Lecture 21
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.
Today’s lecture
 CSTR With Heat Effects
 Multiple Steady States
 Ignition and Extinction Temperatures
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CSTR with Heat Effects
Courtesy of Pfaudler, Inc.
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Unsteady State Energy balance
 
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
Unsteady State Energy balance
We obtain after some manipulation:
dT
dt

 
Q  W
 Fi 0 C Pi T  Ti 0     H Rx T  rA V 
S
NC
Collecting terms with Q  UA Ta
rates, W S  0 and Fi 0  FA 0  i
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i
Pi
 T
and high coolant flow
Unsteady State Energy balance
  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










  






Unsteady State Energy balance
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 
Unsteady State Energy balance
dT
dt
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 G T   R T 
If G(T) > R(T)
Temperature Increases
If R(T) > G(T)
Temperature Decreases
Steady State Energy balance for CSTRs
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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Steady State Energy balance for CSTRs
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
Energy balance for CSTRs
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 
Energy balance for CSTRs
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   
Energy balance for CSTRs
R(T)
Increasing T0
T
Variation of heat removal line with inlet temperature.
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Energy balance for CSTRs
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
1) Mole Balance:
2) Rate Law:
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V 
FA 0 X
 rA
 rA  kC
A
3) Stoichiometry:
4) Combine:
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 
Multiple Steady States (MSS)
Variation of heat generation curve with space-time.
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Multiple Steady States
Finding Multiple Steady States with T0 varied
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Multiple Steady States
Finding Multiple Steady States with T0 varied
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Multiple Steady States
Temperature ignition-extinction curve
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Multiple Steady States
Stability of multiple state temperatures
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MSS - Generating G(T) and R(T)
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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MSS - Generating G(T) and R(T)
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.
End of Lecture 21
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