Lattice Boltzmann simulation of counter-current imbibition of oil and water in porous media at the equivalent capillarity

Abstract

The characterization of oil and water displacement in porous media often relies on the capillary number (Ca = μv/σ cos θ). However, limited investigations have been conducted to explore the relative significance of interfacial tension and wettability in determining oil recovery, particularly under the imbibition mode. To address this research gap, the modified color gradient lattice Boltzmann method has been employed. This study aims to systematically investigate the transient imbibition characteristics, pore-scale events, and morphological features of the two-phase distribution in the matrix, all under the same capillarity but varying capillary numbers. The obtained results indicate that, for a given capillary number, a more water–wet condition generally leads to a higher imbibition recovery. Conversely, the influence of capillary number on oil recovery is complex and contingent upon the capillarity value, i.e., the interfacial tension between oil and water. Additionally, the oil recovery data from all cases have been effectively fitted using the Minkowski functionals, demonstrating a linear correlation. Moreover, an attempt has been made to elucidate the mechanism behind the varying oil recovery observed in different capillarity combinations. This analysis considers factors such as energy conversion, the transient change of the ratio of viscous force over capillarity, and the capillary valve effect. The findings of this study contribute to our understanding of the use of chemical agents to enhance oil recovery and provide valuable insights for determining key two-phase parameters in reservoir simulations.