## 4 Experimental Results
### Influence of Ambient Temperature and Threaded Groove on the Gas Sealing Performance of Alloy Plug
#### 4.1.2 The Influence of Threaded Groove on Gas Sealing Performance  
Comparing the smooth hole casing samples, the gas sealing performance of the alloy plug sample with M84 \(\times\) 6 threaded grooves on the inner surface increased by 1.18 MPa on average, while the gas sealing performance of the smooth casing sample with M84 \(\times\) 3 threaded grooves on the inner surface increased by 1.89 MPa on average, as shown in Figure 12.  
Figure 11: Roughness waveform of alloy plug sample after wire cutting.  
Figure 10: Schematic diagram of roughness measurement of wire-cut alloy plug sample.  
The flow path was formed by the contact between the alloy and the casing. And the flow path theoretically increased when the inner surface of the smooth hole casing was processed through threaded grooves, as shown in Figure 13. Assuming that the total length of the path on the axial surface of the alloy casing is \(L_{M}\), the relationship between the total length of the path and the length of the thread is as follows due to the regularity of the thread itself [18]:  
\[L_{M}=\frac{L_{0}}{P}L_{p} \tag{1}\]  
In Equation (1), \(L_{0}\) is the length of the threaded area, mm; \(P\) is the pitch, mm; and \(L_{p}\) is the path length of the single thread, mm.  
Since the threaded groove turned on the inner surface of the casing is a normal threaded groove, the following formula for calculating the single threaded path length can be deduced from the design criteria for normal threads [18]:  
\[L_{p}=\frac{P}{8}+\left(1-\frac{1}{4}-\frac{1}{8}\right)P\cdot sec\frac{\theta }{2}+\frac{180^{\circ}-\theta}{360^{\circ}}\cdot 2\pi\cdot\frac{P}{8 sin\theta} \tag{2}\]  
In Equation (2), \(\theta\) is the normal pitch angle, \(\theta=60^{\circ}\).  
Figure 12: Gas sealing performance of threaded tube alloy plugs at different ambient temperature conditions.  
Figure 13: Schematic diagram of the path of the alloy plug–casing interface.  
The above formula \(L_{M}\approx 1.526\ L_{0}\) can be simplified to obtain the path length of a standard ordinary thread. From this formula, it can be concluded that for the ordinary threaded casing designed according to the same standard, its path length will not change because of the change of pitch, and its path length is only related to the thread length.  
In summary, after the 100 mm threaded groove is turned on the inner surface of the casing, it can be seen that the effective plugging length of the alloy plug increases by 52.6 mm relative to the actual plugging length. So, the gas sealing performance of the 100 mm threaded casing alloy plug sample should be close to that of the 150 mm smooth hole casing alloy plug. The increase in the gas sealing performance of the alloy plug with a large pitch is close to its theoretical value. But the increase in the gas sealing performance of the alloy plug with a small pitch exceeds its theoretical value. This indicates that the decrease in pitch can also improve the gas sealing performance of the alloy plug.  
1.3 The Influence of Length-to-Diameter Ratio and Roughness on Gas Sealing Performance of Alloy Plug  
The gas sealing performance of alloy plugs in smooth casings, medium-roughness casting, and high-roughness casing of the same plugging length under the same test conditions did not show a significant difference, as shown in Figure 14.  
In order to research the effect of the length-to-diameter ratio on the gas sealing performance of the alloy plug, gas sealing tests on different length-to-diameter ratios of alloy plugs at the same ambient temperature were conducted. The results are shown in Figure 14. The results show that the gas sealing performance of the alloy plugs in the smooth hole casing shows an obvious linear growth relationship with the increase in the plugging length. And the gas sealing performance of alloy plugs in threaded casing increases with the increase in the length-to-diameter ratio, and the growth trend is consistent.