Lecture 19 Tuesday 3/18/08Gas Phase ReactionsTrends and Optimuns

User Friendly Equations Relate T and X or Fi

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

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

WbV

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

2y

TT0

WV

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)

TT0 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

dTdV rA HRx Ua T Ta

FA0 iCPi

dTa

dV

Ua T Ta Ý m CPcool

, V0 Ta Tao

dTa

dV

Ua Ta T Ý m CPcool

V0 Ta ?

Endothermic

PFR

A B

dX

dV

k 1 1 1

KC

X

0 , Xe

KC

1KC

XEB iCPi

T T0 HRx

CPA

ICPI T T0 HRx

T0

XXEB

Xe

TT0 HRx X

CPAICPI

PFR Adiabatic

FA0

FT

1. Irreversible A B Liquid Phase, Keep FA0 Constant

A. First order

dX

dV rA

FA0kCA

FA0k

FA0

1 X FA0

k 1 X

kCA0 1 X FA0

Constant density liquid

0 volumetric flow rate without inert

0FA0 FI

FA0

0 1I

dX

dV

k 1 X 0 1I

First Order Irreversible

I

ISO

V

T

I

V

k ISO

I

1

1I

IOPT

I

k 1 y I k

1 I

I

IOPT

X

k

1I

IOPT

Adiabatic

Exothermic

Endothermic

T

V

KC

V

Xe

V

XeX

V

k

V

KC

V

XeX

V

T

V

Xe

V

k

V

Xe

XFrozen

V

OR

Heat Exchange

Exothermic

Endothermic

T

V

KC

V

Xe

V

XeX

V

T

V

KC

V

Xe

V

XeX

V

(d) Gas Phase Counter Current Heat Exchange Vf = 20 dm3

Matches

Gas phase heat effects

Example: PBR A ↔ B

VW b

1) Mole balance:

2) Rates:

3) Stoich (gas):

0

'

A

A

F

r

dW

dX

TTR

Hkk

TTR

Ekk

kCCkr

RCC

CBAA

11exp

11exp

22

11

'

000

00

000

00

0

0

00

122

1

1

1

1

1

1

T

TX

yT

T

F

F

ydW

dy

T

Ty

X

XCC

T

Ty

X

XC

T

T

P

P

Xv

XFC

T

T

P

PXvv

T

T

AB

AAA

C

Ce

eA

eA

Ae

BeC k

kX

TTyXC

TTyXC

C

Ck

1

1 00

00

4) Heat effects

5) Parameters….

- for adiabatic: Ua = 0

- constant Ta:

- co-current: equations as is

- counter-current:

0dW

dTa

T)-T toT-T flip(or 1 aadW

dT

PCC

ab

a

a

PiiA

ab

aRa

Cm

TTU

dW

dT

CF

TTU

Hr

dW

dT

0

Co-current, (Ta-T) for counter-current

Exothermic Case: Endothermic Case:

kC

T

Xe

T

kC

T T

Xe

~1

As T0 decreases the conversion X will increase, however the reaction will progress slower to equilibrium conversion and may not make it in the volume of reactor that you have.

Therefore, for exothermic reactions there is an optimum inlet temperature, where X reaches Xeq right at the end of V. However, for endothermic reactions there is no temperature maximum and the X will continue to increase as T increases.

As inert flow increases the conversion will increase. However as inerts increase, reactant concentration decreases, slowing down the reaction. Therefore there is an optimal inert flow rate to maximize X.

Adiabatic:

T

X Adiabatic T and Xe

T0

exothermic

T

X

T0

endothermic

PIIPA

R

CC

XHTT

0

X

T

X

T

V1 V2

X

TT0

I

0I

VkdV

dX

I

11

1

I

k

1

I

Ioptimum