Improvement of the adsorption model for CH₄ and CO₂ in coal across supercritical states based on monolayer adsorption and adsorption potential theory

Objective and Method The adsorbed phase density is a key parameter for determining the gas adsorption capacity in coal. In this study, bituminous coal samples from the Huainan-Huaibei mining area in Anhui Province were selected to conduct high-pressure isothermal adsorption experiments of CO₂ and CH₄ at temperatures of 24 ℃, 36 ℃, and 48 ℃. Combined with the quantitative characterization of the coal pore structure using low-temperature nitrogen adsorption and mercury intrusion porosimetry, the high-pressure near-critical and supercritical adsorption processes of CH₄ and CO₂ in coal were analyzed. Based on the principle of Gibbs excess adsorption, the intercept method was used to calculate the adsorbed phase volume and maximum adsorbed phase density of CO₂ and CH₄ in coal. Furthermore, on the basis of the monolayer adsorption Langmuir model and the adsorption potential-based modified Dubinin–Astakhov (D–A) model, an adsorption model suitable for describing the high-pressure near-critical and supercritical adsorption of CH₄ and CO₂ in coal was established. Results and Conclusions Under the experimental conditions of 24~48 ℃ and 0~32 MPa, the excess adsorption of CH₄ and CO₂ shows a declining trend after reaching a peak, due to the increasing product of the free phase density (ρ_f) and the adsorbed phase volume (V_a) at high pressures. Specifically, for CH₄, the free phase density increases linearly with adsorption pressure, resulting in a linear decrease in excess adsorption in the high-pressure range. In contrast, for CO₂, the free phase density increases linearly in the low-pressure range (0~7 MPa) but exhibits an “S”-shaped variation at higher pressures (>7 MPa), leading to a more complex change in excess adsorption. Based on the linear decrease in excess adsorption of CH₄ at high pressures, the intercept method was used to calculate the adsorbed phase volume and maximum adsorbed phase density. Furthermore, an expression for the adsorbed phase density was derived using the modified Dubinin–Astakhov (D–A) model, thereby establishing a model for the absolute adsorption capacity of CH₄ under high-pressure conditions. By substituting the maximum adsorbed phase density of CO₂ for the hypothetical saturated vapor pressure in the above model, an improved model was developed to fit the adsorbed phase density and absolute adsorption capacity of CO₂ in the high-pressure near-critical and supercritical adsorption processes. The improved model achieved coefficients of determination (R²) greater than 0.98 for fitting the absolute adsorption capacities of CH₄ and CO₂. However, larger fitting deviations were observed for CO₂ adsorption in the low-pressure range. By introducing the Langmuir model to describe the adsorption process in this low-pressure stage, a combined model was developed, which further improved the fitting accuracy of the absolute adsorption capacity of CH₄ and CO₂ across the entire pressure range (R² > 0.99). This study provides a theoretical basis and methodological optimization for investigating high-pressure near-critical and supercritical adsorption processes of gases in coal and for evaluating the CO₂ sequestration capacity of deep coal seams.