Question

We are separating a mixture that is 10 mol% methanol, 20 mol% ethanol, 30 mol% n-propanol and 40 mol% n-butanol in a distillation column. The feed is a saturated liquid. We desire to recover 98% of the ethanol in the distillate and 97% of the n-propanol in the bottoms product. The column has a total condenser and a partial reboiler and a feed rate of 100 kmol/hour at 1 atm pressure. The external reflux ratio is 5. In the enriching (rectifying) section of the column:

the liquid flow rate > vapor flow rate

the liquid flow rate = vapor flow rate

the liquid flow rate < vapor flow rate

Answer 1

Distillate product = ethanol = LK

Bottom product = propanol= HK

Methanol = LNK = distillate

butanol = HNK = bottom

Fractional recovery of ethanol in distillate FRe_D = 0.98

Fractional recovery of ethanol in bottom FRe_W = 0.02

Fractional recovery of propanol in distillate FRp_D = 1-0.97

= 0.03

Fractional recovery of propanol in bottom FRp_W = 0.97

Ethanol balance at distillate

DX_{D, E} = FRe_D x F x z_{F, E}

= 0.98 x 100 x 0.20

= 19.6 kmol/h

At bottom

BX_B,E = FRe_B x F x z_{F, E}

= 0.02 x 100 x 0.20

= 0.4 kmol/h

Similarly for propanol

At bottom

BXp_,B = FRp,_B x F x z_{F, p}

= 0.97 x 100 x 0.30

= 29.1 kmol/h

At distillate

DX_D,p = FRp_D x F x z_{F, p}

= 0.03 x 100 x 0.30

= 0.90 kmol/h

Methanol balance at distillate

DX_{D, M} = F x z_{F, M} = 100 x 0.10 = 10 kmol/h

At bottom

X_{B, M} = 0

BX_{B, M} = 0

Total distillate

D = 10 + 19.6 + 0.90 = 30.5 kmol/h

Reflux ratio R = L/D

L = 5 x 30.5 = 152.5 kmol/h

V = L + D = 152.5 + 30.5 = 183 kmol/h

Vapor flow rate (183)> Liquid flow rate (152.5)