Lecture 13

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 13

Today’s lectureComplex Reactions

A +2B CA + 3C D

Liquid Phase PFRLiquid Phase CSTRGas Phase PFRGas Phase Membrane Reactor Sweep Gas Concentration Essentially

Zero Sweep Gas Concentration Increases

with Distance Semi Batch Reactor

2

Reactor Mole Balance SummaryReactor

TypeGas Phase Liquid Phase

Vrdt

dNA

A AA r

dtdC

Batch

Vrdt

dNA

A VCr

dtdC A0

AA

Semibatch

0BBB FVr

dtdN

VCCr

dtdC B0B0

BB

3

Reactor Mole Balance SummaryReactor Type

Gas Phase Liquid Phase

A

A0A

rF FV

A

A0A0 r

CCV

CSTR

AA

0 rdV

dCA

A rdVdF

PFR

AA

0 rdWdC A

A rdWdF PBR

4 Note: The reaction rates in the above mole balances are net rates.

Reactor Mole Balance Summary

5

The new things for multiple reactions are:

Rates:1. Rate Law for every reaction2. Relative Rates for every

reaction3. Net Rates of Reaction

Gas Phase Multiple Reactions

6

Note: We could use the gas phase mole balance for liquids and then just express the concentration as:

Flow: CA=FA/v0

Batch: CA=NA/V0

Note: The reaction rates in the above mole balances are net rates. The new things for multiple reactions are:

1. Rate Law for every reaction2. Relative Rates for every reaction3. Net Rates of Reaction

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Net Rate of Reaction for species A

For N reactions, the net rate of formation of species A is:

N

1iiAA rr

For a given reaction i:

(i) aiA+biB ciC+diD:

i

iD

i

iC

i

iB

i

iA

dr

cr

br

ar

8

VNC B

B

BB

FC

TT

PP

NNVV 00

0T

T0

TT

PP

VN

NNC 0

00

0T

T

BB

TT

PP

NNCC 0

0T

B0TB

TT

PP

FF 00

0T

T0

TT

PP

FFCC 0

0T

B0TB

TT

PPF

FFC 0

00

0T

T

BB

Batch Flow

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Example A: Liquid Phase PFR

NOTE: The specific reaction rate k2C is defined with respect to species C.

)2( DA2C3 2A

3CC2C2 CCkr

)1( CB2A 2BAA1A1 CCkr

NOTE: The specific reaction rate k1A is defined with respect to species A.

The complex liquid phase reactions follow elementary rate laws

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Last Lecture

Example B: Liquid Phase CSTRSame reactions, rate laws, and rate constants as example A




)2( DA2C3 2A

3CC2C2 CCkr

11

Complex Reactions

Example B: Liquid Phase CSTRThe complex liquid phase reactions take place in a 2,500 dm3 CSTR. The feed is equal molar in A and B with FA0=200 mol/min, the volumetric flow rate is 100 dm3/min and the reation volume is 50 dm3.

Find the concentrations of A, B, C and D existing in the reactor along with the existing selectivity.

Plot FA, FB, FC, FD and SC/D as a function of V12

CSTR (1) A + 2B →C (2) 2A + 3C → D

3C

2AC2C2

2BAA1A1

CCkr

CCkr

4 0VrCV0 D3 0VrCV0 C2 0VrCVCV B1 0VrCVCV A

DD0

CC0

BB00B0

AA00A0

1) Mole balance:

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Example B: Liquid Phase CSTR

2) Rates:

14r31r 13r

32r

12rr 11r2r1

r3

r2

r 1r

2r

1r

10rr 9rrr 8rr 7rrr

6 CCkr

5 CCkr

C2D2C2A2

A1C1A1B1

D2C2A2C1B1A1

D2DC2C1C

B2BA2A1A

3C

2AC2C2

2BAA1A1

15 0001.0C

C0001.0F

FSD0

C0

D

CD/C

3) Parameters: 00B0AC2A1 V ,V ,C ,C ,k ,k 14

Same reactions, rate laws, and rate constants as example A




)2( DA2C3 2A

3CC2C2 CCkr

15

Complex ReactionsExample C: Gas Phase PFR, No ΔP

1) Mole balance:

4 rdVdF D 2 r

dVdF B

3 RrdVdF C 1 r

dVdF A

DD

BB

CCC

AA

2) Rates: Same as CSTR (5)-(14)

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Example C: Gas Phase PFR, No ΔP

3) Stoich:

19 FFFFF

18 yFFCC 17 y

FFCC

16 yFFCC 15 y

FFCC

DCBAT

T

D0TD

T

C0TC

T

B0TB

T

A0TA

20 0 else FF then 00001.0V if

FFS

D

C

D

C

4) Selectivity:

21 1y 17

Example C: Gas Phase PFR, No ΔP

Same reactions, rate laws, and rate constants as example A




)2( DA2C3 2A

3CC2C2 CCkr

18

Complex ReactionsExample D: Membrane Reactor with ΔP

We need to reconsider our pressure drop equation. When mass diffuses out of a membrane reactor there will be a decrease in the superficial mass flow rate, G. To account for this decrease in calculating our pressure drop parameter, we will take the ratio of the superficial mass velocity at any point in the reactor to the superficial mass velocity at the entrance to the reactor. The superficial mass flow rates can be obtained by multiplying the species molar flow rates, Fi, by their respective molecular weights, Mwi, and then summing over all species:

2

1

1

2

1

2

Ci0i

Cii

Ci0i

Cii

C1

C2

1

2

AMWFAMWF

AMWFAMWF

AmAm

GG

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Example D: Membrane Reactor with ΔP

Because the smallest molecule is the one diffusing out and has the lowest molecular weight, we will neglect the changes in the mass flow rate down the reactor and will take as first approximation.1) Mole Balance:

4 rdVdF D 2 r

dVdF B

3 RrdVdF C 1 r

dVdF A

DD

BB

CCC

AA

CCsg R

dVdF

We also need to account for the molar rate of desired product C leaving in the sweep gas FCsg

20


)mm( 0

2) Rates: Same (5)-(14)3) Stoich: Same (15)-(20)

21 FF

y2dVdy ;

FF

y2dWdy

0T

T

0T

T

CSweepCCC CCkR

4) Sweep Gas Balance:

CCsg

CVVCsgVCsg

RdV

dF

0VRFF

21


CsgC CC

RC kCCCC

Case 1 Large sweep gas velocity

Case 2 Moderate to small sweep gas velocity

sg

CCsg

sgF

C

sg0

Csgsg00sgsg F

FF

Vary υsg to see changes in profiles

0CCsg

22


Example E: Liquid SemibatchSame reactions, rate laws, and rate constants as example A




)2( DA2C3 2A

3CC2C2 CCkr

23

Complex Reactions

Example E: Liquid SemibatchThe complex liquid phase reactions take place in a semibatch reactor where A is fed to B with FA0=3 mol/min. The volumetric flow rate is 10 dm3/min and the initial reactor volume is 1,000 dm3.The maximum volume is 2,000 dm3 and CA0=0.3 mol/dm3 and CB0=0.2 mol/dm3. Plot CA, CB, CC, CD and SS/D as a function of time.

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1) Mole balance:(1) A + 2B →C (2) 2A + 3C → D

B

FA0

0AAA FVr

dtdN

Vrdt

dNB

B

Vrdt

dNC

C

Vrdt

dND

D

0N 0A

000.2VCN 00B0B

0N 0C

0N 0D 25

Example E: Liquid Semibatch

2) Rates: Same (5)-(14)

19 V

NC 18 VNC

17 V

NC 16 V

NC

15 tvVV

DD

CC

BB

AA

00

20 )0( else NN then )0001.0t( ifS

D

CD/C

Net Rates, Rate Laws and relative rates – are the same as Liquid and Gas Phase PFR and Liquid Phase CSTR

mindm10 30 3

0 dm100V minmol3F 0A

3) Selectivity:

4) Parameters:26

Example E: Liquid Semibatch

End of Lecture 13

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Lecture 13

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