Lecture 20 Thursday 3/20/08 Multiple Reactions with Heat Effects.
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Transcript of Lecture 20 Thursday 3/20/08 Multiple Reactions with Heat Effects.
Lecture 20 Thursday 3/20/08
Multiple Reactions with Heat Effects
User Friendly Equations Relate T and X or 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
W bV
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
2yTT0
W V
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)
T T0 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
dT
dV
rA HRx Ua T Ta FA0 iCPi
dTa
dV
Ua T Ta Ý m CPcool
, V 0 Ta Tao
dTa
dV
Ua Ta T Ý m CPcool
V 0 Ta ?
User Friendly Equations Relate T and X or Fi
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
Multiple reactions with heat effects
Multiple Rxns
Mole balances – every species (no conversion!)
Rates – rate laws
net/relative rates
Stoichiometry –
Heat effects – 00
00
2 T
T
F
F
ydW
dy
T
Ty
F
FCC
T
T
T
ATA
j)i, matching have(must
removedheat
producedheat
Rijijg
r
gPii
rg
Pii
aaRa
HrQ
Q
QCF
dV
dT
CF
TTUHr
dV
dT
A molcal000,10 32 )2(
A molcal000,20 2 )1(
232
22
12
11
ARCACC
ARBAAA
HCCkrDCA
HCCkrCBA
Rate is given for 2C, but ΔHR is given for 2A!
PAPCPDAPRAPARAR
PAPBPCAPRAPARAR
CCCCTTCHH
CCCCTTCHH
2/32/1
2
220
22
11011
Make sure it is in respect to A; A needs a coefficient of 1!!!!!!!
ARAARARijijgPii
rg HrHrHrQCF
dV
dT2211
1) Mole balance:
DD
BB
CC
AA
AA
AA
rdV
dFr
dV
dF
rdV
dFr
dV
dF
rdV
dFr
dW
dF
B''
2) Rate laws:
3) Stoich:
4) Heat effects:
Parameters:,.... , , 021 AFEE
CDCA
ABAC
DDCCC
BBBAA
CCCACC
AABAAA
rrrr
rrrr
rrrrr
rrrrr
TTREkkCCkr
TTREkkCCkr
2222
1111
221
121
222232
22
11112
11
3/1 3/2
2
11exp
11exp
00
00
00
00
00
2
T
T
F
F
ydV
dyFFFFF
T
Ty
F
FCC
T
Ty
F
FCC
T
Ty
F
FCC
T
Ty
F
FCC
T
TDCBAT
T
DTD
T
CTC
T
BTB
T
ATA
Pcooli
aaa
Pii
rg
Cm
TTU
dV
dT
CF
dV
dT
PDDPCCPBBPAAP
aar
ARAARAg
CFCFCFCFC
TTUQ
HrHrQ 2211