Catalyst Effectiveness Factor & Thiele Modulus Calculator
Evaluate pore diffusion resistance, Thiele modulus (Φ), internal effectiveness factor (η), and Weisz-Prater criterion for spherical pellet catalysts.
Pellet Geometry & Diffusivity
Thiele Modulus & Effectiveness Factor
Recommended Tools & Equipment
Tested hardware and components for high reliability
Pore Diffusion & Heterogeneous Catalysis
In heterogeneous catalysis, porous catalyst pellets provide massive active surface area ($100 - 400\text{ m}^2/\text{g}$). However, reactant molecules must diffuse through labyrinthine micropores to reach internal catalytic sites. The Thiele Modulus ($\Phi$) represents the ratio of intrinsic surface reaction rate to pore diffusion rate: $$\Phi = R_p \sqrt{\frac{k_v}{D_e}}$$
Weisz-Prater Criterion ($C_{WP}$)
When intrinsic rate constants are unknown, the Weisz-Prater parameter evaluates internal diffusion resistance using solely measured observable quantities: $$C_{WP} = \frac{-r'_{obs} \rho_c R_p^2}{D_e C_{As}} = \eta \Phi^2$$ If $C_{WP} \ll 1$, internal diffusion resistance is negligible ($\eta \approx 1.0$). If $C_{WP} > 1$, severe internal concentration gradients exist, and the catalyst core remains unutilized.