In HDA process a column separating $H_2,C{H}_4$ from Beazene. Column feed is $400mo\frac{l}{h}r$ and mole fraction $x_{H2}=0\mathrm{.}0055$;$x_{CH}=0\mathrm{.}0324$;$x_{snn}=0\mathrm{.}961$;$x_{\text{T}\text{a}\text{l}}=0\mathrm{.}0011$; 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. MES index $800.$ Textbook $2$ for additional information.

a$.$ Estimate the annual loss of benzene if Equilibrium value of Benzene $K_{\text{B}\text{e}\text{r}}=0\mathrm{.}03$ by assuming liquid in the reflux dram is pure benzene, benzene price is $\frac{105}{m}ol$ and designed for $8000hr$ year.

b$.$ Estimate the column overhead vapor distillate flow $($D$),$ Liquid flow $($L$)$ and

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vapor $(y),$ liquid $(x)$ composition if the value of equilibrium $K_{H2}=550$;$K_{CH}=240$ and $K_{\text{B}\text{e}\text{s}\text{s}}=0\mathrm{.}04.$

c$.$ Estimate the annual cost of the column by assuming following.

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Relative volatility is $72$ ; Reflux ratio $R-2R$ mis; $H=0\mathrm{.}3$;$H_0=20ft$ for column top and bottom space $\frac{M}{M}o=78$;$Tb=400$ oF and $P=150$ psia.

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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$$$1000$gal,$T=30F$ and $Q_{\text{c}\text{a}\text{n}\text{d}}=3038Bt\frac{u}{h}r.$ Steam available at $2\frac{\text{\$}}{1000}lb$ and Qreboiler $=17\mathrm{.}2Bt\frac{u}{h}r.$ assume no purge losses.

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