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 2/26/2013 � Complex Reactions:
A +2B à C A + 3C à D
� Example A: Liquid Phase PFR � Example B: Liquid Phase CSTR � Example C: Gas Phase PFR � Example D: Gas Phase Membrane Reactors
Sweep Gas Concentration Essentially Zero Sweep 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 Reaction 2. Mole Balance on every species 3. 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 àciC+diD:
∑=
=N
iiAA rr
1
3222
211
CACC
BAAA
CCkrCCkr
−=
−=
i
iD
i
iC
i
iB
i
iA
dr
cr
br
ar
==−
=−
Reactor Mole Balance Summary
5
Reactor Type
Gas Phase Liquid Phase
Vr
dtdN
AA = A
A rdtdC
=Batch
VrdtdN
AA = V
CrdtdC A
AA 0υ−=Semibatch
0BBB FVr
dtdN
+= [ ]VCCr
dtdC BB
BB −
+= 00υ
Reactor Mole Balance Summary
6
Reactor Type
Gas Phase Liquid Phase
A
AA
rFFV
−
−=
0 ( )A
AA
rCCV
−
−= 0
0υCSTR
AA r
dVdC
=0υAA r
dVdF
=PFR
AA r
dWdC
ʹ′=0υAA r
dWdF
ʹ′=PBR
Note: The reaction rates in the above mole balances are net rates.
VNC B
B = υB
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
00υυ =
TT
PP
FFCCT
BTB
0
00=
TT
PPF
FFC T
T
BB
0
00
0
υ=
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:
CA =CT 0FAFT
!
"#
$
%& p
T0T
!
"#
$
%& FT = FA +FB +FC +FD
0υA
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 Rates Reaction 1
DDCCC
BBBAAA
rrrrrrrrrrr
221
2121
0 )8( )6( )7( )5(
+=+=
+=+=
3222
211
)10(
)9(
CACC
BAAA
CCkrCCkr
−=
−=
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 Rates Reaction 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
CCkCCkrCCkr
CCkCCkr
=
−=
−=
−−=
Example A: Liquid Phase PFR
13
3) Stoichiometry Liquid
( ) 0 else then 00001.0 ~ )19(
)18( )17( )16( )15(
0
0
0
0
⎟⎟⎠
⎞⎜⎜⎝
⎛>=
=
=
=
=
D
CDC
DD
CC
BB
AA
FFVifS
FCFCFCFC
υ
υ
υ
υ
Example A: Liquid Phase PFR
14
Others 4) Parameters
NeededNot – Liquid )20(NeededNot – Liquid )19(
NeededNot – Liquid
0 =
=
=
T
T
C
Fα
100 )26(200 )28(200 )26(
2500 )25(Liquid )24(
Liquid )23(20 )22(
10 )21(
0
0
0
0
2
1
=
=
=
=
=
=
=
=
υ
α
B
A
f
T
C
A
FFVC
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
CCkrCCkr
−=
−=
00)4(00)3(
0)2(0)1(
0
0
000
000
=+−
=+−
=+−
=+−
VrCDVrCC
VrCCBVrCCA
DD
CC
BBB
AAA
υ
υ
υυ
υυ
1) Mole Balance
Example B: Liquid Phase CSTR
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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
FSυ
υ
00021 , , , , , υVCCkk BACA
Example B: Liquid Phase CSTR
19
(1) A + 2B →C (2) 2A + 3C → D
3222
211
CACC
BAAA
CCkrCCkr
−=
−=
00001.0)19(
)18()17()16()15(
0
0
0
0
+=
=
=
=
=
D
CDC
DD
CC
BB
AA
FFS
FCFCFCFC
υ
υ
υ
υ
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
CCkrCCkr
−=
−=
1) Mole Balance (1–4) 2) Rates (5–14) 3) Stoichiometry: (15–19)
In terms of concentration
( ) VrCCCf AAAA +−= 000)1( υυ (=0)
( ) VrCCCf BBBB +−= 000)2( υυ (=0)
( ) VrCCf CCC +−= 00)3( υ (=0)
( ) VrCCf DDD +−= 00)4( υ (=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
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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
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3) Stoichiometry: Gas: Isothermal T = T0
Packed Bed with Pressure Drop
(15) CA =CT 0FAFT
p (16) CB =CT 0FBFT
p
(17) CC =CT 0FCFT
p (18) CD =CT 0FDFT
p
(19) FT = FA +FB +FC +FD
dpdW
= −α2p
FTFT 0
"
#$
%
&'TT0
"
#$
%
&'= −
α2p
FTFT 0
Example C: Gas Phase PFR, No ΔP
24
4) Selectivity
p =1 21( )
( ) ( ) ( )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 ααα
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 −=
dpdW
= −α2p
FTFT 0
dpdV
= −ρα2p
FTFT 0
21( )
CCsg
CVVCsgVCsg
RdVdF
VRFF
=
=Δ+−Δ+
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.
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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 =υ 3
0 dm100V = minmol3F 0A =33
Example E: Liquid Phase Semibatch
3) Selectivity and Parameters:
End of Lecture 13
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