Lecture 9
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.
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Lecture 9 – Thursday 2/7/2013
Balances in terms of molar flow rates
 Block 1: Mole Balances
Balance Equation on Every Species
 Block 2: Rate Laws
Relative Rates
Transport Laws
 Block 3: Stoichiometry
 Block 4: Combine
 Membrane Reactors:
Used for thermodynamically limited reactions
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Review Lecture 1
Reactor Mole Balances Summary
The GMBE applied to the four major reactor types
(and the general reaction AB)
Reactor
Batch
Differential
NA

N A0
V 
dFA
 rA
dV
Integral
t
dN A
 rAV
dt
CSTR
PFR
Algebraic
FA 0  FA
rA
V
dN A
rAV
FA

FA 0
t
dFA
drA
PBR
3

dFA
 rA
dW
W

FA 0
FA
V

FA
NA
dFA
rA
FA
W
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Membrane Reactors
Membrane reactors can be used to achieve
conversions greater than the original equilibrium
value. These higher conversions are the result of
Le Chatelier’s principle; you can remove the
reaction products and drive the reaction to the right.
To accomplish this, a membrane that is permeable
to that reaction product, but impermeable to all
other species, is placed around the reacting
mixture.
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Membrane Reactors
Dehydrogenation Reaction:
C3H8 ↔ H2 + C3H6
A↔B+C
Thermodynamically Limited:
exothermic
Xe
Xe
XEB
T
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Membrane Reactors
Cross section of IMRCF
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Cross section of CRM
Membrane Reactors
Schematic of IMRCF for mole balance
Membrane Reactors
sweep
FA0
W = ρbV = solids weight
B
ρb = (1-ϕ)ρC= bulk solids density
A,B,C
B
H2
H2
ρC = density of solids
𝜌𝑏 =
𝑣𝑜𝑙𝑢𝑚𝑒 𝑠𝑜𝑙𝑖𝑑𝑠 𝑚𝑎𝑠𝑠 𝑜𝑓 𝑠𝑜𝑙𝑖𝑑𝑠
∗
𝑣𝑜𝑙𝑢𝑚𝑒 𝑡𝑜𝑡𝑎𝑙 𝑣𝑜𝑙𝑢𝑚𝑒 𝑠𝑜𝑙𝑖𝑑𝑠
CBS
CB
A,C stay behind since they are
too big
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Membrane Reactors
Mole Balance on Species A:
Species A:
In – out + generation = 0
FA V  FA V V  rA V  0
dFA
 rA
dV
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Membrane Reactors
Mole Balance on Species B:
Species B:
In – out – out membrane + generation = 0
FB V  FB V V  RB V  rB V  0
dFB
 (rB  RB )
dV
RB 
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moles of B through sides
volume of reactor
Membrane Reactors
molar flow rate through membrane  mol 
'
WB  kC (CB  CBS ) 
 m 2  s 
surface area of membrane
membrane surface area DL 4
a
 2 
D
reactor volume
D
L
4
RB  WB a  kC' aCB  CBS 
kC  kC' a
RB  kC CB  CBS 
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 m ol 
 m3  s 
Neglected most of the time
 m2 
 3
m 
Membrane Reactors
Mole Balances:
1
2
3
dFA
 rA
dV
dFB
 rB  RB
dV
dFC
 rC
dV
Rate Law:
4
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
C B CC 
rA   k C A 

KC 

Membrane Reactors
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Relative Rates:
 rA rB rC
 
1
1
1
Net Rates:
Transport Law:
5
6
rA  rB , rA  rC
Stoichiometry:
7
C A  CT 0
RB  kC CB
FA
(isothermal, isobaric)
FT
8 CB  CT 0 FB
FT
FC
9 CC  CT 0
FT
10 FT  FA  FB  FC
Parameters: CTO = 0.2, FA0= 5, k = 4, KC = 0.0004, kC = 8
Membrane Reactors
Example: The following reaction is to be carried out
isothermally in a membrane reactor with no
pressure drop. The membrane is permeable to
product C, but impermeable to all other species.
Inert Sweep Gas
C6H12  C6H6  3H2 C6H12 (A)
A
B
 3C
Inert Sweep Gas
H2 (C)
C6H6 (B)
For membrane reactors, we cannot use conversion. We
have to work in terms of the molar flow rates FA, FB, FC.
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Membrane Reactors
Mole Balances
C6H12  C6H6  3H2
A
dFA
 rA
dW
dFB
 rB
dW

dFC
 rC   kC CC
dW
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B
Inert Sweep Gas
 3C
H2 (C)
C6H12 (A)
Inert Sweep Gas
C6H6 (B)
Membrane Reactors
Rate Law:
Relative Rates:
Net Rates:
3


C
C
B C

 rA  k A C A 

KC 

rA rB rC 


1 1
3
rB  rA
rC   3rA
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Membrane Reactors
Stoichiometry:
Isothermal, no Pressure Drop
P0
CT 0 
RT0
FA
C A  CT 0
FT
FB
CB  CT 0
FT
CC  CT 0
FC
FT
FT  FA  FB  FC
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Membrane Reactors
Combine: - Use Polymath
Parameters:
CT 0
mol
 0 .2 3
dm
dm3
k A  10
kg cat s
m ol2
K C  200
dm6
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mol
FA0  10
s
dm3
kC  0.5
kg cat s
Membrane Reactors
C6H12 (A)
C6H6 (B)
Ci
H2 (C)
W
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End of Lecture 9
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