A theoretical model investigation on coalbed methane seepage related to temperature–stress

Permeability constitutes a pivotal element in coalbed methane (CBM) migration in coal reservoirs, with temperature–stress coupling effects intensifying as depth increases. Developing a quantitative expression of the correlations between methane transport dynamics and its influencing factors in deep coal reservoirs is of critical importance for enhancing deep CBM development efficiency. This paper introduces the effective deformation coefficient fm, which characteristics the coal matrix–fracture interaction. Furthermore, it establishes a permeability model considering temperature and stress impacts. The model is refined for various conditions, such as constant external stress, constant pore pressure, constant effective stress, and uniaxial strain, and validated against actual experimental data with satisfactory agreement across various boundary conditions. Additionally, the comprehensive discussion has addressed the influence of pore pressure and temperature on fm. The findings demonstrate that variations in fm with pore pressure are contingent upon the boundary conditions. At uniaxial strain, the fm increases with rising pore pressure. In contrast, when external stress remains constant, the fm decreases as the pore pressure increases. Furthermore, the fm exhibits fluctuations with rising pore pressure when effective stress remains constant. Significantly, irrespective of the boundary conditions, the fm tends to increase and then decrease with rising temperature. We have also discussed the governing mechanism of the fm on coal permeability. The analysis reveals an inverse correlation between permeability variation and fm. Based on experimental validation, it is recommended that an fm within 0–0.48 be adopted for reliable permeability prediction in CBM production.