A distillation column separates a binary mixture of $2-$butanol $($component $1)$ and $2-$propanol

$($or isopropyl$-$alcohol, component $2)$ into almost pure $2-$butanol at the bottom $(98$ mol$\%$ pure$)$ and almost pure $2-$propanol in the distillate $(98$ mol$\%$ pure$).$ The feed stream $(10$ kmol$/$hr$)$ is a saturated liquid with $45$ mol$\%2-$propanol.

$($a$)$ Determine the proper fluid package needed to model this distillation problem in Aspen. Estimate the Relative volatility between $2-$butanol and $2-$propanol using the heuristic formula. Compare the x$-$y diagram generated based on the CRV assumption and the x$-$y diagram generated from Aspen simulation.

$($b$)$ Using McCabe$-$Thiele method, determine the minimum number of stages at total reflux, the minimum reflux ratio, the number of equilibrium stages when the column is operated at $20\%$ above the minimum reflux, the feed stage location.

$($c$)$ Assuming a tray efficiency of $70\%$ and using all design heuristics, estimate the diameter and height of the column, as well as the pressure drop within the distillation column.

$($d$)$ Simulate the distillation process in Aspen HYSYS$.$ Report liquid composition profile within the column, temperature profile within the column, and reboiler and condenser heat duties.