Objective and Method  Adsorbed phase density represents a key parameter for determining gas adsorption capacity in coals. Using bituminous coal samples from the Huainan and Huaibei mining areas in Anhui Province, this study carried out high-pressure isothermal adsorption experiments of CO₂ and CH₄ at temperatures of 24 ℃, 36 ℃, and 48 ℃. In combination with the quantitative characterization of pore structures in coals using low-temperature liquid nitrogen adsorption (LNA) experiments and mercury intrusion porosimetry (MIP), this study analyzed the high-pressure trans-critical CH₄ and CO₂ adsorption processes in coals. Meanwhile, based on the Gibbs excess adsorption, the adsorbed phase volumes and maximum adsorbed phase densities of CO₂ and CH₄ in coals were calculated using the intercept method. Furthermore, by integrating the Langmuir model based on the monolayer adsorption theory and the modified Dubinin-Astakhov (D-A) model based on the adsorption potential theory, this study established a model of high-pressure trans-critical CH₄ and CO₂ adsorption in coals.

Results and Conclusions  Under the experimental conditions of 24 ℃‒48 ℃ and 0‒32  MPa, the excess adsorption capacities of CH₄ and CO₂ showed gradually declining trends after peaking due to an increase in the product of their free phase density (ρ_f) and adsorbed phase volumes (V_a) in the high-pressure range. Specifically, the free phase density of CH₄ increased linearly with adsorption pressure, resulting in a linear decrease in the excess adsorption capacity in the high-pressure range. In contrast, the free phase density for CO₂ increased linearly in the low-pressure range (0‒7  MPa) but exhibited an S-shaped trend in the high-pressure range (> 7  MPa), leading to more complex variations in the excess adsorption capacity. Given the linearly decreasing trend in the excess adsorption capacity of CH₄ in the high-pressure range, the adsorbed phase volume and maximum adsorbed phase density of CH₄ were calculated using the intercept method. Then, an expression of the adsorbed phase density was derived using the modified D-A model. As a result, a model of the absolute adsorption capacity of CH₄ under high pressures was established. By substituting the maximum adsorbed phase density of CO₂, used as a substitute for the hypothetical saturated vapor pressure, into the above model, an improved model was developed to fit the adsorbed phase density and absolute adsorption capacity of CO₂ in the high-pressure trans-critical adsorption processes. The improved model yielded coefficients of determination (R²) greater than 0.98 for the fitting of the absolute adsorption capacities of CH₄ and CO₂. However, large deviations were observed during the fitting of CO₂ adsorption in the low-pressure range. To address this, the Langmuir model was introduced to describe the adsorption process in the low-pressure range. The resulting combined model further enhanced the fitting accuracy of the absolute adsorption capacities of CH₄ and CO₂ across the entire pressure range (R² > 0.99). The results of this study provide a theoretical basis and optimized method for exploring the high-pressure trans-critical adsorption processes of gases in coals and for assessing the CO₂ sequestration capacity in deep coal seams.