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Lecture 9
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Transcript of 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.
Lecture 9
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Lecture 9 – Thursday 2/7/2013
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Balances in terms of molar flow ratesBlock 1: Mole Balances
Balance Equation on Every Species Block 2: Rate Laws
Relative RatesTransport Laws
Block 3: StoichiometryBlock 4: Combine
Membrane Reactors: Used for thermodynamically limited reactions
Reactor Differential Algebraic Integral
The GMBE applied to the four major reactor types (and the general reaction AB)
V FA 0 FA
rA
CSTR
Vrdt
dNA
A 0
A
A
N
N A
A
VrdNtBatch
NA
t
dFA
dVrA
A
A
F
F A
A
drdFV
0
PFRFA
V
dFA
dW r A
A
A
F
F A
A
rdFW
0
PBRFA
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Reactor Mole Balances SummaryReview Lecture 1
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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
C3H8 ↔ H2 + C3H6 A ↔ B + C
Dehydrogenation Reaction:
Thermodynamically Limited:
Xe
T
exothermic
Xe
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Membrane Reactors
XEB
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Membrane Reactors
Cross section of IMRCF Membrane Reactors
Cross section of CRM Schematic of IMRCF for mole balance
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Membrane ReactorsW = ρbV = solids weight
ρb = (1-ϕ)ρC= bulk solids density
ρC = density of solidsA,B,C
sweep
FA0
B
B
A,C stay behind since they are too big
H2 H2 CBS
CB
𝜌𝑏=𝑣𝑜𝑙𝑢𝑚𝑒𝑠𝑜𝑙𝑖𝑑𝑠𝑣𝑜𝑙𝑢𝑚𝑒𝑡𝑜𝑡𝑎𝑙 ∗
𝑚𝑎𝑠𝑠𝑜𝑓 𝑠𝑜𝑙𝑖𝑑𝑠𝑣𝑜𝑙𝑢𝑚𝑒𝑠𝑜𝑙𝑖𝑑𝑠
Membrane Reactors
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Mole Balance on Species A:
AA r
dVdF
0A A AV V VF F r V
Species A: In – out + generation = 0
Membrane Reactors
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Mole Balance on Species B:
reactor of volume
sides through B of molesBR
Species B: In – out – out membrane + generation = 0
0
VrVRFF BBVVBVB
)( BBB Rr
dVdF
Membrane Reactors
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2
molar flow rate through membrane' ( )surface area of membraneB C B BS
molW k C Cm s
3
2
4
2
4lumereactor vo
areasurface membranemm
DL
DLaD
BSBCBB CCakaWR '
smmolCCkR BSBCB 3
Neglected most of the time
akk CC'
Membrane Reactors
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Mole Balances:
Rate Law:
3 CC r
dVdF
2 BBB Rr
dVdF
1 AA r
dVdF
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C
CBAA K
CCCkr
Membrane Reactors
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Relative Rates:
Net Rates:Transport Law:
Stoichiometry:
Parameters: CTO = 0.2, FA0= 5, k = 4, KC = 0.0004, kC = 8
,5 CABA rrrr
6 BCB CkR
7 0T
ATA F
FCC (isothermal, isobaric)
8 0T
BTB F
FCC
9 0T
CTC F
FCC
10 CBAT FFFF
111CBA rrr
Membrane Reactors
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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.
C6H12 C6H6 3H2
A B 3C
For membrane reactors, we cannot use conversion. We have to work in terms of the molar flow rates FA, FB, FC.
Inert Sweep GasC6H6 (B)
Inert Sweep Gas
C6H12 (A)H2 (C)
Membrane Reactors
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C6H12 C6H6 3H2
A B 3C
Inert Sweep GasC6H6 (B)
Inert Sweep Gas
C6H12 (A)H2 (C)
AA r
dWdF
BB r
dWdF
CCCC Ckr
dWdF
Mole Balances
C
CBAAA K
CCCkr3
Rate Law:
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Relative Rates:
Net Rates:
311
CBA rrr
AC
AB
rr
rr
3
Membrane Reactors
Stoichiometry:Isothermal, no Pressure Drop 0
00 RT
PCT
T
ATA F
FCC 0
T
BTB F
FCC 0
CBAT FFFF T
CTC F
FCC 0
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Membrane Reactors
Combine: - Use Polymath
Parameters: 30 2.0dmmolCT
smolFA 100
scatkgdmkC
5.03
scatkg
dmkA 10
3
6
2
200dmmolKC
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Membrane Reactors
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Ci
W
C6H12 (A)
H2 (C)C6H6 (B)
Membrane Reactors
End of Lecture 9
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