The finite element method (FEM) is used to solve the diffusion-reaction equation for spherical particles that are partially wetted by the liquid reagent in a trickle-bed reactor. Boundary conditions are specified using true wetting geometries from photographs of spherical particles that were partially wetted under trickle-flow conditions. Three types of reactions were investigated: completely liquid-limited reactions, completely gas-limited reactions, and reactions that are dependent on both the gas and the liquid reagent, following elementary kinetics. The study is limited to spheres, since wetting geometries were only available for these particles. Both monodispersed and eggshell catalysts were simulated. On the basis of the results, existing models for trickle-bed pellet efficiency factors were verified and models are proposed for the prediction of reaction rates in a partially wetted eggshell and monodispersed catalysts for gas-limited reactions, liquid-limited reactions, and elementary reactions for which both gas- and liquid-reagent concentrations are of importance.