Q $2.$ Consider the hydro dealkylation of toluene $($HDA$)$ process to produce benzene. The desired

production rate for benzene is $265$kmo$\frac{l}{h}.$ Toluene feed is pure, but the feed gas contains

$95\%$ hydrogen and $5\%$ methane. The following reactions take place.

Toluene $+H_2$ Benzene $+C{H}_4$

$2$Benzene $$ Diphenyl $+H_2$

Based on intrinsic kinetics, the selectivity for benzene $($S$)$ is related to toluene conversion $(x)$

as $S=1-\frac{0\mathrm{.}0036}{(1-x{)}^{1\mathrm{.}544}}.$ In order to reduce the excess hydrogen feed, it is decided to separate the

recycle gas $($instead of simple recycle and purge$).$ To this end, a membrane separation unit

is installed which takes the flash vapor and separates it into $95\%$ hydrogen enriched stream

$($similar to feed gas$)$ and purge stream of pure methane. For this design alternative,

$($a$)$ Consider that reactor conversion is $0\mathrm{.}7$ and 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.

$($b$)$ The reactor outlet temperature has a maximum limit of $1300F.$ Assess the feasibility

of adiabatic operation. Heat of reaction $(1)$ is $-21530Bt\frac{u}{m}ol.$ Assume negligible heat

effects for reaction $(2).$ Consider that reactor inlet temperature is $1150F.$

You can use the following data for calculations.

$***$ This is the cost of feed gas with $95\%$ hydrogen in it$.$