The main source of production in the middle and late stages of shale gas extraction is the adsorbed gas in shale, and the adsorbed gas in shale mainly comes from organic matter casein and clay minerals in shale; therefore, this paper uses sodium-based montmorillonite to characterize the clay minerals in shale and study the CH₄ adsorption law in clay minerals, and this study has certain guiding significance for shale gas extraction. In addition, this paper also conducts a study on the competitive adsorption law of CH₄ and CO₂, and at the same time, predicts the theoretical sequestration of CO₂ in shale clay minerals, which is a reference value for the study of CO₂ burial in shale and is beneficial to the early realization of carbon neutral. In this paper, the slit model of sodium-based montmorillonite and the fluid model of CH₄ and CO₂ were constructed using Materials Studio software, and the following two aspects were studied based on the Monte Carlo method: Firstly, the microscopic adsorption behavior of CH₄ in sodium-based montmorillonite was studied, and the simulations showed that the adsorption capacity of montmorillonite decreases with increasing temperature, increases and then decreases with increasing pressure, and decreases with increasing pore size. CH₄ has two states of adsorption and free state in the slit. The adsorption type of CH₄ in montmorillonite is physical adsorption. Secondly, the competitive adsorption of CH₄ and CO₂ in sodium-based montmorillonite was studied, and the simulations showed that the CO₂ repulsion efficiency increased with increasing CO₂ injection pressure, and the CO₂/CH₄ competitive adsorption ratio decreased with increasing pressure. The amount of CO₂ storage decreased with increasing temperature and increased with increasing CO₂ injection pressure.

Deep high-temperature and high-pressure (HTHP) oil reservoirs have limited experimental MMP data, large differences between reservoir and saturation pressures, low gas–oil ratios, and pressure-sensitive CO₂–oil phase behavior, which make both minimum miscibility pressure (MMP) prediction and miscibility-mechanism identification challenging. To address these gaps, this study determines the MMP of a CO₂–oil system by integrating slim-tube experiments, empirical formula methods, the Multiple Mixed-Cell (MMC) method, the Method of Characteristics (MOC), compositional numerical simulation, and three intelligent algorithm models (GWO-RBF, GWO-LSSVM, and GWO-SVM). The slim-tube MMP of 44.13 MPa at 140 °C is used as the experimental reference for comparing prediction errors, whereas PVTsim and literature data are used for consistency checks and model benchmarking. The results show that when the injected CO₂ mole fraction exceeds 0.88, the formation oil under original reservoir conditions cannot achieve first-contact miscibility with CO₂, and the maximum dissolved CO₂–oil molar ratio is 7.3:1. Supercritical CO₂ forms dual displacement mechanisms, including front-end vaporizing miscible drive and rear-end condensing miscible drive, but the dominant mechanism for this CO₂–oil system is vaporizing miscible drive. During the vaporizing gas drive, the CO₂ + N₂ + C₁ content in the liquid phase increases from less than 60% to nearly 90%, indicating significant CO₂ dissolution into oil and associated density and viscosity reduction; meanwhile, the C₇₊ content in the gas phase increases to nearly 10%, indicating extraction of heavy components. Relative to the slim-tube reference at 140 °C, the deviations of MMC, GWO-SVM, GWO-LSSVM, compositional numerical simulation, GWO-RBF, MOC, and empirical formula methods are 2.97%, 3.08%, 3.40%, 4.24%, 4.26%, 11.62%, and 19.74%, respectively. The MMC method is the most suitable approach for this specific HTHP oil system, while intelligent algorithms should be regarded as supplementary predictors whose reliability depends on training-domain coverage and independent validation.