Elements
of Chemical
Reaction
Engineering
Fifth Edition
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Elements
of Chemical
Reaction
Engineering
Fifth Edition
H. SCOTT FOGLER
Ame and Catherine Vennema Professor of Chemical Engineering
and the Arthur F. Thurnau Professor
The University of Michigan, Ann Arbor
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Library of Congress Cataloging-in-Publication Data
Fogler, H. Scott, author.
Elements of chemical reaction engineering / H. Scott Fogler.—Fifth edition.
pages cm
Includes index.
ISBN 978-0-13-388751-8 (hardcover : alk. paper)
1. Chemical reactors. I. Title.
TP157.F65 2016
660'.2832—dc23
2015032892
Copyright © 2016 Pearson Education, Inc.
All rights reserved. Printed in the United States of America. This publication is protected by copyright, and
permission must be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval
system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or
likewise. For information regarding permissions, request forms and the appropriate contacts within the Pearson Education Global Rights & Permissions Department, please visit www.pearsoned.com/permissions/.
ISBN-13: 978-0-13-388751-8
ISBN-10: 0-13-388751-0
Text printed in the United States on recycled paper at RR Donnelley in Kendallville, Indiana.
First printing, January 2016
Dedicated to
Janet Meadors Fogler
For her companionship, encouragement,
sense of humor, love, and support throughout the years
This page intentionally left blank
Contents
PREFACE
xvii
ABOUT THE AUTHOR
CHAPTER 1
1.1
1.2
1.3
1.4
1.5
CHAPTER 2
2.1
2.2
2.3
2.4
2.5
xxxiii
MOLE BALANCES
1
The Rate of Reaction, –rA
4
The General Mole Balance Equation
8
Batch Reactors (BRs)
10
Continuous-Flow Reactors
12
1.4.1
Continuous-Stirred Tank Reactor (CSTR)
1.4.2
Tubular Reactor
14
1.4.3
Packed-Bed Reactor (PBR)
18
Industrial Reactors
22
12
CONVERSION AND REACTOR SIZING
Definition of Conversion
32
Batch Reactor Design Equations
32
Design Equations for Flow Reactors
35
2.3.1
CSTR (Also Known as a Backmix Reactor or a Vat)
36
2.3.2
Tubular Flow Reactor (PFR)
36
2.3.3
Packed-Bed Reactor (PBR)
37
Sizing Continuous-Flow Reactors
38
Reactors in Series
47
2.5.1
CSTRs in Series
48
2.5.2
PFRs in Series
52
2.5.3
Combinations of CSTRs and PFRs in Series
53
2.5.4
Comparing the CSTR and PFR Reactor Volumes and Reactor
Sequencing
57
vii
31
viii
Contents
2.6
CHAPTER 3
3.1
3.2
3.3
3.4
CHAPTER 4
4.1
4.2
4.3
CHAPTER 5
5.1
5.2
5.3
5.4
5.5
5.6
Some Further Definitions
58
2.6.1
Space Time
58
2.6.2
Space Velocity
60
RATE LAWS
69
Basic Definitions
70
3.1.1
Relative Rates of Reaction
71
The Reaction Order and the Rate Law
72
3.2.1
Power Law Models and Elementary Rate Laws
72
3.2.2
Nonelementary Rate Laws
76
3.2.3
Reversible Reactions
80
Rates and the Reaction Rate Constant
83
3.3.1
The Rate Constant k
83
3.3.2
The Arrhenius Plot
90
Present Status of Our Approach to Reactor Sizing and Design
93
STOICHIOMETRY
Batch Systems
107
4.1.1
Batch Concentrations for the Generic Reaction,
Equation (2-2)
109
Flow Systems
113
4.2.1
Equations for Concentrations in Flow Systems
4.2.2
Liquid-Phase Concentrations
114
4.2.3
Gas-Phase Concentrations
115
Reversible Reactions and Equilibrium Conversion
126
105
114
ISOTHERMAL REACTOR DESIGN: CONVERSION
Design Structure for Isothermal Reactors
140
Batch Reactors (BRs)
144
5.2.1
Batch Reaction Times
145
Continuous-Stirred Tank Reactors (CSTRs)
152
5.3.1
A Single CSTR
152
5.3.2
CSTRs in Series
155
Tubular Reactors
162
Pressure Drop in Reactors
169
5.5.1
Pressure Drop and the Rate Law
169
5.5.2
Flow Through a Packed Bed
170
5.5.3
Pressure Drop in Pipes
174
5.5.4
Analytical Solution for Reaction with Pressure Drop
5.5.5
Robert the Worrier Wonders: What If…
181
Synthesizing the Design of a Chemical Plant
190
139
177
ix
Contents
CHAPTER 6
ISOTHERMAL REACTOR DESIGN:
MOLES AND MOLAR FLOW RATES
6.1
6.2
6.3
6.4
6.5
6.6
CHAPTER 7
7.1
7.2
7.3
7.4
7.5
7.6
7.7
CHAPTER 8
8.1
8.2
8.3
8.4
The Molar Flow Rate Balance Algorithm
208
Mole Balances on CSTRs, PFRs, PBRs, and Batch Reactors
6.2.1
Liquid Phase
208
6.2.2
Gas Phase
210
Application of the PFR Molar Flow Rate Algorithm to a
Microreactor
212
Membrane Reactors
217
Unsteady-State Operation of Stirred Reactors
225
Semibatch Reactors
227
6.6.1
Motivation for Using a Semibatch Reactor
227
6.6.2
Semibatch Reactor Mole Balances
227
207
208
COLLECTION AND ANALYSIS OF RATE DATA
243
The Algorithm for Data Analysis
244
Determining the Reaction Order for Each of Two Reactants Using the
Method of Excess
246
Integral Method
247
Differential Method of Analysis
251
7.4.1
Graphical Differentiation Method
252
7.4.2
Numerical Method
252
7.4.3
Finding the Rate-Law Parameters
253
Nonlinear Regression
258
Reaction-Rate Data from Differential Reactors
264
Experimental Planning
271
MULTIPLE REACTIONS
Definitions
280
8.1.1
Types of Reactions
280
8.1.2
Selectivity
281
8.1.3
Yield
282
Algorithm for Multiple Reactions
282
8.2.1
Modifications to the Chapter 6 CRE Algorithm for Multiple
Reactions
284
Parallel Reactions
285
8.3.1
Selectivity
285
8.3.2
Maximizing the Desired Product for One Reactant
285
8.3.3
Reactor Selection and Operating Conditions
291
Reactions in Series
294
279
x
Contents
8.5
8.6
8.7
8.8
CHAPTER 9
Complex Reactions
304
8.5.1
Complex Gas-Phase Reactions in a PBR
304
8.5.2
Complex Liquid-Phase Reactions in a CSTR
307
8.5.3
Complex Liquid-Phase Reactions in a Semibatch
Reactor
310
Membrane Reactors to Improve Selectivity
in Multiple Reactions
312
Sorting It All Out
317
The Fun Part
317
REACTION MECHANISMS, PATHWAYS, BIOREACTIONS,
AND BIOREACTORS
9.1
9.2
9.3
9.4
CHAPTER 10
10.1
10.2
333
Active Intermediates and Nonelementary Rate Laws
334
9.1.1
Pseudo-Steady-State Hypothesis (PSSH)
335
9.1.2
Why Is the Rate Law First Order?
338
9.1.3
Searching for a Mechanism
339
9.1.4
Chain Reactions
343
Enzymatic Reaction Fundamentals
343
9.2.1
Enzyme–Substrate Complex
344
9.2.2
Mechanisms
346
9.2.3
Michaelis–Menten Equation
348
9.2.4
Batch-Reactor Calculations for Enzyme Reactions
354
Inhibition of Enzyme Reactions
356
9.3.1
Competitive Inhibition
357
9.3.2
Uncompetitive Inhibition
359
9.3.3
Noncompetitive Inhibition (Mixed Inhibition)
361
9.3.4
Substrate Inhibition
363
Bioreactors and Biosynthesis
364
9.4.1
Cell Growth
368
9.4.2
Rate Laws
369
9.4.3
Stoichiometry
371
9.4.4
Mass Balances
377
9.4.5
Chemostats
381
9.4.6
CSTR Bioreactor Operation
381
9.4.7
Wash-Out
383
CATALYSIS AND CATALYTIC REACTORS
Catalysts
399
10.1.1 Definitions
400
10.1.2 Catalyst Properties
401
10.1.3 Catalytic Gas-Solid Interactions
403
10.1.4 Classification of Catalysts
404
Steps in a Catalytic Reaction
405
10.2.1 Step 1 Overview: Diffusion from the Bulk to the External
Surface of the Catalyst
408
10.2.2 Step 2 Overview: Internal Diffusion
409
399
xi
Contents
10.3
10.4
10.5
10.6
10.7
CHAPTER 11
11.1
11.2
11.3
11.4
10.2.3 Adsorption Isotherms
410
10.2.4 Surface Reaction
416
10.2.5 Desorption
418
10.2.6 The Rate-Limiting Step
419
Synthesizing a Rate Law, Mechanism, and Rate-Limiting Step
421
10.3.1 Is the Adsorption of Cumene Rate-Limiting?
424
10.3.2 Is the Surface Reaction Rate-Limiting?
427
10.3.3 Is the Desorption of Benzene Rate-Limiting?
429
10.3.4 Summary of the Cumene Decomposition
430
10.3.5 Reforming Catalysts
431
10.3.6 Rate Laws Derived from the Pseudo-SteadyState Hypothesis (PSSH)
435
10.3.7 Temperature Dependence of the Rate Law
436
Heterogeneous Data Analysis for Reactor Design
436
10.4.1 Deducing a Rate Law from the Experimental Data
438
10.4.2 Finding a Mechanism Consistent with Experimental
Observations
439
10.4.3 Evaluation of the Rate-Law Parameters
440
10.4.4 Reactor Design
443
Reaction Engineering in Microelectronic Fabrication
446
10.5.1 Overview
446
10.5.2 Chemical Vapor Deposition
448
Model Discrimination
451
Catalyst Deactivation
454
10.7.1 Types of Catalyst Deactivation
456
10.7.2 Reactors That Can Be Used to Help Offset Catalyst
Decay
465
10.7.3 Temperature–Time Trajectories
465
10.7.4 Moving-Bed Reactors
467
10.7.5 Straight-Through Transport Reactors (STTR)
472
NONISOTHERMAL REACTOR DESIGN–THE STEADYSTATE ENERGY BALANCE AND ADIABATIC
PFR APPLICATIONS
Rationale
494
The Energy Balance
495
11.2.1 First Law of Thermodynamics
495
11.2.2 Evaluating the Work Term
496
11.2.3 Overview of Energy Balances
498
The User-Friendly Energy Balance Equations
502
11.3.1 Dissecting the Steady-State Molar Flow Rates
to Obtain the Heat of Reaction
502
11.3.2 Dissecting the Enthalpies
504
11.3.3 Relating H Rx (T), HRx (T R), and C P
505
Adiabatic Operation
508
11.4.1 Adiabatic Energy Balance
508
11.4.2 Adiabatic Tubular Reactor
509
493
xii
Contents
11.5
11.6
11.7
CHAPTER 12
Adiabatic Equilibrium Conversion
518
11.5.1 Equilibrium Conversion
518
Reactor Staging
522
11.6.1 Reactor Staging with Interstage Cooling or Heating
11.6.2 Exothermic Reactions
523
11.6.3 Endothermic Reactions
523
Optimum Feed Temperature
526
522
STEADY-STATE NONISOTHERMAL REACTOR
DESIGN—FLOW REACTORS WITH HEAT EXCHANGE
12.1
12.2
12.3
12.4
12.5
12.6
12.7
12.8
CHAPTER 13
13.1
13.2
539
Steady-State Tubular Reactor with Heat Exchange
540
12.1.1 Deriving the Energy Balance for a PFR
540
12.1.2 Applying the Algorithm to Flow Reactors with Heat
Exchange
542
Balance on the Heat-Transfer Fluid
543
12.2.1 Co-current Flow
543
12.2.2 Countercurrent Flow
544
Algorithm for PFR/PBR Design with Heat Effects
545
12.3.1 Applying the Algorithm to an Exothermic Reaction
548
12.3.2 Applying the Algorithm to an Endothermic Reaction
555
CSTR with Heat Effects
564
12.4.1 Heat Added to the Reactor, Q̇
564
Multiple Steady States (MSS)
574
12.5.1 Heat-Removed Term, R(T )
575
12.5.2 Heat-Generated Term, G(T )
576
12.5.3 Ignition-Extinction Curve
578
Nonisothermal Multiple Chemical Reactions
581
12.6.1 Energy Balance for Multiple Reactions in Plug-Flow
Reactors
581
12.6.2 Parallel Reactions in a PFR
582
12.6.3 Energy Balance for Multiple Reactions in a CSTR
585
12.6.4 Series Reactions in a CSTR
585
12.6.5 Complex Reactions in a PFR
588
Radial and Axial Variations in a Tubular Reactor
595
12.7.1 Molar Flux
596
12.7.2 Energy Flux
597
12.7.3 Energy Balance
598
Safety
603
UNSTEADY-STATE NONISOTHERMAL REACTOR DESIGN
Unsteady-State Energy Balance
630
Energy Balance on Batch Reactors
632
13.2.1 Adiabatic Operation of a Batch Reactor
633
13.2.2 Case History of a Batch Reactor with Interrupted Isothermal
Operation Causing a Runaway Reaction
640
629
xiii
Contents
13.3
13.4
13.5
CHAPTER 14
14.1
14.2
14.3
14.4
14.5
CHAPTER 15
15.1
15.2
15.3
15.4
15.5
15.6
Semibatch Reactors with a Heat Exchanger
Unsteady Operation of a CSTR
651
13.4.1 Startup
651
Nonisothermal Multiple Reactions
656
646
MASS TRANSFER LIMITATIONS IN REACTING SYSTEMS
679
Diffusion Fundamentals
680
14.1.1 Definitions
681
14.1.2 Molar Flux
682
14.1.3 Fick’s First Law
683
Binary Diffusion
684
14.2.1 Evaluating the Molar Flux
684
14.2.2 Diffusion and Convective Transport
685
14.2.3 Boundary Conditions
685
14.2.4 Temperature and Pressure Dependence of DAB
686
14.2.5 Steps in Modeling Diffusion without Reaction
687
14.2.6 Modeling Diffusion with Chemical Reaction
687
Diffusion Through a Stagnant Film
688
The Mass Transfer Coefficient
690
14.4.1 Correlations for the Mass Transfer Coefficient
690
14.4.2 Mass Transfer to a Single Particle
693
14.4.3 Mass Transfer–Limited Reactions in Packed Beds
697
14.4.4 Robert the Worrier
700
What If . . . ? (Parameter Sensitivity)
705
DIFFUSION AND REACTION
Diffusion and Reactions in Homogeneous Systems
720
Diffusion and Reactions in Spherical Catalyst Pellets
720
15.2.1 Effective Diffusivity
721
15.2.2 Derivation of the Differential Equation Describing Diffusion
and Reaction in a Single Catalyst Pellet
723
15.2.3 Writing the Diffusion with the Catalytic Reaction Equation in
Dimensionless Form
726
15.2.4 Solution to the Differential Equation for a First-Order
Reaction
729
The Internal Effectiveness Factor
730
15.3.1 Isothermal First-Order Catalytic Reactions
730
15.3.2 Effectiveness Factors with Volume Change with
Reaction
733
15.3.3 Isothermal Reactors Other Than First Order
733
15.3.4 Weisz–Prater Criterion for Internal Diffusion
734
Falsified Kinetics
737
Overall Effectiveness Factor
739
Estimation of Diffusion- and Reaction-Limited Regimes
743
15.6.1 Mears Criterion for External Diffusion Limitations
743
719
xiv
Contents
15.7
15.8
15.9
Mass Transfer and Reaction in a Packed Bed
744
Determination of Limiting Situations from Reaction-Rate Data
Multiphase Reactors in the Professional Reference Shelf
751
15.9.1 Slurry Reactors
752
15.9.2 Trickle Bed Reactors
752
15.10 Fluidized Bed Reactors
753
15.11 Chemical Vapor Deposition (CVD)
753
CHAPTER 16
RESIDENCE TIME DISTRIBUTIONS OF
CHEMICAL REACTORS
16.1
16.2
16.3
16.4
16.5
16.6
CHAPTER 17
750
General Considerations
767
16.1.1 Residence Time Distribution (RTD) Function
769
Measurement of the RTD
770
16.2.1 Pulse Input Experiment
770
16.2.2 Step Tracer Experiment
775
Characteristics of the RTD
777
16.3.1 Integral Relationships
777
16.3.2 Mean Residence Time
778
16.3.3 Other Moments of the RTD
778
16.3.4 Normalized RTD Function, E()
782
16.3.5 Internal-Age Distribution, I()
783
RTD in Ideal Reactors
784
16.4.1 RTDs in Batch and Plug-Flow Reactors
784
16.4.2 Single-CSTR RTD
785
16.4.3 Laminar-Flow Reactor (LFR)
786
PFR/CSTR Series RTD
789
Diagnostics and Troubleshooting
793
16.6.1 General Comments
793
16.6.2 Simple Diagnostics and Troubleshooting Using the RTD for
Ideal Reactors
794
PREDICTING CONVERSION DIRECTLY FROM THE
RESIDENCE TIME DISTRIBUTION
17.1
17.2
17.3
17.4
767
Modeling Nonideal Reactors Using the RTD
808
17.1.1 Modeling and Mixing Overview
808
17.1.2 Mixing
808
Zero-Adjustable-Parameter Models
810
17.2.1 Segregation Model
810
17.2.2 Maximum Mixedness Model
820
Using Software Packages
827
17.3.1 Comparing Segregation and Maximum Mixedness
Predictions
829
RTD and Multiple Reactions
830
17.4.1 Segregation Model
830
17.4.2 Maximum Mixedness
831
807
xv
Contents
CHAPTER 18
MODELS FOR NONIDEAL REACTORS
845
18.1
Some Guidelines for Developing Models
846
18.1.1 One-Parameter Models
847
18.1.2 Two-Parameter Models
848
18.2 The Tanks-in-Series (T-I-S) One-Parameter Model
848
18.2.1 Developing the E-Curve for the T-I-S Model
849
18.2.2 Calculating Conversion for the T-I-S Model
851
18.2.3 Tanks-in-Series versus Segregation for a First-Order
Reaction
852
18.3 Dispersion One-Parameter Model
852
18.4 Flow, Reaction, and Dispersion
854
18.4.1 Balance Equations
854
18.4.2 Boundary Conditions
855
18.4.3 Finding Da and the Peclet Number
858
18.4.4 Dispersion in a Tubular Reactor with Laminar Flow
858
18.4.5 Correlations for Da
860
18.4.6 Experimental Determination of Da
862
18.5 Tanks-in-Series Model versus Dispersion Model
869
18.6 Numerical Solutions to Flows with Dispersion and Reaction
870
18.7 Two-Parameter Models—Modeling Real Reactors with Combinations of
Ideal Reactors
871
18.7.1 Real CSTR Modeled Using Bypassing and Dead Space
872
18.7.2 Real CSTR Modeled as Two CSTRs with Interchange
878
18.8 Use of Software Packages to Determine the Model Parameters
880
18.9 Other Models of Nonideal Reactors Using CSTRs and PFRs
882
18.10 Applications to Pharmacokinetic Modeling
883
APPENDIX A
A.1
A.2
A.3
A.4
A.5
A.6
NUMERICAL TECHNIQUES
Useful Integrals in Reactor Design
897
Equal-Area Graphical Differentiation
898
Solutions to Differential Equations
900
A.3.A
First-Order Ordinary Differential Equations
A.3.B
Coupled Differential Equations
900
A.3.C
Second-Order Ordinary Differential Equations
Numerical Evaluation of Integrals
901
Semilog Graphs
903
Software Packages
903
897
900
901
APPENDIX B
IDEAL GAS CONSTANT AND CONVERSION FACTORS
905
APPENDIX C
THERMODYNAMIC RELATIONSHIPS INVOLVING
THE EQUILIBRIUM CONSTANT
909
xvi
Contents
APPENDIX D
SOFTWARE PACKAGES
D.1
915
Polymath
915
D.1.A
About Polymath
915
D.1.B
Polymath Tutorials
916
MATLAB
916
Aspen
916
COMSOL Multiphysics
917
D.2
D.3
D.4
APPENDIX E
RATE LAW DATA
919
APPENDIX F
NOMENCLATURE
921
APPENDIX G
OPEN-ENDED PROBLEMS
925
G.1
G.2
G.3
G.4
G.5
G.6
G.7
G.8
G.9
G.10
APPENDIX H
APPENDIX I
I.1
I.2
I.3
INDEX
Design of Reaction Engineering Experiment
Effective Lubricant Design
925
Peach Bottom Nuclear Reactor
925
Underground Wet Oxidation
926
Hydrodesulfurization Reactor Design
926
Continuous Bioprocessing
926
Methanol Synthesis
926
Cajun Seafood Gumbo
926
Alcohol Metabolism
927
Methanol Poisoning
928
925
USE OF COMPUTATIONAL CHEMISTRY
SOFTWARE PACKAGES
929
HOW TO USE THE CRE WEB RESOURCES
931
CRE Web Resources Components
931
How the Web Can Help Your Learning Style
933
I.2.1
Global vs. Sequential Learners
933
I.2.2
Active vs. Reflective Learners
934
Navigation
934
937
Preface
The man who has ceased to learn ought not to be allowed
to wander around loose in these dangerous days.
M. M. Coady
A. Who Is the Intended Audience?
This book and interactive Web site is intended for use as both an undergraduate-level and a graduate-level text in chemical reaction engineering. The level
will depend on the choice of chapters, the Professional Reference Shelf (PRS)
material (from the companion Web site) to be covered, and the type and degree
of difficulty of problems assigned. It was written with today’s students in
mind. It provides instantaneous access to information; does not waste time on
extraneous details; cuts right to the point; uses more bullets to make information easier to access; and includes new, novel problems on chemical reaction
engineering (e.g., solar energy). It gives more emphasis to chemical reactor
safety (Chapters 12 and 13) and alternative energy sources—solar (Chapters 3,
8, and 10) and biofuel production (Chapter 9). The graduate material on topics
such as effectiveness factors, non-ideal reactors, and residence time distribution is in Chapters 14–18 and now includes the software solutions for maximum mixedness and segregation models. A draft version of this book was class
tested at the University of Michigan and other leading universities; then the
text was further revised, taking into account the suggestions of more than
100 students. Much of the material was revised and reworked based on that
feedback.
B. What Are the Goals of This Book?
B.1
To Have Fun Learning Chemical Reaction Engineering (CRE)
Chemical reaction engineering (CRE) is one of two core courses that is unique
to chemical engineering and that separates the chemical engineer from other
xvii
xviii
Preface
engineers. CRE is a great subject that is fun to learn and is the heart of chemical
engineering. I have tried to provide a little Michigan humor as we go. Take a
look at the humorous YouTube videos (e.g., “Black Widow” or “Chemical Engineering Gone Wrong”) that illustrate certain principles in the text. These videos
were made by chemical engineering students at the universities of Alabama and
Michigan. In addition, I have found that students very much enjoy the Interactive
Computer Games (ICGs) that, along with the videos, are linked from the CRE
homepage (http://www.umich.edu/~elements/5e).
B.2
To Develop a Fundamental Understanding of Reaction
Engineering
The second goal of this book is to help the reader clearly understand the fundamentals of CRE. This goal is achieved by presenting a structure that allows the
reader to solve reaction engineering problems through reasoning rather than
through memorization and recall of numerous equations and the restrictions and
conditions under which each equation applies. The algorithms presented in the
text for reactor design provide this framework, and the homework problems give
the reader practice using the algorithms described in Figures P-1 and P-2, shown
in Section C. The conventional homework problems at the end of each chapter
are designed to reinforce the principles in the chapter. These problems are about
equally divided between those that can be solved with a calculator and those that
require a personal computer with a numerical software package, such as Polymath, AspenTech, or COMSOL.
To give a reference point as to the level of understanding of CRE required
in the profession, a number of reaction engineering problems from the California Board of Registration for Civil and Professional Engineers—Chemical
Engineering Examinations (PECEE) are included in the text.1 Typically, these
problems should each require approximately 30 minutes to solve.
Finally, the companion Web site should greatly facilitate learning the
fundamentals of CRE because it includes Summary Notes of the material in
each chapter, PowerPoint slides of class lecture notes, additional examples,
expanded derivations, and self-tests. A complete description of these learning
resources is in Appendix I.
B.3.
To Enhance Thinking Skills
A third goal of this text is to enhance critical thinking skills and creative thinking skills. How does the book help enhance your critical and creative thinking
skills? We discuss ways to achieve this enhancement in Section I of the
Preface.
1
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 95814, is gratefully acknowledged. (Note: These problems have been copyrighted by the California
Board of Registration and may not be reproduced without its permission.)
xix
Preface
C. What Is the Structure of CRE?
C.1
What Are the Concepts that Form the Foundation of CRE?
The strategy behind the presentation of material is to build continually on a
few basic ideas in CRE to solve a wide variety of problems. These ideas,
referred to as the Pillars of Chemical Reaction Engineering (Figure P-1), are
the foundation on which different applications rest. They represent not only
components of chemical reaction analysis, but also the physical phenomena of
diffusion and contacting that affect chemical reactor design.
Figure P-2 shows the first building blocks of CRE and the primary algorithm
that allows us to solve CRE problems through logic rather than memorization. We
start with the Mole Balance Building Block (Chapter 1) and then place the other
blocks one at a time on top of the others until we reach the Evaluate Block (Chapter 5), by which time we can solve a multitude of isothermal CRE problems. As
we study each block we need to make sure we understand everything in that block
and don’t leave anything out so we don’t wind up with a cylindrical block. A tower
containing cylindrical blocks would be unstable and would fall apart as we study
later chapters. See the end of Chapter 1 lecture notes on the CRE Web site to see
the tower of CRE fall if you have blocks with rounded edges.
MULTIPLE REACTIONS
MASS TRANSFER OPERATIONS
NONISOTHERMAL OPERATION, MULTIPLE STEADY STATES
MODELING REAL REACTORS, RTD, DISPERSION, SEGREGATION
ANALYSIS OF RATE DATA, LABORATORY REACTORS, LEAST-SQUARES ANALYSIS
DESIGN OF CHEMICAL REACTORS, PFR, CSTR, BATCH, SEMIBATCH, PACKED BEDS
M
O
L
E
R
A
T
E
B
A
L
A
N
C
E
S
L
A
W
S
Figure P-1
S
T
O
I
C
H
I
O
M
E
T
R
Y
E
N
E
R
G
Y
B
A
L
A
N
C
E
S
D
I
F
F
U
S
I
O
N
C
O
N
T
A
C
T
I
N
G
Pillars of Chemical Reaction Engineering.
Evaluate
Combine
Stoichiometry
Rate Law
Mole Balance
Figure P-2
Building blocks.
From these pillars and building blocks, we construct our CRE algorithm:
Mole Balance + Rate Laws + Stoichiometry + Energy Balance + Combine → Solution
With a few restrictions, the contents of this book can be studied in virtually
any order after students have mastered the first six chapters. A flow diagram
showing the possible paths is shown in Figure P-3.
The reader will observe that although metric units are used primarily in this
text (e.g., kmol/m3, J/mol), English units are also employed (e.g., lbm/ft3, Btu).
This choice is intentional! We believe that whereas most papers published today
use the metric system, a significant amount of reaction engineering data exists in
the older literature in English units. Because engineers will be faced with extracting information and reaction rate data from older literature as well as from the current literature, they should be equally at ease with both English and metric units.
xx
Preface
Ch. 1
Mole
Balances
Ch. 2
Conversion and
Reactor Sizing
Ch. 10
Catalysis and
Catalytic
Reactors
Ch. 3
Rate Laws
Ch. 4
Stoichiometry
Ch. 9
Reaction
Mechanisms,
Pathways,
Bioreactions, and
Bioreactors
Ch. 14
Mass Transfer
Limitations in
Reacting Systems
Ch. 12
Steady-state
Nonisothermal
Reactor Design─
Flow Reactors
with Heat
Exchange
Ch. 13
Unsteady-State
Nonisothermal
Reactor Design
Figure P-3
C.2
Ch. 6
Isothermal Reactor
Design: Moles and
Molar Flow Rates
Ch. 7
Collection and
Analysis of Rate
Data
Ch. 8
Multiple
Reactions
Ch. 11
Nonisothermal
Reactor Design─
The Steady-State
Energy Balance
and Adiabatic
PFR Applications
Ch. 15
Diffusion and
Reaction
Ch. 5
Isothermal
Reactor Design:
Conversion
Ch. 16
Residence Time
Distributions of
Chemical
Reactors
Ch. 17
Predicting
Conversion
Directly from the
Residence Time
Distribution
Ch. 18
Models for
Nonideal
Reactors
Sequences for study using this text.
What Is the Sequence of Topics in which This Book Can Be
Used?
Table P-1 shows examples of topics that can be converged in a graduate
course and an undergraduate course. In a four-hour undergraduate course at the
University of Michigan, approximately thirteen chapters are covered in the following order: Chapters 1 through 7 (Exam 1); Chapters 8, 11, and 12 (Exam
2); and Chapter 13 and parts of Chapters 9 and 10 (Exam 3).
There are notes in the margins, which are meant to serve two purposes.
First, they act as guides or commentary as one reads through the material. Second, they identify key equations and relationships that are used to solve CRE
problems.
D. What Are the Components of the CRE Web Site?
The companion, interactive Web site material is an updated version of the CRE
Web site and is a novel and unique part of this book. The main purposes of the
Web site are to serve as an enrichment resource and as a “professional reference shelf.” The home page for the CRE Web site (http://www.umich.edu/~elements/5e/index.html) is shown in Figure P-4. For discussion of how to use the
Web site and text interactively, see Appendix I.
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Preface
TABLE P-1
UNDERGRADUATE/GRADUATE COVERAGE
Undergraduate Material/Course
Mole Balances (Ch. 1)
Smog in Los Angeles Basin (PRS Ch. 1)
Reactor Staging (Ch. 2)
Hippopotamus Stomach (PRS Ch. 2)
Rate Laws (Ch. 3)
Stoichiometry (Ch. 4)
Reactors (Ch. 5):
Batch, PFR, CSTR, PBR
Reactors (Ch. 6):
Semibatch, Membrane
Data Analysis: Regression (Ch. 7)
Multiple Reactions (Ch. 8)
Bioreaction Engineering (Ch. 9)
Adiabatic Reactor (Ch. 11)
Steady-State Heat Effects (Ch. 12):
PFR and CSTR with and without a
Heat Exchanger
Multiple Steady States
Unsteady-State Heat Effects (Ch. 13)
Reactor Safety
Catalysis (Ch. 10)
OF
CRE
Graduate Material/Course
Short Review (Ch. 1–8, 11–12)
Collision Theory (PRS Ch. 3)
Transition State Theory (PRS Ch. 3)
Molecular Dynamics (PRS Ch. 3)
Aerosol Reactors (PRS Ch. 4)
Multiple Reactions (Ch. 8):
Fed Membrane Reactors
Bioreactions and Reactors (Ch. 9, PRS 9.3–9.5)
Polymerization (PRS Ch. 9)
Co- and Countercurrent Heat Exchange
(Ch. 12)
Radial and Axial Gradients in a PFR
COMSOL (Ch. 12)
Reactor Stability and Safety (Ch. 12, 13, PRS
12.3)
Runaway Reactions (PRS, Ch. 12)
Catalyst Deactivation (Ch. 10)
Residence Time Distribution (Ch. 16, 17)
Models of Real Reactors (Ch. 18)
Applications (PRS): Multiphase Reactors,
CVD Reactors, Bioreactors
Figure P-4 Screen shot of the book’s companion Web site (http://www.umich.edu/~elements/
5e/index.html).
The objectives of the Web site are fourfold:
(1) To facilitate the learning of CRE by using the companion Web site to
actively address the Felder/Solomon Inventory of Learning Styles 7
discussed in Web Appendix I
(2) To provide additional technical material
xxii
Preface
(3) To provide tutorial information and self-assessment exercises
(4) To make the learning of CRE fun through the use of interactive games
The following sections (D.1 through D.4) are listed at the end of most
chapters and can be accessed from each chapter in the companion Web site.2
D.1
Expanded Material
The expanded material consists of material that was removed from the printed
text and moved to the Web site to reduce the size and weight of the physical
textbook. Reducing the weight makes it easier for the students to carry the
book with them at all times, such as while on the campus shuttle or while eating at the cafeteria or the student union. The expanded material includes derivations, examples, and novel applications of CRE principles.
D.2
Learning Resources
The Learning Resources give an overview of the material in each chapter and
provide extra explanations, examples, and applications to reinforce the basic
concepts of CRE; the Learning Resources are described in Appendix I. The
CRE Web site includes the following additional resources:
1. Summary Notes and PowerPoint Slides
The Summary Notes give an overview of each chapter and provide
on-demand additional examples, derivations, and audio comments, as
well as self-tests to assess each reader’s understanding of the material.
Copies of the PowerPoint slides are available from this course taught
at the University of Michigan as well as those from Professor Mary
Kraft’s class at the University of Illinois.
2. What Entertainment Is on the Web Site?
2.A. YouTube Videos
We have included links to humorous YouTube Videos made by
students in Professor Alan Lane’s 2008 chemical reaction engineering class at the University of Alabama, as well as videos
from the University of Michigan 2011 class. Specifically, check
out “The Black Widow Murder Mystery” (Chapter 3), “CRF
Reactor,” and “Diet Coke and Mentos” (Chapter 4); learn a new
dance and song (“CSTR” to the tune of “YMCA”); hear a rap
song (“Find Your Rhythm,” an “Ice Ice Baby” remix (Chapter
5)); and watch University of Michigan videos, including the
ever-popular chemical engineering classic, “Reaction Engineering Gone Wrong.”
2.B. Interactive Computer Games (ICGs)
Students have found the Interactive Computer Games to be both
fun and extremely useful to review the important chapter concepts and then apply them to real problems in a unique and
2
http://www.ncsu.edu/felder-public/ILSdir/styles.htm
xxiii
Preface
entertaining fashion. The following ICGs are available on the
Web site:
•
•
•
•
•
•
Quiz Show I (Ch. 1)
Reactor Staging (Ch. 2)
Quiz Show II (Ch. 4)
Murder Mystery (Ch. 5)
Tic Tac (Ch. 5)
Ecology (Ch. 7)
•
•
•
•
•
The Great Race (Ch. 8)
Enzyme Man (Ch. 9)
Catalysis (Ch. 10)
Heat Effects I (Ch. 12)
Heat Effects II (Ch. 12)
As you play these interactive games, you will be asked a number of questions related to the corresponding material in the
textbook. The ICG keeps track of all the correct answers and at
the end of the game displays a coded performance number that
reflects how well you mastered the material in the text. Instructors have a manual to decode the performance number.
2.C. Web Modules
The Web Modules are a number of examples that apply key
CRE concepts to both standard and nonstandard reaction engineering problems (e.g., glow sticks, the use of wetlands to
degrade toxic chemicals, and pharmacokinetics of death from a
cobra bite). The Web Modules can be loaded directly from the
CRE Web site (http://www.umich.edu/~elements/5e/web_mod/
index.html).
3. Solved Problems
A number of solved problems are presented along with problem-solving heuristics. Problem-solving strategies and additional worked
example problems are available in the Problem Solving section of the
CRE Web site.
D.3
Professional Reference Shelf
This section of the CRE Web site contains
1. Material from the fifth edition of Elements of Chemical Reaction
Engineering that is not included in the printed textbook.
2. Material that is important to the practicing engineer, such as details of
the industrial reactor design for the oxidation of SO2 and design of
spherical reactors and other material that is typically not included in
the majority of chemical reaction engineering courses but is included
here.
E. Why Do We Assign Homework Problems?
The working of homework problems facilitates a true understanding of CRE.
After reading a chapter the student may feel they have an understanding of the
material. However, when attempting a new or slightly different application of
CRE in a homework problem, students sometimes need to go back and re-read
xxiv
Preface
different parts of the chapter to get the level of understanding needed to eventually solve the homework problem.
The end-of-chapter problems numbered “2” (e.g., P3-2A, P11-2B) ask
questions about the example problems in that chapter. These example problems
are a key resource. These number-2-level problems should be worked before
tackling the more challenging homework problems in a given chapter. The subscript letter (A, B, C, or D) after each problem number denotes the difficulty
of the problem (i.e., A = easy; D = difficult).
F.
What Is a Living Example Problem (LEP)?
The example problems that use an Ordinary Differential Equation (ODE)
solver (e.g., Polymath) are referred to as “Living Example Problems” or
“LEPs” because students can load the Polymath program directly onto their
own computers in order to study the problem. Students are encouraged to
change parameter values and to “play with” the key variables and assumptions.
Using the LEPs to explore the problem and asking “what if…?” questions provide students with the opportunity to practice critical and creative thinking
skills.
G. What Software Is Available to Solve the LEPs?
Polymath. Polymath was developed by Professors Michael Cutlip and Mordechai Shacham. The Polymath software includes an ordinary differential equation (ODE) solver, a nonlinear equation solver, and nonlinear regression. As
with previous editions of this book, Polymath is used to explore the example
problems and to solve the homework problems. Polymath tutorials with screen
shots are given on the CRE Web site Summary Notes in Chapter 1 and can also
be accessed from the Home Page by going to Living Example Problems (LEPs)
and then clicking on Polymath. Most chemical engineering departments in the
United States have site licenses for Polymath. If your department does not have
a site license and would like one, have your instructor e-mail the CACHE Corporation at cache@uts.cc.utexas.edu to learn how to obtain one. The LEPs need
to be copied from the CRE Web site and pasted into the Polymath software.
The Polymath software used in the examples in the text is available in most
department computer labs in the United States. If you want to have Polymath
on your personal laptop computer, you will need to purchase the program. An
educational version of the software has been made available by Professors Cutlip and Shacham to students for $20 for a 4-month license, $30 for a 12-month
license, or for $39 for a perpetual-use license. Polymath 6.1 is compatible with
Windows XP, Windows Vista, Windows 7, and Windows 8. See the Polymath
Web site (http://www.polymath-software.com) to obtain the laptop version.
A special Polymath Web site (http://www.polymath-software.com/fogler) has
been set up for this book by Polymath authors Professors Cutlip and Shacham.
AspenTech. AspenTech is a process flow sheet simulator used in most senior
chemical engineering design courses. It is now routinely introduced in earlier
chemical engineering courses, such as thermodynamics, separations, and now
in CRE. See the AspenTech Web site (http://www.aspentech.com) for more
xxv
Preface
information. Like Polymath, AspenTech site licenses are available in most
chemical engineering departments in the United States. Four AspenTech simulation examples specific to CRE are provided on the CRE Web site with
step-by-step tutorial screen shots.
As with Polymath programs, the input parameters in AspenTech can be
varied to learn how they change the temperature and concentration profiles.
Further details are given in Appendix D.
COMSOL Multiphysics. The COMSOL Multiphysics software is a partial differential equation solver that is used with Chapters 12 and 18 to view both
axial and radial temperature and concentration profiles. For users of this text,
COMSOL has provided a special Web site that includes a step-by-step tutorial,
along with examples. See http://www.comsol.com/ecre. Further details are
given in Appendix D.
Further details of these three software packages can be found in Appendix D.
H. Are There Other Web Site Resources?
FAQs. The Frequently Asked Questions (FAQs) page on the CRE Web site
contains a compilation of questions collected over the years from undergraduate students taking reaction engineering.
Visual Encyclopedia of Equipment (http://encyclopedia.che.engin.umich.edu).
This section was developed by Dr. Susan Montgomery at the University of
Michigan. Here, a wealth of photographs and descriptions of real and ideal
reactors are given. Students with visual, active, sensing, and intuitive learning styles of the Felder/Solomon Index will particularly benefit from this
section.
Reactor Lab (http://www.ReactorLab.net). Developed by Professor Richard
Herz at the University of California at San Diego, this interactive tool will
allow students not only to test their comprehension of the CRE material, but
also to explore different situations and combinations of reaction orders and
types of reactions.
CRE Web Site. The CRE Web site (http://www.umich.edu/~elements/5e/
index.html) will be used to update the text and identify typographical and other
errors in the first and later printings of this text—available under Updates and
FAQs on the CRE Web site home page. Additional material may also be added
to include more solved problems, as well as additional Web Modules, which
will also be found under Updates and FAQs.
xxvi
Preface
I.
How Can Critical Thinking and Creative Thinking
Skills Be Enhanced?
I.1.
Enhance Critical Thinking Skills
A third goal of this book is to enhance critical thinking skills. How does one
enhance their critical thinking skills? Answer by learning how to ask the critical thinking questions in Table P-2 and carry out the actions in Table P-3. A
number of homework problems have been included that are designed for this
purpose. Socratic questioning is at the heart of critical thinking, and a number
of homework problems draw from R. W. Paul’s six types of Socratic questions,3 shown in Table P-2 and given in the expanded material on the Web site.
TABLE P-2
SIX TYPES
OF
SOCRATIC QUESTIONS USED
IN
CRITICAL THINKING
(1) Questions for clarification: Why do you say that? How does this relate to our discussion?
“Are you going to include diffusion in your mole balance equations?”
(2) Questions that probe assumptions: What could we assume instead? How can you verify or
disprove that assumption?
“Why are you neglecting radial diffusion and including only axial diffusion?”
(3) Questions that probe reasons and evidence: What would be an example?
“Do you think that diffusion is responsible for the lower conversion?”
(4) Questions about viewpoints and perspectives: What would be an alternative?
“With all the bends in the pipe, from an industrial/practical perspective, do you think diffusion and dispersion will be large enough to affect the conversion?”
(5) Questions that probe implications and consequences: What generalizations can you make?
What are the consequences of that assumption?
“How would the results be affected if you neglected diffusion?”
(6) Questions about the question: What was the point of this question? Why do you think I
asked this question?
“Why do you think diffusion is important?”
It is important to know these six types and be able to apply them when
investigating a problem such as “Is there a chance the reactor will run away
and explode?” or “Why did the reactor explode?”
Critical thinking skills are like any skill, they must be practiced. Scheffer
and Rubenfeld4,5 describe how to practice critical thinking skills using the
activities, statements, and questions shown in Table P-3. The reader should try
to practice using some or all of these actions every day, as well as asking the
critical thinking questions in Table P-1 and on the Web site.
3
R. W. Paul, Critical Thinking (Santa Rosa, CA: Foundation for Critical Thinking,
1992).
4 Courtesy of B. K. Scheffer and M. G. Rubenfeld, “A Consensus Statement on Critical
Thinking in Nursing,” Journal of Nursing Education, 39, 352–359 (2000).
5 Courtesy of B. K. Scheffer and M. G. Rubenfeld, “Critical Thinking: What Is It and
How Do We Teach It?” Current Issues in Nursing (2001).
xxvii
Preface
TABLE P-3
CRITICAL THINKING ACTIONS6
Analyzing: separating or breaking a whole into parts to discover their nature, function, and
relationships
“I studied it piece by piece.”
“I sorted things out.”
Applying Standards: judging according to established personal, professional, or social rules or
criteria
“I judged it according to….”
Discriminating: recognizing differences and similarities among things or situations and distinguishing carefully as to category or rank
“I rank ordered the various….”
“I grouped things together.”
Information Seeking: searching for evidence, facts, or knowledge by identifying relevant
sources and gathering objective, subjective, historical, and current data from those sources
“I knew I needed to look up/study….”
“I kept searching for data.”
Logical Reasoning: drawing inferences or conclusions that are supported in or justified by
evidence
“I deduced from the information that….”
“My rationale for the conclusion was….”
Predicting: envisioning a plan and its consequences
“I envisioned the outcome would be….”
“I was prepared for….”
Transforming Knowledge: changing or converting the condition, nature, form, or function of
concepts among contexts
“I improved on the basics by….”
“I wondered if that would fit the situation of ….”
I have found that the best way to develop and practice critical thinking
skills is to use Tables P-2 and P-3 to help students write a question on any
assigned homework problem and then to explain why the question involves
critical thinking.6
More information on critical thinking can be found on the CRE Web site
in the section on Problem Solving (http://www.umich.edu/~elements/5e/probsolv/index.htm).
I.2
Enhance Creative Thinking Skills
The fourth goal of this book is to help enhance creative thinking skills. This
goal is achieved by using a number of problems that are open-ended to various
degrees. With these, students can practice their creative skills by exploring the
example problems, as outlined at the beginning of the home problems of each
chapter, and by making up and solving an original problem. Problem P5-1 in
the text gives some guidelines for developing original problems. A number of
techniques that can aid students in practicing and enhancing their creativity
6
R. W. Paul, Critical Thinking (Santa Rosa, CA: Foundation for Critical Thinking,
1992); B. K. Scheffer and M. G. Rubenfeld, “A Consensus Statement on Critical
Thinking in Nursing,” Journal of Nursing Education, 39, 352–359 (2000).
xxviii
Preface
can be found in Fogler, LeBlanc, and Rizzo7 (and its companion Web site),
Strategies for Creative Problem Solving, Third Edition. The Web site for that
book can be accessed from the CRE Web site home page. We use these techniques, such as Osborn’s checklist and de Bono’s lateral thinking (which
involves considering other people’s views and responding to random stimulation) to answer add-on questions such as those in Table P-4.
TABLE P-4
PRACTICING CREATIVE THINKING
(1) Brainstorm ideas to ask another question or suggest another calculation that can be made for
this homework problem.
(2) Brainstorm ways you could work this homework problem incorrectly.
(3) Brainstorm ways to make this problem easier or more difficult or more exciting.
(4) Brainstorm a list of things you learned from working this homework problem and what you
think the point of the problem is.
(5) Brainstorm the reasons why your calculations overpredicted the conversion that was measured when the reactor was put on stream. Assume you made no numerical errors in your
calculations.
(6) “What if…” questions: The “What if…” questions are particularly effective when used with
the Living Example Problems, where one varies the parameters to explore the problem and
to carry out a sensitivity analysis. For example, what if someone suggested that you should
double the catalyst particle diameter, what would you say?
One of the major goals at the undergraduate level is to bring students to
the point where they can solve complex reaction problems, such as multiple
reactions with heat effects, and then ask “What if . . . ?” questions and look for
optimum operating conditions and unsafe operating conditions. The solution to
one problem exemplifies this goal: the Manufacture of Styrene (Chapter 12,
Problem P12-26C). This problem is particularly interesting because two reactions are endothermic and one is exothermic.
(1) Ethylbenzene → Styrene + Hydrogen: Endothermic
(2) Ethylbenzene → Benzene + Ethylene: Endothermic
(3) Ethylbenzene + Hydrogen → Toluene + Methane: Exothermic
The student could get further practice in critical and creative thinking
skills by adding any of the following exercises (x), (y), and (z) to any of the
end-of-chapter homework problems.
(x) How could you make this problem easier? More difficult?
(y) Critique your answer by writing a critical thinking question.
(z) Describe two ways you could work this problem incorrectly.
To summarize, it is this author’s experience that both critical and creative
thinking skills can be enhanced by using Tables P-2, P-3, and P-4 to extend
any of the homework problems at the end of each chapter.
7
H. S. Fogler, S. E. LeBlanc, with B. Rizzo, Strategies for Creative Problem Solving,
3rd Ed. (Upper Saddle River, N.J.: Prentice Hall, 2014).
xxix
Preface
J.
What’s New in This Edition?
J.1
Pedagogy
This book maintains all the strengths of the fourth edition of Elements of
Chemical Reaction Engineering by using algorithms that allow students to
learn chemical reaction engineering through logic rather than memorization. It
has the added strength of breaking down the material into smaller bites, as
there are now 18 chapters to cover the same concepts as the 14 chapters in the
fourth edition.
At the same time, this edition provides new resources that allow students to go beyond solving equations in order to get an intuitive feel and
understanding of how reactors behave under different situations. This understanding is achieved through more than 80 interactive simulations (LEPs)
provided on the Web site. The Web site has been greatly expanded to address
the Felder/Solomon Inventory of Different Learning Styles8 through interactive Summary Notes and new and updated Interactive Computer Games
(ICGs). For example, as discussed in Appendix I the Global Learner can get
an overview of the chapter material from the Summary Notes; the Sequential
Learner can use all the
hot buttons; and the active learner can
interact with the ICGs and use the
hot buttons in the Summary
Notes.
A new pedagogical concept is introduced in this text through expanded
emphasis on the example problems. Here, the students simply load the Living
Example Problems (LEPs) onto their computers and then explore the problems
to obtain a deeper understanding of the implications and generalizations before
working the homework problems for that chapter. This exploration helps students get an innate feel for reactor behavior and operation, as well as develop
and practice their creative thinking skills.
To develop critical thinking skills, instructors can assign one of the new
homework problems on troubleshooting, as well as ask the students to expand
homework problems by asking a related question that involves critical thinking
using Tables P-2 and P-3.
Creative thinking skills can be enhanced by exploring the example
problems and asking “What if . . . ?” questions, by using one or more of the
brainstorming exercises in Table P-4 to extend any of the homework problems, and by solving the open-ended problems. For example, in the case
study on safety, students can use the LEP on the CRE Web site to carry out
a postmortem analysis on the nitroaniline explosion in Example 13-2 to learn
what would have happened if the cooling had failed for five minutes instead
of ten minutes. To this end, a new feature in the text is an Analysis paragraph
at the end of each example problem. Significant effort has been devoted to
developing example and homework problems that foster critical and creative
thinking.
8
http://www.ncsu.edu/felder-public/ILSdir/styles.htm
xxx
Preface
J.2
Content
The following areas have an increased emphasis in this new edition over previous CRE editions by including thorough example problems and homework
problems:
1. Safety: Three industrial explosions are discussed and modeled.
a. Ammonium Nitrate CSTR Explosion (Chapters 12 and 13)
b. Nitroaniline Batch Reactor Runaway (Chapter 13)
c. T2 Laboratories Batch Reactor Runaway (Chapter 13)
d. Resources from SAChE and CCPS (Chapter 12)
2. Solar Energy: Three examples of solar energy conversion are discussed.
a. Solar Chemical Reactions (Chapter 3)
b. Solar Thermal Reactors (Chapter 8)
c. Solar Catalytic Water Splitting (Chapter 10)
3. Alternative Fuels:
a. Production of Algae for Biomass (Chapter 9)
4. AspenTech: An AspenTech tutorial for chemical reaction engineering
and four example problems are provided on the CRE Web site. The
example problems are
a. Production of Ethylene from Ethane
b. The Pyrolysis of Benzene
c. Adiabatic Liquid Phase Isomerization of Normal Butane
d. Adiabatic Production of Acetic Anhydride
However, all intensive laws tend often to have exceptions. Very important concepts take orderly, responsible statements. Virtually all laws intrinsically are
natural thoughts. General observations become laws under experimentation.
K. How Do I Say Thank You?
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 again acknowledge all my friends, students, and colleagues for their contributions to the fifth edition of Elements of Chemical Reaction Engineering.
I would like to give special recognition as follows.
First of all, I am indebted to Ame and Catherine Vennema, whose gift of
an endowed chair greatly facilitated the completion of this project. My colleague Dr. Nihat Gürmen coauthored the original Web site during the writing
of the fourth edition of this book. He has been a wonderful colleague to work
with. I also would like to thank University of Michigan undergraduate students
Arthur Shih, Maria Quigley, and Brendan Kirchner, who worked on earlier
versions of the Web site. Their hard work and suggestions are greatly appreciated. Ben Griessmann was instrumental in making everything come together
for the Web site for the fifth edition, including converting the fourth edition’s
physical CD-ROM to online-only content for this new edition.
Preface
xxxi
The many stimulating discussions on activation energy with Professor
Michael Stamatakis in the Chemical Engineering Department at University
College London are greatly appreciated. Michael B. Cutlip, coauthor of Polymath, not only gave suggestions and a critical reading of many sections, but
also, most importantly, provided continuous support and encouragement
throughout the course of this project. Professor Chau-Chyun Chen provided
two AspenTech examples. Ed Fontes at COMSOL Mutiphysic not only provided encouragement, but also provided a COMSOL Web site containing a
tutorial with CRE examples. Bernard Goodwin and Laura Lewin, editors at
Prentice Hall, were extremely encouraging, helpful, and supportive throughout.
Julie Nahil, full-service production manager at Prentice Hall, was fantastic
throughout. She provided encouragement, attention to detail, and a great sense
of humor, which were greatly appreciated. Indian Institute of Technology (IIT)
students Darshan Shah, Anamika Singh, and Sravya Jangareddy, along with
Fan Zhang, a University of Michigan student, and Keyvan Edrisi from Swedish
Royal Institute of Technology, not only participated in the preparation of the
solutions manual, but along with Maithri Venkat worked on the Web site to
place many of the LEPs in Wolfram. Richa Motwani from IIT Guwahati, and
Gunish Handa and Prafful Bhansali from IIT Bombay, did an extraordinary job
in proofreading the galley proofs of the manuscript and making helpful suggestions for changes as well as putting the solution manual in final form.
Thank you to students Krittin Binabdullah, Apirak Hanpan, and Thanaphoom
Khrutphisit from Chulalongkorn University in Bangkok, along with Ph.D. candidate Cláudio Vilas Bôas Fávero for help in meeting the final deadline for this
manuscript.
I very much appreciated the patience of all my Ph.D. students during the
period in which this book was written, Michael Senra, Zhenyu Huang, Michael
Hoepfner, Nasim Haji Akbari Balou, Claudio Vilas Boas Favero, and Mark
Sheng Zheng. Mark helped proofread a number of chapters of the page proofs;
Professor Michael Senra class-tested the draft version of the fifth edition, and
he and his students gave many valuable suggestions to this edition. There are
others I would like to thank for a variety of different reasons: David Bogle,
Lee Brown, Brice Carnahan, John Chen, Stu Churchill, Rane Curl, Jim Duderstadt, Tom Edgar, John Falconer, Rich Felder, Asterios Gavriilidis, Joe Goddard, Jay Jorgenson, Costas Kravaris, Steve LeBlanc, Joe Martin, Susan
Montgomery, Max Peters, Phil Savage, Johannes Schwank, Mordechai Shacham, Klaus Timmerhaus, Ron West, Jim Wilkes, June Wispelwey, Max, Joe
(aka “Jofo”), Sophia, Nicolas, and to the Starbucks staff at Plymouth Road
Mall, where most of my final editing of this book was accomplished.
Laura Bracken is very much a part of this book. I appreciate her excellent deciphering of equations and scribbles, her organization, her discovery of
mistakes and inconsistencies, and her attention to detail in working with the
galleys and proofs. Through all this was her ever-present wonderful disposition. Thanks, Radar!!
Finally, to my wife Janet, love and thanks. Not only did she type the first
edition of this book—on a Royal Select typewriter!—she also was a sounding
board for so many things in this edition. She was always willing to help with
xxxii
Preface
the wording and sentence structure. For example, I often asked her, “Is this the
correct phrase or word to use here?” or “Should I mention Jofostan here?” Jan
also helped me learn that creativity also involves knowing what to leave out.
Without her enormous help and support the project would never have been
possible.
HSF
Ann Arbor, Michigan
November 2015
For updates and new and exciting applications, go to the Web site:
http://www.umich.edu/~elements/5e/index.html
For typographical errors, click on Updates & FAQ on the Home page to find
http://www.umich.edu/~elements/5e/updates/index.html
About the Author
H. Scott Fogler is the Ame and Catherine Vennema professor
of chemical engineering and the Arthur F. Thurnau professor
at the University of Michigan in Ann Arbor, and was the 2009
National President of the American Institute of Chemical
Engineers, a 50,000-member organization. He received his
B.S. from the University of Illinois and his M.S. and Ph.D.
from the University of Colorado. He is also the author of the
Essentials of Chemical Reaction Engineering and co-author,
with Steven LeBlanc and Benjamin Rizzo, of Strategies for Creative Problem
Solving, Third Edition.
Professor Fogler’s research interests include flow and reaction in porous
media, wax and asphaltene deposition, asphaltene flocculation kinetics, gellation kinetics, colloidal phenomena, and catalyzed dissolution. He has been
research advisor to more than forty-five Ph.D. students and has more than two
hundred thirty-five refereed publications in these areas. Fogler has chaired
ASEE’s Chemical Engineering Division, served as director of the American
Institute of Chemical Engineers, and earned the Warren K. Lewis Award from
AIChE for contributions to chemical engineering education. He also received
the Chemical Manufacturers Association’s National Catalyst Award and the
2010 Malcom E. Pruitt Award from the Council for Chemical Research
(CCR). He is the recipient of 11 named lectureships and is associate editor of
Energy & Fuels.
xxxiii
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Mole Balances
1
The first step to knowledge
is to know that we are ignorant.
—Socrates (470–399 B.C.)
How is a chemical
engineer different
from other
engineers?
The Wide Wild World of Chemical Reaction Engineering
Chemical kinetics is the study of chemical reaction rates and reaction mechanisms. The study of chemical reaction engineering (CRE) combines the study
of chemical kinetics with the reactors in which the reactions occur. Chemical
kinetics and reactor design are at the heart of producing almost all industrial
chemicals, such as the manufacture of phthalic anhydride shown in Figure 1-1.
It is primarily a knowledge of chemical kinetics and reactor 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 produces a large amount of undesirable product, subsequent purification and separation of the desired product could make the entire process economically unfeasible.
1
2
Mole Balances
Figure 1-1
Chapter 1
Manufacture of phthalic anhydride.
The chemical reaction engineering (CRE) principles learned here can
also be applied in many areas, such as waste treatment, microelectronics, nanoparticles, and living systems, in addition to the more traditional areas of the
manufacture of chemicals and pharmaceuticals. Some of the examples that
illustrate the wide application of CRE principles in this book are shown in
Figure 1-2. These examples include modeling smog in the Los Angeles (L.A.)
basin (Chapter 1), the digestive system of a hippopotamus (Chapter 2 on the
CRE Web site, www.umich.edu/~elements/5e/index.html), and molecular CRE
(Chapter 3). Also shown are the manufacture of ethylene glycol (antifreeze),
where three of the most common types of industrial reactors are used (Chapters 5 and 6), and the use of wetlands to degrade toxic chemicals (Chapter 7
on the CRE Web site). Other examples shown are the solid-liquid kinetics of
acid-rock interactions to improve oil recovery (Chapter 7); pharmacokinetics of
cobra bites (Chapter 8 Web Module); free-radical scavengers used in the
design of motor oils (Chapter 9); enzyme kinetics (Chapter 9) and drug delivery pharmacokinetics (Chapter 9 on the CRE Web site); heat effects, runaway
reactions, and plant safety (Chapters 11 through 13); and increasing the octane
number of gasoline and the manufacture of computer chips (Chapter 10).
3
Mole
Balances
Section
Hippo Digestion (Ch. 2)
Smog (Ch. 1)
H 2, C 2H 4
C2H6
1
C2H6
O2, C2H4, N2, C2H4O
5
C2H4 +
Separator
C2H4O
H2O
Transition State
(dashed lines show transition
state electron delocalization)
C2H6
C 2H 4
O
Ag
1
O
CH2
CH2
2 2
Separator
4-Pentenal
2
C2H4 + H2
V = 81 ft3
X = 0.8
6
Vinyl Allyl Ether
(arrows indicate
electron movement)
W = 45,440 lb
X = 0.60
8
7
3
Molecular CRE (Ch. 3)
H2O
0.9 wt % H2SO4
4
Air
Waste
water
Absorber
C2H4O(aq)
V = 197 ft
X = 0.80
C2H4O + H2O
Cat. CH2
OH
CH2
OH
Chemical Plant for Ethylene Glycol (Ch. 5)
Marsh
Wetlands Remediation of Pollutants (Ch. 7 on the CRE Web site)
Pulmonary
OIL
WELL
~~
~~
ACID
Oil Recovery (Ch. 7)
Evaporation
200 million lb
EG/year
9
3
Go Blue
Motor Oil
Heart
Muscle
Effective Lubricant
Design Scavenging
Free Radicals
Lubricant Design (Ch. 9)
Pharmacokinetics
of Cobra Bites
Multiple Reactions
in a Batch
(Body) Reactor
Cobra Bites (Ch. 8 on the CRE Web site)
Nitroanaline Plant Explosion
Exothermic Reactions That
Run Away
Plant Safety (Ch.11 to Ch.13)
Liver
Intestines
Pharmacokinetics (Ch. 9 on the CRE Web site)
Etch and Then Remove Photoresist
Microelectronic Fabrication Steps (Ch. 10)
Figure 1-2
The wide world of CRE applications.
4
Mole Balances
Chapter 1
Overview—Chapter 1. This chapter develops the first building block of
chemical reaction engineering, mole balances, which will be used continually throughout the text. After completing this chapter, the reader will
be able to:
•
•
•
Describe and define the rate of reaction
Derive the general mole balance equation
Apply the general mole balance equation to the four most common types of industrial reactors
Before entering into discussions of the conditions that affect chemical reaction rate mechanisms and reactor design, it is necessary to account
for the various chemical species entering and leaving a reaction system.
This accounting process is achieved through overall mole balances on individual species in the 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 reaction, –rA, 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 Reactor (BR)
Continuous-Stirred Tank Reactor (CSTR)
Plug-Flow Reactor (PFR)
Packed-Bed Reactor (PBR)
In developing these equations, the assumptions pertaining to the
modeling of each type of reactor are delineated. Finally, a brief summary
and series of short review questions are given at the end of the chapter.
1.1 The Rate of Reaction, –rA
CH3
CH3
p-xylene
The rate of reaction tells us how fast a number of moles of one chemical species are being consumed to form another chemical species. The term chemical
species refers to any chemical component or element with a given identity. The
identity of a chemical species is determined by the kind, number, and configuration of that species’ atoms. For example, the species para-xylene is made up
of a fixed number of specific atoms in a definite molecular arrangement or
configuration. The structure shown illustrates the kind, number, and configuration of atoms on a molecular level. Even though two chemical compounds
have exactly the same kind and 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 hydrogen atoms; however, the atoms
in this compound can form two different arrangements.
H
—
C —C
CH3
CH3
H
cis-2-butene
CH3
—
C —C
CH3
H
H
and
trans-2-butene
Section 1.1
5
The Rate of Reaction
Reaction, –r
–rA
A
When has a
chemical reaction
taken place?
As a consequence of the different configurations, these 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 number 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 these atoms. In this classical
approach to chemical change, it is assumed that the total mass is neither created nor destroyed when a chemical reaction occurs. The mass referred 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
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 reaction. In order for a particular species to “appear” in the system, some prescribed fraction of another species must lose its chemical identity.
There are three basic ways a species may lose its chemical identity:
decomposition, combination, and isomerization. In decomposition, the molecule loses its identity by being broken down into smaller molecules, atoms, or
atom fragments. For example, if benzene and propylene are formed from a
cumene molecule,
CH(CH3)2
A species can
lose its identity by
• Decomposition
• Combination
• Isomerization
+ C3 H6
cumene
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
chemical identity is through combination with another molecule or atom. In
the above reaction, the propylene molecule would lose its chemical identity if
the reaction were carried out in the reverse direction, so that it combined with
benzene to form cumene. The third way a species may lose its chemical identity is through isomerization, such as the reaction
CH3
CH2—
—C—CH2CH3
CH3
CH3C—
— CHCH3
Here, although the molecule neither adds other molecules to itself nor breaks
into smaller molecules, it still loses its identity through a change in configuration.
6
Mole Balances
Chapter 1
To summarize this point, we say that a given number of molecules (i.e.,
moles) 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. To illustrate, consider the reaction of chlorobenzene and chloral
to produce the banned insecticide DDT (dichlorodiphenyl-trichloroethane) in
the presence of fuming sulfuric acid.
CCl3CHO + 2C6H5Cl ⎯→ (C6H4Cl)2CHCCl3 + H2O
Letting the symbol A represent chloral, B be chlorobenzene, C be DDT, and D
be H2O, we obtain
A + 2B ⎯→ C + D
The numerical value of the rate of disappearance of reactant A, –rA, is a positive number.
What is –rA?
The rate of reaction, –rA, is the number of moles of A (e.g., chloral) reacting
(disappearing) per unit time per unit volume (mol/dm3⋅s).
Example 1–1
Chloral is being consumed at a rate of 10 moles per second per m3 when reacting
with chlorobenzene to form DDT and water in the reaction described above. In symbol form, the reaction is written as
A + 2B ⎯→ C + D
Write the rates of disappearance and formation (i.e., generation) for each species in
this reaction.
Solution
(a) Chloral[A]:
The rate of reaction of chloral [A] (–rA) is given as
10 mol/m3·s
Rate of disappearance of A = –rA = 10 mol/m3·s
Rate of formation of A = rA = –10 mol/m3·s
(b) Chlorobenzene[B]: For every mole of chloral that disappears, two moles of
chlorobenzene [B] also disappear.
Rate of disappearance of B = –rB = 20 mol/m3·s
Rate of formation of B = rB = –20 mol/m3·s
(c) DDT[C]:
For every mole of chloral that disappears, one mole of
DDT[C] appears.
Rate of formation of C = rC = 10 mol/m3·s
Rate of disappearance of C = –rC = –10 mol/m3·s
(d) Water[D]:
Same relationship to chloral as the relationship to DDT
Rate of formation of D = rD = 10 mol/m3·s
Rate of disappearance of D = –rD = –10 mol/m3·s
Section 1.1
7
The Rate of Reaction
Reaction, –r
–rA
A
Analysis: The purpose of this example is to better understand the convention for the
rate of reaction. The symbol rj is the rate of formation (generation) of species j. If
species j is a reactant, the numerical value of rj will be a negative number. If species
j is a product, then rj will be a positive number. The rate of reaction, –rA, is the rate
of disappearance of reactant A and must be a positive number. A mnemonic relationship to help remember how to obtain relative rates of reaction of A to B, etc., is
given by Equation (3-1) on page 71.
A + 2B → C + D
The convention
–rA = 10 mol A/m3⋅s
rA = –10 mol A/m3⋅s
–rB = 20 mol B/m3⋅s
rB = –20 mol B/m3⋅s
rC = 10 mol C/m3⋅s
What is –r A′ ?
Definition of rj
In Chapter 3, we will delineate the prescribed relationship between the
rate of formation of one species, rj (e.g., DDT [C]), and the rate of disappearance of another species, – ri (e.g., chlorobenzene [B]), in a chemical reaction.
Heterogeneous reactions involve more than one phase. In heterogeneous
reaction systems, the rate of reaction is usually expressed in measures other
than volume, such as reaction surface area or catalyst weight. For a gas-solid
catalytic reaction, the gas molecules must interact with the solid catalyst surface for the reaction to take place, as described in Chapter 10.
The dimensions of this heterogeneous reaction rate, –r A′ (prime), are
the number of moles of A reacting per unit time per unit mass of catalyst
(mol/s⋅g catalyst).
Most of the introductory discussions on chemical reaction engineering in
this book focus on homogeneous systems, in which case we simply say that rj
is the rate of formation of species j per unit volume. It is the number of moles
of species j generated per unit volume per unit time.
We can say four things about the reaction rate rj. The reaction rate law
for rj is
•
•
•
The rate law does
not depend on
the type of
reactor used!!
•
What is –rA
a function of?
The rate of formation of species j (mole/time/volume)
An algebraic equation
Independent of the type of reactor (e.g., batch or continuous flow)
in which the reaction is carried out
Solely a function of the properties of the reacting materials and
reaction conditions (e.g., species concentration, temperature, pressure, or type of catalyst, if any) at a point in the system
However, because the properties and reaction conditions of the reacting
materials may vary with 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 law is essentially an algebraic equation
involving concentration, not a differential equation. 1 For example, the algebraic form of the rate law for –rA for the reaction
A ⎯→ products
may be a linear function of concentration,
–r A = kC A
(1-1)
or, as shown in Chapter 3, it may be some other algebraic function of concentration, such as
1
For further elaboration on this point, see Chem. Eng. Sci., 25, 337 (1970); B. L. Crynes
and H. S. Fogler, eds., AIChE Modular Instruction Series E: Kinetics, 1, 1 (New York:
AIChE, 1981); and R. L. Kabel, “Rates,” Chem. Eng. Commun., 9, 15 (1981).
8
Mole Balances
Chapter 1
2
–r A = kC A
(1-2)
or
k1C A
–r A = ------------------1 + k2C A
The rate law is an
algebraic equation.
The convention
For a given reaction, the particular concentration dependence that the rate law
2
follows (i.e., –r A = kC A or –r A = kC A or …) must be determined from experimental observation. Equation (1-2) states that the rate of disappearance of A is
equal to a rate constant k (which is a function of temperature) times the square
of the concentration of A. As noted earlier, by convention, rA is the rate of formation of A; consequently, –rA is the rate of disappearance of A. Throughout this
book, the phrase rate of generation means exactly the same as the phrase rate of
formation, 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 is referred to as the system
volume. We shall perform a mole balance on species j in a system volume,
where species j represents the particular chemical species of interest, such as
water or NaOH (Figure 1-3).
Figure 1-3
Mole balance on species j in a system volume, V.
A mole balance on species j at any instant in time, t, yields the following
equation:
Rate of flow
Rate of flow
of j into – of j out of +
the system
the system
(moles/time) (moles/time)
Mole balance
Rate of
Rate of generation
accumulation
of j by chemical
= of j within
reaction within
the system
the system
(moles/time)
(moles/time)
In
–
Out
+
Generation
F j0
–
Fj
+
Gj
= Accumulation
dN j
--------=
(1-3)
dt
Section 1.2
9
The General Mole Balance Equation
In this equation, Nj represents the number of moles of species j in the system
at time t. If all the system variables (e.g., temperature, catalytic activity, and
concentration of the chemical species) are spatially uniform throughout the
system volume, the rate of generation of species j, Gj , is just the product of the
reaction volume, V, and the rate of formation of species j, rj .
Gj = rj⋅V
moles
moles
-------------- = ------------------------------ ⋅ volume
time
time ⋅ volume
Now suppose that the rate of formation of species j for the reaction varies
with position in the system volume. That is, it has a value r j1 at location 1,
which is surrounded by a small volume, ΔV 1 , within which the rate is uniform; similarly, the reaction rate has a value r j2 at location 2 and an associated
volume, ΔV 2 , and so on (Figure 1-4).
Figure 1-4
Dividing up the system volume, V.
The rate of generation, ΔG j1 , in terms of r j1 and subvolume ΔV 1 , is
ΔG j1 = r j1 ΔV 1
Similar expressions can be written for ΔG j2 and the other system subvolumes,
ΔV i . 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, the total rate of generation is
M
M
i=1
i=1
G j = ∑ ΔG ji = ∑ r ji ΔV i
10
Mole Balances
Chapter 1
By taking the appropriate limits (i.e., let M → ∞ and ΔV → 0 ) and making
use of the definition of an integral, we can rewrite the foregoing equation in
the form
V
Gj =
∫
r j dV
From this equation, we see that rj will be an indirect function of position, since
the properties of the reacting materials and reaction conditions (e.g., concentration, temperature) can have different values at different locations in the reactor volume.
We now replace Gj in Equation (1-3)
dN
Fj0 – Fj + G j = ----------j
dt
(1-3)
by its integral form to yield a form of the general mole balance equation for
any chemical species j that is entering, leaving, reacting, and/or accumulating
within any system volume V.
This is a basic
equation for
chemical reaction
engineering.
F j0 – F j +
∫
V
dN
r j dV = ---------j
dt
(1-4)
From this general mole balance equation, we can develop the design equations
for the various types of industrial reactors: batch, semibatch, and continuous-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 reactants into products.
1.3 Batch Reactors (BRs)
When is a batch
reactor used?
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., filled) through the holes at the top (see Figure 1-5(a)). 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 the
disadvantages of high labor costs per batch, the variability of products from
batch to batch, and the difficulty of large-scale production (see Industrial Reactor Photos in Professional Reference Shelf [PRS] on the CRE Web site,
www.umich.edu/~elements/ 5e/index.html).
Section 1.3
11
Batch Reactors (BRs)
Figure 1-5(b) Batch reactor mixing patterns.
Further descriptions and photos of the batch
reactors can be found in both the Visual
Encyclopedia of Equipment and in the
Professional Reference Shelf on the
CRE Web site.
Figure 1-5(a) Simple batch homogeneous
batch reactor (BR). [Excerpted by special
permission from Chem. Eng., 63(10), 211
(Oct. 1956). Copyright 1956 by McGraw-Hill,
Inc., New York, NY 10020.]
A batch reactor has neither inflow nor outflow of reactants or products while
the reaction is being carried out: Fj0 = Fj = 0. The resulting general mole balance on species j is
dN
---------j =
dt
V
∫
r j dV
If the reaction mixture is perfectly mixed (Figure 1-5(b)) so that there is no
variation in the rate of reaction throughout the reactor volume, we can take rj
out of the integral, integrate, and write the mole balance in the form
Perfect mixing
dN j
--------- = r jV
dt
(1-5)
Let’s consider the isomerization of species A in a batch reactor
⎯→ B
A⎯
dNA
dt
= rAV
Batch Reactor
As the reaction proceeds, the number of moles of A decreases and the number
of moles of B increases, as shown in Figure 1-6.
12
Mole Balances
Chapter 1
NA0
NB1
NB
NA
NA1
0
t1
Figure 1-6
t
0
t1
t
Mole-time trajectories.
We might ask what time, t1, is necessary to reduce the initial number of moles
from NA0 to a final desired number NA1. Applying Equation (1-5) to the
isomerization
dN A
---------- = r AV
dt
rearranging,
dN
dt = ---------Ar AV
and integrating with limits that at t = 0, then NA = NA0, and at t = t1, then
NA = NA1, we obtain
t1 =
∫
N A0
N A1
dN A
-----------–r A V
(1-6)
This equation is the integral form of the mole balance on a batch reactor. It
gives the time, t1, necessary to reduce the number of moles from NA0 to NA1
and also to form NB1 moles of B.
1.4 Continuous-Flow Reactors
Continuous-flow reactors are almost always operated at steady state. We will
consider three types: the continuous-stirred tank reactor (CSTR), the
plug-flow reactor (PFR), and the packed-bed reactor (PBR). Detailed physical descriptions of these reactors can be found in both the Professional Reference Shelf (PRS) for Chapter 1 and in the Visual Encyclopedia of Equipment,
encyclopedia.che.engin.umich.edu, and on the CRE Web site.
1.4.1 Continuous-Stirred Tank Reactor (CSTR)
What is a CSTR
used for?
A type of reactor commonly used in industrial processing is the stirred tank
operated continuously (Figure 1-7). It is referred to as the continuous-stirred
tank reactor (CSTR) or vat, or backmix reactor, and is primarily used for
Section 1.4
13
Continuous-Flow Reactors
Fj 0
Fj
Figure 1-7(a) CSTR/batch
reactor. (Photo courtesy of
Pfaudler, Inc.)
Figure 1-7(b) CSTR mixing patterns.
Also see the Visual Encyclopedia of
Equipment on the CRE Web site.
liquid-phase reactions. It is normally operated at steady state and is assumed
to be perfectly mixed; consequently, there is no time dependence or position
dependence of the temperature, concentration, or reaction rate inside the
CSTR. That is, every variable is the same at every point inside the reactor.
Because 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 of nonideal mixing is discussed in Chapters 16,
17, and 18 on nonideal reactors.
When the general mole balance equation
F j0 – F j +
∫
V
dN
r j dV = ---------j
dt
(1-4)
is applied to a CSTR operated at steady state (i.e., conditions do not change
with time),
dN j
--------- = 0
dt
14
Mole Balances
Chapter 1
in which there are no spatial variations in the rate of reaction (i.e., perfect
mixing),
The ideal CSTR is
assumed to be
perfectly mixed.
V
∫
r j dV = V r j
it takes the familiar form known as the design equation for a CSTR
A
FA0
F j0 – F j
V = ---------------–r j
FAO – FA
– rA
CSTR
V=
FA
(1-7)
The CSTR design equation gives the reactor volume V necessary to
reduce the entering flow rate of species j from Fj0 to the exit flow rate Fj , when
species j is disappearing at a rate of –rj. We note that the CSTR is modeled such
that the conditions in the exit stream (e.g., concentration and temperature) are
identical to those in the tank. The molar flow rate Fj is just the product of the
concentration of species j and the volumetric flow rate v
Fj = C j ⋅ v
moles
moles- volume
-------------- = ----------------⋅ -----------------time volume time
(1-8)
Similarly, for the entrance molar flow rate we have Fj0 = Cj0 · v0. Consequently, we can substitute for Fj0 and Fj into Equation (1-7) to write a balance
on species A as
v0C A0 – vC A
V = ---------------------------–r A
(1-9)
The ideal CSTR mole balance equation is an algebraic equation, not a
differential equation.
1.4.2 Tubular Reactor
When is a tubular
reactor most
often used?
In addition to the CSTR and batch reactors, another type of reactor commonly
used in industry is the tubular reactor. It consists of a cylindrical pipe and is
normally operated at steady state, as is the CSTR. Tubular reactors are used
most often for gas-phase reactions. A schematic and a photograph of industrial
tubular reactors are shown in Figure 1-8.
In the tubular reactor, the reactants are continually consumed as they
flow down the length of the reactor. In modeling the tubular reactor, we
assume that the concentration varies continuously in the axial direction
through the reactor. Consequently, the reaction rate, which is a function of concentration for all but zero-order reactions, will also vary axially. For the purposes of the material presented here, we consider systems in which the flow
field may be modeled by that of a plug-flow profile (e.g., uniform velocity as
Section 1.4
15
Continuous-Flow Reactors
Figure 1-8(a) Tubular reactor schematic.
Longitudinal tubular reactor. [Excerpted by
special permission from Chem. Eng., 63(10),
211 (Oct. 1956). Copyright 1956 by
McGraw-Hill, Inc., New York, NY 10020.]
Figure 1-8(b) Tubular reactor photo.
Tubular reactor for production of Dimersol G.
(Photo courtesy of Editions Techniq Institut
français du pétrole.)
in turbulent flow), as shown in Figure 1-9. That is, there is no radial variation
in reaction rate, and the reactor is referred to as a plug-flow reactor (PFR).
(The laminar-flow reactor is discussed in Chapters 16 through 18 on nonideal
reactors.)
Plug flow–no radial variations in velocity,
concentration, temperature, or reaction rate
Also see PRS and
Visual Encyclopedia of Equipment.
Figure 1-9
Plug-flow tubular reactor.
The general mole balance equation is given by Equation (1-4)
F j0 – F j +
∫
V
dN
r j dV = ---------j
dt
(1-4)
The equation we will use to design PFRs at steady state can be developed in
two ways: (1) directly from Equation (1-4) by differentiating with respect to
volume V, and then rearranging the result or (2) from a mole balance on species j in a differential segment of the reactor volume ΔV . Let’s choose the second way to arrive at the differential form of the PFR mole balance. The
differential volume, ΔV , shown in Figure 1-10, will be chosen sufficiently
small such that there are no spatial variations in reaction rate within this volume.
Thus the generation term, ΔG j , is
ΔG j =
ΔV
∫
r j dV = r j ΔV
16
Mole Balances
Chapter 1
DV
Fj0
Fj
DGj
V
Figure 1-10
Fj
V + DV
Mole balance on species j in volume
ΔV .
Molar rate of
Molar rate of
Molar flow
Molar flow
Accumulation
Generation
rate of species j – rate of species j +
=
of species j
of species j
Out at ( V + ΔV )
In at V
within ΔV
within ΔV
moles/time
moles/time
moles/time
moles/time
In
Fj
V
–
Out
+ Generation = Accumulation
–
Fj
+
V + ΔV
r jΔV
=
0
(1-10)
Dividing by ΔV and rearranging
–Fj
Fj
V + ΔV
V
------------------------------- = rj
ΔV
the term in brackets resembles the definition of a derivative
f (x + Δx) – f ( x )
df
lim ------------------------------------- = ----Δx
dx
Δx → 0
Taking the limit as ΔV approaches zero, we obtain the differential form of
steady state mole balance on a PFR
dF j
-------- = r j
dV
(1-11)
We could have made the cylindrical reactor on which we carried out our
mole balance an irregularly shaped reactor, such as the one shown in Figure
1-11 for reactant species A.
However, we see that by applying Equation (1-10), the result would yield
the same equation (i.e., Equation (1-11)). For species A, the mole balance is
dF
---------A- = r A
dV
(1-12)
Section 1.4
17
Continuous-Flow Reactors
,
Picasso’s
reactor
FA (V + ⌬V)
FA (V)
⌬V
Figure 1-11
Pablo Picasso’s reactor.
Consequently, we see that Equation (1-11) applies equally well to our model of
tubular reactors of variable and constant cross-sectional area, although it is
doubtful that one would find a reactor of the shape shown in 1-11 unless it
were designed by Pablo Picasso.
The conclusion drawn from the application of the design equation to Picasso’s reactor is an important one: the degree of completion of a reaction
achieved in an ideal plug-flow reactor (PFR) does not depend on its shape,
only on its total volume.
Again consider the isomerization A → B, this time in a PFR. As the reactants proceed down the reactor, A is consumed by chemical reaction and B is
produced. Consequently, the molar flow rate FA decreases, while FB increases
as the reactor volume V increases, as shown in Figure 1-12.
FA0
V=
F A0
∫
FA
dF A
---------–r A
FA
FB
F B1
FA1
0
V1
0
V
Figure 1-12
V1
V
Profiles of molar flow rates in a PFR.
We now ask what is the reactor volume V1 necessary to reduce the entering molar flow rate of A from FA0 to FA1. Rearranging Equation (1-12) in the
form
dF
dV = ---------ArA
and integrating with limits at V = 0, then FA = FA0, and at V = V1, then FA = FA1
V1 =
∫
FA1
F A0
dF A
---------- =
rA
∫
FA0
F A1
dF
---------A–r A
(1-13)
18
Mole Balances
Chapter 1
V1 is the volume necessary to reduce the entering molar flow rate FA0 to some
specified value FA1 and also the volume necessary to produce a molar flow rate
of B of FB1.
1.4.3 Packed-Bed Reactor (PBR)
The principal difference between reactor design calculations involving homogeneous reactions and those involving fluid-solid heterogeneous reactions is
that for the latter, the reaction takes place on the surface of the catalyst (see
Chapter 10). The greater the mass of a given catalyst, the greater the reactive
surface area. Consequently, 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 species A is defined as
– r A′ = mol A reacted/(time x mass of catalyst)
The mass of solid catalyst is used because the amount of catalyst is what is
important to the rate of product formation. We note that by multiplying the
mass ⎞
- , we
heterogeneous reaction rate, – r A′ , by the bulk catalyst density, ρb ⎛⎝ ----------------volume⎠
can obtain the homogeneous reaction rate, –rA
–rA = ρb (– r A′ )
mol-⎞
g ⎞ ⎛ -------mol ⎞ ⎛ --------⎛ -------------=
⎝ dm3 ⋅ s⎠ ⎝ dm3⎠ ⎝ g ⋅ s ⎠
The reactor volume that contains the catalyst is of secondary significance.
Figure 1-13 shows a schematic of an industrial catalytic reactor with vertical
tubes packed with solid catalyst.
Figure 1-13 Longitudinal catalytic packed-bed reactor. [From Cropley, American Institute of
Chemical Engineers, 86(2), 34 (1990). Reproduced with permission of the American Institute of
Chemical Engineers, Copyright © 1990 AIChE. All rights reserved.]
Section 1.4
19
Continuous-Flow Reactors
PBR
Mole Balance
In the three idealized types of reactors just discussed (the perfectly mixed
batch reactor, the plug-flow tubular reactor [PFR]), and the perfectly mixed continuous-stirred tank reactor [CSTR]), the design equations (i.e., mole balances)
were developed based on reactor volume. The derivation of the design equation
for a packed-bed catalytic reactor (PBR) will be carried out in a manner analogous to the development of the tubular design equation. To accomplish this derivation, we simply replace the volume coordinate in Equation (1-10) with the
catalyst mass (i.e., weight) coordinate W (Figure 1-14).
FA0
FA
W
FA(W + ΔW)
FA(W)
Figure 1-14
Packed-bed reactor schematic.
As with the PFR, the PBR is assumed to have no radial gradients in concentration, temperature, or reaction rate. The generalized mole balance on species A over catalyst weight ΔW results in the equation
In
–
FA W –
Out
+
F A ( W + ΔW )
Generation =
+
r A′ ΔW
Accumulation
=
0
(1-14)
The dimensions of the generation term in Equation (1-14) are
moles A
moles A
( r′A ) ΔW ≡ --------------------------------------------------------- ⋅ (mass of catalyst) ≡ ------------------(time)(mass of catalyst)
time
Use the differential
form of design
equation for
catalyst decay and
pressure drop.
which are, as expected, the same dimensions of the molar flow rate FA . After
dividing by ΔW and taking the limit as ΔW → 0, we arrive at the differential
form of the mole balance for a packed-bed reactor
dF
---------A- = r′A
dW
(1-15)
When pressure drop through the reactor (see Section 5.5) and catalyst
decay (see Section 10.7 on the CRE Web site Chapter 10) are neglected, the
integral form of the packed-catalyst-bed design equation can be used to calculate the catalyst weight
You can use the
integral form
only when there
is no ΔP and no
catalyst decay.
FA
W=
∫
F A0
dF A
--------- =
rA′
F A0
∫
FA
dF A
--------–rA′
(1-16)
W is the catalyst weight necessary to reduce the entering molar flow rate of
species A, FA0, down to a flow rate FA.
20
Mole Balances
Chapter 1
For some insight into things to come, consider the following example of
how one can use the tubular reactor design in Equation (1-11).
Example 1–2 How Large Is It?
Consider the liquid phase cis – trans isomerization of 2–butene
which we will write symbolically as
A ⎯⎯→ B
The reaction is first order in A (–rA = kCA) and is carried out in a tubular reactor in
which the volumetric flow rate, v, is constant, i.e., v = v0 .
CA0
v0
A→B
V
V=0
CA = 0.1CA0
v
V1
1. Sketch the concentration profile.
2. Derive an equation relating the reactor volume to the entering and exiting
concentrations of A, the rate constant k, and the volumetric flow rate v0 .
3. Determine the reactor volume, V1, necessary to reduce the exiting concentration to 10% of the entering concentration, i.e., CA = 0.1CA0, when the volumetric flow rate is 10 dm3/min (i.e., liters/min) and the specific reaction rate,
–1
k, is 0.23 min .
Solution
1. Sketch CA as a function of V.
Species A is consumed as we move down the reactor, and as a result, both
the molar flow rate of A and the concentration of A will decrease as we
move. Because the volumetric flow rate is constant, v = v0 , one can use
Equation (1-8) to obtain the concentration of A, CA = FA/ v0 , and then by
comparison with the Figure 1-12 plot, obtain the concentration of A as a
function of reactor volume, as shown in Figure E1-2.1.
CA0
CA
0.1CA0
0
Figure E1-2.1
V1
V
Concentration profile.
Section 1.4
21
Continuous-Flow Reactors
2. Derive an equation relating V, v0, k, CA0, and CA.
For a tubular reactor, the mole balance on species A (j = A) was shown to be
given by Equation (1-11). Then for species A (j = A)
dF
---------A- = r A
dV
Mole Balance:
(1-12)
For a first-order reaction, the rate law (discussed in Chapter 3) is
Rate Law:
Reactor sizing
–r A = kC A
(E1-2.1)
Because the volumetric flow rate, v , is constant ( v = v0), as it is for most all
liquid-phase reactions,
dF A d (C Av ) d ( C A v0 )
dC
---------- = ------------------ = -------------------- = v0 ---------A- = r A
dV
dV
dV
dV
(E1-2.2)
Multiplying both sides of Equation (E1-2.2) by minus one and then substituting Equation (E1-2.1) yields
Combine:
v0 dC A
- = –r A = kC A
– --------------dV
(E1-2.3)
Separating the variables and rearranging gives
v ⎛ dC ⎞
– ----0- ⎜ ---------A-⎟ = dV
k ⎝ CA ⎠
Using the conditions at the entrance of the reactor that when V = 0,
then CA = CA0
V
v CA dC
– ----0- ∫ ---------A- = ∫ dV
k CA0 C A
0
(E1-2.4)
Carrying out the integration of Equation (E1-2.4) gives
v
C A0
V = ----0- ln -------k
CA
Solve:
(E1-2.5)
We can also rearrange Equation (E1-2.5) to solve for the concentration of A
as a function of reactor volume to obtain
Concentration
Profile
C A= C A0exp ( –k V ⁄ v0)
B
A
CA
V
22
Mole Balances
Chapter 1
1
3. Calculate V. We want to find the volume, V1, at which C A = ------ C A0
10
–1
3
for k = 0.23 min and v 0 = 10 dm /min.
Evaluate:
Substituting CA0 , CA , v 0 , and k in Equation (E1-2.5), we have
C A0
10 dm3
10 dm3 /min- ---------------ln
= ----------------- ln10 = 100 dm3 (i.e., 100 L; 0.1 m3 )
V = --------------------------–1
0.1C
0.23
A0
0.23 min
Let’s calculate the volume to reduce the entering concentration to CA = 0.01
CA0. Again using Equation (E1-2.5)
C A0
10 dm3
10 dm3 /min- ------------------= ----------------- ln 100 = 200 dm3
ln
V = --------------------------–1
0.01C A0
0.23
0.23 min
Note: We see that a larger reactor (200 dm3) is needed to reduce the exit concentration to a smaller fraction of the entering concentration (e.g., CA = 0.01 CA0).
We see that a reactor volume of 0.1 m3 is necessary to convert 90% of species
A entering into product B for the parameters given.
Analysis: For this irreversible liquid-phase first order reaction (i.e., –rA = kCA)
being carried out in a PFR, the concentration of the reactant decreases exponentially
down the length (i.e., volume V) of the reactor. The more species A consumed and
converted to product B, the larger must be the reactor volume V. The purpose of the
example was to give a vision of the types of calculations we will be carrying out as
we study chemical reaction engineering (CRE).
1.5 Industrial Reactors 2
Be sure to view the actual photographs of industrial reactors on the CRE Web
site. There are also links to view reactors on different Web sites. The CRE Web
site also includes a portion of the Visual Encyclopedia of Equipment,
encyclopedia.che.engin.umich.edu, “Chemical Reactors” developed by Dr. Susan
Montgomery and her students at the University of Michigan. Also see Professional Reference Shelf on the CRE Web site for “Reactors for Liquid-Phase
and Gas-Phase Reactions,” along with photos of industrial reactors, and
Expanded Material on the CRE Web site.
In this chapter, and on the CRE Web site, we’ve introduced each of the
major types of industrial reactors: batch, stirred tank, tubular, and fixed bed
(packed bed). Many variations and modifications of these commercial reactors
(e.g., semibatch, fluidized bed) are in current use; for further elaboration, refer
to the detailed discussion of industrial reactors given by Walas. 3
2
Chem. Eng., 63(10), 211 (1956). See also AIChE Modular Instruction Series E, 5
(1984).
3 S. M. Walas, Reaction Kinetics for Chemical Engineers (New York: McGraw-Hill,
1959), Chapter 11.
Chapter 1
23
Summary
The CRE Web site describes industrial reactors, along with typical feed
and operating conditions. In addition, two solved example problems for Chapter 1 can be found on the CRE Web site.
Closure. The goal of this text is to weave the fundamentals of chemical
reaction engineering into a structure or algorithm that is easy to use and
apply to a variety of problems. We have just finished the first building
block of this algorithm: mole balances.
Mole Balance
This algorithm and its corresponding building blocks will be developed
and discussed in the following chapters:
•
•
•
•
•
•
Mole Balance, Chapters 1 and 2
Rate Law, Chapter 3
Stoichiometry, Chapter 4
Combine, Chapter 5
Evaluate, Chapter 5
Energy Balance, Chapters 11 through 13
With this algorithm, one can approach and solve chemical reaction engineering problems through logic rather than memorization.
SUMMARY
Each chapter summary gives the key points of the chapter that need to be remembered and carried
into succeeding chapters.
1. A mole balance on species j, which enters, leaves, reacts, and accumulates in a system volume V, is
V
F j0 – F j +
∫
r j dV = dN
---------j
dt
(S1-1)
If, and only if, the contents of the reactor are well mixed will the mole balance (Equation (S1-1)) on
species A give
dN
FA0 – FA + r AV = ----------A
dt
(S1-2)
2. The kinetic rate law for rj is
• The rate of formation of species j per unit volume (e.g., mol/s⋅dm3)
• Solely a function of the properties of reacting materials and reaction conditions (e.g., concentration
[activities], temperature, pressure, catalyst, or solvent [if any]) and does not depend on reactor
type
• ...
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