This paper explores significant advancements in the numerical simulation of multiphase, multi-physics flows within underground reservoirs, driven by the necessity to understand and manage complex geological and engineered systems. It delves into the latest research in numerical simulation techniques at both the pore and Darcy scales, emphasizing the integration of traditional methods with emerging machine learning technologies. Key simulation methods reviewed at the pore scale include the lattice Boltzmann method, level set method, phase field method, and volume of fluid method, each offering unique advantages and facing limitations related to computational efficiency and stability. Special attention is given to spontaneous imbibition, where capillary action facilitates the movement of wetting fluids into porous media. Discussions at the Darcy scale focus on macroscopic simulation methods that simplify microscale interactions but face challenges in accurately modeling the multiscale and heterogeneous nature of fractured media. Furthermore, an overview of the basic principles, limitations, and potential of integrating machine learning algorithms with traditional numerical methods emphasizes their role in enhancing simulation efficiency and stability. Future research will aim to address existing challenges and maximize the use of advanced computational technologies to refine the accuracy, efficiency, and practical applicability of multiphase and multifield flow simulations in underground reservoirs.

Multiphase flow is a common scenario in industrial and environmental applications. Especially at microscopic scale, accurately describing flow processes is challenging due to fluid-fluid, fluid-solid, and solid-solid interactions. Pore-scale microfluidics and numerical simulation methods considering complex topology are increasingly being applied to study multiphase flow phenomena. This work focuses the recent applications of microfluidic experiments and new numerical simulations in complex flows for enhanced oil recovery. Two types of coupling algorithms are provided to integrate the advantages of pore network model and direct numerical simulation methods. For fines migration, the computational fluid dynamics-discrete element method is proposed to describe the coupling process between fluid and solid particles. Pore-scale microfluidic experiments and simulation methods deals with complex flow processes at micro/nano scales, providing effective solutions for complex industrial processes.

The lattice Boltzmann method and pore network model are two types of the most popular pore-scale fluid flow simulation methods. As a direct numerical simulation method, lattice Boltzmann method simulates fluid flow directly in the realistic porous structures, characterized by high computational accuracy but low efficiency. On the contrary, pore network model simulates fluid flow in simplified regular pore networks of the real porous media, which is more computationally efficient, but fails to capture the detailed pore structures and flow processes. In past few years, significant efforts have been devoted to couple lattice Boltzmann method and pore network model to simulate fluid flow in porous media, aiming to combine the accuracy of lattice Boltzmann method and efficiency of pore network model. In this mini-review, the recent advances in pore-scale fluid flow simulation methods coupling lattice Boltzmann method and pore network model are summarized, in terms of single-phase flow, quasi-static two-phase drainage flow and dynamic two-phase flow in porous media, demonstrating that coupling the lattice Boltzmann method and pore network model offers a promising and effective approach for addressing the up-scaling problem of flow in porous media.