Ethylene can be produced by the thermal cracking of ethane

$C3H6C2H4+H2$

$C2H60\mathrm{.}5C2H4+Ch4$

The reaction takes place at $1500$ of and $50$ psia. We desire to produce $875mo\frac{l}{h}r$ of ethylene with $75\%$ purity. Assume that the selectivity is given by

$S=\frac{mol{C}_2{H}_4\text{F}\text{o}\text{r}\text{m}\text{e}\text{d}}{mol{C}_2{H}_6\text{C}\text{o}\text{n}\text{v}\text{e}\text{r}\text{t}\text{e}\text{d}}=1-\frac{0\mathrm{.}0381}{(1-x{)}^{0\mathrm{.}241}}$

The ethane feed contains $5\%CH4$ and cost $$\frac{1\mathrm{.}65}{m}ol.$ Ethylene at $95\%$ composition is worth $$\frac{6\mathrm{.}15}{m}ol.$ Fuel is worth $$4{10}^{-6}$ per Btu.

Draw the input output flowsheet and plot economic potential.