End-Member Mixing Model for Methane Carbon Isotope Fractionation During Shale Gas Desorption and Its Application

Unlike conventional natural gas reservoirs, shale gas development involves systematic changes in methane carbon isotopes that cannot be effectively described by existing isotope fractionation models and mechanisms. Therefore, based on fundamental theories such as Rayleigh fractionation, mass transfer flow, and mass conservation, this study established isotopic fractionation equations for methane in adsorbed and free gas. By considering adsorbed and free gases as two end-members and using an isotope mixing model, a fractionation model for methane carbon isotopes during shale gas desorption was constructed. This model quantifies the isotopic fractionation effects during shale gas desorption and elucidates the mechanism of methane carbon isotope fractionation. Using on-site desorbed gas content and isotope data, parameter fitting and model calculations were conducted to characterize methane carbon isotope variations throughout the process of shale core field desorption. The results show a pattern of "initially negative and then turning positive," consistent with those of physical simulation experiments. It was clarified that differences in mixing the two end-members and isotopic fractionation play key roles in the variation of methane carbon isotopic composition in shale gas. By applying the methane carbon isotope fractionation model, the contribution of adsorbed gas during shale gas production was explored. It was found that in the early stage of development, the adsorbed gas in Well JY 1 was negligible. After nearly seven years of development, the contribution of adsorbed gas in the later stage has only reached nearly 15%, indicating that the production contribution of adsorbed gas is still less than 0.3 million cubic feet per day. The open flow of Well JY 6-2 is more conducive to the production of adsorbed gas, but the production capacity is still mainly contributed by free gas, indicating that the shale gas production capacity in the later stage in the Jiaoshiba gas field is still primarily dominated by free gas.