Effectiveness factor for catalyst pellets of non-basic shapes

Abstract

The shape of a catalyst pellet affects the overall rate of reaction when the reaction is influenced by mass and heat transfer processes. While traditional modeling approaches often assume simple, basic pellet shapes (such as spheres or cylinders), this work focused on the numerical modeling of catalyst pellets with non-basic geometries, which are commonly used in industry. Using numerical techniques, the effectiveness factors of catalyst pellets with various non-basic shapes as functions of the Thiele modulus were investigated. Results indicate that the effectiveness factors of catalyst pellets of non-basic shapes, such as a hollow cylinder, cone, parallelepiped and finite cylinder with hemispherical caps, may be given by a single relationship with a generalized Thiele modulus λ_p, much as for the cases of basic shapes of a sphere, a long cylinder and a flat slab. This definition of the generalized modulus further provides unified numerical criteria for negligible effects of pore diffusion as λ_p ≤ 0.3 where $E\approx 1$ within ∼10 % error (or λ_p ≤ 0.1 if an accuracy within ∼1 % is required) and for reaching large λ_p asymptotic condition as λ_p ≥ 3 where $E\approx \frac{1}{{\lambda }_p}$ within ∼10 % error (or λ_p ≥ 10 if an accuracy within ∼1 % is required). Finally, for any shape of the catalyst pellets, the effectiveness factor can be expressed by the following single equation:

$E=\frac{1}{\sqrt{1+{\lambda }_p^2}}$