Open Access

ARTICLE

Regulation of Critical Capillary Number: High-Efficiency Displacement Mechanism of Deep Coalbed Methane Considering Wettability Heterogeneity of Proppants between Fractures

Zeliang Liang^1,2, Jia Tan^1,*, Jiachao She², Fengnian Wang², Yi Wang², Donghao Li³, Rugang Duan³, Haotian Chu⁴
1 Xinjiang Yaxin Coalbed Methane Investment and Development (Group) Co., Ltd., Urumqi, China
2 Xinjiang Yaxin Coalbed Methane Resources and Technology Research Co., Ltd., Urumqi, China
3 School of Energy and Mining, China University of Mining and Technology-Beijing, Beijing, China
4 School of Sustainable Energy, China University of Geosciences, Wuhan, China
* Corresponding Author: Jia Tan. Email:
(This article belongs to the Special Issue: Multi-Scale Heat and Mass Transfer: From Intensification to System Integration)

Frontiers in Heat and Mass Transfer https://doi.org/10.32604/fhmt.2026.078050

Received 23 December 2025; Accepted 22 January 2026; Published online 20 July 2026

Abstract

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.

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Keywords

Heterogeneous wettability; gas-water two-phase flow; capillary number; seepage path regulation

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