#### Diffusion and Reaction in Porous Catalysts: Screencasts

Uses a shell balance to determine the rate of product formed with respect to time for a spherical catalyst.

We suggest that after watching this screencast, you list the important points as a way to increase retention.

Calculates the concentration gradient and the effectiveness factor for a catalyst pore with catalyst on the walls by carrying out a differential material balance.

We suggest that after watching this screencast, you list the important points as a way to increase retention.

##### Important Equations:

For a first-order reaction:

$\eta_{sphere} = \frac{3}{\phi ^2} (\phi coth \phi \,- \, 1)$

$\phi = R \left( \frac{k}{D_e} \right) ^{\frac{1}{2}}$

where $$\eta _{sphere}$$ = effectiveness factor (or internal effectiveness factor) for a sphere

$\eta = \frac{rate\,\, of\,\, reaction\,\, in\,\, catalyst\,\, pellet}{rate \,\,of\,\, reaction\,\, in\,\, pellet \,\,if\,\, C_A = C_{As}}$

where $$C_A$$ = reactant concentration

$$C_{As}$$ = reactant concentration at $$r = R$$

where $$r$$ = radius within the catalyst pellet

$$\phi$$ = Thiele modulus

$\phi = \frac{reaction \,\,rate}{diffusion\,\, rate}$

$$R$$ = particle radius (cm)

$$k$$ = first order rate constant ($$s^{-1}$$)

$$D_e$$ = effective diffusivity ($$\frac{cm^2}{s}$$)

rate of raction in catalyst pellet = rate of diffusion into the pellet = $$4\Pi RD_e\, \left.\frac{dC_A}{dr}\right|_{r=R}$$

At $$r = R$$, $$C_A = C_{As}\,$$.