Consider the hydro dealkylation of toluene $($HDA$)$ process to produce benzene. The desired production rate for benzene is $265$ kmol$/$h$.$ Toluene feed is pure, but the feed gas contains $95\%$ hydrogen and $5\%$ methane. The following reactions take place.

Toluene $+$ H$2->$ Benzene $+$ CH$4(1)2$Benzene $$ Diphenyl $+$ H$2(2)$

Based on intrinsic kinetics, the selectivity for benzene $($S$)$ is related to toluene conversion $($x$)$ as S $=10\mathrm{.}0036.$ In order to avoid selectivity loss to diphenyl, it is decided to recycle the

$(1$x$)1\mathrm{.}544$

diphenyl back into the reactor $($rather than taking as byproduct$).$ The equilibrium constant for reaction $(2)$ is $0\mathrm{.}24.$ For this design alternative,

$($a$)$ Draw the corresponding level $2$ and level $3$ process flowsheets. Briefly justify elements in these flowsheets.

$($b$)$ Consider reactor conversion of $0\mathrm{.}75$ and mole fraction of hydrogen in purge as $0\mathrm{.}4.$ Also consider that hydrogen to toluene ratio of $5$:$1($mol to mol$)$ is maintained at the reactor inlet. Perform appropriate material balance and compute level $2$ economic potential.

$($c$)$ The reactor exit stream is vapor and is cooled to $100$ F to obtain vapor$-$liquid split. Using approximate flash calculations, estimate the value of benzene lost through purge.