Lecture 20 Thursday 3/20/08

Multiple Reactions with Heat Effects

User Friendly Equations Relate T and X or Fi

Heat Exchange

Elementary gas phase reaction carried out in a PBR

The feed consists of both inerts I and Species A with the ratio of inerts to the species A being 2 to 1.(a) Adiabatic. Plot X, Xe, T and the rate of disappearance as a function of V up to

V = 40 dm3. (b) Constant Ta. Plot X, Xe, T, Ta and Rate of disappearance of A when there is a

heat loss to the coolant and the coolant temperature is constant at 300 K for V = 40 dm3. How do these curves differ from the adiabatic case?

• Variable Ta Co-Current. Plot X, Xe, T, Ta and Rate of disappearance of A when there is a heat loss to the coolant and the coolant temperature varies along the length of the reactor for V = 40 dm3. The coolant enters at 300 K. How do these curves differ from those in the adiabatic case and part (a) and (b)?

(d) Variable Ta Counter Current. Plot X, Xe, T, Ta and Rate of disappearance of A when there is a heat loss to the coolant and the coolant temperature varies along the length of the reactor for V = 20 dm3. The coolant enters at 300 K. How do these curves differ from those in the adiabatic case and part (a) and (b)?

Ta

AA B

Heat Exchange Fluid

Ý m C

FA0

FI

Mole Balance (1)

Rate Law (2)

(3)

(4)

dXdW

r A FA0

W bV

dXdV

r AB

FA0

rA

FA0

rA k CA CB

KC

k k1 expER

1T1

1T

KC KC2 expHRx

R1T2

1T

Stoichiometry (5)

(6)

Parameters (7) – (15)

CA CA0 1 X y T0 T

CB CA0Xy T0 T

dydW

y

FT

FT0

TT0

2yTT0

W V

dydV

b

2yTT0

FA0 , k1, E, R, T1, KC2 , HRx , T2 , CA0 , T0 , , b

Energy Balance

Adiabatic and CP = 0

(16A)

Additional Parameters (17A) & (17B)

Heat Exchange

(16B)

T T0 HRx XiCPi

T0 , iCPiCPA

ICPI

dTdV

rA HRx Ua T Ta

FiCPi

FiCPiFA0 iCPi

CPX , if CP 0 then

dTdV

rA HRx Ua T Ta

FA0 iCPi

(16B)

A. Constant Ta (17B) Ta = 300

Additional Parameters (18B – (20B): Ta, , Ua,

B. Variable Ta Co-Current

(17C)

C. Variable Ta Counter Current

(18C)

Guess Ta at V = 0 to match Ta = Tao at exit, i.e., V = Vf

dT

dV

rA HRx Ua T Ta FA0 iCPi

dTa

dV

Ua T Ta Ý m CPcool

, V 0 Ta Tao

dTa

dV

Ua Ta T Ý m CPcool

V 0 Ta ?

User Friendly Equations Relate T and X or Fi

Heat Exchange

Elementary liquid phase reaction carried out in a PFR

The feed consists of both inerts I and Species A with the ratio of inerts to the species A being 2 to 1.

Ta

AA B

Heat Exchange Fluid

Ý m C

FA0

FI

Multiple reactions with heat effects

Multiple Rxns

Mole balances – every species (no conversion!)

Rates – rate laws

net/relative rates

Stoichiometry –

Heat effects – 00

00

2 T

T

F

F

ydW

dy

T

Ty

F

FCC

T

T

T

ATA

j)i, matching have(must

removedheat

producedheat

Rijijg

r

gPii

rg

Pii

aaRa

HrQ

Q

QCF

QQ

dV

dT

CF

TTUHr

dV

dT

A molcal000,10 32 )2(

A molcal000,20 2 )1(

232

22

12

11

ARCACC

ARBAAA

HCCkrDCA

HCCkrCBA

Rate is given for 2C, but ΔHR is given for 2A!

PAPCPDAPRAPARAR

PAPBPCAPRAPARAR

CCCCTTCHH

CCCCTTCHH

2/32/1

2

220

22

11011

Make sure it is in respect to A; A needs a coefficient of 1!!!!!!!

ARAARARijijgPii

rg HrHrHrQCF

QQ

dV

dT2211

1) Mole balance:

DD

BB

CC

AA

AA

AA

rdV

dFr

dV

dF

rdV

dFr

dV

dF

rdV

dFr

dW

dF

B''

2) Rate laws:

3) Stoich:

4) Heat effects:

Parameters:,.... , , 021 AFEE

CDCA

ABAC

DDCCC

BBBAA

CCCACC

AABAAA

rrrr

rrrr

rrrrr

rrrrr

TTREkkCCkr

TTREkkCCkr

2222

1111

221

121

222232

22

11112

11

3/1 3/2

2

11exp

11exp

00

00

00

00

00

2

T

T

F

F

ydV

dyFFFFF

T

Ty

F

FCC

T

Ty

F

FCC

T

Ty

F

FCC

T

Ty

F

FCC

T

TDCBAT

T

DTD

T

CTC

T

BTB

T

ATA

Pcooli

aaa

Pii

rg

Cm

TTU

dV

dT

CF

QQ

dV

dT

PDDPCCPBBPAAP

aar

ARAARAg

CFCFCFCFC

TTUQ

HrHrQ 2211