Ethylbenzene is converted to styrene in the catalytic dehydrogenation reaction:

$C_8{H}_{10}(g)C_8{H}_8(g)+H_2,H_{rxn}^0(600C)=124\mathrm{.}5k\frac{J}{m}ol$

A flowchart of simplified version of the commercial process is shown here:

Fresh and recycled liquid ethylbenzene combine and are heated from $25C$ to $500C(A),$ and the heated ethylbenzene is mixed adiabatically with steam at $700C(B)$ to produce the feed to the reactor at $600C($The steam suppressed undesired side reactions and removes carbon deposited on the catalyst surface$).$ A once$-$through conversion of $35\%$ is achieved in the reactor $($C$),$ and the products emerge at $560C.$ The product steam is cooled to $25C($D$),$ condensing essentially all of the water, ethylbenzene, and styrene and allowing hydrogen to pass out as a recoverable by$-$product of the process.

The water and hydrocarbon liquids are immiscible and are separated in a settling tank decanter $($E$).$ The water is vaporized and heated $(F)$ to produce the steam that mixes with the ethylbenzene feed to the reactor. The hydrocarbon stream leaving the decanter is fed to a distillation tower $($G$),$ which separates the mixture into essentially pure styrene and ethylbenzene, each at $25C$ after cooling and condensation steps have been carried out. The ethylbenzene is recycled to the reactor preheater, and the styrene is taken off as a product.

a$.$ Calculate on the basis of $100k\frac{g}{h}$ styrene produced the required fresh ethylbenzene feed rate, the flow rate of recycled ethylbenzene, and the circulation rate of water, all in $mo\frac{l}{h}($Assume $P=1$atm.

b$.$ Calculate the required rates of heat input or withdrawal in $k\frac{J}{h}$ for the ethylbenzene preheater $(A),$ steam generator $(F),$ and reactor $(C).$

c$.$ Suggest possible ways to improve the energy economy of this process.

Physical Property Data:

Ethylbenzene:

$(C_p{)}_{\text{l}\text{i}\text{q}\text{u}\text{i}\text{d}}=182\frac{J}{\text{m}\text{o}\text{l}-C}$

$(H_v)=36k\frac{J}{m}olat136C$

$(C_p{)}_{\text{v}\text{a}\text{p}\text{o}\text{r}}=118+0\mathrm{.}3T(C)$

Styrene

$(C_p{)}_{\text{l}\text{i}\text{q}\text{u}\text{i}\text{d}}=209\frac{J}{\text{m}\text{o}\text{l}C}$

$(H_v)=37\mathrm{.}1\frac{kJ}{\text{m}\text{o}\text{l}}at145C$

$(C_p{)}_{\text{v}\text{a}\text{p}\text{o}\text{r}}=115+0\mathrm{.}27T(C)$