You are a process engineer in a petrochemical complex. Your complex has $2\mathrm{.}5\backslash$times $106$ kmol$/$yr of an ethylene$-$rich stream $(96\%$ ethylene, $3\%$ propylene and $1\%$ methane$).$ As such $($relatively$)$ impure ethylene stream cannot be put into ethylene pipeline $($which requires more than $99\mathrm{.}99\%$ purity$),$ the company is exploring a possibility of valorization of this stream. One option is to convert it into ethanol using the following reaction:

Ethylene $+$ W ater $$ Ethanol $(15)$

The chemist working on this reaction reported that the reaction is carried out at high tem$-$ perature $(535-575$ K$)$ and pressure $(68-69$ bar$).$ The reactor ethylene conversion is typically $7\%.$ Furthermore, there is a possibility of subsequent condensation of $2$ ethanol molecules to get diethyl ether via the following reaction:

$2$Ethanol $$ Diethylether $+$ W ater $(16)$

The chemist reported that for every $100$ molecules of ethanol produced by reaction $(15),10$ molecules undergo such condensation via reaction $(16).$ Furthermore, under the reaction conditions, propylene can also react with water to produce isopropyl alcohol via the following reaction:

Propylene $+$ Water $$ Isopropyl alcohol $(17)$

Typical propylene conversion for reaction $(17)$ is $1\%.$ Equilibrium constants for reactions $(15),(16)$ and $(17)$ are $1\mathrm{.}1$ bar$1,0\mathrm{.}7$ and $0\mathrm{.}3$ bar$1,$ respectively. Furthermore, the chemist advised to keep the methane mole fraction at reactor inlet to be less than $10\%$ to prevent coking. As ethanol forms azeotrope with water, the company is planning sell this ethanol$-$water azeotrope $(190$ proof ethanol$)$ with $85\mathrm{.}44\%$ mol ethanol and $14\mathrm{.}56\%$ mol water. You are tasked to explore economic feasibility of this process. For this process,

$($a$)$ Develop level $3$ flowsheet for the given conditions and constraints. You are required to justify the relevant decisions leading to this flowsheet.

$($b$)$ Perform appropriate material balance and compute level $2$ economic potential. If re$-$ quired, you can assume appropriate values of design variables. $[$Hint: There will be $2$ such design variables$]\backslash$table$[[$Component$,$Value $(\frac{\text{\$}}{k}$mol$),$Fuel potential $($GJ$/$kmol$),$Boiling point $(C)$