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 19 - Tuesday 3/26/2013
CSTR With Heat Effects
 Multiple Steady States
 Ignition and Extinction Temperatures
2
CSTR with Heat Effects
Courtesy of Pfaudler, Inc.
3
Unsteady State Energy Balance
 
Q  W
S
n
F
i0
i 1
n
d Eˆ sys
i 1
dt
H i 0   Fi H i 
Neglect
Using Eˆ sys 
NE
dE sys
dt
i

i
 N H

i
d  N iH i
dt
dH i
dt
dN i
4
dt

i
 PV i  
N
 C Pi
dH i
i
dt
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
i
Pi
Collecting terms with Q  UA Ta  T  and
coolant flow rates, and Fi 0  FA 0  i
5
 0
W
S
high
Unsteady State Energy Balance
  H Rx
dT

dt

6
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  


7
UA
FA 0 C P 0
TC 
T0   Ta
1 
Unsteady State Energy Balance
dT
dt
8
 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 
10
FA 0 X    H Rx   UAT
a
 FA 0   i C Pi T 0
UA  FA 0   i C Pi
Steady State 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 
Steady State 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   
Steady State Energy Balance for CSTRs
R(T)
Increasing T0
T
Variation of heat removal line with inlet temperature.
13
Steady State Energy Balance for CSTRs
κ=∞
κ=0
R(T)
Increasing κ
Ta
14
T0
T
Variation of heat removal line with κ (κ=UA/CP0FA0)
V 
FA 0 X
 rA  X , T 
A  B
1) Mole Balances:
2) Rate Laws:
15
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 (MSS)
Finding Multiple Steady States with T0 varied
18
Multiple Steady States (MSS)
Finding Multiple Steady States with T0 varied
19
Multiple Steady States (MSS)
Temperature ignition-extinction curve
20
Multiple Steady States (MSS)
Stability of multiple state temperatures
21
MSS - Generating G(T) and R(T)
dT
dt
1
G T   X     H Rx

R  C P0  1     T  T C 
Need to solve for X after combining mole
balance, rate law, and stoichiometry.
22
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 Web Lecture 23
Class Lecture 19
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