Mole Fraction :Distillation Column Problem
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A distillation column is separating 1000 mol/h of a 30 mol% methanol and 70 mol% water mixture.On entering the distillation column, 40% of the feed is vaporized. The column is well insulated and has a total condenser. Instead of using a reboiler, 100 mol/h of saturated steam at 1 atm is introduced directly into the bottom of the column to provide boil-up. External reflux ratio (L/D) is 3 and the reflux is returned as saturated liquid. The compositions in the distillate and bottoms for the methanol are 0.9 and 0.05 mole fractions, respectively. The column operates at 1 atm. 200mol/h is taken off as saturated liquid somewhere in the column such that the side stream composition is 0.6 mole fraction methanol. Assuming CMO is valid, find the followings:
a. Derive the middle operating line equation.
b. The optimal side stream stage.
c. The optimal feed stage.