Question

A binary mixture of benzene and toluene will be separated by continuous distillation. The mixture consists of 20% mol of benzene and 80% mol of toluene at the bubble point of 91ºC. The binary mixture is available at 100 mol h-1 and the separation should deliver a distillate product that has a concentration of 90% mol of benzene and that contains half of the benzene in the feed stream. a) Plot the equilibrium line for benzene. b) Determine the minimum reflux ratio. b) Determine the minimum number of stages required to achieve this separation. Note: You may require looking for properties of components◢

volatilities of components need to looked up

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Answer 1

A- benzene

B- Toluene

F = 100 mol/h

x_b = 0.20

x_t = 0.80

The mole fraction of benzene in distillate = 0.90

And half of benzene in feed is present in distillate

Amount of benzene in feed = 100(0.20) = 20 mol/h

Amount of benzene in distillate = 20/2 = 10 mol/h

Distillate(D) flowrate =( 10/0.90) = 11.11 mol/h

Doing overall balance

F = D+ B

B = 100-11.111 = 88.889 mol/h

Doing benzene balance we get

100(0.20) = 11.111(0.90) +88.889(x_b)

x_b = 0.11249

A)

The feed is at bubble point so it is a saturated liquid

q = 1

T = 91°C = 364 K

From Perry handbook , antonie constants of benzene

A: 4.7258 , B: 1660.652 , C: -1. 461

Antonie constants of toluene are

A: 4.078, B: 1343.943 , C : -53. 173

P_i = 10^{(A-(B/(T+C)) )}

P is in bar and T is in Kelvin

T = 364 K

(V. P) _b = 10^{(4.7258-(1660.652/(364-1.461) ))}

(V.P) _b = 1.396 bar

(V.P) _t = 10^{(4.078-(1343.943/(364-53.173) ))}

(V.P) _t = 0.5678 bar

Benzene is more volatile component

Relative volatility ()= (V.P) _b/(V.P) _t = (1.396/0.5678) = 2.4586

The above relationship can be used to generate equilibrium curve for benzene

x	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1
y	0.214	0.38	0.512	0.62	0.71	0.786	0.85	0.90	0.95	1

The equilibrium curve is shown below

B) q = 1

R_min = (x_d- y') /(y'-x')

From graph

y' = 0.38

x' = 0.20

x_d = 0.90

R_min = (0.90-0.38) /(0.38-0.20)

R_min​​​​​​ = 2.88

C)

Fenksy equation is given by

Substiting x_d = 0.90

x_b = 0.11249

Relative volatility = 2.4586

We get

N_m = 4.738 ~ 5

Number of minimum stages = 5 including partial reboiler

Excluding partial reboiler ,minimum stages = 5-1 = 4 stages

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