In HDA process a column separating $H_2,C{H}_4$ from Benzene. Column feed is $400mo\frac{l}{h}r$ and mole fraction $x_{H2}=0\mathrm{.}0055$;$x_{CH4}=0\mathrm{.}0324$;$x_{\text{B}\text{e}\text{n}2}=0\mathrm{.}961$;$x_{\text{T}\text{o}\text{l}}=0\mathrm{.}0011$; Assume $99\mathrm{.}85\%$ recovery of benzene from feed at the bottom of the column and $100\%$ recovery of $H_2$ and $C{H}_4$ at column overhead. M&S index $800.$ Textbook $2$ for additional information.

a$.$ Estimate the annual loss of benzene if Equilibrium value of Benzene $K_{\text{B}\text{e}\text{n}\text{z}}=0\mathrm{.}03$ by assuming liquid in the reflux drum is pure benzene, benzene price is $10\frac{\text{\$}}{m}ol$ and designed for $8000h\frac{r}{?}$ year.

b$.$ Estimate the column overhead vapor distillate flow $($D$),$ Liquid flow $($L$)$ and vapor $(y_i),$ liquid $(x_i)$ composition if the value of equilibrium $K_{H2}=550$;$K_{CH4}=240$ and $K_{\text{B}\text{e}\text{n}\text{z}}=0\mathrm{.}04.$

c$.$ Estimate the annual cost of the column by assuming following, Relative volatility is $72$; Reflux ratio $R=2R_{\text{m}\text{i}\text{n}}$;$F=0\mathrm{.}3$;$H_0=20ft$ for column top and bottom space. $\frac{M}{M_G}=78$;$Tb=400oF$ and $P=150$ psia.

$20$

d$.$ Calculate the Economic potential, if condenser and reboiler area $50f{t}^2$ and $40f{t}^2$ respectively. Cooling water available at $0\mathrm{.}06\frac{\text{\$}}{1000}$gal,$T=30F$ and $Q_{\text{c}\text{o}\text{n}\text{d}}=3038Bt\frac{u}{h}r.$ Steam available at $2\frac{\text{\$}}{1000}lb$ and Qreboiler $=17\mathrm{.}2Bt\frac{u}{h}r.$ assume no purge losses.