# Shape Modelling and Volume Optimisation of Salt Caverns for Energy Storage
## 3 Results
### Strength/Stress Ratio (SSR)  
In the analysed time (9.5 years), there was a major difference in the value and distribution of the strength/stress ratio (SSR) between withdrawal and injection periods. The SSR in the initial period ranged from 4.0 to 6.0 (green and light blue area) at the walls of the caverns. It locally decreased to 3.0-3.5 (dark blue area) in the caverns with an initial maximum initial diameter of 120 m, precisely at the roof of the enlarged-top caverns (from se to ss2, Figure 14 A-C) and in the bottom of the enlarged-bottom caverns with se and ss1 (Figure 14E,F). In the first withdrawal period, a low SSR (1.80-2.5) was indicated in an area below the bottom of the enlarged bottom caverns with a maximum initial diameter of 120 m from se to ss2 (Figure 15A-C). In this group, but with a maximum initial diameter of 90 m, this low SSR (1.80-2.5) occurred locally in the caverns with se and ss1; however, the caverns with a maximum initial diameter of 75 m were only characterised by the se (Figure 15I-L). The SSR increased to 3.0-4.0 below the bottom of the caverns with an enlarged top and a  
Figure 13: The vMS in the enlarged top and bottom caverns; the last cycle: (**A**,**E**,**L**,**M**) a maximum initial diameter of 120 m: (**A–C**,**E–G**,**I–K**,**M–O**) a maximum initial diameter of 90 m, (**D**,**H**,**L**,**P**) a maximum initial diameter of 75 m.  
In the first injection period, the lowest SSR reached 6.0-7.0 in the area below the bottom of the caverns with an enlarged bottom and a maximum initial diameter of 120 m (Figure 16). Results of numerical simulations for the last injection and withdrawal period were similar to those of the first cycle. There were only some differences in the SSR value, which slightly decreased to 1.75-2.0 (Figure 16). The SSR seemed to be more influenced by caverns' dimensions and shape than by the \"smoothing\" of the sharp edges (Figures 14-17). This is illustrated by the performance of the cylindrical caverns compared to the caverns with a maximum initial diameter of 120 m (Figures 15 and 17) in the withdrawal periods. In the cylindrical caverns, the SSR values of 2.5-3.5 occurred locally below the bottom and in the middle part of the cavern with se and s1 (Figure 18A,B). An SSR in a range of 1.75-2.5 covered the area below the bottom of all simulated caverns with an enlarged bottom and a diameter of 120 m, regardless of the \"smoothing\" of their edges (Figure 15A,B and Figure 17C,F). The caverns with an enlarged top showed better performance than the enlarged-bottom caverns (Figure 15E-H). The lowest SSR registered in these caverns was 3.0-4.0 in the withdrawal periods. respectively (Figure 23F,H). The convergence of the cylindrical cavern with se was 5.81%. The \"smoothing\" of sharp edges had an impact on convergence, but this impact was stronger in the caverns with a maximum initial diameter of 120 and 90 m. The convergence in the cavern with an enlarged top, ss3 and a maximum initial diameter 120 m was 8.50%, but with a maximum initial diameter of 75 m, it decreased to 5.61%. Results for the enlarged bottom caverns were similar: the convergence of caverns with a diameter of 120 m was 8.83% and that of caverns with a diameter of 75 m was 5.65% (Figure 23). The cylindrical shape was less affected by the \"smoothing\" of the sharp edges. Consequently, the convergence in cylindrical caverns ranged from 5.81% for se to 5.13% in ss3 (Figure 23). The volumetric closure in simulated caverns is related to their dimensions and the operating pressure.