We wish to distill \(0.10 \mathrm{kmol} / \mathrm{s}\) of a feed at \(25^{\circ} \mathrm{C}\) and \(15.0 \mathrm{~atm}\). The feed is \(10.0 \mathrm{~mol} \%\) ethane, \(35.0 \mathrm{~mol} \%\) propane, \(45.0 \mathrm{~mol} \% \mathrm{n}\)-butane, and \(10.0 \mathrm{~mol} \% \mathrm{n}-\mathrm{pentane.} \mathrm{Use} \mathrm{the} \mathrm{Peng-Robinson} \mathrm{VLE} \mathrm{correlation.} \mathrm{Design}\) a column with \(\mathrm{N}\) (Aspen notation) \(=35\) and the feed on stage 16 . The column operates at \(15.0 \mathrm{~atm}\), has a partial condenser, and produces a vapor distillate with \(\mathrm{D}=0.0450 \mathrm{kmol} / \mathrm{s}\). A kettle-type reboiler is used. Reflux ratio is \(\mathrm{L} / \mathrm{D}=2.4\).

a. Do tray sizing using the Fair flooding method with \(70 \%\) flooding, \(0.6 \mathrm{~m}\) distance between plates, and default values for the other tray parameters. Find the largest column diameter and the mole fractions of distillate (vapor) and bottoms.

b. Do tray rating for this single-section column with one pass, with weir height of \(0.0508 \mathrm{~m}\), the same diameter calculated in part a, and default values for the other parameters. Leave the Downcomers tab blank. Report the worst downcomer backup (amount and stage) and the weir loading \(\mathrm{m}^{2} / \mathrm{s}\).

c. Design a two-pass system and compare it to the one-pass system.