in order to rationally improve a packed$-$bed reactor, it is helpful to know if the productivity of the system

is limited by external mass transfer, or internal mass transfer, or both, or neither.

Use the Mears and Weisz$-$Prater criteria to make this determination for the $2$ cases below.

For both cases use:

$$ Density of solid catalyst bead $=1$e$6$ g$/$m$3$

$$ Catalyst bead diameter dp $=3$e$-3$ m

$$ Assume $1$st order rxn

$$ Void fraction in packed bed $=0\mathrm{.}5$

$$ v$0=1$e$-6$ m$3/$s

$$ Reactor tube radius $=2$e$-2$ m

Assume the pores are large enough that the diffusion coefficient inside the bead is about the same as

outside the bead.

Case $1$:

$$ gas phase CA$0=1$e$-3$ mole m$-3$

$$ measured $-$rA $=2$e$-9$ mole gcat$-1$ s$-1$

$$ Gas kinematic viscosity $=1$e$-5$ m$2/$s

$$ Diffusion coefficient of A in gas: D$=2$e$-6$ m$2/$s

Case $2$:

$$ liquid phase C A$0=1$ mole m$-3$

$$ measured $-$rA $=2$e$-7$ mole gcat$-1$ s$-1$

$$ Liquid kinematic viscosity $=1$e$-6$ m$2/$s

$$ Diffusion coefficient of A in liquid: D$=2$e$-9$ m$2/$s