## 4 Results and Discussion
### Evaluation of the Trap Dynamic Sealing Capacity
#### 4.4.2 Evaluation of the Static Sealing Capacity of Cap Rock  
Due to the disturbance of the stress field caused by the cyclic injection and production stage of the underground storage in the depleted gas reserve, when the shear stress applied to the fault exceeds the product of the effective normal stress and the friction coefficient, the fault will undergo unstable slip, ultimately leading to longitudinal seal failure. Therefore, the dynamic sealing performance of the fault is usually described using the fault slip index. \[\beta=\frac{\tau_{s}}{\sigma_{n}} \tag{6}\]  
where \(\beta\) is the fault slip index; \(\tau_{s}\) is the tangential stress of fault, Pa; \(\sigma_{n}\) is the effective normal stress of fault, Pa. The fault slip index represents the degree to which the fault deviates from the critical slip state at any given time in the underground storage in a depleted gas reserve. In geological mechanics research, it is generally considered that the friction coefficient of the fault is 0.6. Therefore, when the fault slip index is less than 0.6, it indicates strong fault stability, and no-slip will occur. However, when the fault slip index exceeds 0.6, the tangential frictional resistance caused by the normal stress cannot balance the tangential stress on the fault, leading to a certain degree of fault slip. Figure 22: Shear safety index distribution of direct caprock before reservoir construction. When the designed upper-pressure limit conditions are reached, the distribution of the slip index of various faults is shown in Figure 23a-c. The results indicate that under the current design pressure range, the risk of activation of internal and peripheral fault slips in the underground storage in depleted gas reserves is very low, with an average slip index of only around 0.1. According to the statistical data of the fault grid slip index in Figure 24, it can also be seen that the faults have strong dynamic sealing characteristics. Figure 23: The distribution map of the current design upper limit pressure slip index should be listed as: (**a**) Penetrate through cap rock, reservoir, and layers below the cap rock; (**b**) Penetrate through cap rock and reservoir; (**c**) Penetrate through layers below the reservoir. Figure 24: The grid slip index statistics of faults. Considering that the injection phase in the underground storage in depleted gas reserve will continuously increase the formation pressure, analysis the fault activation limit pressure when the fault is in the critical slip state, the activation limit pressure of faults in reservoir segments F1, F3, F4, F5, F6, F10, and F11 are all distributed between 37.9 MPa and 50.6 MPa, with fault F5 having the smallest activation limit pressure. Based on fault activation theory, the analysis of fault-related parameters is shown in Table 5, and the results indicate that the dynamic sealing of faults within the gas-bearing zone and around it, as well as the covering faults, is strong. Thus, the combined static and dynamic evaluation shows that the overall sealing integrity of the fault in the gas reservoir is good, and it meets the conditions for construction. Specifically, based on the dynamic development data of oil and gas reservoirs and geological data of depleted gas reservoirs, we have performed an inversion of a three-dimensional stress model of the underground gas storage before construction. We describe the stress state of the cap rock and reservoir in the underground gas storage before construction. Based on this, we assessed the sealing of the cap rock and faults of the underground storage in depleted gas reserves from both static and dynamic perspectives to further determine the feasibility and sealing of the depleted gas reservoir as an optimal site for underground gas storage. This article did not address the determination of the corresponding operating upper pressure and lower pressure after this inversion of the pre-construction stress state.