Machine learning (ML) models offer rapid and low-cost prediction of methane (CH4) and carbon dioxide (CO2) adsorption in shale, which is crucial for enhancing recovery and achieving CO2 geological sequestration. However, with adsorption mechanisms model not yet fully established, existing purely data-driven ML lacks reliable physical constraints and exhibits weak interpretability, limited accuracy, and poor generalization. To address this gap, a novel fractal supercritical Dubinin-Radushkevich-Langmuir (FSDR-L) model was derived to describe the adsorption behaviors of CH4 and CO2 in shale and to directly quantify the critical pore size for gas adsorption mechanism transition. The results indicate that increasing temperature shifts CH4/CO2 molecules in shale toward monolayer adsorption, while reducing the contribution of pore-filling. Subsequently, a physics-informed neural network (PINN) model guided by the insights of the FSDR-L model was developed for the first time to predict CH4/CO2 adsorption amounts in shale. The findings reveal that the PINN model achieved reductions of 38.93 % in mean absolute percentage error, 39.47 % in mean absolute error, and 57.46 % in root mean square error compared to the best-performing conventional ML model, demonstrating superior predictive performance and generalization capability in capturing complex shale-gas adsorption behaviors. Finally, to enhance the interpretability of the PINN model, a variance-based sensitivity analysis was conducted, revealing that total organic carbon, pressure, temperature, and pore volume are the key factors governing CH4/CO2 adsorption capacity in shale.
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