Cumene $($isopropyl benzene$)$ is an important petrochemical as it is a raw material for This is the cost of propylene feed gas with propane impurity.

The selectivity for cumene $(S)$ as a function of propylene conversion $(x)$ is given by

$S=1-0\mathrm{.}0171x-0\mathrm{.}0114x^2$the production of phenol. Cumene is manufactured by reaction of benzene and propylene. Unfor$-$ tunately, cumene can get alkylated further to produce undesired p$-$diisopropyl benzene which has only fuel value. In order to selectively get cumene, excess benzene is used in the reactor. The following gas phase exothermic reactions are of interest $($temperature around $350-450$ C$,$ pressure $25$ bar$).$

Benzene $+$ propylene $->$ Cumene $(12)$ Cumene $+$ propylene $->$ p $$ diisopropylbenzene $(13)$

You are tasked to explore economic feasibility of this process. Consider that the desired production rate for cumene is $100$ kmol$/$h$.$ Benzene feed is pure, however, propylene feed has $5\%$ propane as impurity. Consider that the reactor propylene conversion is $0\mathrm{.}8.$ Mol fraction of propylene in purge can be taken as $0\mathrm{.}1.$ Ratio of benzene to propylene at the reactor inlet is $2.$ For this process,

$($a$)$ Develop level $2$ and level $3$ flowsheets for the process. You are required to discuss pros and cons of the relevant decisions leading to these flowsheets with respect to this process.

$($b$)$ Perform appropriate material balance and compute level $2$ economic potential. You can use the following data for calculations.