A multistage fixed bed catalytic reactor was to be designed for the dehydrogenation of ethylbenzene $(C_8{H}_{10}=A)$ into styrene $(C_8{H}_8=S),$ using excess steam to control the reaction temperature. The goal is to reach $90$ percent conversion of ethylbenzene, using a multi$-$stage system if necessary. A new catalyst has been developed, which allows operation at temperatures as high as $1100K,$ compared to the previous catalyst which would undergo sintering at $1000K.$ Assuming that the pseudohomogeneous onedimensional plug flow model is valid, and that each stage operates isobarically:

a$.$ What is the minimum amount of $($new$)$ catalyst required for this process? If you integrate numerically, use a step size of $0\mathrm{.}3.$

b$.$ If the reactor operates adiabatically, how many stages would be required in order to achieve the $90\%$ conversion target with the new catalyst? Assume that the outlet temperature from each stage is $25C$ from equilibrium temperature.

c$.$ How much less catalyst is required with the new catalyst versus the old catalyst? A reasonable estimate is sufficient $($but state your assumptions$)$

Data: $F_{AO}=100mo\frac{l}{s}$;$F_{H2O}=1400mo\frac{l}{s}$;$P_o=\frac{2\mathrm{.}0}{b}ar$ ;$H_{RA}=126k\frac{J}{m}ol$;$c_P=2\mathrm{.}4J{g}^{-1}{K}^{-1}$;

bar;

Graph provided on page $10.$

Numerical answers:

a$)15\mathrm{.}0$ tonnes, by trapezoidal rule