Wetting Dynamics of Spontaneous Imbibition in Porous Media: From Pore Scale to Darcy Scale

Spontaneous imbibition plays an important role in many subsurface and industrial applications. Unveiling pore-scale wetting dynamics, and particularly its upscaling to the Darcy model, are still unresolved. We conduct image-based pore-network modeling of cocurrent spontaneous imbibition and the corresponding quasi-static imbibition in homogeneous sintered glass beads and heterogeneous Estaillades carbonate. We find that pore-scale heterogeneity significantly influences entrapment of the nonwetting fluid, which in Estaillades is mainly because of the poor connectivity of pores. We show that wetting dynamics significantly deviates capillary pressure and relative permeability away from their quasi-static counterparts. Moreover, we propose a nonequilibrium model for wetting permeability that well incorporates flow dynamics. We implement the nonequilibrium model into two-phase Darcy modeling of a 10 cm long medium. Sharp wetting fronts are numerically predicted, which are in good agreement with experimental observations. Our studies provide insights into developing a two-phase imbibition model with measurable material properties.