Investigation of oil/water two-phase flow in carbonate rocks using a multi-relaxation-time lattice Boltzmann phase-field method

Abstract Carbonate reservoirs exhibit complex oil-water two-phase flow behavior owing to their multimodal pore-throat structures, strong heterogeneity, and variable wettability. Traditional Darcy-based models struggle to capture key pore-scale phenomena such as interfacial dynamics and topological evolution, hindering the accurate prediction of displacement processes. In this study, Well A of the Fuman Oilfield in the Tarim Basin was selected as the research target. A high-resolution pore-scale simulation framework was developed by coupling the multi-relaxation-time lattice Boltzmann method (MRT-LBM) with a phase-field model and digital core reconstruction. The effects of interfacial tension, wettability, oil-water viscosity ratio, and capillary number on the displacement efficiency and oil-phase topology evolution were systematically investigated. The results show that interfacial tension strongly regulates droplet breakup and migration. At σ = 0.005 N m −1 , the connected oil volume decreases by 55.4% and isolated droplets increase by 220%, accompanied by a marked increase in the Euler characteristic number, indicating rapid connectivity loss. At σ = 0.01 N m −1 , the breakup and mobility are balanced (72%), with the largest decrease in the isolated-droplet Euler characteristic number, reflecting the highest mobilization capacity. At σ = 0.02 N m −1 , capillary trapping dominates (68%). Wettability governs droplet adhesion and detachment: hydrophilic ( θ = 60°) rapidly forms a water film that cuts the oil phase, increasing the Euler characteristic number significantly (75% recovery), whereas neutral and oil-wet conditions preserve connectivity but retain more residual oil (65% and 55%, respectively). A low viscosity ratio (M = 2) stabilizes the front and enhances the breakup, yielding a large Euler characteristic number growth (72%), whereas a high ratio (M = 10) shows minimal topological change and only 64% recovery. Increasing the capillary number promotes droplet detachment and migration, with high Capillary number (Ca) producing the lowest isolated oil volume peak and largest Euler characteristic number drop, achieving 72% recovery.