized for the reactor shown in Figure 1-6, in a manner simi-
Figure 1-6
lar to that^presented above, by utilizing the volume coordinate
V
ratber tiaan a
linear coordinate
y.
After passing through volume
V,
species 7 enters subvolume
AV at volume Vat a molar flow rate F,(V). Species; leaves subvolume AV at
volume (V
-^
AV), at a molar flow rate F,-(V + AV). As before, AV is chosen
small enough so that there is no spatial variation of reaction rate within the
subvolume:
G.= ) r^dV^rjLV (Ml)
After accounting for steady-state operation in Equation (1-4), it is combined
with Equation (1-11) to yield
Rearranging gives
FjiV)-FjiV^
AV) + rj AV = 0
FjiV+AV)-Fj{V)
AV

and taking the limit as AV->0, we again obtain Equation (1-10);
Tubulor
rsoctar
dV
(1-10)
Consequently, we see that Equation (1-10) applies equally well
to
our model
of tubular reactors of variable and constant cross-sectional area, although it is
14
Mots Balances Chap. 1
Sec. 1.4 Continuous-Flow Reactors
15
doubtful that one would find a reactor of the shape shown in Figure 1-6, unless
designed by Pablo Picasso. The conclusion drawn from the application of the
design equation is an important
one:
The extent of reaction achieved in a plug-flow
tubular reactor (PFR) does not depend on its shape, only on its total volume.
1.4,3 Packed-Bed Reactor
The principal difference between reactor design calculations involving
homogeneous reactions and those involving fluid-solid heterogeneous reac-
tions is that for the latter, the reaction rate is based on mass of solid catalyst,
W, rather than on reactor volume, V. For a fluid-solid heterogeneous system,
the rate of reaction of a substance A is defined as
-
cX
= g mol A reacted/s
•
g catalyst

The mass of solid is used because the amount of the catalyst is what is impor-
tant to the rate of reaction. The reactor volume that contains the catalyst is of
secondary significance.
In the three ideahzed types of reactors just discussed [the perfectly mixed
batch reactor, the plug-flow tubular reactor, and the perfectly mixed continu-
ous-stirred tank reactor (CSTR)], the design equations (i.e., mole balances)
were developed based on reactor volume. The derivaUon of the design equation
for a packed-bed catalytic reactor will be carried out in a manner analogous to
the development of the tubular design equation. To accomplish diis derivation,
we simply replace the volume coordinate in Equation (1-S) with the catalyst
weight coordinate W (Figure 1-7). As with the PFR, the PBR is assumed to have
-AO-
FA
W W +
AW
I
I
' ,AW
FA(W)
F^
[W
+
AW]
Figure 1-7 Packed-bed
reactor
schematic.
no radial gradients in concentration, temperature, or reaction rate. The general-
ized mole balance on species A over catalyst weight AW results in the equation
m
out

4-
generation = accumulation
F^{W) ~ F^iW^LW) + r^AW =
0
(1-12)
The dimensions of the generation term in Equation (1-12) are
(r;)AW^-
moles A
(time) (mass of catalyst)
•
(mass of catalyst) =
moles A
time
Use differential form
of design equation
for catalyst decay
and pressure di'Op
Reactor sizing
which are, as expected, the same dimension of the molar flow rate F^. After
dividing by AW and taking the Hmit as AW -> 0, we arrive at the differential
form of the mole balance for a packed-bed reactor:
dW
(1-13)
When pressure drop through the reactor (see Section 4.4) and catalyst
decay (see Section 10.7) are neglected, the integral form of the packed-cata-
lyst-bed design equation can be used to calculate the catalyst weight.
W
dF.
(1-14)
To obtain some insight into tilings to come, consider the following exam-

ple of how one can use the tubular reactor design equation (1-10).
Example 1-3 l^ow Large Is U?
The first-order reaction
A
is carried out in a tubular reactor in which the volumetric flow rate, v, is coRStant.
Derive an equation relating the reactor volume to the entering and exiting concen-
trations of
A,
the rate constant k, and the volumetric flow rate v. Determine the reac-
tor volume necessary to reduce the exiting concentration to 10% of the entering
concentration when the volumetric flow rate is 10 dm^/min (i.e., Hters/min) and the
specific reaction rate, k, is 0.23 min"' .
Solution
For a tubular reactor, the mole balance on species A (j = A) was shown to be
dV
'•A
For a iirst-order reaction, the rate law (discussed in Chapter 3) is
Since the volumetric flow rate, vn, is constant.
dV
d(C^v^) _ dC^
~^dV~ "° dV
''A
Substituting for r^ in Equation (El-3.1) yields
kC.
(MO)
(El-3.1)
(El-3.2)
CE1~3.3)
16 Mole Balances Chap. l
CA

When is a batch
reactor used?
What are the
advantages and
disadvantages of a
CSTR?
Rearranging gives
•dV
Using the conditions at the entrance of the reactor dial when V = 0, then C^ =
C/^Q,
This equation gives
''^ dC,
k Jc.n C-j
"=1'"^
dV (El-3.4}
(Ei^3.5)
Substinidng C^o, C^.
VQ,
and k in Equation (El-3,5), we have
y = In
A
.'^ = ^;^rr- In 10 = 100 dm^ (i.e., 100 L; 0.1 m^)
0.23 min ^
O-^^^A
0.23
We see that a reactor volume of 0.1
m?
is necessary to convert 90% of species A
entering into product B.
In the remainder of this chapter we look at slightly more detailed draw-

ings of some typical industrial reactors and point out a few of the advantages
and disadvantages of
each.
^
1.5 Industrial Reactors
A batch reactor is used for small-scale operation, for testing new processes that
have not been fully developed, for the manufacture of expensive products, and
for processes that are difficult to convert to continuous operations. The reactor
can be charged (i.e., iilled) through the holes at the top (Figure 1-8). The batch
reactor has the advantage of high conversions that can be obtained by leaving
the reactant in the reactor for long periods of
time,
but it also has die disadvan-
tages of high labor costs per batch and the difficulty of large-scale production.
Liquid-Phase Reactions. Although a semibatch reactor (Figure 1-9) has
essentially the same disadvantages as the batch reactor, it has the advantages of
good temperature control and the capability of minimizing unwanted side reac-
tions through the maintenance of a low concentration of one of the reactants.
The semibatch reactor is also used for two-phase reactions in which a gas is
usually bubbled continuously through the liquid.
A continuous-stirred tank reactor (CSTR) is used when intense agitation
is required. A photo showing a cutaway view of a Pfaudler CSTR/batch reactor
is presented in Figure 1-10. Table l-I gives the typical sizes (along with that of
2
Chem
Eng.,
63{IQ),
211 (1956). See also
AlChE Modular instmcHon Series
E,

Vol
5 (1984).
; ^
Sec.
1.5 Industrial Reactors
17
Hand holes
for
charging reactor
Connection
for
heating
or
cooling jacket
Agitator
Figure 1-S Simple batch homogeneous
reactor, [Excerpted by special permission
from
Chem.
Eng.,
63(10),
21 ]
(Oct 1956).
Copyright 1956 by McGraw-Hill, Inc., New
York, NY 10020,]
Heater
„ or
cooler
r
<3

t
Reactant
B
Figure 1-9 Semibatch reactor, [Excerpted
by special permission from
Chem.
Eng.,
63(10),
2U (Oct. 1956), Copyright 1956 by
McGraw-Hill. Inc., New York, NY 10020.]
^^ ^•
Figure 1-10 CSTRAatch reactor. (Courtesy of Pfaodler, Inc.)