Pore‑Scale Simulation of Methane‑Water Two‑Phase Flow in Deep Coal Seams Using the Volume of Fluid Method

     In deep coal seams, the primary storage space for adsorbed methane resides in the micropores and associated adsorption surfaces of the coal matrix, whereas the fracture network provides the dominant pathway for gas–water transport. Fractures promote the migration and local enrichment of free gas, with their connectivity exerting a fundamental control on methane desorption efficiency and overall seepage capacity. Therefore, elucidating the pore‑scale mechanisms of gas‑driven water displacement is critical for understanding gas–water occurrence and flow dynamics, as well as for assessing the reservoir‑controlling role of different microstructures.In light of the pronounced heterogeneity of coal, this study constructs two pore‑scale digital core models—a matrix‑pore model and a pore–fracture model—based on micro‑CT imaging of low‑rank coal. Utilizing the Volume of Fluid (VOF) method within an immiscible two‑phase displacement framework, we simulate methane‑driven water displacement under reservoir‑formation conditions. The simulation results are used to systematically analyze how the contact angle (θ) and capillary number (Ca) govern displacement morphology, phase connectivity, and residual phase distribution. Furthermore, a capillary‑number–contact‑angle (Ca–θ) phase diagram characterizing the displacement process is established.

       Key findings are summarized as follows: (1) Under gas–water viscosity ratios representative of the reservoir‑formation stage, pore‑scale gas‑driven water displacement exhibits three distinct regimes: capillary fingering, viscous fingering, and a transitional capillary–viscous fingering regime. In the matrix‑pore model, displacement is dominated by capillary fingering due to pore‑throat constrictions and microstructural bottlenecks, resulting in a dispersed and fragmented displacement front. In contrast, displacement in the pore–fracture model is governed by an interconnected fracture network, where capillary forces are substantially weakened, leading to displacement patterns characteristic of viscous fingering. (2) At low Ca, displacement follows the capillary‑fingering regime, and the gas phase predominantly forms a connected flow network after displacement. At high Ca, viscous fingering dominates, generating numerous isolated gas bubbles and yielding poor gas‑phase connectivity. At intermediate Ca, a transitional regime emerges, combining features of both capillary and viscous fingering. (3) The influences of wettability, capillary number, and pore‑structure type on final gas saturation and gas‑phase connectivity differ markedly between the two models. Under identical displacement conditions, the pore–fracture model attains significantly higher gas saturation and superior gas‑phase connectivity compared to the matrix‑pore model. These insights advance the understanding of methane occurrence and migration in deep coal seams and provide a basis for optimizing coal reservoir development strategies.

Keywords：Deep coal;Gas-water two-phase flow;Displacement pattern;Wettability, Capillary number