Estimation of Adsorption Isotherm for Deep Coalbed Methane: A Monolayer-Filling Model Based on Pore Fractal Dimension

Understanding the state of adsorbed methane in coal under high temperatures and pressures is crucial for the exploration and production of deep coalbed methane (CBM). However, the commonly used isothermal adsorption models are inadequate in describing the complex adsorption behavior of methane with multiple occurrence states. Moreover, these models have limited applicability under high-temperature and high-pressure conditions, restricting our understanding of the absorptivity and occurrence mechanism of deep CBM. To address this gap, low-temperature nitrogen adsorption and methane isothermal adsorption experiments under high-temperature and high-pressure conditions were carried out on four high-rank coal samples from the deep CBM block of Daning-Jixian in China's Ordos Basin. Based on the experimental results, a novel methane isothermal adsorption model combining the pore fractal dimension of coal was constructed, and the model exhibits good applicability in studying the adsorption behavior of methane in high-rank coal samples from a deep CBM reservoir. As the pressure increases, the monolayer adsorption amount of methane continues to rise slowly after reaching a certain value, while the adsorption amount in micropores decreases gradually after the pressure exceeds about 12 MPa. This phenomenon can be attributed to the transfer of methane molecules from the micropore filling area to the monolayer adsorption area at high pressures. Furthermore, it is found that the coal in the study area exhibits significant adsorption heterogeneity, with variations in adsorption capacity due to differences in coal composition and pore structure as well as varying degrees of coalification. The adsorption process of methane during the pressure rise can be categorized into three stages: a rapid increase in adsorption amount, conversion of micropore filling to monolayer adsorption, and final stabilization stage.