Determining Supercritical Methane Adsorption Phase Density in Nanoscale Shale: from Polanyi Theory to Machine Learning

The accurate and physically meaningful determination of supercritical methane adsorbed phase density (SMAPD) in shale not only aids in understanding the adsorption mechanisms but also provides crucial design and predictive bases for CO₂ geological sequestration. This paper employs Polanyi theory, in conjunction with the properties of supercritical methane, to evaluate traditional methods for calculating SMAPD. Using isothermal adsorption experiments, an adsorbed phase density Langmuir (APDL) method is derived and validated through nuclear magnetic resonance and molecular simulation. The results indicate that using the micropore volume of shale directly as the adsorbed phase volume is a more physically consistent approximation. Meanwhile, the actual SMAPD may be close to 0.422 g/cm³, as the adsorption characteristic curves show the greatest overlap at this density. The APDL method is particularly effective when calculating the SMAPD in high-temperature and high-pressure. It reveals that under high pressure, the adsorbed phase of supercritical methane exhibits liquid-like properties, while at low pressure, it behaves like a gas. Three machine learning models based on Bayesian optimization (XGBoost, support vector regression, and artificial neural network) were then developed to precisely predict the SMAPD under high temperature and pressure. Among these, the XGBoost model exhibited outstanding generalization capability and high prediction accuracy. Based on the XGBoost model, input parameter sensitivity analysis using the variance-based sensitivity analysis and SHapley Additive exPlanations methods indicated that pressure is the most significant factor affecting SMAPD, while the influence of clay minerals is minimal; the effects of temperature and TOC on SMAPD are comparable, offering new strategies for future regulation of SMAPD through temperature adjustments.