A modified BET equation to investigate supercritical methane adsorption mechanisms in shale

Although the Brunauer-Emmett-Teller (BET) equation is a classic adsorption model for describing the adsorption of gases in adsorbents, it cannot be applied in supercritical conditions because the saturation vapor pressure (p(o)) in this equation is not defined when T > T-c. In this study, a modified BET equation is proposed, and can be applied to investigate supercritical methane adsorption mechanisms in shale by using density instead of pressure in this equation. The observed (excess) high-pressure methane adsorption isotherms always can be well-fitted by the modified BET model when the adsorbed-phase density (p(a)) is not fixed. The fitted results show that the number of adsorption layers (n) ranges from 1.79 to 2.42, with an average value of 2.12, indicating a double layer adsorption mechanism approximately. Moreover, we compare this novel model with the commonly used Langmuir and DR models, and find that all the three models can fit the excess adsorption isotherms equally well. However, a critical advantage of this new model is that it can calculate the number of adsorption layers (n), while other models cannot. It is this advantage that makes it possible to analyze the shale gas adsorption mechanism experimentally. Moreover, the average number of adsorption layers (theta) is much smaller than the number of adsorption layers (n), indicating that there are many empty adsorption sites in the adsorption space and the density of the second layer must be less than the first layer, which is consistent with the molecular simulation results.