We wish to distill an ethanol-water mixture to produce \(2250.0 \mathrm{lbm}\) of distillate product per day. The distillate product is \(80.0 \mathrm{~mol} \%\) ethanol and \(20.0 \mathrm{~mol} \%\) water. \(\mathrm{L} / \mathrm{D}=2.0\), and \(\mathrm{p}=1.0 \mathrm{~atm}\). Your boss suggests trying a packed column with 1.0 -in. plastic Pall rings. Calculate the diameter at the top of the column.

Physical properties: \(\mathrm{MW}_{\mathrm{E}}=46, \mathrm{MW}_{\mathrm{W}}=18\), assume ideal gas, \(\mu_{\mathrm{L}}=\) \(0.52 \mathrm{cP}\) at \(176^{\circ} \mathrm{F}, ho_{\mathrm{L}}=0.82 \mathrm{~g} / \mathrm{ml}\).

a. Operation is at \(75 \%\) of flooding. What diameter is required?

b. If Eq. (10-45) is not satisfied, what size of plastic Pall rings should be used?

c. Operation is at a pressure drop of 0.25 in. of water per foot of packing. Use the size of Pall rings found in part \(\mathrm{b}\). What column diameter is required?

d. Repeat part a (with 1.0 -in. Pall rings) but for \(22,500 \mathrm{lbm}\) of distillate product per day. If Eq. (10-45) is not satisfied, find the diameter of plastic Pall rings that work.

e. Repeat part d (with 1.0-in. Pall rings) but for \(225,000 \mathrm{lbm}\) of distillate product per day. If the result does not satisfy best practice, find the diameter of plastic Pall rings that works.

Note: It is not necessary to redo the entire calculation, because D and hence \(\mathrm{V}\) and hence diameter are related to the feed rate.

Equation (10-45)

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Column diameter/Packing diameter > 8 to 12