Inertial Effect on Oil/Water Countercurrent Imbibition in Porous Media from a Pore-Scale Perspective

The color-gradient lattice Boltzmann (LB) method is used to investigate the inertial effect on oil/water countercurrent imbibition characteristics in a matrix-fracture system. The interplay between capillarity, fluid inertia, and viscous force during the imbibition under different viscosity ratios is delineated. Pore-scale dynamics, the interfacial front morphology, and oil recovery under the influence of fluid inertia are also elucidated. Additionally, we study the energy conversion during the imbibition displacement from the perspective of energy balance. Finally, the application of the theoretical scaling model is discussed based on the simulated data. Results show that the pore-scale events involved mainly consist of cooperative pore filling, oil expelled from large pores, and the motion of jetting-like oil clusters under high viscosity ratios. The curve of pressure difference between the fracture inlet and outlet vs. imbibition time can be regarded as a signal to discern the imbibition regime, which is taken together with the energy conversion analysis could further determine how capillarity, external pressure, and viscous dissipation contribute to water imbibition. Capillary force dominates in the cases of low viscosity ratios, and the majority of the surface energy is dissipated. The external pressure becomes increasingly significant and even governs the countercurrent imbibition as the viscosity ratio increases. Furthermore, the oil recovery, interfacial area, and fractal dimension of the nonwetting phase strongly rely on the Ohnesorge (Oh) number when the viscosity ratio is low. In contrast, the inertial effect can be neglected in the cases of high viscosity ratios. Besides, the relationship between the simulated imbibition recovery and imbibition time follows the theoretical scaling model as the external pressure is trivial. The comparable exponents fitted from different Oh numbers reveal that the inertial effect does not alter the imbibition dynamics. In sum, fluid inertia only affects the local fluid behaviors and thus the imbibition oil recovery when the viscosity ratio is low. These results could provide important implications for a range of energy-related and environmental applications, such as the evaluation of fracturing fluids loss, oil recovery by water huff n puff, microfluidic devices, and hydrological sciences.