QUESTION $3$

Question #$3$: $(25$ pts$)$ A column of $1\mathrm{.}0m^2$ cross$-$section and $35m$ height is packed with spherical particles of diameter $10mm$ so as to obtain a bed porosity $()=0\mathrm{.}55.$ A fluid with a density $({}_0)=1\mathrm{.}2k\frac{g}{m^3}$ and viscosity $()=1\mathrm{.}8{10}^{-5}k\frac{g}{m.s}$ flows through the bed at a mass flow rate of $0\mathrm{.}75k\frac{g}{s}.$ The temperature is constant along the length of the column at $270C.$ The entering pressure is $12$atm. Assume solid catalyst density: ${}_c=1453k\frac{g}{m^3}.$

$($a$)$ Calculate the pressure drop in atm as well as in kPa. $)=(101\mathrm{.}33$kPa

$($b$)$ Calculate the catalyst weight $($in $kg)$ required for this column.

$($c$)$ If a second$-$order gas$-$phase reaction $(AB)$ is taking place in this packed$-$bed reactor, calculate the conversion in the absence of pressure drop. $,$ cat.h $($:$)\}$

$($d$)$ Calculate the conversion considering the same pressure drop as in part $($a$).$