Effect of Temperature and Pressure on Effective Stress Coefficient and Permeability Prediction Model in Coal Reservoirs

Effective stress is a critical factor governing the deformation behavior and pore-permeability characteristics of deep coal reservoirs. Accurate determination of the effective stress relies heavily on the effective stress coefficient (α). However, the variation pattern of the effective stress coefficient under thermo-mechanical coupling conditions is not yet fully understood, which impedes precise permeability prediction. To address this issue, permeability experiments were performed on coal samples of different ranks under varying temperatures and confining pressures. By comparing the classical effective stress method, the <i>Bernabé</i> method, and the differential method, this study investigated the response of the effective stress coefficient to temperature and pressure, as well as an accurate approach for predicting permeability in coal reservoirs. The results indicate that the differential method provided the best fit for the permeability-effective stress relationship and was therefore adopted for calculating the effective stress coefficient. Under thermo-mechanical coupling conditions, the effective stress coefficient increases with temperature and decreases with confining pressure. Based on the differential method, a prediction model for the effective stress coefficient was established. By introducing the geothermal gradient and overburden stress gradient, the temperature and pressure were expressed as functions of burial depth. The effective stress coefficient exhibits a quadratic relationship with the coal seam burial depth, while permeability follows a negative exponential decay trend with increasing depth. Formation overpressure contributes to the preservation of pore structures, thereby enhancing both the permeability and free gas enrichment in deep coal reservoirs. These findings offer a theoretical foundation for the accurate prediction of effective stress coefficients, deformation extents, and seepage behavior in deep coal reservoirs.