As a process engineer you are hired to design a chemical plant to produce $80,000$ tons per annum $($t$/$a$)$ of ethylbenzene from benzene and ethylene. Benzene $($assumed pure$)$ and Ethylene $($containing mole fraction of $0\mathrm{.}93$ ethylene, $0\mathrm{.}07$ ethane$)$ feed are available at $\frac{20}{b}ar$ and $298K.$ Ethane is inert.

It may be assumed that the only reactions occurring are:

$C_6{H}_6{?}_{\text{b}\text{e}\text{n}\text{z}\text{e}\text{n}\text{e}}+C_2{H}_4{?}_{\text{e}\text{t}\text{h}\text{y}\text{l}\text{e}\text{n}\text{e}}\{\begin{array}{c}\text{:}[C_6{H}_5{C}_2{H}_5]\\ & \text{e}\text{t}\text{h}\text{y}\text{l}\text{b}\text{e}\text{n}\text{z}\text{e}\text{n}\text{e}& \end{array}$

$C_6{H}_5{C}_2{H}_5{?}_{\text{e}\text{t}\text{h}\text{y}\text{l}\text{b}\text{e}\text{n}\text{z}\text{e}\text{n}\text{e}}+C_2{H}_4{?}_{\text{e}\text{t}\text{h}\text{y}\text{l}\text{e}\text{n}\text{e}}{C}_6{H}_4(C_2{H}_5{)}_2{?}_{\text{d}\text{i}\text{e}\text{t}\text{h}\text{y}\text{l}\text{e}\text{b}\text{e}\text{n}\text{z}\text{e}\text{n}\text{e}}$

The molar ratio of benzene to ethylene are approximated at $8$:$1,$ in order to minimize yielding tri$-$ and higher ethyl benzene.

The plant should operate for $330$ days in a year, to allow for shutdown and maintenance.

You are required to assess the feasibility of such a process by producing the following:

A conceptual design of the process.

A detailed design of the REACTOR AND ONE other major piece of equipment $($such as a heat exchanger, separator, or other equipment$).$

Calculate mass and energy balances to achieve production in kmo$\frac{l}{h}.$

Calculate conversion of the reactions.