In HDA process a column separating H$\_\{2\}$ C$*$H$\_\{4\}$ from Benzene. Column feed is $400$ mol$/$hr and mole fraction X H$2=0\mathrm{.}0055$ X CH$4=0\mathrm{.}0324$; X Bmx $-0\mathrm{.}961$; X Tol $=0$ ; Assume $99\mathrm{.}85\%$ recovery of benzene from feed at the bottom of the column and $100\%$ recovery of H$\_\{2\}$ and CH$4$ at column overhead. M&S index $800.$ Textbook $2$ for additional information.

a$.$ Estimate the annual loss of benzene if Equilibrium value of Benzene K Iant $=0\mathrm{.}03$ by assuming liquid in the reflux drum is pure benzene, benzene price is $10$ $$/$mol and designed for $8000$ hr$/$year$.$

b$.$ Estimate the column overhead vapor distillate flow $($D$),$ Liquid flow $($L$)$ and vapor $($yi$),$ liquid $($xi$)$ composition if the value of equilibrium K H$2=550$; K CH$4=240$ and K Benz $=0\mathrm{.}04.$

c$.$ Estimate the annual cost of the column by assuming following, Relative volatility is $72$; Reflux ratio R$=2$R min ; mu$\_\{$F$\}=0\mathrm{.}3$ H$\_\{$o$\}=20$ft for column top and bottom space.M M$\_\{$G$\}=78$ Tb $=400$ oF and P$150$ psia.

d$.$ Calculate the Economic potential, if condenser and reboiler area $50$f $*$ t $^2$ and $40$ ft respectively. Cooling water available at $0\mathrm{.}06$ $$/1000$ gal, Delta$*$T $=30$ deg$*$ F and $3038$ Btu$/$hr$.$ Steam available at $2$ $$/1000$ lb and Qreboiler $=17\mathrm{.}2$Btu $/$ h $*$ r $.$ no purge losses.