## 3 Selection of Gas Injection and Brine Discharge Method
### Parameter Determination for BWSCs with a Large Height Difference
\[P_{ft}=\frac{\rho_{b}\lambda hv^{2}}{2d} \tag{3}\]  
\[Re=\frac{vd\rho_{b}}{\mu} \tag{4}\]  
\[\varepsilon=\frac{2\Delta}{d} \tag{5}\]  
In addition, the flow friction resistance generated during brine flow within the residue is correlated with the brine flow rate, flow path length, and fluid flow regime. This flow friction resistance can be determined through parameter fitting utilizing a modified dual-well operation approach--one well for brine injection and another for brine extraction [27]. \[P_{fs}=F(Q_{S},L_{S},\lambda_{S}) \tag{6}\]  
Figure 6: GIBD process for large-height-difference butted-well salt caverns. (**a**) Phase one; (**b**) Phase two. The arrow indicates the fluid flow direction. The yellow area represents the region occupied by gas, and the blue area represents the brine region. Gas is injected into the cavity through the wellbore, following the gas pipe flow theory. The gas pressures in the cavity and at the wellhead exhibit the following conversion relationship [28]:  
\[P_{p}=P_{g}exp\left(\frac{0.03415\gamma_{0}h}{\overline{ZT}}\right) \tag{7}\]  
Additionally, according to the gas state equation, the following relationship exists when converting the gas injected into the cavity to ground standard conditions. Figure 5:0  
To facilitate the analysis of the parameters' variation rules, based on the real parameters of the BWSC in Figure 2 and the simplified model shape parameters in Figure 5 (which form Data Table 4), the above formulas are applied to calculate the relationship chart between the gas injection rate, gas injection pressure, casing shoe pressure, and brine discharge rate in the first stage of Figure 6, as shown in Figure 5:1 It can be seen from the figure that as the brine discharge rate increases, the gas pressures both at the wellhead and at the casing shoe increase. Under the given upper-limit allowable pressure of the casing shoe, the maximum brine discharge rate and the wellhead gas-injection rate can be determined according to this chart. Meanwhile, it can also provide parameter guidance for the phased gas injection and brine discharge design. The utilization volume of the residue can be calculated by equivalent calculation of the volume of a cylinder with an equal diameter, combining the wellbore trajectory, the bottom shape of the cavity as measured by sonar, and the volume calculated by Equation (1). The first stage of the OIOD method was tested in a pair of reconstructed BWSCs in a domestic salt mine. Figure 8 presents the gas injection and brine drainage parameters of this test well group along with the fitting results obtained using the established model. It can be observed that the errors between the two are minimal, demonstrating that the constructed model exhibits strong adaptability. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Item** & **Value** & **Item** & **Value** \\ \hline Roof depth of shallow cavern, m & 1526 & Natural gas density, g/cm\({}^{3}\) & 0.56 \\ \hline Bottom depth of shallow cavern, m & 1586 & Gas average compression factor in well & 0.80 \\ \hline Roof depth of deep cavern, m & 1721 & Average temperature in the cavity, \({}^{\circ}\)C & 60 \\ \hline Bottom depth of deep cavern, m & 1781 & Volume of shallow cavern, m\({}^{3}\) & 200,960 \\ \hline Brine discharge pipe depth, m & 1773 & Volume of deep cavern, m\({}^{3}\) & 200,960 \\ \hline Brine discharge pipe size, mm & 114.3 & Pipe roughness, mm & 0.20 \\ \hline Brine discharge wellbore size, mm & 215.9 & Brine density, g/cm\({}^{3}\) & 1.20 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Basic parameters for gas injection and brine discharge in the BWSC with large height difference.