#### 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 \(r = R\), \(C_A = C_{As}\,\).