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Three immiscible fluids systems are often encountered in energy and environmental disciplines, especially in the oil exploration field. It is essential to enhance oil recovery (EOR) by identifying the three-phase fluid flow mechanism of oil-gas-water system in complex geological structures. In the present study, a lattice Boltzmann (LB) color gradient model for three immiscible fluid flow in three-dimensional porous media is employed and validated using five benchmarks (i.e., the multiphase spinodal decomposition; the multiphase Young-Laplace test; the liquid lens; contact angles and 3D channel layered three-phase fluid flow). The effects of wettability, viscosity ratio (M) and capillary number (Ca) on the relative permeability curves are analyzed in detail. When the wetting condition is enhanced, the results indicate that the relative permeability of non-wetting phase raises while that for the wetting phase exhibits a decline. When M is not equal 1, the relative permeability of high viscosity phase is significantly increased, while the other two phases are less affected. Meanwhile, the maximal value of relative permeability does not exceed unity because of the low porosity in the porous medium. For the influence of Ca , simulation results indicate the relative permeability shows weak sensitivity to Ca. • A lattice Boltzmann color gradient model for three-phase fluid flow is proposed. • Pore-scale three-phase fluid flow in porous media is studied. • Three-phase relative permeability is predicted. • Effects of wettability, viscosity ratio and capillary number are explored. [ABSTRACT FROM AUTHOR]