A distillation column with a partial condenser and a partial reboiler is separating 1500.0 kmol/h of a 10.0 mol% ethane, 30.0 mol% n- butane, and 60.0 mol% n-pentane saturated liquid feed at 8.1 atm. The column operates at a constant pressure of 8.0 atm. The distillate is a saturated vapor. In Aspen notation N = 40, and the feed is on stage 25. In an attempt to obtain close to three pure products, a sidestream is withdrawn between the partial condenser and the feed stage. We want a 99.9% recovery of n-pentane in the bottoms (split fraction in bottoms stream > 0.999). Note: Use Petroleum/Wide- boiling convergence in the Configuration tab for the RadFrac Block. List the VLE correlation used.

a. Set distillate flow rate \(\mathrm{D}=150.0 \mathrm{kmol} / \mathrm{h}\) and side withdrawal flow rate \(\mathrm{S}=450.0 \mathrm{kmol} / \mathrm{h}\) (these are appropriate values if the separation is perfect-although the separation is not and cannot be perfect). Put the side withdrawal on stage 12 and make it a liquid. Increase the reflux ratio until the mole fraction of ethane in the distillate is \(>0.98\) (remember that distillate is a vapor). Record the reflux ratio.
b. To improve the ethane mole fraction in the distillate to \(>0.99\), first try increasing the reflux ratio. Find the value necessary and report this reflux ratio.
c. The reflux ratio required for part \(\mathrm{b}\) is rather high. Reduce the reflux ratio to 20.0. Now set \(\mathrm{D}=150.0-\Delta\) and \(\mathrm{S}=450.0+\Delta\). Find the \(\Delta\) value that gives ethane mole fraction in the distillate \(>\) 0.99 . Report \(\mathrm{D}, \mathrm{S}\), and mole fractions in the three products. The reason reducing \(\mathrm{D}\) and increasing \(\mathrm{S}\) works is since the liquid in the sidestream is in equilibrium with the vapor that carries ethane to the distillate, there must be some ethane in the sidestream. Thus, the sidestream is not pure \(\mathrm{n}\)-butane, but our original values for \(\mathrm{D}\) and \(\mathrm{S}\) assumed it was pure. Because there is ethane in the sidestream, the value of \(\mathrm{D}=150.0\) is too large, which forces some n-butane up into the distillate.
d. Keeping everything the same as in part \(\mathrm{c}\), except changing the sidestream to a vapor, run the separation again. Report the mole fractions of the three products (remember to use y values for the sidestream). Why is the separation significantly worse than with a liquid sidestream?
e. We could also put the sidestream below the feed stage (in this case, the feed stage would be closer to the condenser). However, this configuration will not work as well for this separation. Why not?