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. Plain Language Summary The flow of a fluid into a porous matrix by capillary force is encountered in many everyday processes, such as water‐flow to reach the tips of trees and water‐flow through soils. These processes are examples of spontaneous imbibition. Spontaneous imbibition is also crucial to many industrial applications, ranging from oil recovery and geological sequestration of carbon dioxide to inkjet printing, diapers, and paper sensors. Mostly, the imbibition rate, broadening of the wetting front, and entrapment of the nonwetting fluid are of great interest. In this work, we conduct extensive pore‐scale modeling of spontaneous flow in porous media. We illustrate how pore‐scale heterogeneity influences imbibition dynamics and entrapment of the nonwetting fluid. To bridge the gap between pore‐scale flow dynamics and the Darcy‐scale theory of spontaneous imbibition, we develop a nonequilibrium model for wetting permeability that can provide better modeling of spontaneous imbibition at the Darcy scale. Our studies have immediate implications for the applications of oil production from fractured reservoirs, capillary trapping of carbon dioxide, and remediation of nonaqueous liquids in soils. Key Points We conduct image‐based pore‐network modeling of spontaneous imbibition in sintered glass beads and Estaillades carbonate We illust