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 2/22/2011

Complex ReactionsA +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 Reactor2

Gas Phase Multiple Reactions

3

4

The new things for multiple reactions are:1. Number Every Reaction2. Mole Balance on every species3. Rates: (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

i

iD

i

iC

i

iB

i

iA

dr

cr

br

ar

3222

211

CACC

BAAA

CCkr

CCkr

Reactor Mole Balance SummaryReactor

TypeGas Phase Liquid Phase

VrdtdN

AA A

A rdtdC

Batch

VrdtdN

AA V

CrdtdC A

AA 0Semibatch

0BBB FVr

dtdN

VCCr

dtdC BB

BB

00

5

Reactor Mole Balance SummaryReactor 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

6 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: 8

Stoichiometry Concentration Gas:

DCBATT

ATA FFFFF

TTy

FFCC

0

0

0A

AFC

0VNC A

A

Example A: Liquid Phase PFR

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

)2( DA2C3 2322 ACCC CCkr

)1( CB2A 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

9

Complex Reactions

Mole Balance on Each and Every Species

10

DD

CC

BB

AA

rdVdFr

dVdF

rdVdFr

dVdF

)4( )3(

)2( )1(

(1) A 2B C

(2) A 3C D


11

Rates:Net Rates

Laws

Relative RatesReaction 1

DDCCC

BBBAAA

rrrrrrrrrrr

221

2121

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

3222

211

)10(

)9(

CACC

BAAA

CCkr

CCkr

AC

AB

CBA

rrrr

rrr

11

11

111

)12(2 )11(

121


12

Reaction 2

322

3221

21

322

21

3

232

CAC

D

CACBAAC

BAAB

CACBAAA

CCkr

CCkCCkr

CCkr

CCkCCkr

3 )14(

32 )13(

132

22

22

222

CD

CA

DCA

rr

rr

rrr


13

StoichiometryLiquid

0 else then 00001.0 ~ )19(

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

0

0

0

0

D

CDC

BD

CC

BB

AA

FFVifS

FCFCFCFC


14

Others

Parameters

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

NeededNot – Liquid )20(NeededNot – Liquid )19(

NeededNot – Liquid

0

T

T

C

F


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





15

Complex Reactions

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 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 V16

Example B: Liquid Phase CSTR

CSTR (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:

17


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

3) Stoichiometry: same as Liquid Phase PFR : (15)-(18) Same as PFR

4) Parameters:

0001.00001.0 )19(

0

0/

D

C

D

CDC C

CF

FS

18

00021 , , , , , VCCkk BACA


CSTR (1) A + 2B →C (2) 2A + 3C → D

3222

211

CACC

BAAA

CCkr

CCkr

Example B: Liquid Phase CSTRIn terms of Molar Flow Rates

1900001.0

)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)

19

VrFFFf AAAA 0)1( (=0)

VrFFFf BBBB 0)2( (=0)

VrFFf CCC 0)3( (=0)

VrFFf DDD 0)4( (=0)

CSTR (1) A + 2B →C (2) 2A + 3C → D

Example B: Liquid Phase CSTR In terms of Concentration

20

3222

211

CACC

BAAA

CCkr

CCkr

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

FS

1) Mole balance (1–4)

2) Rates (5–14)

3) Stoichiometry (15–19)

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





21

Complex ReactionsExample C: Gas Phase PFR, No ΔP

)4( (2)

)3( )1(

DD

BB

CCC

AA

rdVdFr

dVdF

RrdVdFr

dVdF

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

22

Example C: Gas Phase PFR

1) Mole balance:

23

000 22 T

T

T

T

FF

yTT

FF

ydWdy

StoichiometryGas : 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

Example C: Gas Phase PFR

3) Stoichmetry:

19 FFFFF

18 17

16 15

DCBAT

00

00

yFFCCy

FFCC

yFFCCy

FFCC

T

DTD

T

CTC

T

BTB

T

ATA

20 0 else then 00001.0 if

D

C

D

C

FFV

FFS

4) Selectivity:

21 1y 24

Example C: Gas Phase PFR, No ΔP, (y=1)

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





25

Complex ReactionsExample D: Membrane Reactor with ΔP

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 balance:

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

26

Example D: Membrane Reactor with ΔP

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.

0GG0

0FiMWiFi0MWi

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:

GG0

mAC1m0 AC1

Fi MWi AC1Fi0 MWi AC1

Fi MWi Fi0 MWi

28


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

21 2

; 2 00 T

T

T

T

FF

ydVdy

FF

ydWdy

CSweepCCC CCkR

4) Sweep Gas Balance:

CCsg

CVVCsgVCsg

RdVdF

VRFF

0

29


thenCC CsgC ,

RC kCCCC

Case 1 Large sweep gas velocity

Case 2 Moderate to small sweep gas velocity

sg

CCsg

sgF

C

sg

Csgsgsgsg F

FF

0

00

Vary υsg to see changes in profiles

0CsgC

30


CsgCCCC CCkR

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

)1( CB2A 2

11 BAAA CCkr




31

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.

32

1) Mole balance:(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 DN 33

Example E: Liquid Semibatch

B

FA0

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

19 18

17 16

15 00

VNC

VNC

VNC

VNC

tvVV

DD

CC

BB

AA

20 )0( else then )0001.0( if/

D

CDC N

NtS

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:34

Example E: Liquid Semibatch

End of Lecture 13

35

lecture 13

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