# Shape Modelling and Volume Optimisation of Salt Caverns for Energy Storage
## 5 Conclusions  
In this paper, 28 caverns differing in shape and diameter were evaluated in terms of stability factors such as displacement, effective strain, von Mises stress, the safety factor and the strength/stress factor as well as volumetric closure. The stability performance of these caverns was compared, and the optimal cavern shape and volume in the geological conditions of the bedded salt deposit (the Mechelinki salt deposit) was found. Moreover, the performed evaluation aimed to determine the impact of sharp and smoothed edges on stability factors analysed in numerical simulations. Numerical modelling indicated that the analysed stability factors are sensitive to changes in the initial cavern diameter and shape. Moreover, simulated shapes with sharp edges showed worse performance than shapes with smoothed edges. The caverns with a maximum initial diameter of 75 m (D/H ratio 5/8) with an enlarged top and bottom showed positive results. However, the caverns with sharp edges and ss1 showed a local increase in displacement in the middle part of the caverns and in the effective strain in the cavern's roof and bottom. The smoothing of the sharp edges in ss2 and ss3 contributed to the elimination of these areas. An overall comparison between the enlarged-top and enlarged-bottom caverns tended to favour enlarged-top caverns. This shape also showed promising results for caverns with a maximum initial diameter of 90 m, but only with ss3. The cylindrical caverns showed the best results of all analysed shapes, but their volume was about 22% smaller than the enlarged caverns with a diameter of 75 m. Therefore, in the simulated geological conditions, the most optimal shape is an enlarged top with a maximum initial diameter of 75 m. The enlarged-bottom cavern with a maximum initial diameter of 75 m can also be considered on the grounds of the positive evaluation results. Moreover, the described results indicate that a possible local increase in the cavern diameter resulting from the leaching and petrological diversity of rock salt, causes no danger to cavern stability. The stability performance of all analysed caverns showed a dependence on operating pressure. There was a large difference in the value of each stability factor between the injection and withdrawal period. The lowering of the operating pressure in the withdrawal periods had a negative impact on the evaluated factors. This impact increased in each operation cycle and was most visible in the displacement and effective strain simulation results. In future research, it would be interesting to consider the various values of k (the ratio between horizontal stress to vertical stress) and its impact on the cavern stability factors. The results presented in this paper can be used for the design process of new cavern fields for storing natural gas, compressed air or hydrogen. The described methodology can be adapted for the estimation of cavern storage capacity in bedded salt deposits. The results of the performed evaluation are also applicable to the design of optimal cavern shapes and dimensions. Moreover, the assessment of risks related to the cavern operation cycles and the planning of injection and withdrawal periods can benefit from the results described in this paper. **Supplementary Materials:** The following are available online at [[https://www.mdpi.com/2076-341](https://www.mdpi.com/2076-341)]([https://www.mdpi.com/2076-341](https://www.mdpi.com/2076-341)) 7/11/1/423/s1. SUPPLEMENT A, full results of the displacements analysis. SUPPLEMENT B, full results of the effective strain analysis. SUPPLEMENT C, full results of the von Mises stress analysis. SUPPLEMENT D, full results of the strength/stress ratio analysis. SUPPLEMENT E, full results of the safety factor analysis. Conceptualization, K.C. ; methodology, K.C., M.K. ; software, M.K. ; validation, M.K. ; analysis, K.C. ; writing--original draft preparation, K.C. ; writing--review and editing, K.C. All authors have read and agreed to the published version of the manuscript.