\(1000 \mathrm{kmol} /\) day of a saturated liquid feed that is \(30 \mathrm{~mol} \%\) acetone and \(70 \mathrm{~mol} \%\) ethanol is fed at the optimum feed location to a column with a partial condenser and a partial reboiler. Operation is at \(\mathrm{p}=1 \mathrm{~atm}\). Distillate is \(90 \mathrm{~mol} \%\) acetone, and bottoms is \(10 \mathrm{~mol} \%\) acetone. Boilup ratio \(\approx / \mathrm{B}=1.25\). On the fourth stage above the partial reboiler, a vapor side stream with flow rate \(S=200 \mathrm{kmol} /\) day is withdrawn, condensed to a saturated liquid, and returned to the column as feed at the optimum location. Assume CMO. Find the mole fraction of vapor side stream \(\mathrm{y}_{\mathrm{s}}\), optimum feed location, optimum location to input saturated liquid from intermediate condenser, and total number of equilibrium stages. Equilibrium data are in Problem 4.D7.

Problem 4.D7.

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D7.* A distillation column with a total condenser is separating a feed that is 30 mol% acetone from ethanol. Distillate xD = 0.90, and bottoms xB = 0.13, both mole fractions acetone. Assume CMO is valid. L/V = 0.8. Boilup ratio is /B = 1.0. Find the composition of the liquid leaving the fifth stage below the total condenser. . The column has a partial reboiler that acts as an equilibrium contact. Find the vapor composition leaving the second stage above the partial reboiler. Find optimum feed plate location, total number of stages, and required q value of feed. Equilibrium data for acetone (A) and ethanol at 1 atm (Perry et al., 1963, pp. 13-4): 0 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.50 0.60 0.70 0.80 0.90 1.0 YA O 0.262 0.348 0.417 0.478 0.524 0.566 0.605 0.674 0.739 0.802 0.865 0.929 1.0 TC 78.3 67.3 65.9 63.6 60.4 59.1 58.0 57.0 56.1