Numerical studies of spontaneous imbibition in porous media: Model development and pore-scale perspectives

Spontaneous imbibition is a crucial two-phase flow process in a variety of subsurface and industrial applications. Due to the lack of an efficient and reliable pore-scale model, however, how pore-filling events in spontaneous imbibition influence average transport properties (i.e., capillary pressure and relative permeability curves) and entrapment of the nonwetting fluid has not been fully understood. In this work, we first experimentally verify an image-based dynamic pore-network model of spontaneous imbibition that is computationally efficient. Then, case studies of a Nubian sandstone are conducted. We demonstrate that average capillary pressure in cocurrent spontaneous imbibition is significantly overestimated by the widely used Young-Laplace equation. This is because the effects of dynamic pore-filling and air entrapment on average capillary pressure are not parameterized in the equation. Based on our pore-scale numerical results, we elaborate on the competition of pore-filling events under different viscosity ratios of the wetting to the nonwetting fluids. It is found that the filling mode evolves from the co-filling of neighboring pores to the preferential filling of small pores as the nonwetting viscosity increases. Our model will be a useful numerical tool for quantitatively predicting spontaneous imbibition in geological formations. Our findings will help us bridge the gap between pore-scale flow dynamics and the Darcy theory of spontaneous imbibition.