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

Lecture 13 – Tuesday 2/26/2013Complex Reactions:

A +2B CA + 3C D

Example A: Liquid Phase PFRExample B: Liquid Phase CSTRExample C: Gas Phase PFRExample D: Gas Phase Membrane Reactors

Sweep Gas Concentration Essentially ZeroSweep Gas Concentration Increases with Distance

Example E: Semibatch Reactor

2

Gas Phase Multiple Reactions

3

New things for multiple reactions are:

4

1. Number Every Reaction2. Mole Balance on every species3. Rate Laws (a) Net Rates of Reaction for every species

(b) Rate Laws for every reaction

(c) Relative Rates of Reaction for every reaction For a given reaction i: (i) aiA+biB ciC+diD:

N

iiAA rr

1

3222

211

CACC

BAAA

CCkr

CCkr

i

iD

i

iC

i

iB

i

iA

dr

cr

br

ar

Reactor Mole Balance Summary

5

Reactor Type Gas Phase Liquid Phase

VrdtdN

AA A

A rdtdC

Batch

VrdtdN

AA V

CrdtdC A

AA 0Semibatch

0BBB FVr

dtdN

VCCr

dtdC BB

BB

00

Reactor Mole Balance Summary

6

Reactor Type Gas Phase Liquid Phase

A

AA

rFFV

0

A

AA

rCCV

00CSTR

AA r

dVdC

0AA r

dVdF

PFR

AA r

dWdC 0A

A rdWdF PBR

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

VNC B

B B

BFC

TT

PP

NNVVT

T 00

00

TT

PP

VN

NNC T

T

BB

0

00

0

TT

PP

NNCCT

BTB

0

00

TT

PP

FF

T

T 00

00

TT

PP

FFCCT

BTB

0

00

TT

PPF

FFC T

T

BB

0

00

0

Batch Flow

7

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

Flow:

Batch:

Stoichiometry

8

Concentration of Gas:

DCBATT

ATA FFFFF

TTy

FFCC

0

0

0A

AFC

0VNC A

A

Example A: Liquid Phase PFR

9

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

23)2( DAC 2322 ACCC CCkr

2)1( CBA 211 BAAA CCkr

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

The complex liquid phase reactions follow elementary rate laws:


10

Complex Reactions

1) Mole Balance on each and every species

(1) A 2B C

(2) A 3C D

DD

CC

BB

AA

rdVdFr

dVdF

rdVdFr

dVdF

)4( )3(

)2( )1(


11

2) Rate Laws:Net Rates

Rate Laws

Relative RatesReaction 1

DDCCC

BBBAAA

rrrrrrrrrrr

221

2121

0 )8( )6( )7( )5(

3222

211

)10(

)9(

CACC

BAAA

CCkr

CCkr

11 1

1 1

1 1

1 2 1

(11) 2(12)

CA B

B A

C A

rr r

r rr r


12

Relative RatesReaction 2

3 )14(

32 )13(

132

22

22

222

CD

CA

DCA

rr

rr

rrr

322

3221

21

322

21

3

232

CAC

D

CACBAAC

BAAB

CACBAAA

CCkr

CCkCCkr

CCkr

CCkCCkr


13

3) StoichiometryLiquid

0 else then 00001.0 ~ )19(

)18( )17( )16( )15(

0

0

0

0

D

CDC

DD

CC

BB

AA

FFVifS

FCFCFCFC


14

Others

4) ParametersNeededNot – Liquid )20(

NeededNot – Liquid )19(NeededNot – Liquid

0

T

T

C

F

100 )26(200 )28(200 )26(

2500 )25(Liquid )24(

Liquid )23(20 )22(

10 )21(

0

0

0

0

2

1

B

A

f

T

C

A

FF

VC

kk

Example B: Liquid Phase CSTR

15

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


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




16

The 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 reaction 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 V


17

(1) A + 2B →C (2) 2A + 3C → D

3222

211

CACC

BAAA

CCkr

CCkr

00)4(00)3(

0)2(0)1(

0

0

000

000

VrCDVrCC

VrCCBVrCCA

DD

CC

BBB

AAA

1) Mole Balance


18

2) Rate Laws: (5)-(14) same as PFR

3) Stoichiometry: (15)-(18) same as Liquid

Phase PFR

4) Parameters:

0001.00001.0 )19(

0

0/

D

C

D

CDC C

CF

FS

00021 , , , , , VCCkk BACA


19

(1) A + 2B →C (2) 2A + 3C → D

3222

211

CACC

BAAA

CCkr

CCkr

00001.0)19(

)18()17()16()15(

0

0

0

0

D

CDC

DD

CC

BB

AA

FFS

FCFCFCFC

1) Mole Balance (1–4) 2) Rates (5–14) 3) Stoichiometry: (15–19)

VrFFFf AAAA 0)1( (=0)

VrFFFf BBBB 0)2( (=0)

VrFFf CCC 0)3( (=0)

VrFFf DDD 0)4( (=0)

In terms of molar flow rates

Same as Example A


20

(1) A + 2B →C (2) 2A + 3C → D

3222

211

CACC

BAAA

CCkr

CCkr

1) Mole Balance (1–4) 2) Rates (5–14) 3) Stoichiometry: (15–19)

In terms of concentration

VrCCCf AAAA 000)1( (=0)

VrCCCf BBBB 000)2( (=0)

VrCCf CCC 00)3( (=0)

VrCCf DDD 00)4( (=0)

00001.0 )15(

D

CDC F

FSSame as Example A

Example C: Gas Phase PFR, No ΔP

21

Same reactions, rate laws, and rate constants as Example A:


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

species A.




22

1) Mole Balance

2) Rate Laws: (5)-(14) same as CSTR

)4( (2)

)3( )1(

DD

BB

CC

AA

rdVdFr

dVdF

rdVdFr

dVdF


23

3) Stoichiometry: Gas: Isothermal T = T0

Packed Bed with Pressure Drop

DCBAT

T

DTD

T

CTC

T

BTB

T

ATA

FFFFF

yFFCCy

FFCC

yFFCCy

FFCC

)19(

)18( )17(

)16( )15(

00

00

000 22 T

T

T

T

FF

yTT

FF

ydWdy


24

4) Selectivity

21 1y

20 0 else then 00001.0 if

D

C

D

C

FFV

FFS

Example D: Membrane Reactor with ΔP

25




species A.




26

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

4 2

3 1

DD

BB

CCC

AA

rdVdFDr

dVdFB

RrdVdFCr

dVdFA

CCsg RdVdF

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

mm 0

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 when 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.

ii

ii

MWFMWF

GG

00

00

27


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:

ii

ii

Cii

Cii

C

C

MWFMWF

AMWFAMWF

AmAm

GG

0000 1

1

1

1


28


29

2) Rate Laws: (5)-(14) same as Examples A, B, and C.

3) Stoichiometry: (15)-(20) same as Examples A and B(T=T0)

4) Sweep Gas Balance:

CSweepCCC CCkR

21 2

2 00 T

T

T

T

FF

ydVdy

FF

ydWdy

CCsg

CVVCsgVCsg

RdVdF

VRFF

0

Example E: Liquid Phase Semibatch

30




species A.



The 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.

31


1) Mole Balances:

(1) A + 2B →C (2) 2A + 3C → D

0AAA FVr

dtdN

VrdtdN

BB

VrdtdN

CC

VrdtdN

DD

00 AN

000.2000 VCN BB

00 CN

00 DN32

B

FA0


2) Rate Laws: (5)-(14)

19 18

17 16

15 00

VNC

VNC

VNC

VNC

tvVV

DD

CC

BB

AA

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

20 )0( else then )0001.0( if/

D

CDC N

NtS

mindm10 30 3

0 dm100V minmol3F 0A 33


3) Selectivity and Parameters:

End of Lecture 13

34

Lecture 13

Documents

liquid phase pfrexample

liquid phase pfr14others

liquid phase cstr171

liquid phase cstr201

liquid phase pfr9note

liquid phase cstr191

liquid phase pfr112

liquid phase cstr182