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Lecture 22
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 22
Class Lecture 18-Thursday 3/21/2013
Multiple Reactions with Heat Effects
2
Multiple Reactions with Heat Effects
PFR/PBR:
dT
dV
UaTa T rij H Rxij
n
i 1
m
F C
j 1
j
Pj
CSTR:
UA Ta T FA 0 CPii T T0 rij H Rxij T 0
3
m
q
j1
i 1
These equations are coupled with the mole
balances and rate law equations.
Multiple Reactions with Heat Effects
Multiple Reactions
Make sure it is in respect to A; Subscripts must agree
dT Q g Q r
dV Fi C Pi
4
Q g rij H Rxij r1A H Rx1A r2 A H Rx 2 A
Multiple Reactions with Heat Effects
Multiple Reactions
1) Mole Balances:– every species (no conversion!)
2) Rate Laws:
– relative rates
– net rates
3) Stoichiometry:
5
CA CT 0
FA T0
y
FT T
dy FT T
dW 2 y FT 0 T0
Multiple Reactions with Heat Effects
Multiple Reactions
4) Heat Effects:
dT Q g Q r
dV Fi C Pi
Q g heat produced
Q r heat removed
Q g rij H Rxij
Q r Ua(T - Ta )
6
(must have matching i, j)
Multiple Reactions with Heat Effects
4) Heat Effects:
dT Q g Q r
dV Fi C Pi
Q g r1A H R1A r2 A H R 2 A
Q r Ua T Ta
FC
i
Pi
FA C PA FB C PB FC C PC FD C PD
dTa Ua T Ta
i C Pcool
dV
m
5) Parameters
7
E1 , E 2 , FA0 , Ua , ...etc
Multiple Reactions with Heat Effects
4) Heat Effects:
dT Qg Qr
dV Fi C Pi
23
H Rx1 A 12kJ /(mole of A reacted in reaction 1)
H Rx 2 B 8kJ /(mole of B reacted in reaction 2)
Qg r1 A H Rx1 A r2 B H Rx 2 B
Use relative rates of reaction
to get r2B in terms of the rate law that is given for reaction 2,
e.g. ,
8
-r
(2)
2A
k
3 A 2B - - 2D
3
2A
C C
A
B
then r2B
2
r2A
3
The complex gas phase reactions
(1)
A 2B C
r1A k 1ACAC2B
H Rx1B 15,000 cal mol B
(2)
A C 2D
r2C k 2C CACC
H Rx 2A 10,000 cal mol A
take place in a 10 dm3 PFR with a heat exchanger. Plot the temperature, concentrations, molar
flow rates down the length of the reactor for the following operations. E.g., Note any maximums
minimums on your plot along with how they change for the different types of operations.
or
(a) Adiabatic operation
(b) Heat exchange with constant Ta
(c) Co current heat exchange
(d) Counter current heat exchange
(e) For parts (c) and (d), plot Qr and Qg down the length of the reactor. What do you observe?
Additional Information
C PA 10 cal mol K
C PC 30 cal mol K
C PB 10 cal mol K
C PD 20 cal mol K
s K at 300K and E1 8,000 cal mol
2
k 2C 2 dm3 mol s K at 300K and E 2 12,000 cal mol
k 1A 40 dm3 mol
2
ÝCool 20g s
C T 0 0.2 mol dm3 , C PCool 1cal g K , m
9
Ua 80 cal dm3 s K , Tao 325K , T0 300K
FA0 5 mol s , FB0 10 mol s , FC0 0 , FD0 0
10
11
12
13
Multiple Reactions with Heat Effects
Multiple Reactions
4) Heat Effects:
UaT Ta
dT
rA H Rx
dV
FiCPi
dT Qg Qr
dV Fi C Pi
Qg rij H Rij
14
Qg heat produced
Qr heat removed
(must have matching i, j)
Multiple Reactions with Heat Effects
in a PFR and CSTR
Examples:
(1) A 2B C
r1A k1A CA CB2
and
HR1A 20,000cal mol A
(2) 2A 3C D
r2C k2C CA2 CC3
and
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HR 2A 10,000cal mol A
Example A: Liquid Phase CSTR
(1) A 2 B C
r1A k1A CA CB2
NOTE: The specific reaction rate k1A is defined with respect to
species A.
(2) 3C 2 A D
r2C k2C CC3 CA2
NOTE: The specific reaction rate k2C is defined with respect to
species C.
16
Example A: Liquid Phase CSTR
The complex liquid phase reactions take place in a
2,500 dm3 CSTR. The feed is equal molar in A and B
with FA0=200 mol/min, the volumetric flow rate is 100
dm3/min and the reation volume is 50 dm3.
Find the concentrations of A, B, C and D existing in
the reactor along with the existing selectivity.
Plot FA, FB, FC, FD and SC/D as a function of V
17
Example A: Liquid Phase CSTR
Solution
Liquid Phase CSTR
1) Mole Balances:
(1)
f CA 0CA 0 0CA rAV
(2)
f CB 0CB 0 0CB rBV
(3)
f CC 0CC rCV
(4)
f CD 0CD rDV
2) Net Rates:
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(5)
rA r1A r2A
Example A: Liquid Phase CSTR
3) Stoichiometry:
(16)
CA FA 0
(17)
CB FB 0
(18)
CC FC 0
(19)
CD FD 0
4) Parameters:
19
(20)
0 100 dm3 min
(21)
k1A 10 dm mol
(22)
15 dm
3
k 2C
3
mol
2
4
min
min
Example B: Liquid Phase PFR
Takes place in a PFR. The feed is equal molar in A and
B and FA0=200 mol/min and the volumetric flow rate is
100 dm3/min. The reaction volume is 50 dm3 and the
rate constants are:
k1A 10 dm mol min
3
2
k2C 15 dm mol min
3
4
Rate laws are the same as Example A.
Plot FA, FB, FC, FD and SC/D as a function of V.
20
Example B: Liquid Phase PFR
1) Mole Balances:
21
Example B: Liquid Phase PFR
2) Net Rates:
(5)
(6)
(7)
22
rA r1A r2A
rB r1B
rC r1C r2C
rD r2D
(8)
2) Rate Laws:
2
(9)
r
k
C
C
1A
1A
A
B
2 3
r2C k2C CA CC
(10)
Example B: Liquid Phase PFR
2) Relative Rates:
r1A r1B r1C
1 2 1
(11)
(12)
r1B 2r1A
r1C r1A
r2A r2C r2D
2 3 1
23
Reaction 1
(13)
r2A 2 3r2C
(14)
r2D 1 3r2C
Reaction 2
Example B: Liquid Phase PFR
2) Rate Laws:
r1 A k1 AC AC B2
r2C k 2C C A2 CC3
rA r1 A r2 B
rC r1C r2C
r1C r1 A
r2 A 2 / 3r2C
24
5 k1 A k1 A1 expE1 R 1 T1 1 T 6
7 k 2C k 2C 2 expE2 R 1 T2 1 T 8
9 rB r1B 10
11 rD r2 D 12
13 r1B 2r1 A 13
15 r2 D 1 / 3r2C 16
Example B: Liquid Phase PFR
3) Stoichiometry:
C A CT 0
FA T0
y
FT T
17
CC CT 0
FC T0
y
FT T
19
FT FA FB FC FD
25
21
CB CT 0
FB T0
y
FT T
18
CD CT 0
FD T0
y
FT T
20
dy FT T
dV
2 y FT 0 T0
22
Multiple Reactions with Heat Effects
4) Heat Effects:
Qg Qr
dT
dV Fi C Pi
dTa UaT Ta
i C Pcool
dV
m
23
26
24
25
Qr UaT Ta
CP FACPA FBCPB FC CPC FDCPD 27
Qg r1 A H R1 A r2 A H R 2 A
Parameters:
26
E1 , E2 , FA0 ,....
Selectivity
If one were to write SC/D=FC/FD in the Polymath
program, Polymath would not execute because at V=0,
FC=0 resulting in an undefined volume (infinity) at V=0.
To get around this problem we start the calculation 10-4
dm3 from the reactor entrance where FD will not be zero
and use the following IF statement.
(15)
27
S˜C D
FC
if V 0.001 then else 0
FD
Selectivity
3) Stoichiometry:
(16)
CA FA 0
(17)
CB FB 0
(18)
CC FC 0
(19)
CD FD 0
Parameters:
28
(20)
0 100 dm3 min
(21)
k1A 10 dm3 mol
(22)
k 2C
15 dm
3
mol
2
4
min
min
End of Web Lecture 22
Class Lecture 18
29