Determining Supercritical\nMethane Adsorption Phase\nDensity in Nanoscale Shale: from Polanyi Theory to Machine Learning

The\naccurate and physically meaningful determination\nof supercritical\nmethane adsorbed phase density (SMAPD) in shale not only aids in understanding\nthe adsorption mechanisms but also provides crucial design and predictive\nbases for CO<sub>2</sub> geological sequestration. This paper employs\nPolanyi theory, in conjunction with the properties of supercritical\nmethane, to evaluate traditional methods for calculating SMAPD. Using\nisothermal adsorption experiments, an adsorbed phase density Langmuir\n(APDL) method is derived and validated through nuclear magnetic resonance\nand molecular simulation. The results indicate that using the micropore\nvolume of shale directly as the adsorbed phase volume is a more physically\nconsistent approximation. Meanwhile, the actual SMAPD may be close\nto 0.422 g/cm<sup>3</sup>, as the adsorption characteristic curves\nshow the greatest overlap at this density. The APDL method is particularly\neffective when calculating the SMAPD in high-temperature and high-pressure.\nIt reveals that under high pressure, the adsorbed phase of supercritical\nmethane exhibits liquid-like properties, while at low pressure, it\nbehaves like a gas. Three machine learning models based on Bayesian\noptimization (XGBoost, support vector regression, and artificial neural\nnetwork) were then developed to precisely predict the SMAPD under\nhigh temperature and pressure. Among these, the XGBoost model exhibited\noutstanding generalization capability and high prediction accuracy.\nBased on the XGBoost model, input parameter sensitivity analysis using\nthe variance-based sensitivity analysis and SHapley Additive exPlanations\nmethods indicated that pressure is the most significant factor affecting\nSMAPD, while the influence of clay minerals is minimal; the effects\nof temperature and TOC on SMAPD are comparable, offering new strategies\nfor future regulation of SMAPD through temperature adjustments.