$P5-20$ B The irreversible first$-$order $($wrt partial pressure of A$)$ gas$-$phase reaction

$AB$

is carried out isothermally in a "fluidized" catalytic CSTR containing $50kg$ of catalyst.

Currently, $50\%$ conversion is realized for pure A entering at a pressure of $20$atm. There is virtually no pressure drop in the CSTR$.$ It is proposed to put a PBR containing the same catalyst weight in series with the CSTR$.$ The pressure drop parameter for the PBR$,,$ given by Equation $(5-29)$ is $=0\mathrm{.}018k{g}^{-1}.$ The particle size is $0\mathrm{.}2mm,$ the bed porosity is $40\%,$ and the viscosity is the Fluidized CSTR same as that of air at $200C.$

$($a$)$ Should the PBR be placed upstream or downstream of the CSTR in order to achieve the highest conversion? Explain qualitatively using concepts you learned in Chapter $2.$

$($b$)$ What is the conversion coming out of the first reactor?

$($c$)$ What is the conversion exiting the last reactor? $($Ans$.$: $x=0\mathrm{.}76)$

$($d$)$ What is the pressure at the exit of the packed bed? $($Ans$.$: $P=6\mathrm{.}32$atm $)$

$($e$)$ How would your answers change if the catalyst diameter were decreased by a factor of $2$ and the