QUESTION $2$ Answer BOTH parts $($a$)$ and $($b$)$

A reaction $AR$ takes place in a porous spherical catalyst particle with radius $10mm$ and effective diffusivity, $D_{eA}={10}^{-6}\frac{m^3}{ms}.$ The concentration of the reactant outside the particle is $1mo\frac{l}{m^3}.$ The reaction exhibits saturation kinetics and the rate equation is:

$-r_A=\frac{k_1{C}_A}{k_2+C_A}mo\frac{l}{m^3\text{c}\text{a}\text{t}\text{a}\text{l}\text{y}\text{s}\text{t}s}$

$($a$)$ Calculate the effectiveness factor of the catalyst particles under the condition of strong pore diffusion resistance.

$($b$)$ The catalyst particles are packed into a multi$-$tubular column for chemical adsorption of reactant $A.$ The molar flow rate and concentration of $A$ in the feed are $1mo\frac{l}{s}$ and $1mo\frac{l}{m^3}$ respectively. Calculate the number of packed tubes required to achieve $99\%$ conversion of $A.$ The effectiveness factor mav be assumed constant and equal to the value obtained in $($a$).$

Data:

$k_1=1mo\frac{l}{m^3(s)},k_2=1mo\frac{l}{m^3}$

Internal diameter of tubes, $d_t=0\mathrm{.}02m$

Length of tubes, $L_t=10m$

Particle density, $r_p=2500k\frac{g}{m^3}$

Bulk density of packed beds packed bed