McCabe$-$Thiele method vs$.$ Aspen simulation $(40$ points$)$

We are interested carrying out the separation of $50-50$ mixture of benzene and toluene as

summarized in Table $1$ using a distillation column shown in Figure $1.$

a$)$ Employ McCabe$-$Thiele method to estimate $R_{\text{m}\text{i}\text{n}}$ needed for the separation

b$)$ For $R$ such that $\frac{R}{R}$min$=3,$ use McCabe$-$Thiele method analytically or graphically to

estimate number of stages and optimal feed stage location

c$)$ Model the separation in Aspen to compute the stage by stage compositions for $\frac{R}{R}$min$=3$

and computed number of stages rounded up to the nearest integer $($if McCabe$-$Thiele method

requires $4\mathrm{.}6$ stages, use $5$ stages in Aspen$).$ Assign feed stage in Aspen to be the optimal feed

stage computed in part b$.$ Report the values of distillate and bottoms purity computed via Aspen

and compare it against that computed by McCabe$-$Thiele method.

d$)$ Plot the benzene composition in the liquid leaving each stage of the column computed via

McCabe$-$Thiele method and the Aspen simulation.

What is your comment on these results obtained in part $c$ and $d?$

Figure $1.$ A process to separate a $50\%$

benzene$-50\%$ toluene mixture into a

benzene$-$rich and toluene$-$rich stream

Table $1.$ stream information of the process in Figure $1$