## 1 Introduction  
With the continued exploitation and large-scale application of fossil fuels such as coal, oil, and natural gas in countries all over the world, the content of greenhouse gases such as CO\({}_{2}\) in the atmosphere has been rising, leading to global warming and the frequent occurrence of extreme weather. For this reason, countries around the world are paying more and more attention to how to effectively control greenhouse gas emissions and complete sustainable development [1]. In recent years, the international community has reached a unanimous consensus on CO\({}_{2}\) emission reduction, and carbon capture, utilization, and storage (CCUS) is an important means of CO\({}_{2}\) emission reduction [2]. Currently, the main methods of CO\({}_{2}\) storage include geological storage, oceanic storage, chemical storage, etc. Among them, geological storage aims to inject CO\({}_{2}\) into the Earth's strata so that the CO\({}_{2}\) is stored underground in a supercritical state, and this method can complete permanent storage of CO\({}_{2}\) and improve the extraction efficiency of crude oil under certain conditions [3]. Ideal CO\({}_{2}\) sequestration sites are often located in concentrated oil and gas development blocks, where abandoned wellbores are common, and the risk of CO\({}_{2}\) leakage along the abandoned wellbores increases dramatically when the abandoned wellbores penetrate the cap layer. Great plugging performance is the key to complete downhole carbon-sequestration technology; therefore, how to complete great long-term plugging of wellbores is important to CCUS [4]. Currently, cement is the main plugging material used in CO\({}_{2}\) geological storage operations, but in most cases, there are leakage channels at the cement plug-casing interface that make it difficult to complete long-term CO\({}_{2}\) plugging [3; 5]. The main reasons for the generation of leakage channels include (1) cement shrinkage during solidification caused by hydration or phase changes, which destroy the integrity of the wellbore [6]; (2) the acidity of CO\({}_{2}\) gas, which can seriously damage the cement plug by hydration of the silicate cement system [7] and cause serious breakage of the seal at the cement plug-casing interface; (3) the cement's low tensile strength after solidification, which makes it prone to fractures and other defects in the high-pressure environment downhole, reducing the plugging effect. In order to solve the problem of gas flurries caused by these cementitious materials, [PERSON] [8] proposed the adoption of low-melting-point alloys to complete downhole plugging. In 2018, Bi-Sn UK [9] proved the feasibility of alloy plugging in 12 wells in Oklahoma and 2 wells in Alaska. [PERSON] [10] used a total of 35 bismuth alloy plugs to seal 30 wells abandoned offshore of Norway and showed experimentally that the seals should last at least 1000 years. In the same year, [PERSON] [11] conducted experimental tests on the sealing effect of alloy plugs in brine wells and confirmed the feasibility of alloy plugs for brine well plugging. In 2023, [PERSON] [12] experimentally verified that alloy plugs have great mechanical pressure-bearing properties and can withstand large axial loads. The alloy plug mainly relies on volume expansion in the solidification process to generate a certain radial force, which brings the inner wall of the casing and the alloy body into close contact to complete the plugging, and its sealing path is the inner wall of the casing and the alloy contact position of the circular surface. However, the alloy plugging smooth hole casing method needs to position a plug with a longer sealing length downhole; therefore, this paper proposes a sealing method in which the downhole casing is processed with threaded grooves and then plugged with a low-melting-point alloy plug.