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TitleIntroduction to chemical reaction engineering and kinetics
File Size17.1 MB
Total Pages692
Table of Contents
Chapter 1: Introduction
Chapter 2: Kinetics & ideal reactor models
Chapter 3: Experimental methods in kinetics: measurement of rate of reaction
Chapter 4: Development of the rate law for a simple system
Chapter 5: Complex systems
chapter 6: Fundamentals of reaction rates
Chapter 7: homogeneous reaction mechanisms & rate laws
Chapter 8: Catalysis & catalytic reactions
Chapter 9: Multiphase reacting systems
Chapter 10: biochemical reactions: enzyme kinetics
chapter 11: Preliminary considerations in chemical reaction engineering
Chapter 12: bath reactors (BR)
Chapter 13: Ideal Flow
Chapter 14: Continuous Stirred-tank reactors (CSTR)
Chapter 15: Plug flow reactors (PFR)
Chapter 16: Laminar flow reactors (LFR)
Chapter 17: Comparisons & combinations of ideal reactors
Chapter 18: Complex Reactions in ideal reactors
Chapter 19: Nonideal flow
Chapter 20: Reactor performance with nonideal flow
Chapter 21: fixed-bed catalytic reactors for fluid-solid reactins
Chapter 22: Reactors for fluid-solid (noncatalytic) reactions
Chapter 23: Fluidized-bed & other moving-particle reactors for fluid-solid reactions
Chapter 24: reactors for fluid-fluid reactions
Appendix A
Appendix B: Bibliography
Appendix C: Answers to selescted problems
Appendix D: Use of E-Z solve for equation solving & parameter estimation
Author index
Subject index
Document Text Contents
Page 346

328 Chapter 13: Ideal Flow

Limit as C-b 0

t Figure 13.6 Motivation for Dirac delta function, s(t - b)

Consider an element of fluid (as “tracer”) entering the vessel at t = 0. Visualizing
what happens to the element of fluid is relatively simple, but describing it quantita-
tively as E(t) requires an unusual mathematical expression. The element of fluid moves
through the vessel without mixing with fluid ahead of or behind it, and leaves the vessel
all at once at a time equal to the mean residence time (f = V/q for constant density).
Thus, E(t) = 0 for 0 < t < t; but what is E(t) at t = t?

To answer this question, away from the context of PF, consider a characteristic func-
tion f(t) that, at t = b, is suddenly increased from 0 to l/C, where C is a relatively
small, but nonzero, interval of time, and is then suddenly reduced to 0 at t = b + C,
as illustrated in Figure 13.6. The shaded area of C(W) represents a unit amount of a
pulse disturbance of a constant value (l/C) for a short period of time (C). As C + 0
for unit pulse, the height of the pulse increases, and its width decreases. The limit of this
behavior is indicated by the vertical line with an arrow (meaning “goes to infinity”) and
defines a mathematical expression for an instantaneous (C + 0) unit pulse, called the
Dirac delta function (or unit impulse function):

8(t - b) = liio[j-(t)] = ~0; t = b

= 0;t # b (13.4-6)

such that

8(t - b)dt = 1 (13.4-7)

For E(t), b = t; and hence E(t) for PF is represented mathematically by

E(t) = LS(t - 4 =

Page 347

13.4 Age-Distribution Functions for Ideal Flow 329

Since 0 5 f < ~0, the area under the vertical line representation for PF is unity, as re-
quired by equation 13.3-1.

Another important property of the delta function is, for any function g(t):


g(t)S(t - b)dt = g(b), if tl 5 b i- t2

= 0, otherwise (13.4-10)

Wylie (1960, pp. 341-2) presents a proof of equation 13.4-10, based on approximating
8(t - t) by l/C (Figure 13.6), and using the law of the mean for integrals, but it is omitted

In terms of dimensionless time, 8, for PF

E(B) = a(0 - 1) = ~0; 8 = 6 = 1

=o;ez1 (PF) (13.4-11)

For E(B) in PF, what are the mean value 6 and the variance ai?


We use the property of the delta function contained in equation 13.4-10, and the definitions
of I!? and (T; in the 13 analogues of equations 13.3-14 and 13.3-16a, respectively, to obtain



fj= e&e - 1)de = 1

a ; =

e26(e - 1)de - fP = l2 - l2 = 0

0 I

The second result confirms our intuitive realization that there is no spread in residence
time for PF in a vessel. F for PF
For PF, the F function requires another type of special mathematical representation.
For this, however, consider a sudden change in a property of the fluid flowing that is
maintained (and not pulsed) (e.g., a sudden change from pure water to a salt solu-
tion). If the change occurs at the inlet at t = 0, it is not observed at the outlet until
t = t. For the exit stream, F(t) = 0 from t = 0 to t = t; since the fraction of the
exit stream of age less than t is 0 for

Page 691

Directory of Examples 8olved Using E-Z !%lve

12-2 I 300 1 exl2-2.msp I performance of a amstant-volume batch reactor I

3 1 1
3 4 1

exl2S.msp adiabatic operaticn of a batch reach
exl2-6.msp optimization of batch-reactor operation
exl2-7.msp semibatch operation
exl4-3.msp translent operation of a CBTR
exl4-6.msc (yas&)e &(-jn in 9 r-!-l-R





3 6 1

..Y.s.. -m u, , . .

--.- dwity operation of a PFR
158 I 379 I exl6-8.msp IeffectofpreswedroponPFRperfcrmance

exl6-3.msp sizing of an LFR
ex17-2.msp comparison of CBTR and PFR performance
exl7-7.msp reactor combination for autocatalytic readion
exl8-l.msp effect of reach staging on conversion for a reversible readion

1 18-6 I 436 I exl8-6.msp I reactofdesignfor parallel readicn netwrk I
141 4 6 1 exlQ-l.msp RTD analysis for a pulse input
192 464 exl92msp RTD analysis for a step input
19-3 466 exlQ-3.msp RTD analysiswtth a reactive tracer
194 469 exlSl.msp RTD analysis - pulse input tith tailing
197 477 exl97.msp caiculation of gamma timction
198 I 478 1 exl9-3.msp I parameter estimation fortanks-irweries mcdel
IQ-9 1 481 I ex19-2.msp I parameter estimation fortanks-in-seties model

21-6 I 640
22-2 1 668

exZlb.msp I design ofafixed bed reactortith cokhhotccding
I ex22-2.msp I gassdid reaction: spherical particles in PF, particle size distribution

22-3 660 ex22-3.msp gas&d reaction: cylindrical particles in BMF
22-4 663 ex22Amsp gas-solid reaction: sensitivity of design to rate-limiting process
22-5 666 ex22S.m.y gas-solid reaction tith more than one rate limiting process
23-2 577 ex2%2.msp minimum fluidhtion velocity in a fluidized-bed reactor
23-3 I 687 I ex23-3.msp I design of a fluidized-bed reactor l~orderreaction- - - - - I

8 1 %

ex23-4.msp series reactions in a fluidized-bed reactor
ex23-6.msp operation of fluidized-bed reactor in intermediate particle regime
ex24-2.msp gas-liquid systems: perfcrmance of a bubbleGdumn reactor
ex24-3 msn aas-tinuid svstnms ripsinn nf R tank reactor

Page 692

udents read through this text, they’ll find a comprehensive, introduc
ent of reactors for single-phase and multiphase systems that expc 2733;

range of reactors and key design features. They’ll gain L ” DE G - CUCEI

sight on reaction kinetics in relation to chemical reactor design. They ~~~~~

also utilize a special software package that helps them quickly solve systems of 1

Solving problems in chemical reaction engineering
and kinetics is now easier than ever!

q; $
V\*& Thorough coverage is provided on the relevant principles of kinetics in order8” \Yi \tt*a “* ; I3 1 $” ui* to develop better designs of chemical reactors.: 8 t.l 1“I *at E-Z Solve software, on CD-ROM, is included with the text. Bv utilizina this

; ;,i gq;“:
:‘,,I ,‘A!,. “), \
,,, \d$t*%f,,~.‘,:‘a,f~?;n$,, software, students’can have m&e time to focus on the de;elopm&t of.!>I ~>Q~*~/q~r~(“ti~,jr ’Y * : ; 1 i,y ,‘ , , * , !bts; ,\‘-i,,b:Y,$‘:,*, design models and on the interpretation of calculated results. The software“::*,,Fp\:h;‘I ;\‘,,lt?,,, ; , I * also facilitates exploration and discussion of realistic, industrial design prob-

*i\, 1 *v lems.
( :su

>I I ;“&
More than 500 worked examples and end-of-chapter problems are included

* ‘I
:, :Y$&:l

to help students learn how to apply the theory to solve design problems.
‘:*(t ~)\\\I”, I

A web site,, provides additional resources

\ \ \.’ :b’
including sample files, demonstrations, and a description of the E-Z Solve

‘- * ‘;*I

““Z \I
About the Authors

1 :;$:; RONALD W. MISSEN is Professor Emeritus (Chemical Engineering) at the
’ University of Toronto. He received his BSc. and M.Sc. in chemical engineering

from Queen’s University, Kingston, Ontario, and his Ph.D. in physical chemistry
from the University of Cambridge, England. He is the co-author of CHEA4ICAL

I I REACTION EQUlLBRlUM ANALYSIS, and has authored or co-authored about
$\:;i;i;, 50 research articles. He is a fellow of the Chemical Institute of Canada and the

: ~~~~~~ Canadian Society for Chemical Engineering, and a member of the American
,‘;l>$$ Institute of Chemical Engineers and Professional Engineers Ontario.
* II0
yiI,tj:: CHARLES A. MIMS is a Professor of Chemical Engineering and Applied

,~i~~y;$ Chemistry at the University of Toronto. He earned his B.Sc. in chemistry at the
” “’ university of Texas, Austin, and his Ph.D. in physical chemistry at the

University of California, Berkeley. He has 15 years of industrial research experi-
ence at Exxon, is the author of over 65 research publications, and holds three
patents. His research interests focus on catalytic kinetics in various energy and

*i i hydrocarbon resource conversion reactions, and the fundamentals of surface.-I\ i
i- ,‘A” reactions.

~ & BRADLEY A. SAVILLE is an Associate Professor of Chemical Engineering at

--I “>ii:;; the University of Toronto. He received his BSc. and Ph.D. in chemical engi-
* ;+$>;

neering at the University of Alberta. He is the author or co-author of over 25

+;I ;2j research articles on enzyme kinetics, pharmacokinetics, heterogeneous reactions
%%% in biological systems, and reactors for immobilized enzymes. He is a member*r*+<
%&@ of the Chemical Institute of Canada, the Canadian Society of Chemical I5
‘%$%! Engineering, and Professional Engineers Ontario.g&-&&

9 ;

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