lecture 19 tuesday 3/18/08 gas phase reactions trends and optimuns
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Heat Exchange
Elementary liquid phase reaction carried out in a PFR
The feed consists of both inerts I and Species A with the ratio of inerts to the species A being 2 to 1.
Ta
AA B
Heat Exchange Fluid
Ý m C
FA0
FI
Heat Exchange
Elementary gas phase reaction carried out in a PBR
The feed consists of both inerts I and Species A with the ratio of inerts to the species A being 2 to 1.(a) Adiabatic. Plot X, Xe, T and the rate of disappearance as a function of V up to
V = 40 dm3. (b) Constant Ta. Plot X, Xe, T, Ta and Rate of disappearance of A when there is a
heat loss to the coolant and the coolant temperature is constant at 300 K for V = 40 dm3. How do these curves differ from the adiabatic case?
• Variable Ta Co-Current. Plot X, Xe, T, Ta and Rate of disappearance of A when there is a heat loss to the coolant and the coolant temperature varies along the length of the reactor for V = 40 dm3. The coolant enters at 300 K. How do these curves differ from those in the adiabatic case and part (a) and (b)?
(d) Variable Ta Counter Current. Plot X, Xe, T, Ta and Rate of disappearance of A when there is a heat loss to the coolant and the coolant temperature varies along the length of the reactor for V = 20 dm3. The coolant enters at 300 K. How do these curves differ from those in the adiabatic case and part (a) and (b)?
Ta
AA B
Heat Exchange Fluid
Ý m C
FA0
FI
Mole Balance (1)
Rate Law (2)
(3)
(4)
dXdW
r A FA0
WbV
dXdV r AB
FA0
rA
FA0
rA k CA CB
KC
k k1 expER
1T1
1T
KC KC2 expHRx
R1T2
1T
Stoichiometry (5)
(6)
Parameters (7) – (15)
CA CA0 1 X y T0 T
CB CA0Xy T0 T
dydW
y
FT
FT0
TT0
2y
TT0
WV
dydV b
2yTT0
FA0 , k1, E, R, T1, KC2 , HRx , T2 , CA0 , T0 , , b
Energy Balance
Adiabatic and CP = 0
(16A)
Additional Parameters (17A) & (17B)
Heat Exchange
(16B)
TT0 HRx XiCPi
T0 , iCPiCPA
ICPI
dTdV rA HRx Ua T Ta
FiCPi
FiCPiFA0 iCPi
CPX , if CP 0 then
dTdV rA HRx Ua T Ta
FA0 iCPi
(16B)
A. Constant Ta (17B) Ta = 300
Additional Parameters (18B – (20B): Ta, , Ua,
B. Variable Ta Co-Current
(17C)
C. Variable Ta Counter Current
(18C)
Guess Ta at V = 0 to match Ta = Tao at exit, i.e., V = Vf
dTdV rA HRx Ua T Ta
FA0 iCPi
dTa
dV
Ua T Ta Ý m CPcool
, V0 Ta Tao
dTa
dV
Ua Ta T Ý m CPcool
V0 Ta ?
Endothermic
PFR
A B
dX
dV
k 1 1 1
KC
X
0 , Xe
KC
1KC
XEB iCPi
T T0 HRx
CPA
ICPI T T0 HRx
T0
XXEB
Xe
TT0 HRx X
CPAICPI
PFR Adiabatic
FA0
FT
1. Irreversible A B Liquid Phase, Keep FA0 Constant
A. First order
dX
dV rA
FA0kCA
FA0k
FA0
1 X FA0
k 1 X
kCA0 1 X FA0
Constant density liquid
0 volumetric flow rate without inert
0FA0 FI
FA0
0 1I
dX
dV
k 1 X 0 1I
Gas phase heat effects
Example: PBR A ↔ B
VW b
1) Mole balance:
2) Rates:
3) Stoich (gas):
0
'
A
A
F
r
dW
dX
TTR
Hkk
TTR
Ekk
kCCkr
RCC
CBAA
11exp
11exp
22
11
'
000
00
000
00
0
0
00
122
1
1
1
1
1
1
T
TX
yT
T
F
F
ydW
dy
T
Ty
X
XCC
T
Ty
X
XC
T
T
P
P
Xv
XFC
T
T
P
PXvv
T
T
AB
AAA
C
Ce
eA
eA
Ae
BeC k
kX
TTyXC
TTyXC
C
Ck
1
1 00
00
4) Heat effects
5) Parameters….
- for adiabatic: Ua = 0
- constant Ta:
- co-current: equations as is
- counter-current:
0dW
dTa
T)-T toT-T flip(or 1 aadW
dT
PCC
ab
a
a
PiiA
ab
aRa
Cm
TTU
dW
dT
CF
TTU
Hr
dW
dT
0
Co-current, (Ta-T) for counter-current
Exothermic Case: Endothermic Case:
kC
T
Xe
T
kC
T T
Xe
~1
As T0 decreases the conversion X will increase, however the reaction will progress slower to equilibrium conversion and may not make it in the volume of reactor that you have.
Therefore, for exothermic reactions there is an optimum inlet temperature, where X reaches Xeq right at the end of V. However, for endothermic reactions there is no temperature maximum and the X will continue to increase as T increases.
As inert flow increases the conversion will increase. However as inerts increase, reactant concentration decreases, slowing down the reaction. Therefore there is an optimal inert flow rate to maximize X.
Adiabatic:
T
X Adiabatic T and Xe
T0
exothermic
T
X
T0
endothermic
PIIPA
R
CC
XHTT
0
X
T
X
T
V1 V2
X
TT0
I
0I
VkdV
dX
I
11
1
I
k
1
I
Ioptimum