## 4 Materials, Exergy Storage Tool, and Methodology
### Exergy Storage Tool
Parts (**a**-) show graphs for differing injection/withdrawal rates (108/108 kg/s and 108/417 kg/s) or fill and pressure reduction rates (108 kg/s/1.5 MPa/h) for all potentially available cavers, 15% of available cavers and estimates based upon the number of UCS cavers in the basins. Additionally shown, by basin, the percentage of UK electricity demand for 92% of stored energy to work. Key common to all, see Figure 3.  
Figure 8: Plots of dynamic energy storage and energy to work estimates for the preferred CHT model, over the depth range 500-1500 m and cavern heights 100–150 m considered for CAES. Parts (**a–e**) show graphs for differing injection/withdrawal rates (108/108 kg/s and 108/417 kg/s) or fill and pressure reduction rates (108 kg/s/1.5 MPa/h) for all potentially available cavers, 1% of available cavers and estimates based upon the number of UCS cavers in the basins. Additionally shown, by basin, the percentage of UK electricity demand for 92% of stored exergy to work. Key common to all, see Figure 4.0  
In practice, realistic CAES cavern operation lies somewhere between the two endmember cases, and the convective heat transfer (CHT) wall condition for a practical (diabatic) cavern operational scenario was developed and is thought to more accurately represent actual storage conditions: during the cavern charging period, thermal energy of the air stored in the cavern is lost to the immediate surrounding rock mass, whilst the air temperature still increases due to the internal compression [38]. The two-end member scenarios produce slightly greater (isothermal) and smaller (adiabatic) exergy values, bracketing the CHT model (see Figure 3 and S2, Tables S3 and S4). Consequently, we have further refined the modelling tool for CHT conditions to implement their equations and predict the exergy stored when charging an uncompensated isochoric (constant volume, variable pressure) cavern or set of caverns. Results of this scenario are presented and discussed here. Input parameters to the exergy modelling tool are summarised in S2, Table S2. Cavern surface areas and the calculation of heat transfer from the cavern void into the walls are necessary for CAES, estimates of which were derived relative to each cavern mid-point depth. They were calculated using the geothermal gradient for each specific basin, with an average annual surface temperature of 9.5 \({}^{\circ}\)C and pressure of 1 bar (14.5 psi). The tool imports the depths, volumes, temperatures, and min/max storage pressures calculated for each cavern and models iteratively, as well as the cavern-fill (exergy storage) from the starting point of the minimum to maximum permissible storage pressures. Results for the three differing cavern wall heat transfer models for each cavern over the two cavern depth ranges are output to a spreadsheet as the 'working exergy' storage in megawatt hours (MWh), together with the maximum pressure (pascals) and stored air mass (kg). However, energy losses occur during generation, most notably through heat exchangers and in the turbines. From an energy and exergy analysis for 10 salt caverns of 100 m plus height in the Cheshire Basin, it was calculated that a full charge of all 10 caverns could store a net exergy of 25.32 GWh, of which \(\approx\)92% (23.19 GWh) could be converted to work via the turbines [41]. Therefore, alongside stored exergy estimates in Figures 3-8, we also present estimates of the stored exergy to work available, data behind which are provided in S2, Tables S3-S8.