## 2 Materials and Methods  
### Sn58 Bi Alloy Plugging Casing Method  
In this study, the low-melting-point alloy used is Sn58 Bi alloy, which is a eutectic alloy consisting of 58% Bi and 42% Sn. The properties of this alloy are shown in Table 1.  
Sn58 Bi alloy has the following advantages [15; 16]:  
1. Low melting point: Its melting process requires low energy that does not affect the strength of the casing body;
2. Micro-expansion: This alloy expands in volume (similar to water freezing) when it solidifies from the liquid state to the solid state;  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Properties** & **Melting Point (\(\lx@math@degree\)C)** & **Surface Tension at** & **Thermal Expansion** & **Volume Change** & **Density at** \\  & & **155 \(\lx@math@degree\)C (mPa-s)** & **Coefficient (\(\lx@math@degree\)C\(\lx@math@degree\)–1)** & **(from Liquid to Solid)** & **21 \(\lx@math@degree\)C (g/cm\({}^{3}\))** \\ \hline Value & 138 & 438 & \(1.5\times 10^{-7}\) & +0.77\% & 8.72 \\ \hline \end{tabular}
\end{table}
Table 1: The properties of Sn58 Bi alloys [13; 14].  
* Corrosion resistance: The alloy is able to resist corrosion, especially H2S and CO2;
* High density: Due to the high density of the alloy, other impurities in the wellbore float to the top during the melting and solidification process, assisting in forming a pure alloy plug for seal integrity;
* High mobility in liquid-state alloys is capable of completing seals in tiny gaps and irregular shapes. This kind of alloy can be formed into a series of alloys with melting points of 138 \({}^{\circ}\)C-263 \({}^{\circ}\)C based on different alloy ratios [17], which makes it easy to optimize the selection based on the formation temperature.  
There is no wettability between the Sn58 Bi alloy and the metal casing [15], and the sealing of the alloy plug is completed by the expansion of the alloy, which is caused by its conversion from a liquid to a solid within the downhole casing, as shown in Figure 1.  
The alloy plugging smooth hole casing method proposed by [PERSON] [8] mainly relies on the radial force generated after the alloy solidifies and expands, as shown in Figure 1a, which makes the alloy plug come into close contact with the casing and thus completes the plugging, and the sealing path is the round surface of the inner wall of the casing in contact with the alloy. This paper proposes a sealing method wherein the downhole casing is processed with threaded grooves and then plugged by low-melting-point alloy plug. As shown in Figure 1b, the length of alloy plug in the threaded casing (the inner surface of the casing was turned threads) is similar to the length of alloy plug in the conventional alloy plugging casing method with the same amount of alloy. When the sealing surface changes from a round surface to a threaded surface, the sealing path increases, which might increase the gas sealing performance of the alloy plug.  
Compared with cement plugging casing method, the advantages of alloy plugging threaded casing method are as follows:  
1. High stability of sealing: Sn58 Bi alloy itself has the characteristics of denseness, corrosion resistance, high strength, etc., and the alloy plug formed is able to withstand the interference of most unfavorable factors downhole;
2. Compared with the curing time during the molding process of cement plugs, the alloy plug can complete the sealing function after cooling naturally at the bottom of the well, and the operation time is greatly reduced;
3. After turning threads in the casing, the sealing path per unit sealing length is increased and gas sealing performance is improved, while the threaded structure increases the axial pressure-bearing capacity of the alloy plug.  
Figure 1: Schematic diagram of downhole alloy plug and casing structure.