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

1

Lecture 9 – Thursday 2/3/2011Membrane Reactors:

Used for Thermodynamically Limited Reactions

Balances in Terms of Molar Flow RatesBlock 1: Mole Balances

Balance Equation on Every Species Block 2: Rate Laws

Relative RatesTransport Laws

Block 3: Stoichiometry Block 4: Combine

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Reactor Mole Balance Summary

Reactor

Differential Algebraic Integral

The GMBE applied to the four major reactor types (and the general reaction AB)

A

AA

r

FFV

0CSTR

Review Lecture 1

Vrdt

dNA

A 0

A

A

N

N A

A

Vr

dNtBatch

NA

t

AA r

dV

dF

A

A

F

F A

A

dr

dFV

0

PFRFA

V

AA r

dW

dF

A

A

F

F A

A

r

dFW

0

PBRFA

W3

4

Membrane ReactorsMembrane 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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C3H8 ↔ H2 + C3H6 A ↔ B + C

Dehydrogenation Reaction:

Thermodynamically Limited:

XC

T

exothermic

endothermicXC

T6

Membrane Reactors

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Cross section of IMRCF Membrane Reactors

Cross section of CRM Schematic of IMRCF for mole balance

Membrane Reactors

W = ρbV

ρb = (1-ϕ)ρC

A,B,C

sweep

FA0

B

B

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A,C stay behind since they are too big

H2 H2 CBS

CB

Membrane Reactors

AA r

dV

dFA:

Mole Balance:

0

VrFF AVVAVA

Species A: In – out + generation = 0

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Membrane Reactors

RB moles of B through sides

volume of reactor

Species B: In – out – out membrane + generation = 0

0

VrVRFF BBVVBVB

)( BBB Rr

dV

dFB:

10

Membrane Reactors

sm

molCCkW BSBCB 2

)('

3

2

4

2

4

lumereactor vo

areasurface membrane

m

m

DL

DLa

D

11

BSBCBB CCakaWR '

sm

molCCkR BSBCB 3

Neglected most of the time

akk CC'

Membrane Reactors

4

C

CBAA K

CCCkr

1 AA r

dV

dF

2 BBB Rr

dV

dF

3 CC r

dV

dF

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Mole Balance:

Rate Laws:

Membrane Reactors

Parameters: CTO = 0.2, FA0= 5, k = 4, KC

= 0.0004, kC = 8

111CBA rrr

Relative Rates:

,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

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Net Rates:

Transport Law:

Stoichiometry:

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.

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 Gas

C6H6 (B)

Inert Sweep Gas

C6H12 (A)H2 (C)

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Membrane Reactors

AA r

dW

dF

BB r

dW

dF

CCCC Ckr

dW

dF

Mole Balances:

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Inert Sweep Gas

C6H6 (B)

Inert Sweep Gas

C6H12 (A)H2 (C)

Membrane Reactors

C

CBAAA K

CCCkr

3

Rate Law:

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Rates:

Relative Rates:

Net Rate:

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 2.0

dm

molCT

s

molFA 100

scatkg

dmkC

5.03

scatkg

dmkA

103

6

2

200dm

molKC

18

Membrane Reactors

Membrane Reactors

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Ci

W

C6H12 (A)

H2 (C)

C6H6 (B)

End of Lecture 9

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