You desire $99\%$ recovery of ethane in the distillate and $99\mathrm{.}5\%$ recovery of propane in Multicomponent Distillation $...$ A saturated liquid feed containing methane $(M),$ ethane $(E),$

propane $(P),$ and isobutene $($I$)$ enters a column operating at $1$atm. Use the following data;

You desire $99\%$ recovery of ethane in the distillate and $99\mathrm{.}5\%$ recovery of propane in the bottoms.

The relative volatility given may be assumed to be an average $($of tops and bottoms$)$ for each

component listed.

a$)$ Identify the key components, and

b$)$ Assuming nonkeys do not distribute, estimate distillate and bottoms compositions and flow rates.

c$)$ Use the Fenske equation to find the number of stages necessary at total reflux.

d$)$ Use the Fenske equation to get a revised estimate of the non$-$key component flow rates in the

distillate and bottoms, in other words update the distillate and bottoms compositions.

e$)$ Calculate the minimum reflux using the Underwood equations and the flow rates from part $($b$).$

Hint $/$ Help: Confirm that the Theta root $=3\mathrm{.}2228$ is correct. Use this root to determine $R_{\text{m}\text{i}\text{n}}.$

f$)$ Calculate the total number of stages required for this separation for a reflux ratio of $1\mathrm{.}4R_{\text{m}\text{i}\text{n}}.$

g$)$ Determine, this time using Gilliland $($equations and$/$or graph$),$ an effective $N,R$ combination for

this column.the bottoms. The relative volatility given may be assumed to be an average $($of tops and bottoms$)$ for each component listed.

a$)$ Identify the key components, and

b$)$ Assuming nonkeys do not distribute, estimate distillate and bottoms compositions and flow rates.

c$)$ Use the Fenske equation to find the number of stages necessary at total reflux.

d$)$ Use the Fenske equation to get a revised estimate of the non$-$key component flow rates in the distillate and bottoms, in other words update the distillate and bottoms compositions.

e$)$ Calculate the minimum reflux using the Underwood equations and the flow rates from part $($b$).$

Hint$/$Help: Confirm that the Theta root$=3\mathrm{.}2228$ is correct. Use this root to determine Rmin$-$

f$)$ Calculate the total number of stages required for this separation for a reflux ratio of $1\mathrm{.}4$ R min $.$

g$)$ Determine, this time using Gilliland $($equations and$/$or graph$),$ an effective N$,$ R combination for this column.