Lecture 2
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.
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Lecture 2 – Tuesday 1/15/2013
 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
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Review Lecture 1
Reactor Mole Balances Summary
The GMBE applied to the four major reactor types
(and the general reaction AB)
Reactor
Differential
Algebraic
Integral
NA
Batch
dN
dt
A
N A0
CSTR
PFR
V 
dF A
dV

t
 r AV
dN
 rA
NA
A
rAV
FA 0  FA
 rA
FA
V 

FA 0
FA
dF A
dr A

3
PBR
dF A

dW
FA
 rA
t
W 

FA 0
dF A
V
FA
rA
W
Review Lecture 1
CSTR – Example Problem
Given the following information, Find V
 0  10 dm
3
C A0
FA0   0C A0
Liquid phase

  0
FA   0C A
4
   0  10 dm
min
V ?
C A  0 . 1C A 0
FA  C A
3
min
Review Lecture 1
CSTR – Example Problem
(1) Mole Balance:
V 
FA0  FA
 rA

 0C A0   0C A
(2) Rate Law:
 r A  kC A
(3) Stoichiometry:
CA 
5
FA


FA
0
 rA

 0 C A 0  C A 
 rA
Review Lecture 1
CSTR – Example Problem
(4) Combine:
V 
 0 C A 0  C A 
kC A
(5) Evaluate:
C A  0 . 1C A 0

10 dm
V 
V 
6
3
C A 0  0 . 1C A 0 
min
0 . 23 min

900
2 .3
1
0 .1C 
 391 dm
A0
3

10 1  0 . 1
0 . 23 0 . 1
dm
3
Define conversion, X
Consider the generic reaction:
aAbB
 c C  d D
Chose limiting reactant A as basis of calculation:
A 
b
a
B

c
C
a
Define conversion, X
X 
moles A reacted
moles A fed
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d
a
D
Batch
 Moles A   Moles A   Moles A 

 


remaining
initially
reacted

 
 

NA
dN
A
dN
A
dt
8

N A0
 0  N A 0 dX
  N A0
dX
dt
 r AV

N A0 X
Batch
dN A

dt
r AV
t 0
X 0
N A0
t t
X  X
Integrating,
X
t  N A0 
0
dX
 r AV
The necessary t to achieve conversion X.
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CSTR
Consider the generic reaction:
aAbB
 c C  d D
Chose limiting reactant A as basis of calculation:
A 
b
a
B

c
C
a
Define conversion, X
X 
moles A reacted
moles A fed
10
d
a
D
CSTR
Steady State
dN
dt
Well Mixed
11

0
FA 0  FA
V 
r
A
 rA
A
dV  rAV
CSTR
 Moles A 
 Moles A   Moles A 

  


 leaving 
 entering   reacted 
FA

FA0  FA 
V 
V 
12

FA 0 
FA0
r
A

FA0 X
dV  0
F A 0  F A 0 X 
 rA
FA0 X
 rA
CSTR volume necessary to achieve conversion X.
PFR
dF A
dV
 rA
FA  FA0  FA0 X
Steady State
dF A  0  F A 0 X
dX
dV
13

 rA
FA0
PFR
V 0
X 0
V V
X  X
Integrating,
X
V 
FA0
r
0
dX
A
PFR volume necessary to achieve conversion X.
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Reactor Mole Balances Summary
in terms of conversion, X
Reactor
Differential
Algebraic
Integral
X
X
Batch
N A0
dX
dt
  r AV
0
V 
CSTR
PFR
t  N A0 
FA 0
  rA
dV

 r AV
t
FA 0 X
 rA
X
dX
dX
V 

F A 0 dX
 rA
0
X
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PBR

FA 0
dX
dW
X
  rA
W 

0
F A 0 dX
 r A
W
Levenspiel Plots
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:
FA0
 rA
16
 g(X )
Levenspiel Plots
FA 0
 rA
X

17

CSTR
FA 0
Area = Volume of CSTR
rA
 FA0 
 X1
V  


r
A X

1
X1
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PFR
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Levenspiel Plots
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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)
X
V 
1
r
0
 rA ( X 2 )
FA0
A
dX 
 1

4
1
FA0 



3

r
(
0
)

r
(
X
/
2
)

r
(
X
)
A
A
 A

x
1
 rA
1
 rA ( X 1 )
1
 rA ( 0 )
21
0
X1
X2
Other numerical methods are:
 Trapezoidal Rule (uses two
data points)
 Simpson’s Three-Eight’s
Rule (uses four data points)
 Five-Point Quadrature
Formula
Reactors in Series
Given: rA as a function of conversion, one can also
design any sequence of reactors in series by defining
X:
Xi 
total moles of A reacted up to point i
moles of A fed to first reactor
Only valid if there are no side streams.
Molar Flow rate of species A at point i:
FAi  FA 0  FA 0 X i
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Reactors in Series
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Reactors in Series
Reactor 1:
F A1  F A 0  F A 0 X 1
V1 
F A 0  F A1
 r A1
FA 0
 rA
24

FA0  FA0  FA0 X 1 
 rA1
V1
X1
X

FA0 X 1
 r A1
Reactors in Series
Reactor 2:
X2
V2 
FA0
r
X1
dX
A
V2
FA0
 rA
X1
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X2
X
Reactors in Series
Reactor 3:
F A 2  F A 3  rA 3V 3  0
 F A 0  F A 0 X 2    F A 0  F A 0 X 3   rA 3V 3
V3 
0
F A 0 X 3  X 2 
 rA 3
V3
FA 0
 rA
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X1
X
X2
X3
Reactors in Series
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Reactors in Series
Space time τ is the time necessary to process 1
reactor volume of fluid at entrance conditions.
 
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V
0
KEEPING UP
 The tower of CRE, is it stable?
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Reaction Engineering
Mole Balance
Rate Laws
These topics build upon one another.
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Stoichiometry
Heat Effects
Isothermal Design
Stoichiometry
Rate Laws
Mole Balance
CRE Algorithm
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Mole Balance
Rate Laws
Be careful not to cut corners on any of the
CRE building blocks while learning this material!
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Heat Effects
Isothermal Design
Stoichiometry
Rate Laws
Mole Balance
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Otherwise, your Algorithm becomes unstable.
End of Lecture 2
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