A novel fractal Langmuir and machine learning framework for precise prediction of CH4/CO2 adsorption in heterogeneous shale: Implications for CO2 sequestration

Capturing the adsorption behavior of gases in heterogeneous shale is crucial for CH4 enhanced recovery and CO2 geological sequestration. This study derives a fractal Langmuir adsorption model that incorporates energy heterogeneity across pore sizes to characterize CH4 and CO2 adsorption in real shale. The results show that the fractal Langmuir model provides accurate fitting and high stability, effectively calculating gas adsorption amounts within various shale pore size ranges. It reveals that CH4 and CO2 are primarily adsorbed in micropores, with adsorption amounts influenced by the interplay of pore quantity and adsorption energy. In mesopores and macropores, gas predominantly exists in a free state, and the volume of free gas is dependent on pore volume. Additionally, a variance-based sensitivity analysis was applied to quantitatively assess the impact of shale pore structure (minimum pore diameter, λmin; maximum pore diameter, λmax; and porosity) on gas adsorption. The analysis demonstrates that λmin has the greatest effect on adsorption, followed by porosity, while λmax exerts a lesser influence. Increased porosity significantly enhances the adsorption capacity of shale for both CH4 and CO2. Finally, to overcome the physical assumptions of the fractal Langmuir model, a Convolutional Neural Networks-Gaussian Process Regression machine learning framework was developed that directly uses the N2 adsorption–desorption curve at 77 K as input to predict CH4/CO2 adsorption in shale, achieving comparable accuracy.