A steady-state, countercurrent, staged distillation column is to be used to sepa

Question

A steady-state, countercurrent, staged distillation column is to be used to separate ethylene from propene. The saturated vapor feed at -63 degree C contains a mixture of 57 wt% ethylene and 43 wt% propene. Flow rate of the feed is 155 lb-mol/hr. The column operates at a pressure of 1 atm. The reflux is cooled to saturated liquid. A boilup ratio of V^Overbar/B = 2.4 is being used. We desire a bottoms composition of x_b = 0.1 mol fraction ethylene and a distillate composition of x_d = 0.9 mol fraction ethylene. The system has a total condenser and a partial reboiler. The column is well insulated. Determine D and B. B = 64 lb-mol/hr Find the top and bottom operating lines for the separation. top: y = 0.7x + 0.27 bottom: y = 1, 42x - 0.042

Explanation / Answer

Feed contains 57 weight % ethylene and 43 wt% propene

Molar mass : Ethylene :28.05 and propene =42.08

Basis :100 lb of mixture

Moles : ethylene = 57/28.05 =2.03 and propene =   43/42.08 =1.022

Mole fractions ethylene = 2.03/ (2.03+1.022) =0.665 and propylene = 1.022/(2.03+1.022)= .335

Let F= Feed, D= Distillate and B= Bottoms

Overall mass balance gives F= D+B, 155= D+B, D= 155-B (1)

Component ( ethylene balance gives ) , 155*0.665= D*0.9 +B*0.1 (2)

From Eq.1, Eq.2 becomes 103.075= (155-B)*0.9 +B*0.1

103.075= 155*0.9- B*0.9+B*0.1

B*(0.9-01)= 36.425, B= 45.35 lb moles/hr and D = 155-45.35 =109.65 lb moles/hr

Writing a balance for the bottom section

LJ+i= V+B (3) and LJ+1*xJ+1 = VjYj+B*XB (4)

When Eq.3 and 4 are solved for yJ= [(Vj+B)/Vj]xJ+1- (B/Vj)XB

Given V/B= S = boil up ratio

  

y= (R/R+1)*X+ XD/(R+1)

y= (8.1/(8.1+1)x+ 0.9/(9.81)

y= 0.89x+0.091

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