Tutorial $6$

Catalyst Deactivation

The catalytic cracking of a gas oil charge. A$,$ to form $C_5+(B)$ and to form coke and dry gas $($ C $)$ is to be carried out in a screw$-$type conveyor moving$-$bed reactor at $900F$ :

e

The reaction can also be written as

$A{k}_1$ Products

The reaction follows $2^{nd}$ order rate law with the following specific reaction rate:

$-r_A^{\text{'}}=0\mathrm{.}6\frac{d{m}^6}{(g)\text{c}\text{a}\text{t}\text{.}\text{m}\text{o}\text{l}\text{.}\text{m}\text{i}\text{n}}{C}_A^2$

The catalytic deactivation is independent of gas$-$phase concentration and follows a $1^{st}-$order decay rate law, with a decay constant of $0\mathrm{.}72mi{n}^{-1}.$ The reactor contains $22$ kg of catalyst that moves through the reactor rate of $10k\frac{g}{m}in.$ the gas is fed at a rate of $30mo\frac{l}{m}in$ at a concentration of $0\mathrm{.}075mo\frac{l}{d}{m}^3.$

Given the decay rate law;

$a=e^{-(\frac{k_d}{U_s})W}$

Determine the conversion that can be achieved in this reactor.