Design a horizontal flash drum to separate \(15,000 \mathrm{~kg} / \mathrm{h}\) of a feed with the following mass fractions: methane 0.21 , propane 0.39 , n-butane 0.24 , i-butane 0.11 , and n-pentane 0.05 . The feed is at \(0.0^{\circ} \mathrm{C}\) and a pressure just high enough that it is all liquid. The drum pressure is \(4.0 \mathrm{~atm}\), and the drum is adiabatic (heat duty \(=0\) ).

a. Find the minimum feed pressure (to within a whole number of atm) that keeps the feed a liquid. Report this pressure and the VLE correlation used, and use this as the feed pressure for the flash calculation.

b. Find \(\mathrm{L}, \mathrm{V}\) (in \(\mathrm{kg} / \mathrm{h}\) and in \(\mathrm{kmol} / \mathrm{h}\) ), \(\mathrm{y}_{\mathrm{i}}, \mathrm{x}_{\mathrm{i}}\) (in mole fractions), and \(\mathrm{T}_{\text {drum }}\) (in \(\left.{ }^{\circ} \mathrm{C}\right)\).

c. If a horizontal drum is used, find \(\mathrm{D}_{\min }\). If the liquid holding time is 9 minutes, and the ratio of the drum length to diameter is \(\mathrm{h} / \mathrm{D}=6\), find the surge time that can be accommodated.