CDP$15-K_B$

The oxidation of ethanol is to be carried out in a trickle bed reactor. The reaction is first$-$order with respect to oxygen and zero$-$order with respect to ethanol. The reactor is $30$ cm in diameter and $6m$ long

and the bed porosity is $40\%.$ The $P\frac{d}{A}{l}_2$ O catalyst pellets are $0\mathrm{.}5cm$ in diameter and have a density of $1800k\frac{g}{m^3}.$ The diffusivity of oxygen in ethanol is $4{10}^{-10}\frac{m^2}{s}$ and the equilibrium solubility is

$4{10}^{-2}$kmo$\frac{l}{m^3}$ at reaction conditions. The superficial gas velocity is $10c\frac{m}{s}$ and the corresponding pressure gradient is $30kP\frac{a}{m}.$ The superficial liquid$-$phase velocity is $0\mathrm{.}25c\frac{m}{s}.$ The specific reaction

rate is $0\mathrm{.}03s^{-1}.$ Tortuosity $=3\mathrm{.}9,{}_p=0\mathrm{.}6,=0\mathrm{.}8.$

$($a$)$ Calculate the percent of the total resistance for each transport step.

$($b$)$ Determine the conversion of ethanol.

$($c$)$ Assuming an axial dispersion coefficient of $0\mathrm{.}02c\frac{m^2}{s},$ determine if the plug$-$flow model was a good assumption.