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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 AB)
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
4
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
10
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' aCB 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:
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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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