Pore-Scale Simulations of Counter-Current Spontaneous Imbibition in Heterogeneous Porous Media

Spontaneous imbibition is a fundamental natural process and a key mechanism in a wide range of engineering and industrial applications. It is primarily governed by capillary forces along fluid-fluid interfaces, whose evolution is strongly influenced by pore structure and boundary conditions. In this study, pore-scale spontaneous imbibition is simulated using a lattice Boltzmann color-gradient model under one-end-open (OEO) and two-end-open (TEO) boundary conditions, with particular emphasis on the effects of geometric heterogeneity. The results show that, under both boundary conditions, heterogeneous digital rocks exhibit consistent interfacial evolution: the interface initiates at the open face and subsequently bifurcates into an imbibition front and a drainage front, accompanied by a progressive reduction in low-curvature interfaces and an increase in high-curvature ones. The TEO configuration markedly enhances imbibition efficiency by increasing the available imbibition area. Geometric heterogeneity further improves efficiency by extending the lifetime of the drainage front. In contrast, more homogeneous rocks display limited curvature variation, a short-lived drainage front, and reduced imbibition efficiency, with minimal sensitivity to the location of the open face. This study provides pore-scale insights into the coupled impacts of boundary conditions and heterogeneity on counter-current spontaneous imbibition, offering theoretical guidance for improved prediction and optimization of subsurface multiphase flow processes.