$(50$ marks$)$ A multistage fixed bed catalytic reactor was to be designed for the dehydrogenation

of ethylbenzene $(C_8{H}_{10}=A)$ into styrene $(C_8{H}_8=S),$ in the presence of steam. The Thiele modulus

for the catalyst is $1\mathrm{.}2,$ assumed to be constant. Eighty percent conversion of ethylbenzene is desired.

The maximum operating temperature is $1075K,$ dictated by sintering of the catalyst.

a$)$ Assuming adiabatic operation, how many stages will be required to achieve $80\%$

conversion of ethylbenzene, given that the outlet temperature from each stage differs from

the equilibrium temperature by $25K?$ Show the operating lines on the diagram on the next

page. Provide the inlet and outlet conversion and temperature for each stage.

b$)$ If $30$ percent conversion is achieved in the first stage of this system, how much catalyst is

required, assuming adiabatic, isobaric operation and that the pseudohomogeneous one$-$

dimensional plug flow model is valid. Use a step size of $0\mathrm{.}10$ for the fractional conversion.

c$)$ Identify and justify your preferred mode of operation if your goal is to minimize the catalyst

requirement.

Data: $F_{Ao}=100mo\frac{l}{s}$;$F_{H2O}=1200mo\frac{l}{s}$;$P_o=\frac{2\mathrm{.}0}{b}ar$ ;$H_{RA}=126k\frac{J}{m}ol$;$c_P=2\mathrm{.}4J{g}^{-1}{K}^{-1}$;