Counter-current spontaneous imbibition (SI), in which water and oil flow through the same face in opposite directions, is known as one of the most significant oil recovery mechanisms in naturally fractured reservoirs; however, this mechanism has not received much attention. Understanding the dynamic of water-oil displacement during counter-current SI is very challenging because of simultaneous impacts of multiple factors including geometry complexity and heterogeneity of naturally fractured reservoir materials, e.g., high permeability contrast between the rock matrix and fracture, wettability, and porosity. This study investigates the effects of water injection velocity, fracture aperture, and grain shape during counter-current SI at pore-scale. A robust finite element solver is used to solve the governing equations of multiphase flow, which are the coupled Navier–Stokes and Cahn–Hilliard phase-field equations. The results showed that the case with the highest injection velocity (uinj = 5 mm/s) recovered more than 15% of the matrix oil at the early times and then reached its ultimate recovery factor. However, in the case of the lowest injection velocity, i.e., uinj = 0.05 mm/s, the lowest imbibition rate was observed at the early times, but ultimately 23% of the matrix oil was recovered. The model with uinj = 5 mm/s was able to capture some pore-level mechanisms such as snap-off, oil film thinning, interface coalescence, and water film bridging. The obtained results revealed that changing the fracture aperture has a slight effect on the imbibition rate at the earlier times and ultimate recoveries would be almost equal. To assess the influences of grain shape on the imbibition process, the simulated domain was reconstructed with cubic grains. It was noticed that because of higher permeability and porosity, relatively larger oil drops were formed and resulted in higher oil recovery compared with the model with spherical grains. The developed model can be used as a basis for phase-field counter-current simulations and would be useful to study the qualitative and quantitative nature of this phenomenon.

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