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 $900F$ :

This cracking of gas oil can also be written as

$A{k}_1$ Products

While pure hydrocarbons are known to crack according to a first$-$order rate law, the fact that the gas$-$oil exhibits a wide spectrum of cracking rates gives rise to the fact that the lumped cracking rate is well represented by a second$-$order rate law $($see Web Problem CDP$5-H_B)$ with the following specific reaction rate: ${?}^{31}$

$-r_A^{\text{'}}=600\frac{(dm{)}^6}{((kg)cat)(mol)(min)}{C}_A^2$

The catalytic deactivation is independent of gas$-$phase concentration and follows a first$-$order decay rate law, with a decay constant, $k_d$ of $0\mathrm{.}72$ reciprocal minutes. The feed stream is diluted with nitrogen so that as a first approximation,

${?}^{31}$ Estimated from V$.$ W$.$ Weekman and D$.$ M$.$ Nace, AIChE J$.,16,397(1970).$

Catalysis and Catalytic Reactors

Chapter $10$

volume changes can be neglected with reaction. The reactor contains $22kg$ of catalyst that moves through the reactor at a rate of $10k\frac{g}{m}in.$ The gas$-$oil is fed at a rate of $30mo\frac{l}{m}in$ at a concentration of $0\mathrm{.}075mo\frac{l}{d}{m}^3.$ Determine the conversion that can be achieved in this reactor.

$($PLESE SOLUTION THIS QUSTION IN EULER METHOD $)$

$($AND PLESE DRAW $)$