TY - EJOU AU - Liang, Zeliang AU - Tan, Jia AU - She, Jiachao AU - Wang, Fengnian AU - Wang, Yi AU - Li, Donghao AU - Duan, Rugang AU - Chu, Haotian TI - Regulation of Critical Capillary Number: High-Efficiency Displacement Mechanism of Deep Coalbed Methane Considering Wettability Heterogeneity of Proppants between Fractures T2 - Frontiers in Heat and Mass Transfer PY - VL - IS - SN - 2151-8629 AB - Significant wettability differences between proppants and coal matrices in deep coal reservoirs limit gas–water mass transfer, a key factor for coalbed methane recovery. This study develops a hybrid wettability fracture model using in-situ data, coupling Navier–Stokes equations with a phase-field method to simulate multi-scale gas–water flow. A random wettability mapping technique captures spatial heterogeneity. The critical capillary number (Ca)-balancing capillary and viscous forces-serves as the key threshold governing flow pathways. At low Ca, capillary forces dominate, causing liquid film aggregation and gas blockage; at high Ca, viscous forces break films and open pathways. Wettability gradients drive asynchronous phase transitions through force competition, dynamically reconstructing flow paths. We propose an optimized strategy: operating near the critical Ca breaks confined liquid phases, while a hydrophilic-hydrophobic balanced system enables synergistic film pre-reconstruction and secondary breakage to maximize gas transfer efficiency. This work clarifies how critical Ca regulates flow via wettability heterogeneity, providing a theoretical and optimization framework for enhanced mass transfer in porous media relevant to energy applications. KW - Heterogeneous wettability; gas-water two-phase flow; capillary number; seepage path regulation DO - 10.32604/fhmt.2026.078050