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Rock surface wettability is one of the most important factors impacting the oil recovery efficiency. Carbonate reservoir rocks show highly heterogeneous wettability, which is imposing big challenges in Enhanced Oil Recovery. Because of the complicated porous morphology and interaction between oil/water phases, the mechanism of how surface wettability affects the relative permeability is still unclear. In this work, we develop a Lattice Boltzmann method (LBM) to study the oil-water-rock interaction through systematic water-flooding simulations. Our LBM model is validated by the analytical solution of co-current oil-water flow and lab-scale microchannel oil displacement experiment. To further investigate the effect of rock surface wettability and reveal the pore-scale oil trapping mechanism, a series of water-flooding oil displacement simulations are conducted under different initial oil saturation and surface …