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.精准且具备物理意义的页岩超临界甲烷吸附相密度（supercritical methane adsorbed phase density, SMAPD）测定工作，不仅有助于深化对吸附机理的理解，更为二氧化碳地质封存提供了关键的设计与预测依据。本文采用波拉尼吸附理论（Polanyi theory）结合超临界甲烷的物性特征，对传统SMAPD计算方法进行了系统评估。通过等温吸附实验，推导得到吸附相密度朗缪尔法（adsorbed phase density Langmuir, APDL），并借助核磁共振与分子模拟手段对该方法完成了验证。研究结果显示，直接将页岩微孔体积作为吸附相体积是一种物理一致性更强的近似方式。同时，实际SMAPD可能趋近于0.422 g/cm³，因为在此密度下吸附特征曲线的重合度达到最高。APDL方法在高温高压条件下计算SMAPD时效果尤为显著，其揭示出超临界甲烷的吸附相在高压下表现出类液体特性，而在低压下则呈现类气体行为。随后，本文构建了3种基于贝叶斯优化（Bayesian optimization）的机器学习模型，分别为极端梯度提升（XGBoost）、支持向量回归（support vector regression, SVR）与人工神经网络（artificial neural network, ANN），以实现高温高压条件下SMAPD的精准预测。其中，XGBoost模型展现出优异的泛化能力与较高的预测精度。基于该XGBoost模型，通过基于方差的敏感性分析与SHAP加性解释（SHapley Additive exPlanations, SHAP）方法开展输入参数敏感性分析后发现，压力是影响SMAPD的最显著因素，而黏土矿物的影响微乎其微；温度与总有机碳（TOC）对SMAPD的影响程度相当，这为未来通过调节温度实现SMAPD的调控提供了全新策略。