Chemical Reaction Engineering (CRE) is thefield that studies the rates and mechanisms of

chemical reactions and the design of the reactors inwhich they take place.

Lecture 5c

1

Lecture 5c

2

Balances in terms of molar flow rates Block 1: Mole Balances

Balance Equation on Every Species Block 2: Rate Laws

Relative RatesTransport Laws

Block 3: Stoichiometry Block 4: Combine

Reactor Differential Algebraic Integral

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

CSTR

0

∫=A

A

N

N A

A

Vr

dNtBatch

NA

t

€

dFAdV

= rAPFR

FA

V

∫ ′=

A

A

F

F A

A

r

dFW

0

PBRFA

W3

Reactor Mole Balances SummaryReview Lecture 1

Reactor Differential Algebraic Integral

€

V =FA0X−rA

CSTR

∫ −=

X

AA r

dXFV

0

0PFR

Vrdt

dXN AA −=0

Batch

X

t

€

FA 0dXdW

= − ′ rAPBR

X

W4

Building Block 1: Mole Balancesin terms of conversion, X

Review Lecture 2

Using CA (liquid) and FA (gas) in theMole Balances and Rate Laws

5

There are a number of instances when it is much more convenientto work in terms of the number of moles (NA, NB) or molar flowrates (FA, FB, etc.) rather than conversion.

The main difference is that when conversion is used as our variableto relate one species concentration to that of another speciesconcentration, we needed to write a mole balance on only onespecies, our basis of calculation. When molar flow rates andconcentrations are used as our variables, we must write a molebalance on each species and then relate the mole balances to oneanother through the relative rates of reaction

6

Membrane reactors can be used to achieveconversions greater than the original equilibriumvalue. These higher conversions are the result ofLe Chatelier’s principle; you can remove thereaction products and drive the reaction to the right.

To accomplish this,

7

Membrane Reactors

Dehydrogenation Reaction:

Thermodynamically Limited:

Xe

T

exothermic

Xe

8

Membrane Reactors

X

9

Membrane Reactors

Cross section of IMRCF Membrane Reactors

Cross section of CRM Schematic of IMRCF for mole balance

Inert membrane reactor with catalyst pellets on the feed side

Catalytic Membrane Reactor

10

Membrane Reactors

A,B,C

sweep

FA0

B

B

A,C stay behind since they aretoo big

CBS

CB

= ∗

Membrane Reactors

11

Mole Balance on Species A:

AA r

dV

dF =

Membrane Reactors

12

Mole Balance on Species B:

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

0=∆+∆−−∆+

VrVRFF BBVVBVB

Membrane Reactors

13

2

molar flow rate through membrane' ( )surface area of membraneB C B BS

molW k C C

m s = − = ⋅

[ ]BSBCBB CCakaWR −== '

[ ]

⋅−=

sm

molCCkR BSBCB 3

Neglected most of the time

akk CC'=

Membrane Reactors

14

Mole Balances:

Rate Law:

( )2 BBB Rr

dV

dF −=

( )1 AA r

dV

dF =

Membrane Reactors

15

Relative Rates:

Net Rates:Transport Law:

Stoichiometry:

Parameters:

( ) ,5 CABA rrrr −=−=

( )6 BCB CkR =

( )7 0T

ATA F

FCC = (isothermal, isobaric)

( )8 0T

BTB F

FCC =

( )10 CBAT FFFF ++=

Membrane Reactors

16

Example: The following reaction is to be carried outisothermally in a membrane reactor with nopressure drop. The membrane is permeable toproduct C, but impermeable to all other species.

For membrane reactors, we cannot use conversion. Wehave to work in terms of the molar flow rates FA, FB, FC.

C6H6 (B)

C6H12 (A)H2 (C)

Membrane Reactors

17

Inert Sweep GasC6H6 (B)

Inert Sweep Gas

′= AA r

dW

dF

′= BB r

dW

dF

CCCC Ckr

dW

dF −′=

Mole Balances

18

Relative Rates:

Net Rates:

311

′=

′=

−

′CBA rrr

Membrane Reactors

Stoichiometry:Isothermal, no Pressure Drop

0

00 RT

PCT =

T

ATA F

FCC 0=

T

BTB F

FCC 0=

CBAT FFFF ++=19

Membrane Reactors

Combine: - Use Polymath

Parameters:s

molFA 100 =

scatkg

dmkA 10

3

=

6

2

200dm

molKC =

20

Membrane Reactors

21

Ci

W

C6H12 (A)

H2 (C)C6H6 (B)

Membrane Reactors

End of Lecture 5c

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