## 4 Analysis of Pipeline Overvoltage under the Action of Multi-Tower Flow
### The Influence of \"Tube-Line\" Spacing  
The study investigates the impact of different \"tube\" spacings (\(d_{gp1}\)) on the overvoltage of a natural gas pipeline when subjected to lightning strikes. The fixed soil resistivity (\(\rho\)) is 1000 \(\Omega\cdot\)m and the lightning peak current (I\({}_{0}\)) is 50 kA. The \"tube\" cross angle (\(\beta\)) is 0\({}^{\circ}\). The  
Figure 10: Potential distribution of tower grounding grid and natural gas pipeline at cross-crossing under different soil resistivity. \"tube\" spacing options considered are 40 m, 50 m, 60 m, 70 m, 80 m, and 90 m. Figure 11 illustrates the amplitude of lightning-induced overvoltage on the natural gas pipeline at the intersection. Figure 12 shows the distribution of potential height for the tower grounding grid and the intersecting natural gas pipeline under different \"pipeline\" spacings. Based on the findings of Figure 11a, it was observed that as the spacing between pipelines increases, the induced electric potential of both the metal layer and the insulation layer of the natural gas pipeline decreases. Specifically, when the pipeline spacing increases from 40 m to 90 m, the induced voltage of the metal layer decreases from 42.25 kV to 30.96 kV and the induced voltage of the insulating layer decreases from 47.56 kV to 32.37 kV; these reductions correspond to a decrease of 26.72% and 31.94%, respectively. Figure 11b illustrates that the withstand electric potential of the pipeline insulation layer gradually decreases with the increase in pipeline spacing. However, as the spacing continues to increase, the voltage drop trend of the insulation layer becomes more gradual. For instance, when the spacing increases from 40 m to 70 m, the withstand voltage of the insulating layer decreases from 7.23 kV to 2.53 kV, a decrease of 65.01%. When the spacing further increases from 70 m to 90 m, the withstand voltage of the insulating layer decreases from 2.53 kV to 1.91 kV, representing a decrease of only 24.51%. Figure 11: Influence of “pipeline” spacing on overvoltage of natural gas pipeline at cross-crossing. (**a**) Induced voltage amplitude of metal layer and insulation layer of pipeline. (**b**) Voltage amplitude of pipeline insulation layer. Figure 12: The potential height distribution of tower grounding grid and natural gas pipeline at cross-crossing under different “pipeline” spacings. (**a**) \(d_{gp1}\) = 40 m. (**b**) \(d_{gp1}\) = 50 m. (**c**) \(d_{gp1}\) = 70 m. (**d**) \(d_{gp1}\) = 80 m.  
The reason for studying the variation law mentioned above is that the pipeline's center is closer to the tower grounding grid and the effective dispersion area of the tower grounding grid. This proximity causes a more significant impact of the tower grounding grid dispersion on the center of the pipeline. When the spacing between the pipeline and the tower is small, the center of the pipeline is more affected by the dispersion of the tower grounding grid at both ends. As a result, the induced voltage curve along the insulation layer becomes more prominent. However, when the spacing between the pipeline and the tower increases within a certain range, the difference in the impact of the tower grounding grid dispersion on the center of the pipeline and the two ends reduces. Consequently, the overall curve of the induced voltage along the insulation layer becomes relatively flat. Figure 12 demonstrates that altering the \"tube-line\" spacing dgp1 does not impact the potential height distribution of the grounding grid and the surrounding soil area. In order to ensure that the lightning current components of the scattered current through the T\({}_{0}\) and T\({}_{\text{R1}}\) tower grounding grids are approximately equal, the vertical distance between the natural gas pipeline and the T\({}_{0}\) and T\({}_{\text{R1}}\) tower grounding grids can be adjusted by changing the \"tube-line\" spacing \(d_{gp1}\).