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.
Lecture 13
Lecture 13 – Tuesday 2/26/2013Complex Reactions:
A +2B CA + 3C D
Example A: Liquid Phase PFRExample B: Liquid Phase CSTRExample C: Gas Phase PFRExample D: Gas Phase Membrane Reactors
Sweep Gas Concentration Essentially ZeroSweep Gas Concentration Increases with Distance
Example E: Semibatch Reactor
2
Gas Phase Multiple Reactions
3
New things for multiple reactions are:
4
1. Number Every Reaction2. Mole Balance on every species3. Rate Laws (a) Net Rates of Reaction for every species
(b) Rate Laws for every reaction
(c) Relative Rates of Reaction for every reaction For a given reaction i: (i) aiA+biB ciC+diD:
N
iiAA rr
1
3222
211
CACC
BAAA
CCkr
CCkr
i
iD
i
iC
i
iB
i
iA
dr
cr
br
ar
Reactor Mole Balance Summary
5
Reactor Type Gas Phase Liquid Phase
VrdtdN
AA A
A rdtdC
Batch
VrdtdN
AA V
CrdtdC A
AA 0Semibatch
0BBB FVr
dtdN
VCCr
dtdC BB
BB
00
Reactor Mole Balance Summary
6
Reactor Type Gas Phase Liquid Phase
A
AA
rFFV
0
A
AA
rCCV
00CSTR
AA r
dVdC
0AA r
dVdF
PFR
AA r
dWdC 0A
A rdWdF PBR
Note: The reaction rates in the above mole balances are net rates.
VNC B
B B
BFC
TT
PP
NNVVT
T 00
00
TT
PP
VN
NNC T
T
BB
0
00
0
TT
PP
NNCCT
BTB
0
00
TT
PP
FF
T
T 00
00
TT
PP
FFCCT
BTB
0
00
TT
PPF
FFC T
T
BB
0
00
0
Batch Flow
7
Note: We could use the gas phase mole balances for liquids and then just express the concentration as:
Flow:
Batch:
Stoichiometry
8
Concentration of Gas:
DCBATT
ATA FFFFF
TTy
FFCC
0
0
0A
AFC
0VNC A
A
Example A: Liquid Phase PFR
9
NOTE: The specific reaction rate k2C is defined with respect to species C.
23)2( DAC 2322 ACCC CCkr
2)1( CBA 211 BAAA CCkr
NOTE: The specific reaction rate k1A is defined with respect to species A.
The complex liquid phase reactions follow elementary rate laws:
Example A: Liquid Phase PFR
10
Complex Reactions
1) Mole Balance on each and every species
(1) A 2B C
(2) A 3C D
DD
CC
BB
AA
rdVdFr
dVdF
rdVdFr
dVdF
)4( )3(
)2( )1(
Example A: Liquid Phase PFR
11
2) Rate Laws:Net Rates
Rate Laws
Relative RatesReaction 1
DDCCC
BBBAAA
rrrrrrrrrrr
221
2121
0 )8( )6( )7( )5(
3222
211
)10(
)9(
CACC
BAAA
CCkr
CCkr
11 1
1 1
1 1
1 2 1
(11) 2(12)
CA B
B A
C A
rr r
r rr r
Example A: Liquid Phase PFR
12
Relative RatesReaction 2
3 )14(
32 )13(
132
22
22
222
CD
CA
DCA
rr
rr
rrr
322
3221
21
322
21
3
232
CAC
D
CACBAAC
BAAB
CACBAAA
CCkr
CCkCCkr
CCkr
CCkCCkr
Example A: Liquid Phase PFR
13
3) StoichiometryLiquid
0 else then 00001.0 ~ )19(
)18( )17( )16( )15(
0
0
0
0
D
CDC
DD
CC
BB
AA
FFVifS
FCFCFCFC
Example A: Liquid Phase PFR
14
Others
4) ParametersNeededNot – Liquid )20(
NeededNot – Liquid )19(NeededNot – Liquid
0
T
T
C
F
100 )26(200 )28(200 )26(
2500 )25(Liquid )24(
Liquid )23(20 )22(
10 )21(
0
0
0
0
2
1
B
A
f
T
C
A
FF
VC
kk
Example B: Liquid Phase CSTR
15
Same reactions, rate laws, and rate constants as Example A
2)1( CBA 211 BAAA CCkr
NOTE: The specific reaction rate k1A is defined with respect to species A.
NOTE: The specific reaction rate k2C is defined with respect to species C.
23)2( DAC 2322 ACCC CCkr
Example B: Liquid Phase CSTR
16
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 reaction 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
Example B: Liquid Phase CSTR
17
(1) A + 2B →C (2) 2A + 3C → D
3222
211
CACC
BAAA
CCkr
CCkr
00)4(00)3(
0)2(0)1(
0
0
000
000
VrCDVrCC
VrCCBVrCCA
DD
CC
BBB
AAA
1) Mole Balance
Example B: Liquid Phase CSTR
18
2) Rate Laws: (5)-(14) same as PFR
3) Stoichiometry: (15)-(18) same as Liquid
Phase PFR
4) Parameters:
0001.00001.0 )19(
0
0/
D
C
D
CDC C
CF
FS
00021 , , , , , VCCkk BACA
Example B: Liquid Phase CSTR
19
(1) A + 2B →C (2) 2A + 3C → D
3222
211
CACC
BAAA
CCkr
CCkr
00001.0)19(
)18()17()16()15(
0
0
0
0
D
CDC
DD
CC
BB
AA
FFS
FCFCFCFC
1) Mole Balance (1–4) 2) Rates (5–14) 3) Stoichiometry: (15–19)
VrFFFf AAAA 0)1( (=0)
VrFFFf BBBB 0)2( (=0)
VrFFf CCC 0)3( (=0)
VrFFf DDD 0)4( (=0)
In terms of molar flow rates
Same as Example A
Example B: Liquid Phase CSTR
20
(1) A + 2B →C (2) 2A + 3C → D
3222
211
CACC
BAAA
CCkr
CCkr
1) Mole Balance (1–4) 2) Rates (5–14) 3) Stoichiometry: (15–19)
In terms of concentration
VrCCCf AAAA 000)1( (=0)
VrCCCf BBBB 000)2( (=0)
VrCCf CCC 00)3( (=0)
VrCCf DDD 00)4( (=0)
00001.0 )15(
D
CDC F
FSSame as Example A
Example C: Gas Phase PFR, No ΔP
21
Same reactions, rate laws, and rate constants as Example A:
2)1( CBA 211 BAAA CCkr
NOTE: The specific reaction rate k1A is defined with respect to
species A.
NOTE: The specific reaction rate k2C is defined with respect to species C.
23)2( DAC 2322 ACCC CCkr
Example C: Gas Phase PFR, No ΔP
22
1) Mole Balance
2) Rate Laws: (5)-(14) same as CSTR
)4( (2)
)3( )1(
DD
BB
CC
AA
rdVdFr
dVdF
rdVdFr
dVdF
Example C: Gas Phase PFR, No ΔP
23
3) Stoichiometry: Gas: Isothermal T = T0
Packed Bed with Pressure Drop
DCBAT
T
DTD
T
CTC
T
BTB
T
ATA
FFFFF
yFFCCy
FFCC
yFFCCy
FFCC
)19(
)18( )17(
)16( )15(
00
00
000 22 T
T
T
T
FF
yTT
FF
ydWdy
Example C: Gas Phase PFR, No ΔP
24
4) Selectivity
21 1y
20 0 else then 00001.0 if
D
C
D
C
FFV
FFS
Example D: Membrane Reactor with ΔP
25
Same reactions, rate laws, and rate constants as Example A:
2)1( CBA 211 BAAA CCkr
NOTE: The specific reaction rate k1A is defined with respect to
species A.
NOTE: The specific reaction rate k2C is defined with respect to species C.
23)2( DAC 2322 ACCC CCkr
Example D: Membrane Reactor with ΔP
26
Because the smallest molecule, and the one with the lowest molecular weight, is the one diffusing out, we will neglect the changes in the mass flow rate down the reactor and will take as first approximation:1) Mole Balances
4 2
3 1
DD
BB
CCC
AA
rdVdFDr
dVdFB
RrdVdFCr
dVdFA
CCsg RdVdF
We also need to account for the molar rate of desired product C leaving in the sweep gas FCsg
mm 0
We need to reconsider our pressure drop equation.
When mass diffuses out of a membrane reactor there will be a decrease in the superficial mass flow rate, G. To account for this decrease when calculating our pressure drop parameter, we will take the ratio of the superficial mass velocity at any point in the reactor to the superficial mass velocity at the entrance to the reactor.
ii
ii
MWFMWF
GG
00
00
27
Example D: Membrane Reactor with ΔP
The superficial mass flow rates can be obtained by multiplying the species molar flow rates, Fi, by their respective molecular weights, Mwi, and then summing over all species:
ii
ii
Cii
Cii
C
C
MWFMWF
AMWFAMWF
AmAm
GG
0000 1
1
1
1
Example D: Membrane Reactor with ΔP
28
Example D: Membrane Reactor with ΔP
29
2) Rate Laws: (5)-(14) same as Examples A, B, and C.
3) Stoichiometry: (15)-(20) same as Examples A and B(T=T0)
4) Sweep Gas Balance:
CSweepCCC CCkR
21 2
2 00 T
T
T
T
FF
ydVdy
FF
ydWdy
CCsg
CVVCsgVCsg
RdVdF
VRFF
0
Example E: Liquid Phase Semibatch
30
Same reactions, rate laws, and rate constants as Example A:
2)1( CBA 211 BAAA CCkr
NOTE: The specific reaction rate k1A is defined with respect to
species A.
NOTE: The specific reaction rate k2C is defined with respect to species C.
23)2( DAC 2322 ACCC CCkr
The complex liquid phase reactions take place in a semibatch reactor where A is fed to B with FA0= 3 mol/min. The volumetric flow rate is 10 dm3/min and the initial reactor volume is 1,000 dm3.
The maximum volume is 2,000 dm3 and CA0=0.3 mol/dm3 and CB0=0.2 mol/dm3. Plot CA, CB, CC, CD and SS/D as a function of time.
31
Example E: Liquid Phase Semibatch
1) Mole Balances:
(1) A + 2B →C (2) 2A + 3C → D
0AAA FVr
dtdN
VrdtdN
BB
VrdtdN
CC
VrdtdN
DD
00 AN
000.2000 VCN BB
00 CN
00 DN32
B
FA0
Example E: Liquid Phase Semibatch
2) Rate Laws: (5)-(14)
19 18
17 16
15 00
VNC
VNC
VNC
VNC
tvVV
DD
CC
BB
AA
Net Rate, Rate Laws and relative rate – are the same as Liquid and Gas Phase PFR and Liquid Phase CSTR
20 )0( else then )0001.0( if/
D
CDC N
NtS
mindm10 30 3
0 dm100V minmol3F 0A 33
Example E: Liquid Phase Semibatch
3) Selectivity and Parameters:
End of Lecture 13
34