In this study, the multiphase multicomponent Shan-Chen lattice Boltzmann method is employed to analyze the impact of capillary force on oil-CO₂-water fluid flow and enhanced oil recovery. Various sizes of the single throat are designed to simulate the interaction between displacing and displaced phases as well as their mechanical equilibrium. Several sensitivities are taken into account, such as wettability, miscibility, interfacial tension, and pore aperture. Based on the objective reservoir conditions, supercritical CO₂ as an injection fluid is adopted to study the influence of different displacement patterns on the mechanical equilibrium in both homogenous and heterogeneous porous media, in which enhanced oil recovery is also quantitatively estimated. The results show that the water-alternating-gas injection pattern reduces the moving speed of the leading edge by increasing the swept area of the residual oil, and inhibits the breakthrough effect of the gas, making it the optimal displacement method in terms of the degree of oil production. Compared with the results of different displacement patterns, the enhanced oil recovery of water-alternating-gas injection is the highest, followed by supercritical CO₂ flooding after water flooding, and lastly, continuous supercritical CO₂ flooding.