Ethylbenzene is an important petrochemical as it is a raw material for the production of styrene. Ethylbenzene is manufactured by reaction of benzene and ethylene. Ethylbenzene can get alkylated further to produce undesired diethylbenzene which has only fuel value. For$-$ tunately, diethylbenzene can react with benzene to product ethylbenzene through transalky$-$ lation reaction. The following gas phase exothermic reactions are of interest $($temperature around $400$ C$,$ pressure $20$ bar$).$

Consider that the desired production rate for Ethylbenzene is $90$ kmol$/$h$.$ Ethylene feed has $7\%$ Ethane as impurity. Benzene feed contains $2\%$ toluene impurity. Toluene can react with Ethylene, at the reaction conditions, to give Ethylbenzene by the following reaction.

T oluene $+2$ Ethylene $->$ Ethylbenzene $+$ P ropylene $(21)$

For this process,

$($a$)$ Develop level $2$ flowsheet for the process. You are required to discuss pros and cons of the relevant decisions leading to the flowsheet with respect to this process.

$($b$)$ Set up material balance to compute all the input and output flows. Based on these equations, identify key design variables at level $2.$

$($c$)$ Develop level $3$ flowsheet for the process. You are required to discuss pros and cons of the relevant decisions leading to the flowsheet with respect to this process.