A Lagrangian algebraic slip mixture model (LASMM) has been developed to study gas-oil-water-solid four-phase flow. In this model the slip velocities between continuous and dispersed phases were derived from the Lagrangian movement equation. Therefore the slip velocities are able to consider the effects of various interfacial forces, such as buoyancy, drag, lift, virtual mass and turbulent dispersion. This model is easily coded through the user defined functions (UDFs) linking to the commercial or open source software. The validations were carried out through the comparisons of the numerical simulations to the experiments of gas-water-solid and gas-oil-water three-phase flows. For the validations of gas-water-solid three-phase flows, the simulation results compared to Michele and Hempel's (2002) experiments on a cylindrical bubble column reactor. The comparisons were carried out by the quantitative comparisons on the axial water velocity under different inlet superficial gas velocities. For the validations of gas-oil-water three-phase flows, the simulation results compared to Descamps et al.'s (2007) experiments on a vertical pipe. The comparisons were performed by the quantitative comparisons of the gas volume fractions at different water cuts under different inlet flow conditions. After the validations, this model was used to study the gas-oil-water-solid four-phase flows in the bubble column reactor. The distributions of the solid phase and gas phase under different situations of oil-in-water and water-in-oil flows were studied. It was found that following the increase of the water cuts, in the oil-in-water flows, the solid particles were pushed away from the center of the column; however the solid particles were absorbed into the center of the column in the water-in-oil flows. The CFD work evaluates the aptness of the LASMM to predict the motion of a gas-oil-water-solid mixture to further the understanding of such complex reaction processes. (C) 2015 Elsevier Ltd. All rights reserved.