Modified Dubinin–Astakhov Model for the Accurate Estimation of Supercritical Methane Sorption on Shales

[Image: see text] In order to evaluate the total shale gas-in-place (GIP) resources in deep formations, it is important to study the sorption of supercritical methane in shales. At present, the Dubinin–Astakhov model is used to describe sorption isotherms. However, it still has some shortcomings. The main objective of this study is to establish an optimized model for supercritical methane sorption in shales. A series of high-pressure methane sorption isotherms were measured at different temperatures (from 293 to 333 K) for shale samples collected in the Cengong block, Guizhou, China. The characteristics and causes of shale gas sorption capacity changes were analyzed. By comparing the fitting results of several conventional sorption models, the characteristics and applicable scope of these models are obtained. A four-parameter (V(0), D, m, and ρ(a)) modified supercritical D–A model was developed to accurately estimate the sorption of supercritical methane on shales based on Polanyi sorption potential theory. The results show that the sorption characteristic curve of methane on the shale surface under high pressure is obviously different from that under low pressure. The density of the sorption phase and the virtual saturated vapor pressure have a great influence on the fitting results of the sorption models. The density of the adsorption phase directly determines the ultimate sorption capacity of the shale sample. Also, the modified D–A model can improve the accuracy of the prediction of supercritical methane sorption on shales, and it can accurately describe the isothermal sorption law of gas in the supercritical state.