Spontaneous imbibition, as a fundamental flow phenomenon, is widely utilized in fossil energy production, carbon dioxide and underground hydrogen storage. With the development of computing, the exploration of flow laws of spontaneous imbibition has evolved from macroscopic theoretical models to pore-scale numerical analysis. Currently, the solutions for multiphase flow in pore media mainly consider the volume of fluid and the phase field, and have been classed into level set methods based on macroscopic Navier-Stokes equations and the Shan-Chen, free energy, color gradient, and phase-field methods based on mesoscopic lattice Boltzmann equations. However, no comprehensive review article has summarized the strengths and limitations of these methods. Therefore, this work focuses on critically reviewing and commenting on the fundamentals and limitations of pore-scale models applied to spontaneous imbibition. In addition, recent works applying these methods are systematically reviewed. Our study aims to provide the scientific community with an expert opinion to understand the basic methods for solving the existing problems of spontaneous imbibition in porous media. Future research directions are suggested, namely, focusing on developing the reconstruction pore medium algorithms, establishing modeling methods for non-stationary states, exploring the flow laws in mixed wetting conditions, linking macroscopic and microscopic flow laws, and developing models for coupled multiphase flow numerical computation with machine learning. Overall, this review provides a comprehensive understanding of spontaneous imbibition simulation methods, promotes a thorough knowledge of spontaneous imbibition in porous media, provides guidance on exploring flow laws, and inspires researchers to give more credit to spontaneous imbibition studies.

Hydraulic fracturing technology can improve the geologic structure of unconventional oil and gas reservoirs, yielding a complex fracture network resulting from the synergistic action of hydraulic and natural fractures. However, the impact of spontaneous imbibition associated with hydraulic fracture propagation on the reservoir matrix remains poorly understood. In this study, combining the Cahn-Hilliard phase field method with the Navier-Stokes equations, pore-scale modeling was employed to capture the evolution of the oil-water interface during dynamic spontaneous imbibition for hydraulic fracture propagation in a two-end open mode. This pore-scale modeling approach can effectively circumvent the challenges of conducting spontaneous imbibition experiments on specimens partitioned by hydraulic fractures. A direct correlation was established between the pressure difference curve and the morphology of discharged oil phase in the primary hydraulic fracture, providing valuable insights into the distribution of oil phase in spontaneous imbibition. Furthermore, it was shown that secondary hydraulic fracture propagation expands the longitudinal swept area and enhances the utilization of natural fractures in the transverse swept area during spontaneous imbibition. When secondary hydraulic fracture propagation results in the interconnection of upper and lower primary hydraulic fractures, competitive imbibition occurs in the matrix, leading to reduced oil recovery compared to the unconnected models. Our results shed light upon the spontaneous imbibition mechanism in porous media with hydraulic fracture propagation, contributing to the refinement and application of hydraulic fracturing techniques.