# Shape Modelling and Volume Optimisation of Salt Caverns for Energy Storage
## 1 Introduction  
Salt caverns are the best method for the storage of natural gas due to their large capacity, safety and long operation time [1, 2]. Most previous studies concerning underground gas storage facilities have been limited to pure and homogeneous salt formations in salt domes. However, in the last two decades, increasing attention has been paid to gas storage in bedded salt formations [3, 4, 5, 6]. In recent years, salt caverns have been considered for large-scale hydrogen and compressed air storage [7, 8, 9, 10]. The pressure limits of salt caverns in bedded salt deposits were studied by [PERSON] and [PERSON] [11]. These authors described cavern deformation and bedding plane slips for a variety of cavern configurations. The optimal operating pressure of salt caverns in a bedded salt formation with high insoluble content was analysed by [PERSON] et al. [12] and [PERSON] et al. [13]. The cavern roof stability in a bedded rock salt formation was studied by [PERSON] [14], [PERSON] et al. [15] and [PERSON] et al. [16]. The influence of interlayers on storage operations was analysed by [PERSON] et al. [17] and [PERSON] and [PERSON] [18]. Weakness planes and hydraulic fracturing in bedded salt formation were reported by [PERSON] and [PERSON] [19]. The deformation characteristics of mudstone interbeds and their impact on cavern stability was described by [PERSON] et al. [20], [PERSON] et al. [5], [PERSON] et al. [3] and [PERSON] and [PERSON] [4]. The influence of anhydrite interbeds on cavern stability was studied by [PERSON] et al. [21]. Horizontal caverns in bedded salt deposits were studied by [PERSON] et al. [22] and [PERSON] et al. [23]. As described above, most previous papers were designed to study cavern performance and damage in salt, determine the safety factors and develop guidelines for cavern design. Field engineering experience and literature [3; 24; 25; 26; 27; 28; 29; 30] show that the rational design of a salt cavern's shape and dimensions can improve safety and reduce negative effects [29]. However, finding the optimal shape and dimensions of a salt cavern in mining and geological conditions is still a difficult problem. During the construction of salt caverns, their shapes are the most important concern for safety and stability issues [5; 6]. The shapes and dimensions of salt caverns used for gas storage are greatly differentiated [31]. This variety results from many factors such as the depth of the cavern location, geological and mining conditions, strata lithology and the solubility of salt and admixtures. Some authors have investigated different shapes of salt caverns and their effect on stability. A slender cylinder was chosen as the most effective shape for maintaining stability by [PERSON] and [PERSON] [25]. Caverns with an enlarged top are leached for natural gas and oil storage [30; 32]. Safety factors, volume shrinkage, displacements and ground subsidence were analysed by [PERSON] and [PERSON] [26] for salt caverns with a shape of a cylinder, a cylinder with an enlarged top, a cylinder with an enlarged middle and a cylinder with an enlarged bottom. The same shapes were studied by [PERSON] et al. [29] but in different geological conditions. The enlarged-middle cavern design had the highest safety factor, but the enlarged-bottom design had the lowest performance. The stress distribution, stability and displacements of caverns with a cylindrical, a tapered cylinder and a teardrop shape were studied by [PERSON] [32]. This work determined that a cylindrical shape was the most stable for underground storage. The cylindrical shape was also considered the most optimal in relation to the stability and volume of the salt cavern by other authors [2; 15; 25; 29]. Moreover, the optimal ratio of the short (D) and long (H) axes of ellipsoidal salt caverns for gas storage has been studied. A D/H ratio in a range from 0.40 to 1.00 was evaluated against the effective volume, maximum displacement and safety factor by [PERSON] et al. [27].