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
Today’s lectureComplex Reactions
A +2B CA + 3C D
Liquid Phase PFRLiquid Phase CSTRGas Phase PFRGas Phase Membrane Reactor Sweep Gas Concentration Essentially
Zero Sweep Gas Concentration Increases
with Distance Semi Batch Reactor
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Reactor Mole Balance SummaryReactor
TypeGas Phase Liquid Phase
Vrdt
dNA
A AA r
dtdC
Batch
Vrdt
dNA
A VCr
dtdC A0
AA
Semibatch
0BBB FVr
dtdN
VCCr
dtdC B0B0
BB
3
Reactor Mole Balance SummaryReactor Type
Gas Phase Liquid Phase
A
A0A
rF FV
A
A0A0 r
CCV
CSTR
AA
0 rdV
dCA
A rdVdF
PFR
AA
0 rdWdC A
A rdWdF PBR
4 Note: The reaction rates in the above mole balances are net rates.
Reactor Mole Balance Summary
5
The new things for multiple reactions are:
Rates:1. Rate Law for every reaction2. Relative Rates for every
reaction3. Net Rates of Reaction
Gas Phase Multiple Reactions
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Note: We could use the gas phase mole balance for liquids and then just express the concentration as:
Flow: CA=FA/v0
Batch: CA=NA/V0
Note: The reaction rates in the above mole balances are net rates. The new things for multiple reactions are:
1. Rate Law for every reaction2. Relative Rates for every reaction3. Net Rates of Reaction
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Net Rate of Reaction for species A
For N reactions, the net rate of formation of species A is:
N
1iiAA rr
For a given reaction i:
(i) aiA+biB ciC+diD:
i
iD
i
iC
i
iB
i
iA
dr
cr
br
ar
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VNC B
B
BB
FC
TT
PP
NNVV 00
0T
T0
TT
PP
VN
NNC 0
00
0T
T
BB
TT
PP
NNCC 0
0T
B0TB
TT
PP
FF 00
0T
T0
TT
PP
FFCC 0
0T
B0TB
TT
PPF
FFC 0
00
0T
T
BB
Batch Flow
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Example A: Liquid Phase PFR
NOTE: The specific reaction rate k2C is defined with respect to species C.
)2( DA2C3 2A
3CC2C2 CCkr
)1( CB2A 2BAA1A1 CCkr
NOTE: The specific reaction rate k1A is defined with respect to species A.
The complex liquid phase reactions follow elementary rate laws
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Last Lecture
Example B: Liquid Phase CSTRSame reactions, rate laws, and rate constants as example A
)1( CB2A 2BAA1A1 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.
)2( DA2C3 2A
3CC2C2 CCkr
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Complex Reactions
Example B: Liquid Phase CSTRThe 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 V12
CSTR (1) A + 2B →C (2) 2A + 3C → D
3C
2AC2C2
2BAA1A1
CCkr
CCkr
4 0VrCV0 D3 0VrCV0 C2 0VrCVCV B1 0VrCVCV A
DD0
CC0
BB00B0
AA00A0
1) Mole balance:
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Example B: Liquid Phase CSTR
2) Rates:
14r31r 13r
32r
12rr 11r2r1
r3
r2
r 1r
2r
1r
10rr 9rrr 8rr 7rrr
6 CCkr
5 CCkr
C2D2C2A2
A1C1A1B1
D2C2A2C1B1A1
D2DC2C1C
B2BA2A1A
3C
2AC2C2
2BAA1A1
15 0001.0C
C0001.0F
FSD0
C0
D
CD/C
3) Parameters: 00B0AC2A1 V ,V ,C ,C ,k ,k 14
Same reactions, rate laws, and rate constants as example A
)1( CB2A 2BAA1A1 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.
)2( DA2C3 2A
3CC2C2 CCkr
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Complex ReactionsExample C: Gas Phase PFR, No ΔP
1) Mole balance:
4 rdVdF D 2 r
dVdF B
3 RrdVdF C 1 r
dVdF A
DD
BB
CCC
AA
2) Rates: Same as CSTR (5)-(14)
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Example C: Gas Phase PFR, No ΔP
3) Stoich:
19 FFFFF
18 yFFCC 17 y
FFCC
16 yFFCC 15 y
FFCC
DCBAT
T
D0TD
T
C0TC
T
B0TB
T
A0TA
20 0 else FF then 00001.0V if
FFS
D
C
D
C
4) Selectivity:
21 1y 17
Example C: Gas Phase PFR, No ΔP
Same reactions, rate laws, and rate constants as example A
)1( CB2A 2BAA1A1 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.
)2( DA2C3 2A
3CC2C2 CCkr
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Complex ReactionsExample D: Membrane Reactor with ΔP
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 in 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. 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:
2
1
1
2
1
2
Ci0i
Cii
Ci0i
Cii
C1
C2
1
2
AMWFAMWF
AMWFAMWF
AmAm
GG
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Example D: Membrane Reactor with ΔP
Because the smallest molecule is the one diffusing out and has the lowest molecular weight, we will neglect the changes in the mass flow rate down the reactor and will take as first approximation.1) Mole Balance:
4 rdVdF D 2 r
dVdF B
3 RrdVdF C 1 r
dVdF A
DD
BB
CCC
AA
CCsg R
dVdF
We also need to account for the molar rate of desired product C leaving in the sweep gas FCsg
20
Example D: Membrane Reactor with ΔP
)mm( 0
2) Rates: Same (5)-(14)3) Stoich: Same (15)-(20)
21 FF
y2dVdy ;
FF
y2dWdy
0T
T
0T
T
CSweepCCC CCkR
4) Sweep Gas Balance:
CCsg
CVVCsgVCsg
RdV
dF
0VRFF
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Example D: Membrane Reactor with ΔP
CsgC CC
RC kCCCC
Case 1 Large sweep gas velocity
Case 2 Moderate to small sweep gas velocity
sg
CCsg
sgF
C
sg0
Csgsg00sgsg F
FF
Vary υsg to see changes in profiles
0CCsg
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Example D: Membrane Reactor with ΔP
Example E: Liquid SemibatchSame reactions, rate laws, and rate constants as example A
)1( CB2A 2BAA1A1 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.
)2( DA2C3 2A
3CC2C2 CCkr
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Complex Reactions
Example E: Liquid SemibatchThe 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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1) Mole balance:(1) A + 2B →C (2) 2A + 3C → D
B
FA0
0AAA FVr
dtdN
Vrdt
dNB
B
Vrdt
dNC
C
Vrdt
dND
D
0N 0A
000.2VCN 00B0B
0N 0C
0N 0D 25
Example E: Liquid Semibatch
2) Rates: Same (5)-(14)
19 V
NC 18 VNC
17 V
NC 16 V
NC
15 tvVV
DD
CC
BB
AA
00
20 )0( else NN then )0001.0t( ifS
D
CD/C
Net Rates, Rate Laws and relative rates – are the same as Liquid and Gas Phase PFR and Liquid Phase CSTR
mindm10 30 3
0 dm100V minmol3F 0A
3) Selectivity:
4) Parameters:26
Example E: Liquid Semibatch
End of Lecture 13
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