Adsorption Equilibrium and Thermodynamics of Supercritical High-Pressure Methane Adsorption on the Lower Cambrian Organic-Rich Marine Shuijingtuo Shales Based on the Dubinin-Astakhov (D-A) Model

Characterizing methane (CH4) adsorption behavior in marine shale reservoirs is of great significance for assessing geological natural gas reserves and elucidating adsorption mechanisms within complex pore systems. In this study, supercritical high-pressure CH4 adsorption experiments were conducted on Lower Cambrian organic-rich marine Shuijingtuo shales under reservoir-relevant pressure and temperature conditions (30–90 °C and up to 32 MPa). The measured excess isotherms were analyzed using the Polanyi theory-derived Dubinin-Astakhov (D-A) model, which incorporates a pseudo-saturation pressure correction for supercritical conditions and accounts for the adsorbed phase density. The D-A model yielded excellent fits (R2 = 0.976–0.990) and temperature-independent characteristic curves for all marine shale samples, confirming its suitability for supercritical CH4 adsorption in heterogeneous pore systems. A strong positive correlation (R2 = 0.87) was observed between total organic carbon (TOC) content and adsorption capacity. This relationship is attributable to the abundant nanoscale organic pores developed within the organic matter, which increase the micropore volume and BET surface area, thereby improving the gas uptake potential. Thermodynamic analysis incorporating real gas behavior and adsorbed phase volume reveals that simplified assumptions (assuming an ideal gas or negligible adsorbed phase volume) systematically overestimate the isosteric heat of adsorption, with this deviation being particularly pronounced at high surface coverages. The model-derived isosteric heat decreases with increasing surface coverage across all shale samples, an observation that is highly consistent with the preferential occupation of high-energy sites within a highly heterogeneous marine nanopore system. The theoretical framework of the isosteric heat of adsorption provided in this study is suitable for other gas–solid adsorption systems and establishes a foundation for future research on other thermodynamic analyses such as the adsorbed phase enthalpy and adsorbed phase specific heat capacity.