### Numerical methods to simulate spontaneous imbibition in microscopic pore structures: A review

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#### Abstract

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 porescale 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.

**Document Type:** Invited review

**Cited as:** Zhou, Y., Guan, W., Zhao, C., Zou, X., He, Z., Zhao, H. Numerical methods to simulate spontaneous imbibition in microscopic pore structures: A review. Capillarity, 2024, 11(1): 1-21. https://doi.org/10.46690/capi.2024.04.01

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