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