## Highlights:  
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Salt caverns are extensively used for Underground Natural Gas Storage to regulate the regional and seasonal imbalances in gas demand [5; 6] and Strategic Petroleum Reserves to ensure energy security [7; 8; 9]. Salt caverns can also be used for Compressed Hydrogen Energy Storage (CHES) and compressed air energy storage (CAES) [10; 11; 12]. These are two of the most cost-efficient large-scale energy storage technologies, which can buffer the electricity supply and demand cycles [13; 14]. Currently, all the diabatic utility-scale CHESs and CAESs in the world have been built in salt caverns [15; 16]. At present, there are only three salt caverns in China, and these are mainly used for storing natural gas [17; 18]. As shown in Figure 1, the domestic production of natural gas has increased slowly, and the consumption of natural gas has risen rapidly in China since 2008 [19]. China's natural gas imports and dependency are rising, which highlights the necessity for sufficient storage and peak shaving to ensure energy security. The construction of China's three salt cavern gas storages employed the single-well-vertical method [20; 21; 22], a technique that requires a salt formation of substantial height to secure a large cavity volume. However, most of the salt rock formations in China deemed appropriate for constructing underground gas storage are continental deposits. These are characterized by thin single layers, many interlayers, and a high content of insoluble impurities [23]. The stability of salt caverns is affected by numerous unfavorable factors, resulting in more complex designs and construction processes for the salt caverns within layered salt rock formations [24; 25]. Therefore, the bedded salt formations in China are unsuitable for large-scale straight salt caverns, making horizontal salt cavern construction a preferable alternative [26]. At present, the only successful case is the Volgograd horizontal salt cavern in Russia [27]. Compared with the two-well-horizontal (TWH) method [22; 28], the multi-step horizontal construction method can be implemented in salt layers with a thickness of less than 80 m, can be utilize more salt formations, and does not require an antisolvent [10]. Figure 2 shows the construction process of a multi-step horizontal salt cavern. A directional well is drilled to connect with the vertical well. Then, a tube is put into the directional well. The process is to inject freshwater from the inlet and replace high-concentration brine from the outlet of the vertical well, and injection and discharge are cycled continuously. The injection tube is removed at a certain distance for a certain time, and then the next stage is leaching. After several steps, a multi-step horizontal cavern is formed finally. The modeling of multi-step horizontal salt caverns construction is less frequently conducted due to the complexity of their shape and flow fields. Presently, the theoretical studies on the construction of multi-step horizontal caverns primarily concentrate on numerical simulations and extensive indoor salt rock experimentation. This technology remains in its nascent stages, straddling between theoretical inquiry and preliminary field explorations, and has yet to reach maturity [29; 30; 31]. Figure 1: Schematic diagram of the consumption of natural gas in China. Many models and codes have been developed to simulate the construction of vertical caverns, including SANSMIC, WinUbro, and PCL [32]. However, there are few models for simulating horizontal salt caverns due to their complex shape and flow field. The multi-step horizontal construction method has been proposed [33], highlighting the importance of controlling the step distance to maintain the integrity of step caverns. Based on the floating plume model to describe the flow field, [PERSON] [34] initially simulated the expansion of a horizontal cavern's middle segment using a horizontal cylindrical grid, disregarding the vertical concentration gradient of the brine.