A Lagrange-Euler-Euler computational fluid dynamic approach was developed to represent the evolution of two-phase pressure gradients in trickle-bed reactors undergoing deposition of colloidal/non-colloidal fines under deep-bed filtration conditions. The ballistic trajectory equation to analyze fines interception was extended to two-phase flows using the inclined slit as the basic collector geometry. New equations for the collection efficiencies and filter coefficients were established for the various filtration stages encountered in single-phase flow and trickle flow regime both for monolayer and multilayer collection mechanisms. These slit-based expressions were established for non-polar and nonelectrolytic petroleum-like liquids where there is a need for the refining industry to model deep-bed filtration in multiphase flow. By embedding the new collection efficiency and filter coefficient expressions in an unsteady-state multidimensional computational fluid dynamics code, the deep-bed filtration process in trickle flow reactors was simulated and the increase of pressure drop during plugging was explained by increasing local specific surface area and decreasing local porosity due to fines deposition. The simulations were benchmarked using the experimental pressure drop data and observations of [M.R. Gray, N. Srinivasan, J.H. Masliyah, Pressure build-up in gas-liquid flow through packed beds due to deposition of fine particles, Can. J. Chem. Eng. 80 (2002) 346] in their study of kaolinite-kerosene-air flows in trickle-bed reactors. (C) 2004 Elsevier B.V. All rights reserved.