Precise prediction of methane–ethane adsorption in shale nanopores using multi-component models and machine learning

Methane and ethane are the primary hydrocarbon components of shale gas, predominantly adsorbed within shale as a binary mixture. Accurately predicting the adsorption capacity of methane–ethane binary mixtures is crucial for estimating shale gas reserves. This paper employs the multi-component adsorption models to characterize the adsorption behavior of binary mixtures across various temperatures and methane molar fractions. The results indicate the Extended Langmuir model shows good accuracy for low methane molar fraction mixtures in shale adsorption, while the Ideal Adsorbed Solution Theory model performs better for high methane molar fraction mixtures. Recognizing the time- and labor-intensive nature of parameter acquisition for multi-component models, four common machine learning models optimized by Bayesian methods are developed for the adsorption of single and binary gases, including Gaussian process regression, Support vector regression, Decision trees, and Extreme Gradient Boosting (XGBoost). The XGBoost model showed the superior performance and strong generalization abilities. Additionally, a sensitivity analysis method based on variance, leveraging kernel density estimation theory, is used to assess the importance of input features on XGBoost model hyperparameters. It turned out that the methane molar fraction significantly affects the adsorption capacity of binary gas mixtures, whereas clay minerals exert minimal impact.