Reading$/$References: Ch $7[$Seader$,$ Henley, & Roper $($SHR$)$ Textbook$]$

n$-$Octane $/$ n$-$Decane Separations

A saturated liquid feed of $1000mo\frac{l}{h}r$ containing $42$mole$\%n-$octane is to be fractionated at $101\mathrm{.}325$kPa $($abs$)$ in order to form a distillate containing $94$ mole $\%$ n$-$octane and a bottoms product of $10$ mole $\%n$ octane. Assuming Raoult's Law behavior applies the associated vapor$-$liquid equilibrium has been modeled $($provided below$).$

The column is originally designed for a reflux ratio of $2$:$1.$

a$)$ Calculate the flowrates $(mo\frac{l}{h}r$ of the distillate and bottoms.

b$)$ Determine the minimum reflux ratio, RMIN and the minimum number of theoretical trays at total reflux.

c$)$ Determine the theoretical number of trays and the feed tray number for the specified operational design.

d$)$ Determine the boil$-$up rate $($vapor returned to column compared to bottoms flowrate$).$

Reconsider the design if the feed enters with thermal value, $q=0\mathrm{.}20$ and answer the following $---$

e$)$ Determine the minimum reflux ratio, RMIN and the minimum number of theoretical trays at total reflux.

f$)$ Determine the theoretical number of trays and the feed tray number for the specified operational design.

g$)$ Determine the boil$-$up rate $($vapor returned to column compared to bottoms flowrate$).$

Now consider the following situation: Assume you start with the original design as specified by solutions in parts $($a$)$ through $($d$)$ above. The feed suddenly changes from the saturated liquid to a mixed vapor$-$liquid condition with $q=0\mathrm{.}2.$ The number of trays determined for the original design $($determined in part $($c$))$ does not change, so $...$

h$)$ If the boil$-$up ratio does NOT change $....$

i$)$ What distillate n$-$octane mole fraction results?

ii$)$ Onto what plate does the feed enter?

i$)$ Now if the distillate reflux were to remain the same $...$

i$)$ What bottoms mole fraction results?

ii$)$ Onto what plate does the feed enter?

j$)$ Discuss $($compare$,$ etc$)$ the results found in part $($h$)$ and $($i$).($Discussion question$)$

$\backslash$table$[[T(C),$Vapor Pressure,$x,y$