Chemical Reaction Engineering (CRE) is the field that studies the rates and mechanisms of
chemical reactions and the design of the reactors in which they take place.
Lecture 2
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Lecture 2 – Tuesday 1/15/2013Review of Lecture 1Definition of Conversion, XDevelop the Design Equations in terms of XSize CSTRs and PFRs given –rA= f(X)Conversion for Reactors in SeriesReview the Fall of the Tower of CRE
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Reactor Differential Algebraic Integral
The GMBE applied to the four major reactor types (and the general reaction AB)
V FA 0 FA
rA
CSTR
Vrdt
dNA
A 0
A
A
N
N A
A
VrdNtBatch
NA
t
dFA
dVrA
A
A
F
F A
A
drdFV
0
PFRFA
V
dFA
dW r A
A
A
F
F A
A
rdFW
0
PBRFA
W3
Reactor Mole Balances Summary
Review Lecture 1
4
CSTR – Example Problem
000
0
3
0 mindm 10
AA
A
CFC
AA
AA
CFCC
0
3
0
1.0min
dm 10
0
FA 0CA
Liquid phase
V ?
Given the following information, Find V
Review Lecture 1
5
CSTR – Example Problem (1) Mole Balance:
A
AA
A
AA
A
AA
rCC
rCC
rFFV
000000
AA kCr (2) Rate Law:
(3) Stoichiometry:
0AA
AFFC
Review Lecture 1
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CSTR – Example Problem (4) Combine:
V 0 CA 0 CA
kCA
(5) Evaluate:
3
01
00
3
0
1.023.01.0110
1.0min23.0
1.0min
10
1.0
dmC
CCdm
V
CC
A
AA
AA
3 3913.2
900 dmV
Review Lecture 1
Define conversion, X
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D d C c B b A a Consider the generic reaction:
D ad C
ac B
ab A
Chose limiting reactant A as basis of calculation:
fedA moles reactedA moles X
Define conversion, X
Batch
8
VrdtdXN
dtdN
dXNdNXNNN
reactedAMoles
initiallyAMoles
remainingAMoles
AAA
AA
AAA
0
0
00
0
Batch
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X
AA Vr
dXNt0
0
Integrating,
The necessary t to achieve conversion X.
XXttXt
0 0
0
A A
A
dN r Vdt N
CSTR
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D d C c B b A a Consider the generic reaction:
D ad C
ac B
ab A
Chose limiting reactant A as basis of calculation:
fedA moles reactedA moles X
Define conversion, X
CSTR
11
dNA
dt0Steady State
VrdVr AA
Well Mixed
V FA 0 FA
rA
CSTR
12 CSTR volume necessary to achieve conversion X.
V FA 0 FA 0 FA 0X
rA
A
A
rXFV
0
XFFFreacted
AMolesentering
AMolesleaving
AMoles
AAA 00
00 dVrFF AAA
PFR
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AA r
dVdF
XFFF AAA 00
0A
A
Fr
dVdX
XFdF AA 00 Steady State
PFR
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XXVVXV
0 0
PFR volume necessary to achieve conversion X.
dXr
FVX
A
A
0
0
Integrating,
Reactor Differential Algebraic Integral
V FA 0X rA
CSTR
FA 0dXdV
rA
X
A
A
rdXFV
0
0PFR
VrdtdXN AA 0
0
0
X
AA Vr
dXNtBatch
X
t
FA 0dXdW
r A
X
A
A
rdXFW
0
0PBR
X
W15
Reactor Mole Balances Summaryin terms of conversion, X
Levenspiel Plots
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Reactor SizingGiven –rA as a function of conversion, -rA= f(X), one can size any type of reactor. We do this by constructing a Levenspiel plot. Here we plot either (FA0/-rA) or (1/-rA) as a function of X. For (FA0/-rA) vs. X, the volume of a CSTR and the volume of a PFR can be represented as the shaded areas in the Levenspiel Plots shown as:
)(0 Xgr
F
A
A
Levenspiel Plots
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FA 0
rA
X
FA 0
rA
Area = Volume of CSTR
X1
10
1
Xr
FVXA
A
18
CSTR
19
PFR
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Levenspiel Plots
Numerical Evaluations of IntegralsThe integral to calculate the PFR volume can be
evaluated using method as Simpson’s One-Third Rule: (See Appendix A.4)
)(
1)2/(
4)0(
13 0
0
0
XrXrrFxdX
rFV
AAAA
X
A
A
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Other numerical methods are:Trapezoidal Rule (uses two
data points)Simpson’s Three-Eight’s
Rule (uses four data points)Five-Point Quadrature
Formula
)(1
2XrA
)(1
1XrA
)0(1
Ar
Ar1
0 1X 2X
Given: rA as a function of conversion, one can also design any sequence of reactors in series by defining X:
reactorfirst tofedA of molesipoint toup reactedA of moles total Xi
Only valid if there are no side streams.
Molar Flow rate of species A at point i:
0 0Ai A A iF F F X 22
Reactors in Series
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Reactors in Series
Reactor 1:
1001 XFFF AAA
1
10
1
1000
1
101
A
A
A
AAA
A
AA
rXF
rXFFF
rFFV
V1A
0A
rF
X241X
Reactors in Series
Reactor 2:
dXr
FVX
X A
A
2
1
02
V2
A
A
rF
0
X251X 2X
Reactors in Series
00
33300200
3332
VrXFFXFFVrFF
AAAAA
AAA
V3 FA 0 X3 X2
rA 3
V3
A
0A
rF
X263X1X 2X
Reactors in SeriesReactor 3:
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Reactors in Series
Space time τ is the time necessary to process 1 reactor volume of fluid at entrance conditions.
V0
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Reactors in Series
KEEPING UPThe tower of CRE, is it stable?
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Reaction Engineering
Mole Balance Rate Laws Stoichiometry
These topics build upon one another.
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Mole BalanceRate Laws
StoichiometryIsothermal Design
Heat Effects
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CRE Algorithm
Mole Balance
32
Be careful not to cut corners on any of the CRE building blocks while learning this material!
Rate Laws
Mole Balance
Rate LawsStoichiometry
Isothermal DesignHeat Effects
33Otherwise, your Algorithm becomes unstable.
End of Lecture 2
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