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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
1
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Lecture 2
Review of Lecture 1
Definition of Conversion, X
Develop the Design Equations in terms of X
Size CSTRs and PFRs given –rA= f(X)
Conversion for Reactors in Series
Review the Fall of the Tower of CRE
2
Chapter 2
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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
Vr
dNtBatch
NA
t
dFA
dV rA
A
A
F
F A
A
dr
dFV
0
PFR
FA
V
dFA
dW r A
A
A
F
F A
A
r
dFW
0
PBRFA
W3
Reactor Mole Balances Summary
Review Lecture 1
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CSTR – Example Problem
000
0
3
0 mindm 10
AA
A
CF
C
AA
AA
CF
CC
0
3
0
1.0
mindm 10
0
FA 0CA
Liquid phase
V ?
Given the following information, Find V
Review Lecture 1
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5
CSTR – Example Problem
(1) Mole Balance:
A
AA
A
AA
A
AA
r
CC
r
CC
r
FFV
000000
AA kCr
(2) Rate Law:
(3) Stoichiometry:
0AA
A
FFC
Review Lecture 1
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6
CSTR – Example Problem
(4) Combine:
V 0 CA 0 CA
kCA
(5) Evaluate:
3
0
1
00
3
0
1.023.0
1.0110
1.0min23.0
1.0min
10
1.0
dmC
CCdm
V
CC
A
AA
AA
3 3913.2
900dmV
Review Lecture 1
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Define conversion, X
7
D d C c B b A a
Consider the generic reaction:
D a
d C
a
c B
a
b A
Chose limiting reactant A as basis of calculation:
fedA moles
reactedA moles X
Define conversion, X
Chapter 2
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Batch
8
Vrdt
dXN
dt
dN
dXNdN
XNNN
reacted
AMoles
initially
AMoles
remaining
AMoles
AAA
AA
AAA
0
0
00
0
Chapter 2
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Batch
9
X
A
AVr
dXNt
0
0
Integrating,
The necessary t to achieve conversion X.
XXtt
Xt
0 0
0
A A
A
dN r V
dt N
Chapter 2
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CSTR
10
D d C c B b A a
Consider the generic reaction:
D a
d C
a
c B
a
b A
Chose limiting reactant A as basis of calculation:
fedA moles
reactedA moles X
Define conversion, X
Chapter 2
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CSTR
11
dNA
dt 0Steady State
VrdVr AA
Well Mixed
V FA 0 FA
rA
Chapter 2
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CSTR
12 CSTR volume necessary to achieve conversion X.
V FA 0 FA 0 FA 0X
rA
A
A
r
XFV
0
XFFF
reacted
AMoles
entering
AMoles
leaving
AMoles
AAA 00
00 dVrFF AAA
Chapter 2
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PFR
13
AA r
dV
dF
XFFF AAA 00
0A
A
F
r
dV
dX
XFdF AA 00Steady State
Chapter 2
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PFR
14
XXVV
XV
0 0
PFR volume necessary to achieve conversion X.
dXr
FV
X
A
A
0
0
Integrating,
Chapter 2
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Reactor Differential Algebraic Integral
V FA 0X
rA
CSTR
FA 0
dX
dV rA
X
A
A
r
dXFV
0
0PFR
Vrdt
dXN AA 0
0
0
X
A
AVr
dXNtBatch
X
t
FA 0
dX
dW r A
X
A
A
r
dXFW
0
0PBR
X
W15
Reactor Mole Balances Summaryin terms of conversion, X
Chapter 2
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Levenspiel Plots
16
Reactor Sizing
Given –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
Chapter 2
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Levenspiel Plots
17
FA 0
rA
X
Chapter 2
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FA 0
rA
X 1
Area = Volume of CSTR
10
1
Xr
FV
XA
A
18
CSTR
Chapter 2
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19
PFR
Chapter 2
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Levenspiel Plots
Chapter 2
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Numerical Evaluations of Integrals
The 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(
1
30
0
0
XrXrrF
xdX
r
FV
AAA
A
X
A
A
21
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
Ar
1
0 1X 2X
Chapter 2
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Given: rA as a function of conversion, one can also
design any sequence of reactors in series by defining
X:
reactorfirst tofedA of moles
ipoint toup reactedA of moles total Xi
Only valid if there are no side streams.
22
Reactors in Series
Molar Flow rate of species A at point i:
0 0Ai A A iF F F X
Chapter 2
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23
Reactors in Series
Chapter 2
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Reactor 1:
1001 XFFF AAA
1
10
1
1000
1
101
A
A
A
AAA
A
AA
r
XF
r
XFFF
r
FFV
24
V1
A
0A
r
F
X1X
Reactors in Series
Chapter 2
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Reactor 2:
dXr
FV
X
X A
A
2
1
02
25
V2
A
A
r
F
0
X1X 2X
Reactors in Series
Chapter 2
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0
0
33300200
3332
VrXFFXFF
VrFF
AAAAA
AAA
V3 FA 0 X3 X2
rA 3
26
V3
A
0A
r
F
X 3X1X 2X
Reactors in Series
Reactor 3:
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27
Reactors in Series
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Space time τ is the time necessary to process 1
reactor volume of fluid at entrance conditions.
V
0
28
Reactors in Series
Chapter 2
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KEEPING UP
The tower of CRE, is it stable?
29
Chapter 2
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Reaction Engineering
Mole Balance Rate Laws Stoichiometry
These topics build upon one another.
30
Algorithm
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Mole Balance
Rate Laws
Stoichiometry
Isothermal Design
Heat Effects
31
CRE Algorithm
Algorithm
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Mole Balance
32
Be careful not to cut corners on any of the
CRE building blocks while learning this material!
Rate Laws
Algorithm
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Mole Balance
Rate Laws
Stoichiometry
Isothermal Design
Heat Effects
33
Otherwise, your Algorithm becomes unstable.
Algorithm
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End of Lecture 2
34