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

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, Af

'«r CHEMICAL ENGINEERING

Elements of Chemical

Reaction Engineering

H Scott Fogler Third Edition

Applied Algofitfims + Software Packages a Advanced Tools for Solving Complex ProlJlems

The newest digital techniques, built on the sound foundations of the classic, best-selling text

With a combination of user-friendly software and classic algorithms, students learn to solve

problems through reasoning ratfierthan memorization

Thorough coverage of the fundamentals of cfiemlcal reaction engineering forms the backbone of this trusted

text, presented in a framework that helps develop critical-thinking skilis and practical problem-solving All the

classical elements are covered Elements of Ctiemical Reaction Engineering, Third Edition, builds a strong

understanding of chemical reaction engineering principles and shows how they can be applied to numerous

reactions in a variety of applications

The structured approach helps develop skills In critical thinking, creative thinking, and problem-solving, by

employing open-ended questions and stressing the Socratic method

To enhance the transfer of skills to real-life settings, three styles of problems are Included

for each subject:

• Straightforward problems that reinforce the material

• Problems that encourage students to explore the issues and look for optimum solutions

• Open-ended problems that encourage students to practice creative problem-solving skills

Elements ofChsmicsl Reaction Engineering, Third Edition, remains a leader as the only undergraduate-level book

to focus on computer-based solutions to chemical reaction problems

About the CD-ROM

The enclosed CD offers numerous enrichment opportunities for both students and Instructors, including:

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examples and ask "what-if" questions

• Professional Reference Shelf: detailed derivations, equations, general engineering

materials, and specialty reactors and reaction systems

• Additional Study Materials: extra homework problems, course syllabi, guides to

popular software packages

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TURTON, BAILIE, WHITING, AND SHAEIWITZ Analysis, Synthesis and Design of Chemical Processes

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Elements

of Chemical Reaction Engineering

Third Edition

H SCOTT FOGLER Ame and Catherine Vennema Professor

of Chemical Engineering The University of Michigan, Ann Arbor

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of the University of Michigan whose standards aiid lifelong achievements

serve to inspire us

Contents

PREFACE XV

1 MOLE BALANCES 1

1.1 Definition of the Rate of Reaction, - v/^ 2

1.2 The General Mole Balance Equation • 6

1.3 Batch Reactors 8 1.4 Continaous-Flow Reactors 10

L4.I Continuous-Stirred Tank Reactoi- 10 L4.2 Tubular Reactor 11

1.4.3 Packed-Bed Reactor 14

1.5 Industrial Reactors 16 Summary 25 Questions and Problems 25 CD-ROM Material 31 Supplementary Reading 31

2 CONVERSION AND REACTOR SIZING 33

2.1 Definition of Conversion 33 2.2 Design Equations 34

2.2./ Batch Systems 34 2,2,2 Flow Systems 37

2.3 Applications of the Design Equations for Continuous-Flow Reactors 40

2.4 Reactors in Series 48 2.5 Some Further Definitions 56 Summary 59

mr

VIII

Questions and Probiems 62 CD-ROM Material 66 Supplementary Reading 67

3 RATE LA WS AND STOICHIOMETRY

Contents

6S 3.1 Basic Definitions 68

3.1.1 The Reaction Rate Constant 69

3 J.2 The Reaction Order and the Rate Law 3.1.3 Elementary Rate Laws and Molecularity

3.1.4 Reversible Reactions 77

3.1.5 Nonelementary Rate Laws and Reactions

3.2 PresentStatusof Our Approach to Reactor Sizing

and Design 83 3.3 SloicMometric Table S4

3.3.1 Batch Systems 84 3.3.2 Constant-Volume Reaction Systems 87 3.3.3 Flow Systems 90

3.3.4 Volume Change with Reaction 92

3.4 Expressing Concentrations in Terms Other Than

Conversion 105 3.5 Reactions with Phase Change 107

Summary 111 Questions and Problems 114 CD-ROM Material 123 Supplementary Reading 123

220

73

75

81

4.1 Design Structure for Isothermal Reactors 125

4.2 Scaie-Up of Uquid-Phase Batch Reactor Data to the Design

ofaCSTR 129

4.2.1 Batch Operation 129 4.2.2 Design ofCSTRs 137

4.3 Tubular Reactors 147

4.4 Pressure Drop in Reactors 153

4.4.1 Pressure Drop and the Rate Law 153 4.4.2 Flaw Tlirough a Packed Bed 154 4.4.3 Spherical Packed-Bed Reactors 168 4.4.4 Pressure Drop in Pipes 173

4.5 Synthesizing a Chemical Plant 174

4.6 Using Cfi^ (liquid) and F^ (gas) in the Mole Balances

and Rate Laws 176

4.6.1 CSTRs, PFRs, PBRs, mdBatch Reactors 111 4.6.2 Membrane Reactors 182

4.7 Unsteady-State Operation of Reactors 187

4.7.1 Startup of a CSTR 189 4.7.2 Semibatch Reactors 190 4.7.3 Reactive Distillation 197

4,8 Recycle Reactors 200 Summary 202 ODE Solver Algorithm 204 Questions and Probiems 205 Journal Critique Problems 219 Some Thoughts on Critiquing What You Read CD-ROM Material 220

Supplementary Reading 222

5 COLLECTION AND ANALYSIS OF RATE DATA

5.1 Batch Reactor Data 224

5.1.1 Differential Method of Rate Analysis 224 5.1.2 Integral Method 235

5.2 Melliod of Initial Rates 239 5.3 Method of Half-Lives 242 5.4 Differential Reactors 243 5.5 Least-Square Analysis 2S0

5.5.1 Linearization of the Rate Law 250

5.5.2 Nonlinear Least-Squares Analysis 252

5.5.3 Weighted Least-Squares Analysis 261

5.6 Experimental Planning (CD-ROM) 262 5.7 Evaluation of Laboratory Reactors (CD-ROM) 263

5.7.1 Integral (Fixed-Bed) Reactor 264

5.7.2 Stirred Batch Reactor 264

5.7.3 Stirred Contained Reactor (SCSR) 265 5.7.4 Continuous-Stirred Tank Reactor (CSTR) 265 5.7.5 Straight-Through Transport Reactor 266 5.7.6 Recirculating Transport Reactor 266 5.7.7 Summary of Reactor Ratings 267

Summary 26S Questions and Problems 269 Journal Critique Problems 279 CD-ROM Material 280 Supplementary Reading 280

223

6.1 Maximizing the Desired Product in Parallel Reactions

6.1.1 Maximizing the Rate Selectivity Parameter S

for One Reactant 285

6.1.2 Maximizing the Rate Selectivity Parameter S

for Two Reactants 288

284

6.2 Maximizing the Desired Product in Series Reactions 291

6.3 Algorithm for Solution to Complex Reactions 295

6.3.1 Mole Balances 295 6.3.2 Net Rates of Reaction 296 6.3.3 Rate Laws 297

6.3.4 Stoichiometry: Relative Rates of Reaction 297 6.3.5 Stoichiometry: Concentrations 300

6.3.6 Combining Step 301 6.3.7 Multiple Reactions in a CSTR 307

6.4 Sorting It All Out 314

6.5 The Fun Part 315

6.6 The Attainable Region CD-ROM 316

Summary 318 Questions and Problems 320 Journal Critique Problems 335 CD-ROM Material 335 Supplementary Reading 336

7 NONELEMENTARY REACTION KINETICS

7.5.8 Oxygen-Limited Gennentation

7.5.9 Scale-up 407

Summary 408 Questions and Problems 410 CD-ROM Material 423 Journal Critique Problems 424 Supplemental^ Reading 424

S STEADY-STATE NONISOTHERMAL REACTOR DESIGN

Anionic Polymerization 375

Enzymatic Reaction Fundamentals 383

7.4.1 Definitions and Mechanisms 383 Michaelis-Menten Equation 386 Batch Reactor Calculations 389 Inhibition of Enzyme Reactions 391 Multiple Enzyme and Substrate Systems 392

Bioreactors 393

7.5.1 Cell Growth 394

7.5.2 Rate Laws 396

7.5.3 Stoichiometry 398 7.5.4 Mass Balances 400 7.5.5 Chemostats 404 7.5.6 Design Equations 404

7.5.7 Wash-out 406

7.3.2 7.3.3 7.3.4 7.3.5

7.4.2 7.4.3 7.4.4 7.4.5

8.1 Rationale 426

8.2 The Energy Balance 427

8.2.1 First Law Thennodynamics 427

5.2.2 Evaluating the Work Term 429

8.2.3 Dissecting the Steady-State Molar Flow Rates

to Obtain the Heal of Reaction 430 8.2.4 Dissecting the Enthalpies 432

8.2.5 Relating SHR^CF), m°^, and hCp 434

8.2.6 Constant of Mean Heat Capacities 435 B.2.7 Variable Heat Capacities 436 8.2.8 Heat Added to the Reactor Q 438

8.3 Nonisothermal Continuous-Fiow Reactors 440

8.3.1 Application to the CSTR 441 8.3.2 Adiabatic Tubular Reactor 451

8.3.3 Steady-State Tubular Reactor

with Heat Exchange 458

8.4 Equilibrium Conversion 468

8.4.1 Adiabatic Temperature and Equilibrium

Conversion 468 8.4.2 Optimum Feed Temperature 476

8.5 Nonadiabatic Reactor Operation: Oxidation of Sulfur

Dioxide Example 478

8.5.1 Manufacture of Sulfuric Acid 478 8.5.2 Catalyst Quantities 481 8.5.3 Reactor Configuration 482 8.5.4 Operating Conditions 482

8.6 Multiple Steady States 490

8.6.1 Heat-Removed Term R(T) 491 8.6.2 Heat of Generation, G{T) 492 8.6.3 Ignition-Extinction Curve 493 8.6.4 Runaway Reactions 497 8.6.5 Steady-State Bifurcation Analysis 498

5.7 Nonisothermal Multiple Chemical Reactions 500

8.7.1 Plug-Flow Reactors 500 8.7.2 CSTR 504

Summary 507

Questions and Probiems 511 Journal Cdtique Problems 530 CD-ROM Material 530 Supplementary Reading 532

The General Equation 534

Unsteady Operation of CSTRs and Semibatch Reactors 535

9.2.1 Batch Reactors 537

9.2.2 Adiabatic Operation of a Batch Reactor 537

9.2.3 Transient CSTR, Batch, and Semibatch Reactors with Heat Exchanger—Ambient Temperature Not

Nonisothermal Multiple Reactions 566

Unsteady Operation of Plug-Flow Reactors

Summary 571 Questions and Problems 572 CD-ROM Material 579 Supplementary Reading 579

10.2 Steps in a Catalytic Reaction 591

10.2.1 Adsorption Isotherms 594 10.2.2 Surface Reaction 599 10.2.3 Desorption 601 10.2.4 The Rate-Limiting Step 601

10.3 Synthesizing a Rate Law, Mechanism,

and Rate-Limiting Step 603

10.3.1 Is the Adsorption of Cumene Rate-Limiting? 606

10.3.2 Is the Surface Reaction Rate-Limiting? 609 10.3.3 Is the Desorption of Benzene Rate-Limiting? 610 10.3.4 Summary of the Cumene Decomposition 612

10.3.5 Rate Laws Derived from the Pseudo-Steady-State

Hypothesis 616

10.4 Design of Reactors for Gas-SoUd Reactions 619

10.4.1 Basic Guidelines 619 10.4.2 The Design Equations 619

581

xm

10.5 Heterogeneous Data Analysis for Reactor Design 620

10.5.1 Deducing a Rate Law

from the Experimental Data 622

10.5.2 Finding a Mechanism Consistent

with Experimental Observations 623 10.5.3 Evaluation of the Rate Law Parameters 624 10.5.4 Reactor Design 627

10.6 Chemical Vapor Deposition 631 10.7 Catalyst Deactivation 634

10.7.1 Types of Catalyst Deactivation 636 10.7.2 Temperature-Time Trajectories 647 10.7.3 Moving-Bed Reactors 649 10.7.4 Straight-Through Transport Reactors 655 10.7.5 Determining the Order of Deactivation 660

10.8 Reaction Engineering in Microelectronic

Device Fabrication 662

I0.8.I Etching 664

Summary 665 Questions and Problems 668 Journal Critique Problems 682 CD-ROM Material 683 Supplementary Reading 684

11 EXTERNAL DIFFUSION EFFECTS

11.1 Mass Transfer Fundamentals 687

11.1.1 Definitions 687 11.1.2 MolarFlux 687 11.1.3 Pick's First Law 688

11.2 Binary Diffusion 689

11.2.1 Evaluating the Molar Flux 689 11.2.2 Boundary Conditions 692 11.2.3 Modeling Diffusion Without Reaction 692

11.2.4 Temperature and Pressure Dependence

ofD^^ 691

11.2.5 Modeling Diffusion with Chemical Reaction

11.3 External Resistance to Mass Transfer 699

11.3.1 Mass Transfer Coefficient 699 11.3.2 Mass Transfer to a Single Particle 702

11.3.3 Mass Transfer-Limited Reactions

Contents

n.5.1 Catalyst Regeneration 720

11.5.2 Dissolution of Monodispersed Solid Particles

11.5.3 Flow and Dissolution in Porous Media 726

Summary 728 Questions and Problems 729 Journal Article Problem 735 Journal Critique Problems 735 CD-ROM Materia! 735 Supplementary Reading 736

724

12.1 Diffusion and Reaction in Spherical Catalyst Pellets 739

12.1.1 Effective Diffusivity 739

12.1.2 Derivation of the Differential Equation Describing

Diffusion and Reaction 741 12.1.3 Writing the Equation in Dimensionless Form 743

12.1.4 Solution to the Differential Equation

for a First-Order Reaction 746

12.2 Internal Effectiveness Factor 747 12.3 Falsified Kinetics 753

12.4 Overall Effectiveness Factor 755

12.5 Estimation of Diffusion- and Reaction-Limited

Regimes 758

12.5.1 Weisz-Prater Criterion for Internal Diffusion 758

12.6 Mass Transfer and Reaction in a Packed Bed 761

12.7 Determination of Limiting Situations

from Reaction Data 767 12.8 Multiphase Reactors 768

12.8.1 Slurry Reactors 769 12.8.2 Trickle Bed Reactors 783

12.9 FIuidized-Bed ReactorSoj.KOM

786

12.10 The Overall View 787 12.11 Chemical Vapor Deposition Reactors 789 Summary 793

CD-ROM Material 805

Supplementary Reading 806

13 DISTRIBUTIONS OF RESIDENCE TIMES

13.3 Characteristics of theRTD 819

13.3.1 Integral Relationships 819 13.3.2 Mean Residence Time 821 13.3.3 Other Moments of the RTD 823 13.3.4 Normalized RTD Function, Ex 825 13.3.5 Internal-Age Distribution la 826

13.4 RTD in Ideal Reactors 829

13.4.1 RTDs in Batch and Plug-Flaw Reactors

13.4.2 Single-CSTR RTD 829 13.4.3 Laminar Flow Reactor 831 13.4.4 PFR/CSTR Series RTD 833

13.5 Reactor Modeling with the RTD 836 13.6 Zero-Parameter Models 838

13.6.1 Segregation Model 838 13.6.2 Maximum Mixedness 844 13.6.3 Heat Effects 851

13.7 Using Software Packages 8S1 13.8 RTD and Multiple Reactions 854

13.8.1 Segregation Model 854 13.8.2 Maximum Mixedness 855

Summary 860 Questions and Problems 861 CD-ROM Material 868 Supplementary Reading 869

829

14.1 14.2

14.3

Some Guidelines 871 One-Parameter Models 872

14.2.1 Tmks-in-Series Model 873 14.2.2 Dispersion Model 877

Two-Parameter Models—Modeling Real Reactors with

Combi-nations of Ideal Reactors 893

14.3.1 Real CSTR Modeled Using Bypassing

and Dead Space 893 Solving the Model System for Cj^ and X 894

Using a Tracer to Determine the Model Parameters

in CSTR-with-Dead-Space-and'Bypass

Model 895

Real CSTR Modeled with an Exchange

Volume 899 Solving the Model System for C^ and X 900

14.3.1 A 14.3.1B

14.3.2 14.3.2A

14.4 14.5

!4.6

Contents

14.3.2B Using a Tracer to Determine the Model Parameters

in a CSTR with an Exchange Volume 900

Use of Software Packages to Determine the Model

Parameters 901

Other Models of Nonideal Reactors Using CSTRs

and FFRs 904 Using the RTD Versus Needing a Model 904 Summaiy 907

Questions and Problems 9Q9

CD-ROM Material 916 Supplementary Reading 917

A p p e n d i x A NUMERICAL TECHNIQUES

A 1 Useful Integrals in Reactor Design 921

A.2 Equal-Area Graphical Differentiation 922 A.3 Solutions to Differential Equations 924

A.4 Numerical Evaluation of Integrals 924

A.5 Software Packages 926

Appendix B IDEAL GAS CONSTANT

AND CONVERSION FACTORS

Appendix C THERMODYNAMIC RELATIONSHIPS INVOLVING

THE EQUILIBRIUM CONSTANT Appendix D MEASUREMENT OF SLOPES ON SEMILOG PAPER

Appendix E SOFTWARE PACKAGES

Appendix F NOMENCLATURE

Appendix G MOLECULAR DYNAMICS OF CHEMICAL REACTIONS

G 1 CoUision Theory 941 G.2 Transition State Theory 944 G-3 Moleculai- Dynamics 948

Appendix H OPEN-ENDED PROBLEMS

H 1 Design of Reaction Engineering Experiment

H.2 Effective Lubricant Design 953 H:3 Peach Bottom Nuclear Reactor 953

H.4 Underground Wet Oxidation 954 H.5 Hydrosuifurization Reactor Design 954 H.6 Continuous Bioprocessing 954 H.7 Methanol Synthesis 954 H.8 Cajun Seafood Gumbo 954

HOW TO USE THE CD-ROM USE OF COMPUTATIONAL CHEMISTRY SOFTWARE PACKAGES

INDEX ABOUT THE CD

9 5 6

9 5 8

961

9 7 6

Preface

"The man who has ceased to learn ought not to be allowed to wander around loose in these danger- ous days."

M M Coady (ca 1870)

A The Audience This book is intended for use as both an undergraduate- and graduate-level text in chemical reaction engineering The level of difficulty will ctepend on the choice

of chapters to be covered and the type and degree of difhcully of problems assigned Most problems requiring significant numerical computations can be solved with a personal computer using either POLYMATH or MATLAB

B The Goals B.1, To Develop a Fundamental Understanding

of Reaction Engineering

The first goal of this book is to enable the reader to develop a clear understanding of the fundamentals of chemical reaction engineering This goal will be achieved by presenting a structure that allows the reader to solve reac-tion engineering problems through reasoning rather than through memorization and recall of numerous equations and the restrictions and conditions under which each equation applies To accomplish this, we use (1) conventional problems that reinforce the student's understanding of the basic concepts and principles (included at the end of each chapter); (2) problems whose solution requires reading the literature, handbooks, or odier textbooks on chemical engineering kinetics; and (3) problems that give swdents practice in problem

• T

XX

definition and alternative pathways to solutions The algorithms presented in

die text for reactor design provide a framework through which one can develop

confidence through reasoning rather than memorization

To give a reference point as to the level of understanding required in the

profession, a number of reaction engineering problems from the California

Board of Registration for Civil and Professional Engineers—Chemical

Engi-neering Examinations (PECEE) are included Typically, each problem should

require approximately one-half hour to solve, Hints on how to work the

Califor-nia exam problems can be found in the Summary Notes and in the Tlioughts on

Problem Solving on the CD-ROM

The second and third goals of this book are to increase the student's critical

thinking skills and creative thinking skills by presenting heuristics and problems

that encourage the student to practice these skills,

B.2 To Develop Critical Thinking Skills

Due to the rapid addition of new information and the advancement of

sci-ence and technology that occur almost daily, an engineer must constantly expand

his or her horizons beyond simply gathering infomaation and relying on the basic

engineering principles,

A number of homework problems have been included that are designed to

enhance critical thinking skills Socratic questioning is at die heart of critical

thinking and a number of homework problems draw from R W Paul's six types

of Socratic questions:'

(1) Questions for clarification: Why do you say that? How does this

relate to our discussion?

(2) Questions that probe assumptions: What could we assume instead?

How can you verify or disprove that assumption?

(3) Questions that probe reasons and evidence: What would be an

example?

(4) Questions about viewpoints and perspectives: What would be an

alternative?

(5) Questions that probe implications and consequences: What

generali-zations can you make? What are the consequences of that assumption?

(6) Questions about the question: What was the point of this question?

Why do you think I asked this question?

Practice in critical thinking can be achieved by assigning additional parts to the

problems at the end of each chapter tiiat utilize R, W Paul's approach Most of

these problems have more than one part to them The instructor may wish to

assign all or some of the parts In addition, the instructor could add the following

parts to any of the problems:

• Describe how you went about solving this problem,

• How reasonable is each assumption you made in solving this problem?

' Paul, R W., Critical Thinking (Published fay the Foundation for Critical Thinking,

Santa Rosa, CA, 1992)

Although the students were told that choosing an article with erroneous data or reasoning was not necessary for a successful critique, finding an error made the whole assignment much more fun and interesting Consequently, a select number

of problems at the end of chapters involve the critique of journal articles on tion engineering which may or may not have major or minor inconsistencies, In some cases, a small hint is given to guide the student in his or her analysis

reac-B.3 To Develop Creative Thinking Skills

To help develop creative Uiinking skills, a number of problems are open-ended to various degrees Beginning with Chapter 4, die first problem in each chapter provides students the opportunity to practice their creative skills by making up and solving an original problem Problem 4-1 gives some guidehnes for developing original problems A number of techniques that can aid the stu-dents in practicing their creativity (e.g., lateral thinking and brainstorming) can

be found in Fogler and LeBlanc.^

"What if " problems can serve to develop both critical and creative

dunk-ing skills The second problem of each chapter (e.g., 4-2) contains "What if "

questions that encourage the student to think beyond a single answer or operating condition These problems can be used in conjunction with the living example problems on die CD to explore die problem Here, questioning can be carried out

by varying the parameters in die problems

One of the major goals at the undergraduate level is to bring the students to the point where they can solve complex reaction systems, such as multiple reac-tions with heat effects, and then ask 'TVhat if " questions and look for opti-mum operating conditions One problem whose solution exemplifies this goal is

die Manufacture of Styrene, Problem

8-30-(1) Ethyibenzene -> Styrene + Hydrogen: Endothermic (2) Ethyibenzene -^ Benzene -i- Ediylene; Endothennic (3) Ethyibenzene + Hydrogen -> Toltiene -i- Methane: Exothermic

In this problem, the students can find a number of operating conditions which maximize the yield and selectivity

The parameters can also be easily varied in the example problems by ing die POLYMATH or MATLAB programs from the CD onto a computer to

load-explore and answer "What if " questions

' Fogier, H, S and S E LeBlanc, Strategies far Creative Problem Solving (Upper

Sad-dle River, NJ: Prentice Hall, 1995)

XXM

Margin Notes

C The Structure

The strategy behind the presentation of material is to continually build on a

few basic ideas in chemical reaction engineering to solve a wide variety of

problems These ideas are referred to as the Pillars of Chemical Reaction

Engineering, on which different applications rest The pillars holding up the

application of chemical reaction engineering ai'e shown in Figure P-1

IMULTIPLEREACTJONSI JMflSS TRanSFER OPERATiONS I [NONISOT>ffiRMfll OPERATION, WJLTIPLE BTEADY STATES | IMOOEUNG REAL REACTORS, RTD DISTCRSION SESRECATION]

fettJAt-YSlB OF RATE DATA, LABORATORY REACTORS LEAST-SQUARES ANALYSISl jDESION OF CHEMICAL REACTORS, PFR CSTR BATCH SEMIBATCH, PACKED BEDsl

^ ^ (TO C=vP ^ ^ S

Figure P-1 Pillars of Chemical Reaction Engineering

The architecture and construction of the structure shown in Figure P-1 had many participants, most notably Professors Amundsen, Aris, Smith, Levenspiel,

and Denbigh The contents of this book may be studied in virtually any order

after the fet four chapters, with few restrictions A flow diagram showing

possi-ble paths is shown in Figure P-2

In a three-hour undergraduate course at the University of Michigan, imately eight chapters are covered in the following order: Chapters 1, 2, 3, 4, and

approx-6, Sections 5.1-5.3, and Chapters 8,10, and parts of either 7 or 13 Complete

sam-ple syllabi for a 3-credit-hour course and a 4-credit-hour course can be found on

the CD-ROM

The reader will observe that although metric units are used primarily in this text (e.g., kmol/m^, J/mol), a variety of other units are also employed (e.g.,

Ib/ft^) This is intentional It is our feeling that whereas most papers published in

the future will use the metric system, today's engineers as well as those

graduat-ing over the next ten years will be caught in the transition between EngUsh, SI,

and metric units, As a resuit, engineers will be faced with extracting information

and reaction rate data from older Uterature which uses English units as well as the

current literature using metric units, and they should be equally at ease with both

The notes in the margins are meant to serve two purposes First, they act as guides or as commentary as one reads through the material Second, they identify

key equations and relationships that are used to solve chemical reaction

i

CH,5 COLLECTION AND ANALYSIS OF DATA

*->

CH.S MULTIPLE REACTIONS «-+

CH,7 NONEt£MENTARY HCM)GENEOUS IHEACTimS

<->

CH,8 STEADY STATE HEAT EFFECTS

4~>

CH.tO CATALYSIS

mo

CATALYTIC

< - * •

CH.t3 FIESIDENCE TIME DISTRIBUTION

CH.9 UNSTEADY STATE HEAT EFFECTS

CH.11 EXTERNAL DIFFUSION EFFECTS

C H H NONiDEAL REACTORS

CH.9 UNSTEADY STATE HEAT EFFECTS

CH.11 EXTERNAL DIFFUSION EFFECTS

C H H NONiDEAL REACTORS

"

i

SECTIONS 8.78 9,5 MULTIPLE REACTIONS

c H i a DIFFUSION

!N POROUS

Figure P-2 Sequences for Studying the Text

examples and clear explanations, rather than an outline of the principles and the philosophy of chemical reaction engineering There are many other applications described in the text

D The Applications Important applications of chemical reaction engineering (ORE) of all kinds can

be found both inside and outside the chemical process industries (CPI) In this text, examples from the chemical process industries include the manufacture of ethylene oxide, phthalic anhydride, ethylene glycol, metaxylene, styrene, sul-fur trioxide, propylene glycol, ketene, and t-butane just to aame a few Also, plant safety in the CPI is addressed in both example problems and homework problems These are real industrial reactions with actual data and reaction rate law parameters

Because of the wide versatility of the principles of CRE, a number of examples outside the CPI are included, such as the use of wetlands to degrade toxic chemicals, smog formation, longevity of motor oils, oil recovery, and phar-macokinetics (cobra bites, SADD-MADD, drug delivery) A samphng of the applications is shown graphically in the following figures

XXIV

I^^RVfJlMll fPOuntT'ld

SmogCCh, l.Ch 7) Wetlands (Cti 4)

i'liarmi'ctdiliictfcsyrCulim Bilis [Body) Heatttte

CvoHiErmlc Rfdctlun^Thiii

Oil Recovery Cobra Bites (Ch 6) Lubricant Design PliinC Sufety

(Ch.5) (Ch.7) (Ch,8&9)

Manufacture of Phttialic Anhydride {Ch 3)

Chemical Piaat for Ethylene Glycol using Examples from Ch, 4

E The Components of the CD-ROM The primary purpose of the CD-ROM is to serve as an enrichment resource Its objectives are fourfold: (I) To provide the option/opportunity for further study or clarification on a particular concept or topic through Summary Notes, additional examples, interactive computing modules and web modules, (2) To provide the opportunity to practice critical thinking skills, creative thinking skills, and prob-

lem solving skills through the use of "What if " questions and "living example

problems," (3) To provide additional technical material for the professional ence shelf, (4) To provide other tutorial information, such as additional home-work problems, thoughts on problem solving, how to use computational software

refer-in chemical reaction engrefer-ineerrefer-ing, and representative course structures The lowing components are listed atjhe end of most chapters and can be accessed, by chapter, on the CD

fol-Learning Resources

These resources give an overview of the material in each chapter and provide extra explanations, examples, and applications to reinforce the basic concepts of chemical reaction engineering The learning resources on the CD-ROM include:

1 Summary Nates

These are Summary Notes that will give an overview of each chapter, and are taken from lecmre notes from an undergraduate class at Michigan

3 Interactive Computer Modules

Students can use the corresponding Interactive Computer Modules

to review the important chapter concepts and then apply them to real problems in a unique and entertaining fashion The Murder Mys-tery module has long been a favorite with students across the nation,

4 Solved Problems

A number of solved problems are presented along with

prob-lem-solving heuristics Probprob-lem-solving strategies and additional

worked example problems are available in the Thoughts on

Problem Solving section of the CD-ROM

Living Example Problems

A copy of POLYMATH is provided on the CD-ROM for the students

to use to solve the homework problems The example problems that use an ODE solver (e.g., POLYMATH) are referred to as "living exam-ple problems" because the students can load the POLYMATH program directly onto their own computer in order to study the problem Stu-

xxvi

Preface

dents are encouraged to change pai-ameler values and to "play with"

the key variables and assumptions Using the living example problems

to explore the problem and asking "What if " questions provides the

opportunity to practice critical and creative thinking skills

Professional Reference Shelf

This section of the CD-ROM contains:

1 material that is important to the practicing engineer, although it is

typically not included in the majority of chemical reaction

engi-neering courses

2 material that gives a iTiore detailed explanation of derivations that

were abbreviated in the text The intermediate steps to these

der-ivations are given on the CD-ROM

' Additional Homework Problems

New problems were developed for this edition that provide a greater

opportunity to use today's computing power to solve realistic problems

• Other CD-ROM Material

In addition to the components listed at the end of each chapter the

following components are included on the CD-ROM:

1 Software ToolBox

Instructions on how to use the different software packages

(POLY-MATH, MATLAB, and ASPEN PLUS) to solve examples

2 Representative Syllabi for a 3- and a 4-Credit Course

The syllabi give a sample pace at v/hich the course could be

taught as well as suggested homework problems

3 FAQ

These are Frequently Asked Questions (FAQ's) from

undergradu-ate stadeuts taking reation engineering,

• Virtual Reality Module (WWW)

This module provides an opportunity to move inside a catalyst pellet

to observe surface reactions and coking It can be found at

http://www.engin.umich.edu/labs/vrichel

F The Integration of the Text and the CD-ROM There are a number of ways one can use the CD in conjunction with the text The

CD provides enrichment resouives for the reader in the form of interactive

tutori-a!s Pathways on how to use the materials to learn chemical reaction engineering are shown in Figure P-3 and P-4 The keys to the CRE learning flowsheets are

Primary resources

( CD 1 = Enrichment resources

F.I For the University Student

In developing a fundamental understanding of the material, the student may wish to use only the primary resources wiUiout using the CD-ROM, (i.e

using only the boxes shown in Figure P-3) or the smdent may use a few or ail

of the interacdve tutorials in the CD-ROM (i.e., the circles shown in Figure P-3) However, to practice die skills that enhance cridcal and creative diinking,

the students are strongly encouraged to use the Living Example Problems and

vary tlie model parameters to ask and answer "What if " questions

Start

Figure P-3 A Student Patliway to Iniegraie ihe Class Text and CD

•r

Pfaface

Problems

figure P-4 A Problem-Solving Pathway to IniegraCe the text and the CD,

One notes that while the author recommends studying the living examples before

working home problems, they may be bypassed, as is the case with all the

enrich-ment resources if time is not available However, class tesdng of the enrichenrich-ment

resources reveals that they not only greatly aid in learning the material but they

may also serve to motivate students through the novel use of CRE principles

F.2, For the Practicing Engineer

Practicing engineers may want to first review the CD summary notes or

the summaries at the end of each chapter to refresh their memories as to what

they have previously studied They can then focus on the topics that they want

to study in the text using the web modules, solved problems, and interactive

computer modules as tutorials They can also learn more about specialty topics

by using the CD reference sheif The flow diagram is shown in Figure P-4

G, The Web

The Web site (http://www.engin.umich,edu/ cre) will be used to update the text

and the CD-ROM It will identify typographical and otiier errors in the 3st and

2nd piintings of the 3rd edition of the text In the neai" future, additiofia!

mate-rial will be added to include more solved problems as well as additional Web

Modules

Preface

H What's New

XXIX

The main thrust of the new edition is to enable the student to solve Digital

Age'^ reacdon engineering problems, Consequendy the content, example

prob-lems, and homework problems focus on achieving this goal These problems provide the students an opportunity to pracdce their critical and creative think-ing skills by "playing with" the problems through parameter variations Conse-quently, some of the text material, e.g., control of chemical reactors and safety, was added because it provides opportunities to formulate and solve problems

For example, in the Case Study on safety, the shident can use the CD-ROM to

cany out a post-mortem on the nitroanaline explosion in Example 9-2 to find out what would have happened if the cooling h ^ failed for 5 minutes instead

of 10 minutes Significant effort has been devoted to developing example and homework problems that foster critical and creative thinking

The use of mole balances in terms of concentrations and flow rates rather than conversions is introduced early in the text so diey can be easily applied to membrane reactors and multiple reactions The 3rd edition contains more industrial chemistry with real reactors and real reactions and extends the wide range of applications to which chemical reaction engineering principles can he applied (i.e„ cobra bites, drug medication, ecological engineering) New mate-rial includes spherical reactors, recycle reactors, trickle bed reactors, fluidized bed reactors, regression of rate data, etching of semiconductors, multiple reac-tions in RTD models, the application of process control to CSTRs, safety, col-lision theory, transition state theory, and an- example using computational chemistry to calculate an activation energy The material that has been greatly expanded includes polymerization, heat effects in batch reactors and in multi-ple reactions, catalysts and catalytic reactions, experimental design, and reactor staging The living example problems on the CD-ROM are in both POLY-MATH and MATLAB

A large number of enrichment resources are provided on the CD-ROM that can help the student over difficult spots However, if there is a time con-straint, or the reader's computer breaks down, the reader need only read the text and proceed along the patiiway of the boxes shown in Figures P-3 and P-4,

I Acknowledgments Many of tlie problems at the end of the various chapters were selected from the

California Board of Registration for Civil and Professional ical Engineering Examinations (PECEE) in past years The permission for use

Engineers—Chem-of these problems, which, incidentally, may be obtained from the Documents Section, California Board of Registration for Civil and Professional Engineers— Chemical Engineering, 1004 6th Street, Sacramento, CA 95S14, is gratefully acknowledged (Note: These problems have been copyrighted by the California Board of Registration and may not be reproduced without their permission.)

^ Fogler, H S., "Teaching Critical Tliiniiing, Creative Tliiiiking and Problem Solving in

the Digital Age" (Phillips Lecture, Oklahoma State University Press, April 25, 1997),

However, all intensive laws tend often to have exceptions Very interesting

con-cepts take orderly, responsible statements Virtually ali laws intrinsically are

nat-ural thoughts General observations become laws under experimentation

There are so many colleagues and students who contributed to this book

that it would require another chapter to thank them all in an appropriate manner

I would like to again acknowledge all my friends and colleagues for their

contributions to the 1st and 2nd editions (See Introduction, CD-ROM), For the

3rd edition, I would like to give special recognition to the students who

con-tributed so much to the CD-ROM: In particular" Dieter Schweiss, Anuj Hasija,

Jim Piana, and Susan Fugett, with thanks also to Anurag Murial, Gavin Sy,

Scott Conaway, Mayur Valanju, Matt Robinson, Tim Mashue, Lisa Ingalls, Sean

Conners, Gustavo Boiaiios, and EUyne Buckingham Further, Tim Hubbard,

Jessica Hamman, David Johnson, Kylas Subramanian, Sumate Charoenchaidet,

Lisa Ingalls, Probjot Singh, Abe Sendijarevic, and Nicholas R Abu-Absi

worked on the solution manual Jason Ferns, Rob Drewitt, and Probjot Singh

contributed to the problems, while Professor Andy Hrymak, Probjot Singh,

Marty Johnson, Sumate Charoenchaidet, N Vijay, and K Subramanxan helped

with proofreading the galleys Thanks to my graduate students Venkat

Ram-achandran, Chris Fredd, Dong Kim, Barry Wolf, Probjot Singh, Vaibhav

Nal-waya, and Ann Wattana for their patience and understanding Barbara Zieder

(copy-editing), Lisa Garboski (production), andYvette Raven (CD-ROM) did

an excellent job in bringing the project to a successful completion Bernard

Goodwin of Prentice Hall was extremely helpful and supportive throughout

The stimulating discussions with Professors John Falconer, D B Battacharia,

Richard Braatz, Kristi Anseth, and Al Weimer are greatly appreciated I also

appreciate the friendship and insights provided by Dr Lee Brown, who

contrib-uted to chapters 8, 12, 13, and 14 Professor Mike Cutlip gave not only

sug-gestions and a critical reading of many sections, but most important provided

continuous support and encouragement throughout the course of this project

Laura Bracken is so much a part of this manuscript through her excellent

deci-phering of equations and scribbles, and typing, her organization, and always

present wonderful disposition Thanks Radar]! Finally, to my wife Janet, love

and thanks Without her enormous help and support the project would not have

been possible

HSF Ann Arbor

Elements

of Chemical Reaction Engineering

Third Edition

For updates on the CD and typographical errors for this printing see the web site;

http://www.engin.umich.edu/~cte

Mole Balances ^

The first step to knowledge

is to know that we are ignorant

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

This book focuses on a variety of chemical reaction engineering topics

It is concerned with the rate at which chemical reactions take place, together with the mechanism and rate-Umiting steps that control the reaction process The sizing of chemical reactors to achieve production goals is an important segment How materials behave within reactors, both chemically and physi-cally, is significant to the designer of a chemical process, as is how the data from chemical reactors should be recorded, processed, and interpreted

Before entering into discussions of the conditions that affect chemical reaction rates and reactor design, it is necessary to account for the various chemical species entering and leaving a reaction system This accounting pro-cess is achieved through overall mole balances on individual species m the

http://avibert.blogspot.com

Mote Balances Chap 1

nicotine

reacting system In this chapter we develop a general mole balance that can be

applied to any species (usually a chemical compound) entering, leaving, and/or

remaining within the reaction system volume, After defining the rate of

reac-tion, - r ^ , iuid discussing the earlier difficulties of properly defining the

chem-ical reaction rate, in this chapter we show how the general balance equation

may be used to develop a preliminary form of the design equations of the most

common industrial reactors: batch, continuous-stirred tank (CSTR), and

tubu-lar In developing these equations, the assumptions pertaining to the modeling

of each type of reactor are deUneated Finally, a brief summary and series of

short review questions are given at the end of the chapter

1.1 Definition of the Rate of Reaction, - 0 \

We begin our study by performing mole balances on each chemical species in

the system Here, the tenn chemical species refers to any chemical compound

or element with a given identity The identity of a chemical species is

deter-mined by the kind, number, and configuration of that species' atoms For

example, the species nicotine (a bad tobacco alkaloid) is made up of a fixed

number of specific elements in a definite molecular arrangement or

configura-tion The strucmre shown illustrates the kind, number, and configuration of the

species nicotine (responsible for "nicotine fits") on a molecular level

Even though two chenaical compounds have exactly the same number of atoms of each element, they could still be different species because of different

configurations For example, 2-butene has four carbon atoms and eight

hydro-gen atoms; however, the atoms in this compound can form two different

and

H CH3 CHs H

trans-2-hatsne

As a consequence of the different configurations, tliese two isomers display

different chemical and physical properties Therefore, we consider them as two

different species even though each has the same number of atoms of each

element

We say that a chemical reaction has taken place when a detectable

num-ber of molecules of one or more species have lost their identity and assumed a

new form by a change in the kind or number of atoms in the compound and/or

by a change in structure or configuration of diese atoms In this classical

approach to chemical change, it is assumed that the total mass is neither

cre-ated nor destroyed when a chemical reaction occurs The mass refeixed to is

the total collective mass of all the different species in the system However,

when considering the individual species involved in a particular reaction, we

do speak of the rate of disappearance of mass of a particular species The rate

of disappearance of a species, say species A, is the number of A molecules that

A species can lose its identity by decomposition, combination,

or isomerizacion

What is - T A ? r.'?

lose their chemical identity per unit time per unit volume through the breaking and subsequent re-forming of chemical bonds during the course of the reac-tion In order for a particular species to "appear" in the system, some pre-scribed fraction of anodier species must lose its chemical identity

There are three basic ways a species may lose its chemical identity One

way is by decomposition, in which a molecule is broken down into smaller

molecules, atoms, or atom fragments For example, if benzene and propylene are formed from a cumene molecule,

C H ( C H 3 ) 2

+ C 3 H ,

cvimene benzene propylene

the cumene molecule has lost its identity (i.e., disappeared) by breaking its bonds to form these molecules A second way that a molecule may lose its spe-

cies identity is through combination with another molecule or atom In the

example above, the propylene molecule would lose its species identity if the reaction were carried out in the reverse direction so that it combined with ben-zene to form cumene

The thkd way a species may lose its identity is through isomerization,

such as the reaction

CH

CH2=;C—CH2CH3

CH, CH,C=CHCH, Here, although the molecule neither adds other molecules to itself nor breaks into smaller molecules, it still loses its identity through a change in configura-tion

To summarize this point, we say that a given number of molecules (e.g., mole) of a particular chemical species have reacted or disappeared when the molecules have lost their chemical identity

The rate at which a given chemical reaction proceeds can be expressed in several ways It can be expressed either as the rate of disappearance of reac-

tants or the rate of formation of products For example, the insecticide DDT

(dichlorodiphenylttichloroethane) is produced from chlorobenzene and chloral

in the presence of filming sulfuric acid

2C6H5CI + CCI3CHO -> (QH4Cl)2CHCCl3 + HjO Letting the symbol A represent the chemical chloral, the numerical value of the

rate of reaction, —r^, is defined 2& the number of moles of chloral reacting

(disappearing) per unit time per unit volume (mol/dm^ • s) In the next chapter

we delineate the prescribed relationship between the rate of formation of one

species, r,- (e.g., DDT), and the rate of disappearance of another species, -r,

(e.g., chiorobenzene), in a chemical reaction

In heterogeneous reaction systems, the rate of reacEion is usually

expressed in measures other than volume, such as reaction surface area or

cat-alyst weight Thus for a gas~solid catalytic reaction, the dimensions of tliis

rate, r!^, are the number of moles of A reacted per unit time per unit mass of

catalyst (mol/s-g catalyst) Most of die introductory discussions on chemicai

reaction engineering in this book focus on homogeneous systems

The mathematical definition of a chemical reaction rate has been a source

of confusion in chemical and chemical engineering literature for many years

The origin of this confusion stems from laboratory bench-scale experiments

that were carried out to obtain chemical reaction rate data These eaiiy

experi-ments were batch-type, in which the reaction vessel was closed and rigid;

con-sequently, the ensuing reaction took place at constant volume The reactants

were mixed together at time t = 0 and the concentration of one of the

reac-tants, C^, was measured at various times t The rate of reaction was

deter-mined from the slope of a plot of C^ as a function of time Letting r^ be the

rate of formation of A per unit volume (e.g., g mol/s-dm^), the investigators

then defined and reported the chemical reaction rate as

Sec 1,1

However, this definition was for a constant-volume batch reactor

As a resuU of the limitations and restrictions given, Equation (1-1) is a

rather limited and confusing definition of die chemical reaction rate For

amplification of this point, consider the following steady-flow system in which

the saponification of ethyl acetate is carried out

Example 1-1 Is Sodium Hydroxide Reacting?

Sodium hydroxide and ethyl acetate are continuously fed to a rapidly stirred tank in

which they react to form sodium acetate and ethanol:

KaOH + CH^COOCH, -^ CH.COONa + C H O H

(Figure El-1,1) The product stream, containing sodium acetate and etiianol,

together with the unreacted sodium hydroxide and ethyl acetate, is continuously

withdrawn from the tank at a rate equal to the total feed rate The contents of the

tank in which this reaction is taking place may be considered to be perfectly mixed

Because the system is operated at steady state, if we were to withdraw liquid

sam-ples at some location in the tank at various times and analyze them chemically, we

would find that the concentrations of the individual species in the different samples

were identical That is, the concentration of the sample taken at 1 P.M is the same

as that of the sample taken at 3 P.M Because the species concentrations are constant

and therefore do not change with time,

No OH ond CHsCOOCgHa

Figure El-I.l Well mi-Ked reaction vessel

where A ^ NaOH Substitution of Equation (El-i.l) into Equation (i-I) leads to

'"A = 0 (B1-L2)

which is incorrect because C^HjOH and CHaCOONa are being fomied from NaOH

and CHjCOOCjHj at a finite rate Consequendy, the rate of reaction as defined by

Equation ( M ) cannot apply to a flow system and is incorrect if it is defined in this

manner

By now you should be convinced that Equation ( M ) is not the definition

of the chemical reaction rate We shall simply say that rj is the rate of

forma-tion of species j per unit volume It is the number of moles of species j

gener-ated per unit volume per unit time The rate equation for rj is solely a function

of the properties of the reacting materials [e.g., species concentration (i.e

activities), temperature, pressure, or type of catalyst, if any] at a point in the system and is independent of the type of system (i.e., batch or continuous fiow) m which the reaction is carried out However, since the properties of the

reacting materials can vary widi position in a chemical reactor, rj can in turn

be a function of position and can vary from point to point in the system

The chemical reaction rate is an intensive quantity and depends on perature and concentration The reaction rate equation (i.e., fiie rate law) is essentially an algebraic equation involving concentration, not a differential

tem-equation.' For example, the algebraic form of the rate law -r^ for the reaction

' For further elaboration on this point, see Chem Eng Set, 25, 337 (1970); B L

Crynes and H S Fogler, eds., AICliE Modular Instruction Series E: Kinetics Vol 1 (New York: AIChE, 198!), p i; and R L Kabel, "Rates," Chem Eng Commun., 9,

15 (1981) ^

The rate law is an

For a given reaction., the particular concentration dependence that the rate law

follov/s (i.e., — r^ == /cC^ or -r^^ = iC^or ) must be determined from

exper-imental observation Equation (1-2) states that the rate of disappearance of A is

equal to a rate constant k Umes the square of the concentration of A By

conven-tion, t\ is the rate of formation of A; consequently, -TA is the rate of

disappear-ance of A Throughout this book the phrase rale of generation means exactly the

same as the phrase rate offormation, and these phrases are used interchangeably

1.2 The General Mole Balance Equation

To perform a mole balance on any system, the system boundaries must first be

specified The volume 'enclosed by these boundaries will be referred to as the

system volume We shall perform a mole balance on species j in a system

vol-ume, where species j represents the particular chemicai species of interest,

such as water or NaOH (Figure 1-1)

Mole balance

Figure 1-1 Balance on system volume

A mole balance on species; at any instant in time, i, yields the following

equation:

rate of flow

of j into

the system [(moles/time)

F,

rate of generation

of j by chemical

reaction within the system (moles/time) generation G;

rate of flow

of j out of

the system (moles/dme) out

rate of

accumulation

of ;• within the system (moles/time) accumulation

~df (1-3)

where Nj represents the number of moles of species j in the system at time /

If all the system variables (e.g., temperature, catalytic activity, concentration of

the chemical species) are spatially uniform diroughout the system volume, the rate of generation of species;', G,-, is just the product of the reaction volume,

V, and the rate of formation of species j , rj

Gj rrV

moles time

moles

time - volume volume Suppose now that the rate of formation of species 7 for the reaction varies

with the position in the system volume That is, it has a value rji at location 1,

which is stuTounded by a small volume, AVj, within which the rate is

uni-form: similarly, the reaction rate has a value rj2 at location 2 and an associated

volume, AV2 (Figure 1-2), The rate of generation, AG^,, in terms of ry, and

subvolume AVi is

Figure 1-2 Dividing up the system volume V

AGj, = rj, ^V, Similar expressions can be written for AGj2 and the other system subvolumes

AV; The total rate of generation within the system volume is the sum of all the rates of generation in each of the subvolumes If the total system volume is divided into M subvolumes, die total rate of generation is

M M

G;=X AGj,= 2 0/^^/'

1 = 1 i = i

By taking the appropriate limits (i.e., let M -* °= and A V ^ 0) and making use

of the definition of an integral, we can rewrite the foregoing equation in the form

G, rjdV

1

This is a basic

equation for chemical reaction

engineering

-dNa

= -rAV

L

From this equation we see that rj will be an indirect function of position, since

the properties of the reacting materials (e.g., concentration, temperature) can have different values at different locations in the reactor

We now replace Gj in Equation (1-3),

Sec 1.3 Batch Reactors

or reactor volume (continuous-flow) necessary to convert a specified amount of the reaclants to products

1.3 Batch Reactors

A batch reactor has neither inflow nor outflow of reactaats or products while

the reaction is being carried out; FJQ

If the reaction mixture is perfectiy mixed so tiiat there is no variation in the

rate of reaction throughout the reactor volume, we can take rj out of the

inte-gral and write the mole balance in the form

(1-5)

Figure 1-3 shows two different types of batch reactors used for gas-phase reactions Reactor A is a constant-volume (variable-pressure) reactor and Reac-tor B is a constant-pressure (variable-volume) reactor At time r = 0, the reac-tants are injected mto the reactor and the reaction is initiated To see clearly the different forms the mole balance will take for each type of reactor, consider the following examples, in which the gas-phase decomposition of dimethyl ether is taking place to form methane, hydrogen, and carbon monoxide:

(CH3)20 -> CH4 -h H2 + CO

Figure 1-3 Batch reactors for gas-phase reactions

Example 1-2 Constant Volume or Constant Pressure:

Does It Make a Difference?

Write the moie balance for dimethyl ether in terms of the reactor volume, tration, and rate of formation of dimethyl ether for both a constant-pressure and a constant-volume batch reactor

concen-Solution

To reduce the number of subscripts, we write the reaction symbolically as

A > M-HH + C where A is diraethyi ether, M is methane, H is hydrogen, and C is carbon monoxide For both batch reactors, the mole balance on A is

Constant-pressure batch reactor To write the mole balance for this reactor

in terms of concenuration, we again^use the fact that

10 11

I The difference between equations (El-2.1) and (El-2.3) for the two different types

I of reactors is apparent

1.4 Continuous-Flow Reactors

1.4.1 Continuous-Stirred Tank Reactor

A type of reactor used very commonly in iudustrial processing is a stin-ed

tank operated continuously (Figure 1-4) It is referred to as the continuous-stirred

tank reactor (CSTR) or backmix reactor The CSTR is normally run at steady

state and is usually operated so as to be quite well mixed As a result of die latter

quality, the CSTR is generally modeled as having no spatial variations in

concen-tration, temperature, or reaction rate throughout the vessel Since the temperature

and concentration are identical everywhere within the reaction vessel, they are

the same at the exit point as they are elsewhere in the tank, Thus the temperature

and concentration in the exit stream are modeled as being the same as those

inside the reactor In systems where mixing is highly nonideal, the well-mixed

model is inadequate and we must resort to other modeling techniques, such as

residence-time distributions, to obtain meaningful results This topic is discussed

in Chapters 13 and 14

Reactants

Products

Figure 1-4 ConEinuous-stirred tank reactor

When the general mole balance equation

in which there are no spatial variations in the rate of reaction

it takes the familiar form known as the design equation for a CSTR;

(1-6)

The CSTR design equation gives the reactor volume necessary to reduce

the entering flow rate of species,;, FJQ, to the exit flow rate Fj We note that the

CSTR is modeled such that the conditions in the exit stream (e.g.,

concentra-tion, temperature) are identical to those in the tank The molar flow rate Fj is just theproductof the concentration of species J and the volumetric flow rate u:

(1-7)

1.4.2 Tubular Reactor

In addition to the CSTR and batch reactors, another type of reactor

com-monly used in industry is the tubular reactor It consists of a cylindrical pipe

and is normally operated at steady state, as is the CSTR For the purposes of iiie material presented here, we consider systems in which the flow is highly turbu-lent and the flow field may be modeled by that of plug flow That is, there is no radial variation in concentration and the reactor is referred to as a plug-flow reactor (PFR) (The laminar flow reactor is discussed in Chapter 13.)

In the tubular reactor, the reactants are continually consumed as they flow down the length of the reactor In modeling the mbular reactor, we assume that the concentration varies continuously in the axial direction through the reactor Consequently, the reaction rate, which is a fimction of con-centration for ail but zero-order reactions, will also vary axially The general mole balance equation is given by Equation (1-4):

To develop the PFR design equation we shall divide (conceptually) die reactor into a number of subvolumes so that within each subvolume AV, the reaction rate may be considered spatially uniform (Figure 1-5) We now focus our

attention on the subvolume that is located a distance y firom the entrance of the reactor We let Fj(y) represent the molar flow rate of species ;" into volume AV

at y and Fj{y + Ay) the molar flow of species ; out of the volume at the

loca-tion (y -I- Ay) In a spatially uniform subvolume AV,

Figare 1-5 Tubular reactor

For a tubular reactor operated at steady state

dNj

It" 0

Equation (1-4) becomes

F.(y) FJiy^^y)-^r:^V^O (1-8)

In this expression ry is an indirect fimction ofy That is, rj is a function of

reac-tant concentration, which is a function of the position y down the reactor The

volume A V is the product of the cross-sectional area A of the reactor and the

reactor length Aj

i^V = A^y

We now substitute in Equation (1-8) for AV and then divide by Aj to obtain

> / y + Ay)-Fy(yy

= -Ar:

The term in brackets resembles the definition of the derivative

lim fix + Ax)-fix)

It is usually most convenient to have the reactor volume V rather than the

reactor length y as the independent variable Accordingly, we shall change variables using the relation dV ~ A dy to obtain one forai of the design equa-

tion for a tubular reactor:

djj

We also note that for a reactor in which the cross-sectional area A varies along

the length of the reactor, the design equation remains unchanged This tion can be generalized for the reactor shown in Figure 1-6, in a manner simi-

equa-Figure 1-6

lar to that^presented above, by utilizing the volume coordinate V ratber tiaan a

linear coordinate y After passing through volume V, species 7 enters subvolume

AV at volume Vat a molar flow rate F,(V) Species; leaves subvolume AV at

volume (V -^ AV), at a molar flow rate F,-(V + AV) As before, AV is chosen

small enough so that there is no spatial variation of reaction rate within the subvolume:

Consequently, we see that Equation (1-10) applies equally well to our model

of tubular reactors of variable and constant cross-sectional area, although it is

14 Mots Balances Chap 1 15

doubtful that one would find a reactor of the shape shown in Figure 1-6, unless

designed by Pablo Picasso The conclusion drawn from the application of the

design equation is an important one: The extent of reaction achieved in a plug-flow

tubular reactor (PFR) does not depend on its shape, only on its total volume

1.4,3 Packed-Bed Reactor

The principal difference between reactor design calculations involving

homogeneous reactions and those involving fluid-solid heterogeneous

reac-tions is that for the latter, the reaction rate is based on mass of solid catalyst,

W, rather than on reactor volume, V For a fluid-solid heterogeneous system,

the rate of reaction of a substance A is defined as

- cX = g mol A reacted/s • g catalyst The mass of solid is used because the amount of the catalyst is what is impor-

tant to the rate of reaction The reactor volume that contains the catalyst is of

secondary significance

In the three ideahzed types of reactors just discussed [the perfectly mixed

batch reactor, the plug-flow tubular reactor, and the perfectly mixed

continu-ous-stirred tank reactor (CSTR)], the design equations (i.e., mole balances)

were developed based on reactor volume The derivaUon of the design equation

for a packed-bed catalytic reactor will be carried out in a manner analogous to

the development of the tubular design equation To accomplish diis derivation,

we simply replace the volume coordinate in Equation (1-S) with the catalyst

weight coordinate W (Figure 1-7) As with the PFR, the PBR is assumed to have

Figure 1-7 Packed-bed reactor schematic

no radial gradients in concentration, temperature, or reaction rate The

general-ized mole balance on species A over catalyst weight AW results in the equation

Use differential form

of design equation for catalyst decay and pressure di'Op

Reactor sizing

which are, as expected, the same dimension of the molar flow rate F^ After dividing by AW and taking the Hmit as AW -> 0, we arrive at the differential form of the mole balance for a packed-bed reactor:

When pressure drop through the reactor (see Section 4.4) and catalyst decay (see Section 10.7) are neglected, the integral form of the packed-cata-lyst-bed design equation can be used to calculate the catalyst weight

To obtain some insight into tilings to come, consider the following ple of how one can use the tubular reactor design equation (1-10)

exam-Example 1-3 l^ow Large Is U?

The first-order reaction

A

is carried out in a tubular reactor in which the volumetric flow rate, v, is coRStant

Derive an equation relating the reactor volume to the entering and exiting

concen-trations of A, the rate constant k, and the volumetric flow rate v Determine the

reac-tor volume necessary to reduce the exiting concentration to 10% of the entering concentration when the volumetric flow rate is 10 dm^/min (i.e., Hters/min) and the

specific reaction rate, k, is 0.23 min"'

Solution

For a tubular reactor, the mole balance on species A (j = A) was shown to be

dV '•A

For a iirst-order reaction, the rate law (discussed in Chapter 3) is

Since the volumetric flow rate, vn, is constant

16 Mole Balances Chap l

Using the conditions at the entrance of the reactor dial when V = 0, then C^ = C/^Q,

This equation gives

We see that a reactor volume of 0.1 m? is necessary to convert 90% of species A

entering into product B

In the remainder of this chapter we look at slightly more detailed ings of some typical industrial reactors and point out a few of the advantages and disadvantages of each ^

draw-1.5 Industrial Reactors

A batch reactor is used for small-scale operation, for testing new processes that have not been fully developed, for the manufacture of expensive products, and for processes that are difficult to convert to continuous operations The reactor can be charged (i.e., iilled) through the holes at the top (Figure 1-8) The batch reactor has the advantage of high conversions that can be obtained by leaving the reactant in the reactor for long periods of time, but it also has die disadvan-tages of high labor costs per batch and the difficulty of large-scale production

Liquid-Phase Reactions Although a semibatch reactor (Figure 1-9) has

essentially the same disadvantages as the batch reactor, it has the advantages of good temperature control and the capability of minimizing unwanted side reac-tions through the maintenance of a low concentration of one of the reactants

The semibatch reactor is also used for two-phase reactions in which a gas is usually bubbled continuously through the liquid

A continuous-stirred tank reactor (CSTR) is used when intense agitation

is required A photo showing a cutaway view of a Pfaudler CSTR/batch reactor

is presented in Figure 1-10 Table l-I gives the typical sizes (along with that of

2 Chem Eng., 63{IQ), 211 (1956) See also AlChE Modular instmcHon Series E, Vol

5 (1984)

; ^

Hand holes for charging reactor

Connection for heating or cooling jacket

Agitator

Figure 1-S Simple batch homogeneous reactor, [Excerpted by special permission

from Chem Eng., 63(10), 21 ] (Oct 1956)

Copyright 1956 by McGraw-Hill, Inc., New York, NY 10020,]

Heater

„ or cooler

r t <3

Reactant B Figure 1-9 Semibatch reactor, [Excerpted

by special permission from Chem Eng.,

TABLE l-I REPRESENTATIVE PFAUDLER CSTR/BATCH REACTOR

SIZES AND 1996 PRICES

Sec 1.5 Industriai Reactors

Example 1-4 Liquid-Phase Industrial Process Flowsheet

(Jacuzzi) (gasoline tanker)

A battery of four CSTRs similar to those in Figure 1-10 are shown in the plant sheet (Figtire El-4.1) for the commercial production of nitrobenzene In 1995, 1.65 billion pounds of nitrobenzene were produced

Chem Eng 63(10), 211 (Oct 1956) Copyright 1956 by McGraw-Hill, Inc., New

York, NY 10020.]

the comparable size of a familiar object) and costs for batch and CSTR

reac-tors All reactors are glass lined and the prices include heating/cooling jacket,

motor, mixer, and baffles The reactors can be operated at temperatures between

20 and 450°F and at pressures up to 100 psi

The CSTR can either be used by itself or, in the manner shown in Figure

1-11, as part of a series or battery of CSTRs It is relatively easy to maintain

good temperature control with a CSTR There is, however, the disadvantage

that the conversion of reactant per volume of reactor is the smallest of the flow

reactors Consequently, very large reactors are necessary to obtain high

conversions

If you are not able to afford to purchase a new reactor, it may be possible

to find a used reactor that may fit your needs Previously owned reactors are

much less expensive and can be purchased from equipment clearinghouses

such as Universal Process Equipment or Loeb Equipment Supply

Note: Heat Exchange between Benzene feed and Nitroben/.ene product

Benzene

Crude nitrobenzene

Sulfuric add concentrator

The feed consists of 3 to 1% HNOj, 59 to 67% H2SO4, and 28 to 37% water

Siil-fmic acid is necessary to adsorb the water and energy generated by the heat of tion The plant, which produces 15,000 lb nitrobenzene/h, requires one or two operators per shift together with a plant supervisor and part-time foreman This exo-thermic reacdon is carried out essentially adiabatically, so that the temperature of

reac-the feed stream rises from 90°C to 135°C s-X reac-the exit One observes that reac-the

nitroben-zeae stream from the separator is used to heat the benzene feed However, care miLsi

be taken so that the temperature never exceeds 190°C, where secondary reactions could result in an explosion, One of the safety precautions is the installation of relief valves that will rupmre before the temperature approaches 190°C, diereby aitowin^

a boil-off of water and benzene, which would drop the reactor temperature

Gas-Phase Reactions The tubular reactor [i.e., plug-flow reactor (PFR)J is

relatively easy to maintain (no moving parts), and it usually produces the

high-est conversion per reactor volume of any of the flow reactors The

disadvan-tage of the tubular reactor is that it is difficult to control temperature within the

reactor, and hot spots can occur when the reaction is exothermic The tubular

reactor is commonly found either in the form of one long tube or as one of a

number of shorter reactors arranged in a tube bank as shown in Figure \-\l

Most homogeneous liquid-phase flow reactors are CSTRs, whereas most

homogeneous gas-phase flow reactors are tubular

The costs of PFR and PBR (without catalyst) are similar to the costs oC

heat exchangers and thus can be found in Plant Design and Economics far

Rue gas Product gas

Figure 1-12 Longitudinal tubular reactor [Excerpted by special permission from

Chem Eng., 63(10) 211 (Oct 1956), Copyright 1956 by McGraw-Hill, Inc., New

Institute of Chemical Engineers, 86(2), 34

(1990) ReprodiKed with permission of the American InstitEte of Chemical Engineers, Copyright © 1990 AIChE All rights reserved.]

Compressed air

-Naphlha and

Catalyst \ '^''^^S^

Furnace

Figure 1-14 Fluidized-bed cataEyiic reactor

[Excerpted by special permission from Chem

Eng., 63(10), 211 (Oct 1956) Copyright 1956

by McGraw-Hill, Inc., New York, NY 10020,]

Chemical Engineers, 4th ed., by JVI S Peters and K D Timmerhaus (New

York: McGraw-Hill, 1991) From Figure 15-12 of this book, one can get an

estimate of the purchase cost per foot of $1 for a 1-in pipe and $2 per foot for

a 2-in, pipe for single tubes and approximately $20 to $50 per square foot of surface area for fixed-tube sbeet exchangers

A packed-bed (also called a fixed-bed) reactor is essentially a tubular reactor that is packed with solid catalyst particles (Figure 1-13) This heteroge-neous reaction system is used most frequently to catalyze gas reactions This reactor has the same difficulties with temperature control as other tubular reac-tors, and in addition, the catalyst is usually troublesome to replace On occa-sion, channeling of the gas flow occurs, resulting in ineffective use of parts of the reactor bed The advantage of the packed-bed reactor is that for most reac-tions it gives the highest conversion per weight of catalyst of any catalytic reactor

Another type of catalytic reactor in common use is the fluidized-bed (Figure 1-14) The fluidized-bed reactor is analogous to the CSTR in that its contents, though heterogeneous, are well mixed, resulting in an even tempera-

ture distilbution throughout the bed The fluidized-bed reactor cannot be

mod-eled as either a CSTR or a mbular reactor (PFR), but requires a model of its own The temperature is relatively uniform throughout, thus avoiding hot spots This type of reactor can handle large amounts of feed and solids and has good temperature control; consequently, it is used in a large number of appli-cations The advantages of the ease of catalyst replacement or regeneration are

22 23

Maiing Gasoline

sometimes offset by the high cost of the reactor and catalyst regeneration

equipinent,

Example 1-5 Gas-Phase Industrial Reactor/Process

Synthesis gas contains a mixture of carbon monoxide and hydrogen and c&n be

obtained from the combustion of coal or natural gas This gas can be used to produce synthetic crude by the Fischer-Tropsch reaction Describe two industrial reactors used

to convert synthesis gas to a mixture of hydrocarbons by the Fischer-Tropsch process

Solution

Reaction,s The Fischer-Tropsch reaction converts synthesis gas into a ture of alkanes and allcenes over a solid catalyst usually containing iron The basic reaction for paraffin formation is as follows

mix-nCO + (2«+l)H2 ^ C„Hj„ + 2 + rtH20 (,E1-5.1) For example, when octane, a component of gasoline, is formed, Equation (Ei-5,1) becomes >

-> C=H,s + 8H,0 8CO+17Hi

Similarly, for the formation of olefin.s,

In addition to the simultaneous formadon of paraffins and olefins, side tions also take place to produce small quantities of acids and nonacids (e.g., ethanoj)

reac-Reactors Two types of reactors will be discussed, a straight-tkrougli

trans-port reactor, which is also referred to as a riser or circulating fluidized bed, and a packed-bed reactor (PBR), which is also referred to as & fixed-bed reactor

Riser Because the catalyst used in the process decays rapidly at high

temper-afiares (e.g., 350°C), a straight-through transport reactor (STTR) (Chapter 10) is used This type of reactor is also called a riser and/or a circulating bed A schematic

diagram is shown in Figure EI-5.1 Here the catalyst particles are fed to the bottom

of tlie reactor and are shot up through the reactor together with the entering reactant gas mixture and then separated from the gas in a setlUng hopper The volumetric gas feed rate of 3 X 10^ m^/h is roughly equivalent to feeding die volume of gas con-tained in the University of Michigan football stadium to the reactor each hour

A schematic and photo of an industrial straight-through transport reactor

used at Sasol are shown in Figure El-5.2 together with the composition of the feed and product streams The products that are condensed out of the product stream

Catalyst

Syn crude + other

Catalyst 5.8 - * 9.5 ton/s

Tail Gas 35% CH4 38% HE

7% CO

1 2 % C 0 a

l t % L i g h t C 2 - C s hydrocarbon

Feed 300.000 mSftr @ STP 9% CH4 5B% Hg 32% CO

1 % GO, Figure El-S.l Schematic of Saso! Fischer-Tropsch process

Figure El-5.2 The reactor is 3.5 m in diameter and 38 m tall (Schematic and photo courtesy of Sasol/Sastech FT Limited.)

24

Use to produce wax

for candles and

printing inks

before the stream is recycled include Synoil (a syndiedc crude), water, methyl ethyl ketone (MEK), alcohols, acids, and aldehydes The reactor is operated at 25 atm and 350''C and at any one time contains 150 toas of catalyst The catalyst feed rate is 6

to 9.5 tons/s and the gas recycle rado is 2:1

Packed Bed The packed-bed reactor used at the Sasol plant to cany out cher-Tropsch synthesis reaction is shown in Figure El-5.3, SynEhesis gas is fed at a rate of 30,000 mVh (STP) at 240''C and 27 atm to the packed-bed reactor The reac-tor contains 2050 tubes, each of which is 5.0 cm in diameter and 12 m in length

Fis-The iron-based catalyst that fills these tubes usually contains K^O and Si02 and has

a specific area on the order of 200 m-/g The reaction products are light bons along with a wax that is used in candles and printing inks Approximately 50%

hydrocar-conversion of the reaciant is achieved in Ehe reactor

Figure E1-S.3 Packed-faed reactor (Schematic and photograph courtesy of Sasol/Sastech FT Limited.)

The aim of the preceding discussion on commercial reactors is to give a more detailed picture of each of the major types of industrial reactors: batch, semibatch, CSTR, tubular, fixed-bed (packed-bed), and fluidized-bed Many variations and modifications of these commercial reactors are in current use;

for further elaboration, refer to the detailed discussion of indushial reactors

1 A mole balance on species 7, which enters, leaves, reacts, and

accumu-lates in a system volume V, is

2 The kinedc rate law for rj is:

• Solely a function of properties of reacting materials [e.g., tion (acdvities), temperature, pressure, catalyst or solvent (if any)]

concentra-• An intensive quantity

• An algebraic equation, not a differential equation

For homogeneous catalytic systems, typical units of -r,- may be gram moles per second per liter; for heterogeneous systems, typical

units of rJ may be gram moles per second per gram of catalyst By convention, -r^ is the rate of disappearance of species A and r^ is the

rate of formation of species A

Mole balances on four common reactors are as follows:

Reactor Mole Balance

-t >

Batch CSTR PFR PBR

Q U E S T I O N S A N D P R O B L E M S

I wish I had an answer for that, because I'm getting tired of answering that question

Yogi Berra, New York Yankees

Sports Illustrated, June 11, 1984

The subscript to each of the problem numbers indicates the level of difficulty: A, least difficult; D, most difficult

A = » B = I C = * n >= **

Ineachof the questions and problems below, rather than just drawing a box around your answer, write a sentence or two describing how you solved the problem, the assump-tions yoii made, the reasonableness of your answer, what you learned, and any other

facts that you want to include You may wish to refer to W Strunk and E B White, The

Elements of Style (New York: Macmillian, 1979) and Joseph M Wlliams, Styie: Ten Lessons in Clarity & Grace (Gienview, IlL: Scott, Foresman, 1989) to enhance the qual-

ity of your sentences

Mole Balances Chap, 1

After reading each page, ask yourself a question Make a list of the most

important things that you learned in this chapter

What if:

(a) the benzene feed stream in Example 1-4 were not preheated by the

prod-uct stream? What would be the consequences?

(b) you needed the cost of a 6000-gallon and a 15,000-galion Pfaudler

reac-tor? What would they be?

the exit concentration of A in Example 1-3 were specified at 0.1% of the

entering concentration?

the volume of the movable piston in Example 1.-2 varied in a manner

similar to a car cylinder, y = Vg + V| sin wr?

only one operator showed up to run the nitrobenzene plant, what would

be some of your first concerns?

Calculate the volume of a CSTR for the conditions used to calculate iht;

plug-flow reactor volume in Example 1-3

Calculatethetimetoreduce thenumberof molesof Ato 1% of its initial value

in a constant-volume batch reactor for the reaction and data in Example 1 -3

What assumptions were made in the derivation of the design equation for:

(a) the batch reactor?

(b) the CSTR?

(c) the plug-flow reactor (PFR)?

(d) the packed-bed reactor (PER)?

(e) State in words tlie meanings of - / ' A ' " ' ' A ' ''^^ 'A- ^^ ^^e reaction rate

-TA an extensive quantity? Explain

What is the difference between the rate of reaction for a homogeneous

sys-tem, -r^, and the rate of reaction for a heterogeneous syssys-tem, -rj^l Use the

raole balance to derive an equation analogous to Equation (1-6) for a fluidized

CSTR containing catalyst particles in terms of the catalyst weight, W, and

other appropriate terms,

How can you convert the general mole balance equation for a given species

Equation (1-4), to a general mass balance equation for that species?

The United States produces 24% of the world's chemical products According

to the yearly "Facts and Figures" issue of Chemical and Engineering New.s

{C&E News, June 24, 1996), the following were the 10 most produced

(a) What were the 10 most produced chemicals for the year that just ended'.'

Were there any significant changes from the 1995 statistics?

The same issue of CSiE News gives the following chemical companies as the

top 10 in total sales in 1995 (Also see http://www.chemweek.com)

Type of Reactor Characteristics

Kinds of Phases

P1-10B Schematic diagrams of the Los Angeles basin are shown in Figure Pl-10 The basin floor covers approximately 700 square miles (2 X 10'° fi^) and is almost completely surrounded by mountain ranges If one assumes an inversion height in the basin of 2000 ft, the corresponding volume of air in the basin is

4 X 10'^ ft^ We shall use this system volume to model the accumulation and depletion of air pollutants As a very rough first approximation, we shall treat the Los Angeles basin as a well-mixed container (analogous to a CSTR) in which there are no spatial variations in pollutant concentmtions Consider only the pollutant carbon monoxide and assume that the source of CO is from automobile exhaust and that, on the average, there are 400,000 cars operating

in the basin at any one time Each car gives off roughly 3000 standard cubic

feet of exhaust each hour containing 2 mol % carbon monoxide

Side view

Figure PI-10

We shall perform an unsteady-state mole balance on CO as it is depleted

from the basin area by 2 Santa Ana wind Santa Ana winds are high-velocity

winds that originate in the Mojave Desert just to the northeast of Los Angeies

This clean desert air flows into the basin through a corridor assumed to be 20

miles wide and 2000 ft high (inversion height) replacing the polluted air,

which flows out to sea or toward the south The concentration of CO in the

Santa Ana wind entering the basin is 0.08 ppra (2.04 X lO""'" lb mol/tV)

(a) How many pound moles of gas are in the system volume we have chosen

for the Los Angeles basin if the temperature is 75"? and the pressure is J

atm? (Values of the ideal gas constant may be found in Appendix B.)

What is the rate, fco.A^ ^^ which ail autos emit carbon monoxide into the

basin (lb mol CO/h)?

What is the volumetric flow rate (ft^/h) of a !5-mph wind through the

corridor 20 miles wide and 2000 ft high? (Ans.: 1.67 X 10'^ ftVh.)

At what rate, FQQS, does the Santa Ana wind bring carbon riionoxide

into the basin (lb mol/h}?

Assuming that the volumetric flow rates entering and leaving the basin

are identical, v = UQ, show that the unsteady mole balance on CO within

the basin becomes

(g) If the initial concentration of carbon monoxide in the basin before the

Santa Ana wind starts to How is 8 ppm (2.04 x 10^^ lb mol/ft^),

calcu-late the time required for the carbon monoxide to reach a level of 2 ppm

(h) Repeat parts (b) through (g) for another pollutant, NO The concentration

of NO in the auto exhaust is 1500 ppm (3.84 X IQ-e lb mol/ft^), and the

inidal NO concentration in the basin is 0.5 ppm If there is no NO in the

Santa Ana wind, calculate the time for the NO concentration to reach 0.1

ppm What is the lowest concentration of NO that could be reached?

Chap 1 Questions and Problems

CA = 0.01 CAO) when the entering molar flow rate is 5 mol/h, assuming the

reaction rate - r ^ is:

is canied out isothermally in a IQ-dn? constant-volume batch reactor Twenty

moles ofpure Ais initially placed in the reactor The leactor is well mixed (a) If the reaction is first order;

-r^ = kC^ with k ~ 0.865 min"'

calculate the time necessary to reduce the number of moles of A in the

reactor to 0.2 mol (Note: N^ = C^K) (Ans.: t = 5.3 min)

(b) if the reaction is second order:

-kCl with k ~ 2dm3

raol - min

(c)

(f>)

calculate the time necessary to consume 19.0 mol of A

If the temperature is \2TC, what is the initial total pressure? What is the

final total pressure assuming the reaction goes to completion?

P1-13A (a) How many cubic feet (at STPJ enter the pacfced-bed reactor described in

Example 1-5 every second? How long does a molecule spend, on the

average, in die reactor? [Hint: What is the gas velocity in each tube

assuming a 30% porosity (volume of gas/volume of reactor) for the packed bed?]

Estimate the time that a catalyst particle and a gas-phase molecule spend

in the Sasol straight-through transport reactor (STTR) What is the hulk density of the catalyst (kg cat/m^) in the STTR?

Write a one-paragraph summary of a journal article on chemical kinetics or reaction engineering The article must have been published within the last five years, * What did you learn from this aiticle? Why is the article important?

Pl-15^ (a) What journals, books, or papers give you costs of industrial (not

labora-toiy, e.g., Fisher catalog) chemicals and catalysts?

(b) List various journals, books, or other sources where you will find details about the construcdon and safety of industrial reactors

PI-14

• See the Supplementary Reading list at the end of the chapter, particulariy item 4

30

Pl-16c

P M 7 ,

What are typical operating conditions (temperature, pressure) of a catalytic

cracking reactor used in petroleum refining?

View the photos and schematics on the CD-ROM under Elements of Chemical

Reaction Engineering-Chapter 1, Look al the quicklime videos Write a

para-graph describing two or more of the reactors What similarities and differences

do you observe between the reactors on the Web and in the text?

P1-18A (a) There are initially 500 rabbits (x) and 200 foxes (y) on Farmer Oat's

property, Use POLYMATH or MATLAB to plot the concenti'ation of foxes

and rabbits as a function of time for a period of up to 500 days The

preda-tor-prey relationships are given by the following set of coupled ordinary

Constant for growth of rabbits fc, = 0.02 day"'^

Constant for death of rabbits fcj = 0.00004/(day x no of foxes)

Constant for growth of foxes after eating rabbits k-^ = 0.0004/(day x no

of rabbits)

Constant for death of foxes k^ = 0.04 day"'

What do your results look like for the case of fcj = 0.00004/(day X no

of rabbits) and t^asx = 800 days? Also plot the number of foxes versus the

number of rabbits Explain why the curves look the way they do

Vary the parameters fe,, fcj- ^3' and k^ Discuss which parameters can or

cannot be larger than others Write a paragraph describing what-you find

Use POLYMATH or MATLAB to solve the following set of nonlinear

algebraic equations:

x^y - 4y^ -I- 3JC = 1

dy^ - 9jcy = 5

with initial guesses of J: = 2, y = 2, Try to become famihar with the edit

keys in POLYMATH MatLab See CD-ROM for instructions,

P1-19A (a) Surf the Worid Wide Web and make a list of the links that are relevant to

chemical reaction engineering Pick the five most relevant links and write

two or three sentences about each,

(fa) Check the reaction engineering 3rd ed web site (http://www.engin.umich

edu,/~cre) to learn what material has been added and any typographical

erron that have been found in the first printing,

P1-20A Surf the CD-ROM included with the text

(a) Approximately how many additional solved example problems are there?

(b) List at least one video clip

(c) In what lectures are activation energy discussed?

(d) What photos are in the Wetlands Module?

After Reading Each Page in This Book, Ask Yourself a Question

About What You Read

Chap, 1 Supplementary Reading 31

C D - R O M M A T E R I A L

• Learning Resources

1 Summary Notes for Lectures 1 and 2

2 Web Modules

A Problem Solving Algorithm for Closed-Ended Problems

B Hints for Getting Unstuck on a Pi-oblem

3 Interactive Computer Modules

A Quiz Show 1

4 Salved Problems

A, C D P I - A B Batch Reactor Calculations: A Hint of Things to Come

• Professional Reference Shelf

1 Photograplis of Real Reactors

• FAQ [Frequently Asked Questionsl- In Updates/FAQ icon section

• Additional Homework Probieras

CDP1-AA Calculate the time to consume 80% of species A in a constant-volume

batch reactor for a first- and a second-order reaction (Includes Solution)

CDPI-BA Derive the differential mole balance equation for a foam reactor [2nd

Ed P I - I O B ]

S U P P L E M E N T A R Y R E A D I N G

1 For further elaboration of the development of the general balance equation, see

DIXON, D, C „ Chem Eng Sci 25, 337 (1970)

FELDER, R M., and R, W ROUSSEAU, Elementary Principles of Chemical

Pro-cesses, 2nd ed New York: Wiley, 1986, Chap, 4

HlMMELBLAU, D M., Basic Principles and Calculations in Chemical

Engineer-ing 6th ed Upper Saddle River, N.J.: Prentice Hall, 1996, Chaps, 2 and 6

HOLLAND, C, D., and R G, ANTHONY, Fundamentals of Chemical Reaction

Engi-neering, 2nd ed, Upper Saddle River, N,J.: Prentice Hall, 1989, Chap 1

2 A detailed explanation of a number of topics in this chapter can be found in

CRYNES, B L., and H S FOOLER, eds., AIChE Modular Instruction Series E:

Kinetics, Vols 1 and 2 New York: AIChE, 1981,

3 An excellent description of the various types of corrmiercial reactors used in try is found in Chapter 11 of

indus-WALAS, S M „ Reaction Kinetics for Chemical Engineers New York:

McGraw-Hill, 1959,

A somewhat different discussion of the usage, advantages, and limitations of ous reactor types can be found in

vari-DENBIGH, K G., and J C R TURNER, Chemical Reactor Theory, 2nd ed

Cam-bridge: Cambridge University Press, 1971, pp 1-10,

32 Mo,3 ba:ar,ces

4 A discussion of some of the most important indostrial processes is presented by

MEYERS, R.A„ Handbook of Chemical Production Processes New Yofk:

McGraw-HiU, 1986

See also

MCKETTA, J J., ed., Encyclopedia of Chemical Processes and Dexigji

New-York: Marcel Dekker, 1976,

A similar book, which describes a larger number of processes, is

SHREVE, R N„ and J" A BRINK, JR., Chemical Process Industries, 4th ed New

York: McGraw-Hill, 1977

5 The following journals may be aseful in obtaining information on chemical

reac-tion engineering: Internareac-tional Journal of Chemical Kinetics, Journal of Catalysis,

Journal of Applied Catalysis, AJChE Journal, Chemical Engineering Science,

Canadian Journal of Chemical Engineering, Chemical Engineering

Communica-tions, Journal of Physical Chemistry, and Industrial and Engineering Chemistry

Research-6 The price of chemicals can be found in such journals as the Chemical Marketing

Reporter, Chemical Weekly, and Chemical Engineering News

Conversion 2 and Reactor Sizing

Be more concerned with your character than with your reputation, because character is what you really are while reputation is merely what others think you are

John Wooden, coach, UCLA Bruins

The first chapter focused on the general mole balance equation; the balance was applied to the four most common types of industrial reactors, and a design

equation was developed for each reactor type In Chapter 2 we first define

con-version and then rewrite the design equations in terms of concon-version After

car-rying out tills operation, we show how one may size a reactor (i.e., determine

the reactor volume necessary to achieve a specified conversion) once the

rela-tionship between reaction rate, r^, and conversion is

known-2.1 Definition of Conversion

In defining conversion, we choose one of the reactants as the basis of tion and then relate the other species involved in the reaction to this basis In most instances it is best to choose the hmiting reactant as the basis of calcula-tion We develop the stoichiometric relationships and design equations by con-sidering the general reaction

The uppercase letters represent chemical species and the lowercase letters

rep-resent stoichiometric coefficients Taking species A as our basis of calculation,

we divide the reaction expression through by the stoichiometric coefficient of species A, in order to arrange the reaction expression in the form

33

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34 Conversion and Reactor Sizing Chap, 2 35

Definition of X

a ^'-C + ^-Q (2-2)

to put every quantity on a "per mole of A" basis

Now we ask such questions as "How can we quantify how far a reaction [e.g., Equation (2-2)] has progressed?" or "How many moles of C are formed

for every mole A consumed?" A convenient way to answer these questions i.s

to define a parameter called conversion The conversion X^ is the number of

moles of A that have reacted per mole of A fed to the system:

X,= moles of A reacted

molesof A fed

Because we are defining conversion with respect to our basis of calculation [A

in Equation (2-2)], we eliminate the subscript A for the sake of brevity and let

2.2 Design Equations

2.2.1 Batch Systems

In most batch reactors, the longer a reactant is in the reactor, the more reactant is converted to product until either equilibrium is reached or the reac-

tant is exhausted Consequently, in batch systems the conversion X is a

func-tion of the time the reactants spend in the reactor, If WAO is the number of

moles of A initially, then the total number of moles of A that have reacted after

a time t is [WAO^]

moles of A consumed

moles of A reacted (consumed)

moles of A fed

= [A'AO]

moles of A reacted mole of A fed

iX]

(2-3)

Now, the number of moles of A that remain in the reactor after a time r,

Nj^, can be expressed in terms of N/^Q and X:

The number of moles of A in the reactor after a conversion X has been

reactant A is disappearing; therefore, we multiply both sides of Equation (2-5)

by -1 to obtain the mole balance for the batch reactor in the form

dt {-rAV

The rate of disappearance of A, - T A , in this reaction might be given by a rate

law similar to Equation (1-2), such as - T A =

kCp^Cs-For batch reactors we are interested in determining how long to leave the

reactants in the reactor to achieve a certain conversion X, To determine this

length of time, we ttansform the mole balance Equation (2-5), in terras of conversion by differentiating Equation (2-4),

36 I and nractc:' Si? ng Chap 2

Constant-volume batch reactors are found very frequendy in industry In

par-ticular, tiie laboratory bomb reactor for gas-phase reactions is widely used for

obtaining reaction rate Information on a small scale Liquid-phase reactions in

which the volume change during reaction is insignificant are frequently carried

out in batch reactors when small-scale production is desired or operating

diffi-culties rule out the use of continuous systems For a constant-volume batch

reactor, Equation (2-5) can be arranged into the form

For batch-reactor systems in which the volume varies while the reaction is

pro-ceeding, the volume may usually be expressed either as a function of time

alone or of conversion alone, for either adiabatic or isothermal reactors

Con-sequently, the variables of the differential equation (2-6) can be separated in

one of the following ways:

Vdt = N dX

dt = N^ dX

These equations are integrated with the limits that the reaction begins ;it

time zero (i.e., f = 0, X = 0) When the volume is varied by some externa!

source in a specific manner (such as a car cylinder piston compressing ihe

reacting gas according to the equation V = Vi + V2 sin wt), the equation

relating time and conversion that one would use is

However, for the more common batch reactors in which volume is not a

predetermined function of time, the time t necessary to achieve a conversion X

is

(2-9)

Equation (2-6) is the differential form of \bs design equation, and Equations

(2-8) and (2-9) are the integral forms for a batch reactor The differential form

is generally used in the interpretation of laboratory rate data

Sec 2.2 Des,yi! u-mjations

2.2.2 Flow Systems

37

Normally, conversion increases with die time the reactants spend in the reactor For continuous-flow systems, tiiis time usually increases with increas-ing reactor volume; consequently, the conversion X is a function of reactor vol-

ume V If FAO is flie molar flow rate of species A fed to a system operated at

steady state, the molar rate at which species A is reacting witiiin the entire

sys-tem will be F/^QX

[i^Ao]-ra = moles of A fed moles of A reacted

[PAO'X]

time moles of A reacted time

Rearranging gives

molar rate at which A is consumed within the system

[FAOX]

molar flow rate

at which A leaves the system

The entering molar flow rate, F^o (mol/s), is just die product of tiie entering

concenti-ation, C^o (mol/dra^), and die entering volumetric flow rate, Vn

(dmVs): ^

•^AO = ^ A O ^ 0

For liquid systems, CAO is commonly given in terms of molarity, for example, CAO = 2 mol/dml For gas systems, CAO can be calculated from tiie entering temperature and pressure using the ideal gas law or some other gas law For an ideal gas (see Appendix B);

RTn yAoPo

RT,

38

where C^g ~ entering concentration, mol/dm^

>'AO ~ entering mole fraction of A

PQ = entering total pressure, kPa

TQ = entering temperature, K

P^o ~ entering partial pressure, kPa

R - ideal gas constant e.g., R = 8.314*^ " ^ ; see Appendix B

m o l • K

Example 2-1 Using the Ideal Gas Law to Calculate C^o

A gas mixture consists of 50% A and 50% inerts at 10 am (1013 kPa) and enler:s

the reactor with a flow rate of 6 dmVs at 300°F (422.2 K) Calculate the entering

con-centration of A, CAO, and the entering molar flow rate, ^AO- The ideal gas conslunt is

We could also solve for the partial pressure in terms of the concentration

P^, = C^,RTo (E2-I.2)

Substituting values in Equation (E2-l,l) yields

r ^ 0-5(10 atm) ^ Q ^^^^^ ^

^° 0.082 dm5-atm/mol-K(422.2K) ' dm^

Keeping only the significant figures gives us

CAQ = 0.144 mol/din^ - 0.144 kmol/m^ = 0.144 mol/L

The entering molar flow rate, PAO' IS just the product of the entering concentration,

CAO, and the entering volumetric flow rate, VQ'

Design

equalion F A

39

'^AO = CAO^^O = (0.14442 raol/dm3)(6.0 dmVs) = 0.867 mol/s

We will use this value of PAO together with either Table 2-2 or Figure 2-1 to size a number of reactor schemes in Examples 2-2 through 2-5

Now that we have a relationship [Equation (2-10)] between the molar flow rate and conversion, it is possible to express the design equations (i.e.,

mote balances) in terms of conversion for the flow reactors examined in

Chapter 1

CSTR or Backmix Reactor The equation resulting from a mole balance on

species A for the reaction

A + ^ B ^ E C + ^ D (2-2)

a a

occuring in a CSTR was given by Equation (1-6), which can be arranged to

^ A O - F A ^ - ' - A V (2-11)

We now substitute for the exituig molar flow rate of A, P^- in terms of

the conversion X and the entering molar flow rate, PAO> by using Equation

(2-10) in the form

and combining it with Equation (2-11) to give

^ A O ^ = - ' - A V (2-12)

We can rearrange Equation (2-12) to determine the CSTR volume

neces-sary to achieve a specified conversion X

Since the exit composition from the reactor is identical to the composition inside the reactor, the rate of reaction is evaluated at the exit conditions

T^ibular Flow Reactor (PFR) After multiplying both sides of the tubular

reactor design equation (1-10) by - 1 , we express die mole balance equation for species A in the reaction given by Equation (2-2) as

For a flow system, P^ has previously been given in terms of the entering molar

flow rate PAO and the conversion X:

We now separate the variables and integrate with the limit V = 0 when X = Q

to obtain the plug-flow reactor volume necessary to achieve a specified sion X-

conver-(246)

To carry out the integrations in the batch and plug-flow reactor design equations (2-9) and (2-16), as well as to evaluate the CSTR design equation (2-13), we need to know how the reaction rate —r^ varies with the concentra-tion (hence conversion) of the reacting species This relationship between reac-tion rate and concentration is developed in Chapter 3,

Packed-Bed Reactor The derivation of the differential and integral forms of the design equations for a packed-bed reactor are analogous to those for a PFR [cf Equations (2-15) and (2-16)} That is, substituting for F^ in Equation ( l - l l ) gives

(2-17)

The differential form of the design equation [i.e., Equation (2-17)] must be

used when analyzing reactors fliat have a pressure drop along the length of the reactor We discuss pressure drop in packed-bed reactors in Chapter 4

Integrating with the limits W = 0 aX X = 0 gives

each of the concentrations can be expressed as a function of the conversion X (see Chapter 3); consequently, - r ^ can be expressed as a function of X

A particularly simple functional dependence, yet one that occurs on

many occasions, is - r ^ = kC^oil ~ X), For this dependence, a plot of the

reciprocal rate of reaction ( - l / r ^ ) as a function of conversion yields a curve similar to the one shown in Figure 2-1, where

of A and inerts

TABLE 2-1 RAW DATA

X - r ^ (mol/dm^ - s) 0.0 0.0053 0.1 0.0052 0.2 O.0O50 0,3 0.0045

0.5 0.0033 0.6 0.0025 0.7 0,0018 0.8 0.00125 0.85 0.00100

The rate data in Table 2-1 have been converted to reciprocal rates, I Z - r ^

in Table 2-2, which are now used to arrive at the desired plot of IZ-r^ as a ftinction of X shown in Figure 2-1 We will use this figure to illustrate how one can size each of the reactors in a number of different reactor sequences The volumetric feed to each reactor sequence will be 6.0 dm^/s First, though, some initial conditions should be evaluated If a reaction is carried out isother-mally, the rate is usually greatest at the start of the reaction when the concen-tration of reactant is greatest [i.e., when there is negligible conversion

(^ = 0)]- Hence (IZ-r^,) will be small Near the end of the reaction, when the

reactant concentration is small (i.e., the conversion is large), the reaction rate will be small Consequently, (1/-/-^) is large For irreversible reactions of greater than zero-order

S' «> a s X - > 1

'•A

For reversible reactions in which the equilibrium conversion is X^,

- 1 _ i Qo as X ^ X,

These characteristics are illustrated in Figure 2-1 The majority of reactions

exhibit qualitatively similar curves for isothermal operation

Example 2-2 Sizing a CSTR

(a) Using the data in either Table 2-2 or Figure 2-1, calculate the volume necessav)'

to achieve 80% conversion in a CSTR (b) Shade the area in Figure 2-1 which whcii

multiplied by F^ would give the volume of a CSTR necessary to achieve 80%

con-version (i.e., X = 0,8)

Solution

From Example 2-1, knowing the entering conditions UQ ^ 6 dmVs, PQ = 10 aim,

•y^p = o_5^ x^ = 422.2 K, we can use the ideal gas law to calculate the entering

molar flow rate of A, i.e.,

^AO - t-Ao^o ^f^ "o -:8.314 kPa dmV(raol){K)] (422.2 K) (Q.5)(1013kPa)-6^mVs ^ ^_^^^ ^^^,^

(a) Equation (2-13) gives the volume of a CSTR as a function of FAQ, X and -r/^:

s

800 dm'-s mol 554.9 dm^ = 554,9 L

Figure E2-2.1 Levenspiel CSTR plot

In Figure E2-2,l the value of V/F^o is equal to the area of a rectangle with a height IZ-^A = 800 d m ' - s / m o l a n d a b a s e X = 0.8 This rectangle is shaded in the figure

To calculate the reactor volume, we multiply the area of the rectangle by

FAO-4 FAO-4 Sec 2.3 Applications ot the Design Equations for Continuous-Row Reactors 45

V - 0.867 mol 800 ^HIJ (O.S)

mol = 554.9 dm-' The CSTR volume necessary to achieve 80% conversion at the specified tempera-

tiire and pressure is 555 dm^

Example 2-3 Sizing a PFR

The reaction described by the data in Tables 2-1 and 2-2 is to be carried out in a

PFR The entering molar flow rate is 5 mol/s Calculate the reactor volume

tiec(;s-sary to achieve 80% conversion in a PFR (a) First, use one of the integration

lor-mulas given in Appendix A.4 to determine the PFR reactor volume, (b) Next, shade

the area in Figure 2-1 which when muUiplied by fXo would give the PFR volume,

(c) Make a qualitative sketch of the conversion, X, and the rate of reaction, ~}\y,

down the length (volume) of the reactor

Solution

(a) For the PFR, the differential form of the mole balance is

dX 'dV

Rearranging and integrating gives

= area under the curve between X-=0 and X = 0.8

'A (see appropriate shaded area in Figure E2-3.1)

Conversion, X Figure E2-3.I Levenspiel PFR pioL

The product of this area and F^Q will give the tubular reactor volume necessary to

achieve the specified conversion of A For 80% conversion, the shaded area is roughly equal to 260 dm^-(s/mol) The tubular reactor volume can be determined

by multiplying this area [in dm^-(s/mol)] by F^ (moUs) Consequently, for an

entering molar flow rate of 0.867 mol/s the PFR volume necessary to achieve 80% conversion is 225 dm'

(c) Sketch - r ^ and X down the length of the reactor, We know that as we proceed

down the reactor and more and more of the reactant is consumed, the concentration

of reactant decreases, as does the rate of disappearance of A However, the

conver-sion increases as more and more reactant is converted to product For X = 0,2 we calculate the corresponding reactor volume using Simpson's rule with AX = 0.1

46 Conversion and Reactor Sizing Chap, 2

We can continue in this manner to arrive at Table E2-3.1

TABLE E2-3,l CoNVERSiON P R O F I L E

Figure E2-3.2 Conversion profile

Rather than using Simpson's rule we could have used the data in Table 2-2 to En

— r^(X) to a polynomial and then used POLYMATH to integrate the design

equa-tion to obtain the conversion profile,

Example 2-4 Comparing CSTR and PFR Sizes

It is interesting to compare the volumes of a CSTR and a plug-flow reactor (PFR)

required for the same job To do this we shall use the data in Figure 2-1 to learn

which reactor would require the smaller volume to achieve a conversion of 60%: a

CSTR or a PFR The feed conditions are the same in both cases The entering molar

flow rate is 5 mol/s

Solution

For the CSTR:

47

Generally, the isothermal tubular reactor volume is smaller tlian the CSTR for the same conversion

V_

~ IX = (400) (0.6) = 240 ^ ^ -r^ mol

This is also the area of the rectaigle with vertices (X, M-r^^) of (0, 0), (0, 400),

(0.6, 400), and (0.6,0) The CSTR volume necessary to achieve 60% conversion is

V 5 mol

s 240din^-s moi 1200 dm3 For the plug-flow (tubular) reactor:

dX

K dV

Integrating and rearrangmg Equation (2-15) yields

1 -rA(O.O) 0.3

= - 3 - X [189+ 4(222)+ 400]

- H g d m ^ - s

•'X(0.3) -rA(0.6)

moi The PFR volume necessary to achieve 60% conversion is

V 5 mol 148 dm^ • s

mol 740 dm^

For the same flow rate f^o the plug-flow reactor requires a smaller volume than the CSTR to achieve a conversion of 60% This comparison can be seen in Figure E2-4.1 For isothermal reactions of greater than zero order, the PFR wiU always require a smaller volume than the CSTR to achieve the same conversion,

mol

Mfferaiee between CSIR

Itog Flow Reactor

az 014 ConversiOE X Figure E2-4.1 Levenspiel plot comparing CSTR and PFR size

mr