Lecture 23
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.
Web Lecture 23
Class Lecture 21 - Tuesday 3/22/2011
 CSTR With Heat Effects
 Multiple Steady States
 Ignition and Extinction Temperatures
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Courtesy of Pfaudler, Inc.
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 
Q  W
S
n
F
i0
i 1
Using Eˆ
sys

NE
dE sys
dt
i

i
i
d  N iH i
dt
dH i
dt
dN i
4
dt
d Eˆ sys
i 1
dt
H i 0   Fi H i 
 N H

n

i
 PV i  
N
 C Pi
dH i
i
dt
Neglect
NH
i
 H i
dT
dt
   i rA V  Fi 0  Fi
i
 PV
dN i
dt
We obtain after some manipulation:
dT

 
Q  W
 Fi 0 C Pi T  Ti 0     H Rx T  rA V 
S
dt
Collecting terms with
rates, W S  0 and Fi 0
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NC
i
Pi
  UA T  T 
Q
a
 FA 0  i
and high coolant flow
  H Rx
dT

dt

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FA 0
 N i C Pi
C


P


0


 rA V    FA 0   i C Pi T  T 0    UA T  T a 






 N i C Pi


R  T 
           



G  T 
 



 



rA V 
UA
H R
 T  T a   
  C P0  T  T 0 
FA 0
FA 0 C P S










  






dT

dt
FA 0
 N i C Pi
G T   R T 
G T    rA V  H Rx

R T   C P0 1   T  T 0   T a 
T0   Ta 

R ( T )  C P0 1    T 
  C P0 1   T  T C 
1  


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UA
FA 0 C P 0
TC 
T0   Ta
1 
dT
dt
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 G T   R T 
If G(T) > R(T)
Temperature Increases
If R(T) > G(T)
Temperature Decreases
At Steady State
dT
dt

dN
A
0
dt
 rA V  FA 0 X
G T   R T   0
   H Rx FA 0 X  FA 0   i C P T  T 0   UA T  T a   0
i
Solving for X.
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Solving for X
  i C Pi  T  T 0  
X 
 H
UA
FA 0
T  T a 
 X EB

Rx
Solving for T
T 
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FA 0 X    H Rx   UAT
a
 FA 0   i C Pi T 0
UA  FA 0   i C Pi
X    H Rx
Let  


UA
  C P0  T  T 0 
T  Ta 
FA 0 C P0


UA
FA 0 C P0
X    H Rx
T0   Ta 

  C P0 T   T  T 0   T a   C P0 1    T 

1  

 C P0 1   T  T C 
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TC 
T0   Ta
1 
G (T )
R (T )
    
  


 X  H Rx  C P 0 1   T  T C 
X 
C P 0 1   T  T C 
T  TC 
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 H

 H

Rx
Rx
 X 
C P 0 1   
R(T)
Increasing T0
T
Variation of heat removal line with inlet temperature.
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κ=∞
κ=0
R(T)
Increase κ
Ta
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T0
T
Variation of heat removal line with κ (κ=UA/CP0FA0)
V 
FA 0 X
 rA  X , T 
A  B
V 
FA 0 X
 rA
 rA  kC
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A
C A  C A 0 1  X 
V 
FA 0 X
kC A 0 1  X 
k 
X 
k
1  k

G T   X    H Rx  
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C A00X

kC A 0 1  X 
X
1 X
 E RT
 Ae
1  Ae
 Ae
 E RT
 E RT
1  Ae
 E RT
   H Rx 
Variation of heat generation curve with space-time.
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Finding Multiple Steady States with T0 varied
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Finding Multiple Steady States with T0 varied
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Temperature ignition-extinction curve
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Stability of multiple state temperatures
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dT
1
dt
G T   X     H Rx
R  C P0  1  kappa

  T  T C 
Need to solve for X after combining mole balance rate law
and stoichiometry.
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For a first order irreversible reaction
X 
tau  k
1  tau
E
k  k 1 exp 
R
k
 1
1 



T

T
 1

Parameters
Tau ,    H Rx , k 1 , E , R , T1 , TC , kappa, C P0
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Then plot G and R as a function of T.
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