Dynamic Pore Network Modeling of Imbibition in Real Porous Media with Corner Film Flow

Wetting films can develop in the corners of pore structures during imbibition in a strongly wetting porous medium, which may significantly influence the two-phase flow dynamics. Due to the large difference in scales between main meniscus and corner film, accurate and efficient modeling of the dynamics of corner film remains elusive. In this work, we develop a novel two-pressure dynamic pore network model incorporating the interacting capillary bundle model to analyze the competition between the main meniscus and corner film flow in real porous media. A pore network with four-point star-shaped pore bodies and throat bonds is extracted from the real porous medium based on the pore shape factor and pore cross-sectional area, which is then decomposed into several layers of sub-pore networks, where the first layer of sub-pore network simulates the main meniscus flow while the upper layers characterize the corner film flow. The two-phase flow conductance of throat bonds for different layers of sub-pore networks are determined by high-resolution two-phase lattice Boltzmann modeling, thus inherently considering the viscous coupling effect. In addition, two artificial neural network models are developed to predict the two phases' flow conductance based on the shape of the throat cross section and the fluid properties. The accuracy of the developed model is validated with a lattice Boltzmann simulation of imbibition in a strongly wetting square tube. Then the model is used to simulate imbibition in a strongly wetting sandstone porous medium, and the competition between the main meniscus and the corner film flow is analyzed. The results show that with decreasing capillary number and viscosity ratio between wetting and nonwetting fluids, the development of the wetting corner film becomes more significant.