A distillation column at 101 kPa is used to separate 350 kmol/h of a bubble point mixture of toluene and benzene into an overhead product with 3 mole % toluene and a bottoms product with 98 mole % toluene. The feed contains 0.45 mole fraction benzene. The overhead reflux occurs at saturation temperature (implies it is total condenser – if it was not, you would have a vapor liquid mixture or a partial condenser akin to a partial reboiler). VLE data for the mixture is given below. An average alpha can be found from the VLE data if solving analytically. EQUILIBRIUM DATA IN MOLE- FRACTION BENZENE, 101 kPA
y 0.21 0.37 0.51 0.64 0.72 0.79 0.86 0.91 0.96 0.98
x 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.95

Required:
a. What are the distillate and bottoms flow rates (D and B)?
b. What is the minimum reflux ratio, Rmin (corresponding to N= infinity)?

A)

  D = 158.42 kmol/h

  B =  191.578 kmol/h

B) Rmin = 1.3095

Explanation:

a) Determine the distillate and bottoms flow rates ( D and B )

F = D + B ( 1 )

Given data :

F = 350 kmol/j

Xf = 0.45 mole

yD ( distillate comp ) = 0.97

yB ( bottom comp ) = 0.02

back to equation 1

350(0.45) = 0.97 D + 0.02 B   ( 2 )

where; B = F - D

Equation 2 becomes

350( 0.45 ) = 0.97 D + 0.02 ( 350 - D )   3

solving equation 3

D = 158.42 kmol/h

resolving equation 2

B = 191.578 kmol/h

B) Determine the minimum reflux ratio Rmin

The minimum reflux ratio occurs when the enriching line meets the q line in the VLE curve

first we calculate the value of the enriching line

Y =( Rm / R + 1 m ) x   +  ( 0.97 / Rm + 1 )

q - line ;  y =  ( 9 / 9-1 ) x -  xf/9-1

therefore ; x = 0.45

Finally Rmin

=  (( 0.97 / (Rm + 1 ))  = 0.42

0.42 ( Rm + 1 ) = 0.97

∴ Rmin = 1.3095

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explanation:

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