Problem $5.$ Comparison of Fluidized $($Backmixed Catalyst$)$ vs Fixed$-$bed Reactor

Performance for Catalytic Decomposition $(20$ points$)$

Chemical $R$ is to be produced by the catalytic decomposition of reactant $A,$ and

reaction proceeds at $539C$ and $2$atm with negligible heat effects as follows

$A(g)$catalystR$(g),-r_A^{\text{'}}=k^{\text{'}}{C}_A,k^{\text{'}}={10}^{-2}\frac{m^3}{k}g$ cat $*s$

We want $90\%$ conversion of reactant to product. Catalyst is very expensive and

comes in two sizes, as a $120m$ powder or as $1\mathrm{.}2cm$ pellets, both at the same cost

per $kg.$ The properties of the catalyst are

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

Effective diffusivity of gas in the pellet, $D_{\text{e}\text{f}\text{f}}={10}^{-6}\frac{m^3}{m}$ cat $*s$

We have two choices, to use a packed bed of the large pellets, or a fluidized bed of

powder.

$($a$)$ How many $kg$ of catalyst powder would be needed for a fluidized bed reactor

$($assume mixed flow of gas$)?$

$($b$)$ How many $kg$ of catalyst pellets would be needed for a packed bed reactor

$($assume plug flow of gas$)?$