## 1 Introduction  
With the development and progress of industrial technology, global energy utilization continues to rise. In the context of the post-epidemic era, governments worldwide have implemented economic recovery policies in response to the COVID-19 epidemic. Additionally, due to the international situation resulting from the Russia-Ukraine conflict, global energy consumption has been further increased. According to the \"BP Statistical Review of World Energy (2022)\" statistics, see Figure 1[1], the global primary energy consumption in 2021 reached 595.15 EJ, compared to 564.10 EJ in 2020 during the epidemic containment period. For the first time, the annual average growth rate of primary energy consumption reached a record high of 5.8%. In 2021, the total consumption of fossil fuels such as oil, coal, and natural gas reached 489.66 EJ, accounting for 82.3%, with a year-on-year growth of 5.6%, maintaining its dominant position. However, the combustion of fossil fuels and oxygen produces excessive CO\({}_{2}\), leading to severe carbon emissions exceeding the limit in the atmosphere. Consequently, global temperatures are rapidly rising, Antarctic glaciers are melting, and sea levels are rising, seriously disrupting the ecological balance of oceansand land [2; 3; 4]. To address the worsening ecological and environmental problems caused by excessive carbon emissions, seeking active and effective measures to control carbon emissions and efficient technologies has become a global consensus [5; 6]. In the current global context of the low-carbon transition, renewable energy generates virtually no pollutants throughout the entire energy utilization cycle and has low marginal carbon emissions. However, renewable energy sources such as wind and solar power are subject to significant fluctuations due to environmental and seasonal impacts, necessitating complementary energy storage facilities for sustainable energy supply. Presently, energy storage technology is not yet mature, resulting in high utilization costs for renewable energy and hindering large-scale deployment [7; 8; 9]. At this time, natural gas, as a low-carbon energy source, can meet the low-carbon clean energy supply requirements while reducing the transformation span of the supply-side energy consumption structure. Thus, achieving large-scale, safe, and concealed natural gas reserves is crucial for the smooth transition from high-energy-consuming sources such as coal to clean energy sources like renewable energy. This also provides assurance for national energy supply security and stable industrial energy efficiency. Currently, underground natural gas storage is characterized by high efficiency, safety, and stable operation. It has become the primary way of storing natural gas globally with nearly 13% of the world's natural gas being stored in underground storage for future peak processing. At the same time, with the continuous exploitation of natural gas resources, the pressure in the original gas reservoirs is declining, and some reservoirs are reaching depletion. Nevertheless, due to the completeness of the gas-exploited facilities, these depleted reservoirs are perfect carriers for the economical and efficient construction of underground natural gas storage [10; 11; 12]. Therefore, in the current international scenario where there is a significant rebound in global primary energy consumption, urgent research is needed on the dynamic closure sealing evaluation and site optimization of underground natural gas storage, especially those with depleted gas reservoirs. This is a critical aspect in the construction of underground storage in depleted gas reserves, and it directly impacts the safe and smooth operation of subsequent capacity expansion, production, and cyclic injection and exploitation [13; 14; 15; 16]. According to a large number of statistics, mudstone, carbonate rock, and gypsum-salt rock are the main lithological characteristics of the cap rock in large and medium-sized oil and gas fields, with mudstone being the most common one [16].