Nonlinear Entropy-Enthalpy Correlation for Methane Adsorption on Shale.

The enthalpy-entropy compensation effect is widely recognized in shale gas adsorption studies, where the standard adsorption entropy change is typically reported to vary linearly with the standard adsorption enthalpy change. However, this study reveals that such linear approximations tend to overestimate the standard adsorption entropy change for methane-shale systems. To address this, we established a thermodynamic framework integrating the van't Hoff equation with the Langmuir-Freundlich model. This approach directly leverages excess adsorption isotherms obtained under high-temperature and high-pressure conditions. By analyzing a wide range of literature-reported isotherms from diverse shale samples, we identified a Langmuir-type correlation between the standard adsorption entropy and enthalpy changes. This nonlinearity stems from the physical constraint that entropy change must converge to an asymptotic limit associated with the entropy of the free gas. Our findings show that this limiting value aligns closely with, yet remains lower than, the standard molar entropy of gaseous methane, reflecting the maximum possible loss of molecular degrees of freedom. This physically grounded correlation provides a theoretically consistent description of the thermodynamic behavior of methane adsorption on shale.