Problem $4$ I need explanations and details for answers.

$($Development of PFD and Economic Performance$)$

The hydrodealkylation of side$-$chain aromatics to non$-$substituted parents is a major process in petrochemical processes $[$for example, benzene is the starting raw material for producing a top commodity chemical like isopropyl benzene $($also called cumene$)$ which accounts for about $8\%$ of the total worldwide propylene consumption. Cumene is mostly used to produce phenol and acetone$].$

The conversion of toluene to benzene is carried out via the reaction:

$C_6{H}_5-C{H}_3+H_2{C}_6{H}_6+C{H}_4$

at $30-\frac{50}{b}ar,$ either thermally at $550-700C$ or over a suitable catalys. Thermally, the conversion is $60-80\%$ with selectivity ~~$95\%[$of course, selectivity is higher with catalyst$].$ Other significant side reaction produces diphenyl via reaction:

$2C_6{H}_6{C}_{12}{H}_{10}+H_2$

$($i$)$ Feeds are introduced by mixing pure toluene and hydrogen with $5\%$ methane. Hydrogen is recycled back to the process but to avoid accumulation of methane in process some purge stream of $\frac{H_2}{?}$ methane is added to the process from which valuable methane is recovered via membranes.

$($ii$)$ All toluene is recycled. But ratio $H_2/$toluene of $5$ is maintained at reactor inlet to avoid $C$ formation. We will assume reaction takes place at $40$ bar and temperature of $600C.$

$($iii$)$ Raw feeds will be heated $($in furnace$)$ before introduction to the plug flow reactor and the reactor outlet products will be cooled before sending them to a single stage flash unit. A simulation of the flash unit at $40$ bar & $305K$ using Peng$-$Robinson EOS gives the $K$ values in the table $($table includes operating data too$).$

$\backslash$table$[[$Flow rate$**,$Input$*,(),(),(),$K$-$value$],[H_2,134\mathrm{.}5,37\mathrm{.}0,714\mathrm{.}3,616\mathrm{.}8,7\mathrm{.}23e+01$