A Fractal Adsorption Model for Deep Coal Based on the Kelvin Equation

Gas adsorption in coalbed methane occurs primarily through micropore filling, a process complicated by pronounced structural heterogeneity. This complexity limits the accuracy of conventional adsorption models. To overcome these limitations, we developed a novel fractal adsorption model. This equation uses fractal dimensions, derived from low-temperature gas adsorption and high-pressure mercury intrusion data, to quantitatively describe the complex pore structure. By integrating this structural information with the Kelvin equation, the novel fractal adsorption equation elevates the R 2 value for adsorption capacity prediction to above 0.98. The results demonstrate that while adsorption capacity is influenced by pressure, temperature, and pore complexity, the spatial distribution of the pores themselves is the decisive factor. Ultimately, this model provides a critical distinction between the spaces where gas is stored (adsorption) and the pathways through which it flows. This study establishes a foundational framework for advancing our understanding of gas flow mechanisms in coalbed methane reservoirs.