To investigate the evolution patterns of thermodynamic processes within a hydraulic-compensated isobaric tunnel-type compressed air energy storage (CAES) cavern, a systematic study is conducted via theoretical analysis. Three thermodynamic models, including the adiabatic, isothermal, and convective heat transfer models, accounting for the dynamic variation in the heat exchange area during CAES cavern operation across different cross sections are established to describe changes in the air state in gas storage. Analytical solutions are derived for the adiabatic model, and finite-difference formulations are established for the isothermal and convective heat transfer models. Formulas for calculating the heat transfer area are also provided for circular and gateshaped tunnel-type caverns. Finally, the temperature, pressure, exergy, and air mass variations for all three models are analyzed through a case study. The results demonstrate the following: (1) During charging and discharging, the average temperature of compressed air in the isobaric tunnel-type cavern fluctuates minimally, remaining between the initial cavern air temperature and injected air temperature. (2) The air volume and exergy within the cavern exhibit approximately linear variations. Among the three models, the isothermal model yields the highest exergy values (2.23×10⁶ MJ), whereas the adiabatic model produces the lowest (2.11×10⁶ MJ). The exergy values of the convective heat transfer model fall between these two extremes (2.17×10⁶ MJ). (3) The isothermal model stores the greatest air mass (6.47×10⁶ kg), the adiabatic model stores the least (6.11×10⁶ kg), and the value of the convective heat transfer model lies between them (6.29×10⁶ kg). The relationship between air mass and exergy exhibits the same trend across all three models.