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

W3

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

4

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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