# Shape Modelling and Volume Optimisation of Salt Caverns for Energy Storage
## 4 Discussion  
From the above analysis, it was found that caverns with an enlarged top outperformed caverns with an enlarged bottom when evaluated in terms of stability factors such as displacements, ES, vMS and SSR as well as volumetric closure. These results agree with the findings of [PERSON] and [PERSON] [26] and [PERSON] et al. [29]. The worse performance of caverns with an enlarged bottom was caused by the larger exposure of the cavern surface area to higher pressure. This pressure was caused by the difference between the in situ hydrostatic pressure and the operating gas pressure in the deeper part of the salt beds. However, the SF evaluation showed better results for caverns with an enlarged bottom because of the lower deviatoric stress in the cavern roof. As explained by [PERSON] and [PERSON] [26], in caverns with an enlarged top, the angle of the slope of the cavern walls directs the pressure to hold up the cavern roof, thereby decreasing downward vertical displacement. This decrease in deformation is compensated by higher deviatoric stresses in the cavern roof, resulting in the possibility of dilatant damage and fracturing. Moreover, in the analysed caverns, the higher thickness of the roof pillar compared to the bottom pillar contributed to the better stability performance of the enlarged-top caverns. Referring to the results of earlier works [2; 25; 32; 35], cylindrical caverns showed the best performance of the analysed shapes. The results of the numerical simulation indicated that the cavern dimensions have a great impact on the stability factors. The caverns with a maximum initial diameter of 120 m showed the worst geomechanical performance of all analysed caverns. On the contrary, most of the evaluated factors, except for displacements and SSR, showed similar results in cylindrical caverns with a maximum initial diameter of 75 m. [PERSON] et al. [33] concluded that the dimensions of caverns have a greater effect on cavern deformation than the cavern shape. However, in the analysed cases, the performance of caverns with a maximum initial diameter of 75 m was almost the same, and the caverns with an enlarged top presented better results than caverns with an enlarged bottom if the maximum initial diameter was 90 m or 120 m.  
The \"smoothing\" of the sharp edges performed in the three steps had a significant effect on the cavern performance in all analyses. Shapes with sharp edges had the worst results in the evaluation against stability factors. The assumption that sharp edges are prone to the stress concentration in the rock mass surrounding the caverns that caused the formation of damage zones [35; 36] has been confirmed. The \"smoothing\" steps caused the roof and the bottom of the analysed caverns to be less flat and, as a consequence, better able to withstand deformations and applied load. [PERSON] et al. [42] stated that caverns with a plain bottom should be avoided in design and construction. A flat roof of caverns was mentioned by [PERSON] et al. [43], [PERSON] et al. [44], [PERSON] et al. [45], [PERSON] et al. [2] and [PERSON] et al. [46] as a key factor in incidents of casing and roof stability loss. Moreover, a \"smoothing\" of sharp edges results in the formation of ellipsoidal caverns that are considered optimal for maintaining stability and resistance to volume convergence [3; 29; 47]. For the analysed shapes, the \"smoothing\" effect was stronger in the enlarged caverns than the cylindrical caverns. The geomechanical performance of the cylindrical shape was less affected by \"smoothing\" than the enlarged cavern. Moreover, the \"smoothing\" of the sharp edges contributed to the shrinkage in the volume of analysed caverns, resulting in lower susceptibility to volumetric closure. In addition, all shapes and dimensions evaluated in terms of stability factors had a positive relationship with operating pressure. A high operating pressure (injection periods) improved the stability and performance of the analysed factors.