Question

(Multiple reactions with heat effects). Styrene can be produced from ethylbenzene by the

following reaction:

2

H

styrene

ne

ethylbenze

+

↔

(1)

However, several irreversible side reactions also occur:

ethylene

benzene

ne

ethylbenze

+

→

(2)

methane

toluene

H

ne

ethylbenze

2

+

→

+

(3)

[J. Snyder and B. Subramaniam, Chem. Eng. Sci., 49, 5585 (1994)]. Ethylbenzene is fed at a rate

of 0.00344 kmol/s to a 10.0-

m

3

PFR reactor along with inert steam at a total pressure of 2.4 atm.

The steam/ethylbenzene molar ratio is initially [i.e., parts (a) to (c)] 14.5:1 but can be varied.

Given the following data, find the exiting molar flow rates of styrene, benzene, and toluene for

the following inlet temperatures when the reactor is operated adiabatically.

(a)

T

0

= 800 K

(b)

T

0

= 930 K

(c)

T

0

= 1100 K

(d)

Find the ideal inlet temperature for the production of styrene for a steam/ethyl benzene ratio

of 58:1. (Hint: Plot the molar flow rate of styrene versus T

0

. Explain why your curve looks

the way it does).

(e)

Find the ideal steam/ethyl benzene ratio for the production of styrene at 900 K. [Hint: See

part (d)

Additional information:

Heat capacity at 900 K

Methane:

68 J/mol.K

Styrene:

273 J/

mol.K

Ethylene:

90 J/mol.K

Ethylbenzene:

299 J/mol.K

Benzene:

201 J/mol.K

Hydrogen:

30 J/mol.K

Toluene:

249 J/mol.K

Steam:

40 J/mol.K

ρ

= 2137 kg/m

3

of pellet

φ

= 0.4

∆

H

r1E

= 118,000 kJ/kmol ethylbenzene

∆

H

r2E

= 105,200 kJ/kmol ethylbenzene

∆

H

r3E

= -

53,900 kJ/kmol ethylbenzene













+

+

+

+

+

=

T

]

b

T

)

b

T

[(b

ln(T)

b

T

b

b

exp

K

6

5

4

3

2

1

p1

atm

b

1

= -

17.34

b

4

= -

2.314

×

10

-10

b

2

= -

1.302

×

10

4

b

5

= 1.302

×

10

-6

b

3

= 5.051

b

6

= -

4.931

×

10

-3

The kinetic rate laws for the formation of styrene (St), benzene (B), and toluene (T),

respectively, are as follows.





























=

p1

H2

st

EB

1s

K

P

P

-

P

T

10,925

-

0.08539

-

exp

)

-

(1

r

φ

ρ

(kmol/m

3

.s)

( )

EB

2B

P

T

25,000

-

13.2392

exp

)

-

(1

r













=

φ

ρ

(kmol/m

3

.s)

(

)

H2

EB

3T

P

P

T

11,000

-

0.2961

exp

)

-

(1

r













=

φ

ρ

(kmol/m

3

.s)

(f)

The temperature T is in Kelvin.

[Hint: this is a problem with multiple reactions. Do not use design equation

(i.e. do not use

conversion). Solve for the flow rates of each species (i.e. system of ordinary differential

equations)]

Answer 1