Expansion of infrastructure acquiring electricity from renewable sources determines the necessity of energy storage technology development. For highly urbanized areas specializing in the exploitation of underground coal deposits, due to the progressive decarbonization process, an adiabatic compressed air energy storage system using post-mining mine shafts has been proposed. The adiabatic character of the system is provided using Thermal Energy Storage (TES) tank, which is designed to be installed in a mine shaft volume. The solution determines unique geometrical dimensions compared to the studied and applied heat storage tanks, which affect both the heat transfer intensity and pressure drop of the flowing medium. This paper presents an exergy analysis of the performance of heat storage tanks on a laboratory scale, which was based on a numerical analysis validated on experimental data. It is shown that as the slenderness of the storage tank increases, the exergy efficiency of the heat storage process increases from 90.7% to 98.5% depending on the geometry studied. For the full cycle of the heat storage performance, exergy efficiency values ranging from 56.2% to 69.0% were obtained depending on the studied geometry.