Biorefineries producing ethanol by fermentation have several distillation columns to separate the ethanol from the water. The first column, the beer still, is a stripping column that takes the dilute liquid fermenter product containing up to \(15 \%\) solids and produces a clean vapor product that is sent to the main distillation column. The main column produces a distillate product between about \(65 \mathrm{~mol} \%\) and the ethanol azeotrope concentration, \(89.43 \mathrm{~mol} \%\), and a bottoms product with very little ethanol. The calculated diameter of the main distillation column is much greater at the top than elsewhere. To reduce the size and hence the cost of the main column, you can use a two-enthalpy feed system: split the vapor feed into two parts, condense one part, and then feed both parts to the main column at their optimum feed locations. This method reduces the vapor velocity in the top of the column, which reduces the calculated diameter; however, a few additional stages may be required to obtain the desired purity.

Simulate the following base case and two-enthalpy feed system for the main column using NRTL VLE correlation. The feed for the base case is \(1000.0 \mathrm{kmol} / \mathrm{h}\) of a \(10.0 \mathrm{~mol} \%\) ethanol saturated vapor stream. The feed and the column are at \(2.5 \mathrm{~atm}\). A vapor distillate product from a partial condenser with \(\mathrm{y}_{\mathrm{D}}=79.01 \mathrm{~mol} \%\) ethanol and a liquid bottoms product with \(99.86 \mathrm{~mol} \%\) water are desired. The column has 34 equilibrium stages plus a partial condenser and a kettle reboiler \((\mathrm{N}=36\) in Aspen Plus notation). Tray spacing \(=18 \mathrm{in} .=0.4572 \mathrm{~m}\), operation is at \(80 \%\) of flooding, and the flooding design method developed by Jim Fair is used. For the base case (all feed is a vapor), the feed stage is 23 (in Aspen Plus notation). \(\mathrm{Q}_{\mathrm{R}}=902 \mathrm{~kW}\), and \(\mathrm{D}=125 \mathrm{kmol} / \mathrm{h}\).
For the two-enthalpy feed case, \(600.0 \mathrm{kmol} / \mathrm{h}\) of the feed is condensed to a saturated liquid and is fed to the column on stage 17. Vapor feed remains on stage 23. Other parameters are unchanged from the base case.

a. Simulate the base case and find the product mole fractions and the column diameter.

b. Simulate the two-enthalpy feed and find the product mole fractions and the column diameter.

c. To explain the reduction in column diameter, assume \(\mathrm{CMO}\), and calculate \(\mathrm{V}\) in the top of the column for both cases. Then explain, using the equations in this chapter, how this will reduce the diameter.