With rapid industrial development, gas charging and discharging processes have become critical to energy storage systems. Current research predominantly focuses on specific vessel types or isolated operational stages and therefore lacks a unified thermodynamic framework that
simultaneously addresses isochoric and isobaric constraints, heat transfer, adiabatic and isothermal processes, and the charging, storage, and discharging stages. Based on variable-mass thermodynamics theory, this study establishes a comprehensive modeling system comprising 18
distinct thermodynamic models that cover all combinations of these conditions and derives explicit analytical solutions in both differential and
algebraic forms from fundamental conservation laws. Subsequently, specific case analyses are conducted for all thermodynamic models to assess differences among them, and their correctness is verified through numerical simulation; finally, the engineering implications, limitations, and applicability of the models are discussed. The results indicate that the isochoric adiabatic model exhibits relatively large variations in temperature and pressure, posing serious safety threats to material integrity; the isochoric heat transfer model is susceptible to ambient temperature effects and exhibits somewhat smaller temperature and pressure variations than the former; the isothermal model minimizes variations during the charging stage and restores initial conditions after discharging; and the isobaric model maintains constant temperature and pressure with only volume change, representing the ideal vessel type. This study comprehensively characterizes the thermodynamic behavior of gas vessels under varying conditions, providing a systematic theoretical basis for the engineering design of such vessels.