## 3 Results
### Flow Field Characteristics  
Natural cold gas injection can not only cause the water-ice phase transition but also displace pore water. Therefore, in these experiments, a coupling physical field of two-phase flow and water-ice phase transition existed in the freezing model. The pressure difference between the inlet and outlet of the freezing model could indirectly reflect the change of the gas-water two-phase flow field and reflect the redistribution of water.  
Figure 5 depicts the pressure differences between the inlet and outlet of the freezing model in the experiments. As the flow valve needed to be adjusted irregularly in order to maintain the stability of the flow rate, the flow rate would fluctuate, which was also the reason for the fluctuation of the pressure differences measured in real time. According to the fitting curves of the pressure differences shown in Figure 5, it showed that in the early stages of cold gas injection, the reduction rates of pressure differences was relatively large, and after about 50 minutes, the reduction rates slowed down. In the process of gas injection, water in the pores would redistribute under the displacement of gas flow,  
Figure 4: Comparison of temperature change at the T2 position in different conditions; (**a**,**b**) depict the influence of gas flow rate, (**c**,**d**) depict the influence of initial water content.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Experiment Number**} & \multirow{2}{*}{\begin{tabular}{c} **Freezing Rate of T1–T2** \\ **(cm/min)** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Freezing Rate of T2–T3** \\ **(cm/min)** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Freezing Rate of T3–T4** \\ **(cm/min)** \\ \end{tabular} } \\  & & & \\ \hline
1 & 0.46 & 0.33 & 0.18 \\
2 & 0.60 & 0.52 & 0.47 \\
3 & 0.37 & 0.44 & — \\
4 & 0.61 & 0.52 & — \\ \hline \hline \end{tabular}
\end{table}
Table 3: Freezing rate of each section.  
where numerous smooth and stable gas flow channels gradually formed. Before the formation of the gas channels, part of the pores was filled with water and the path of the gas flow was blocked, resulting in a large pressure difference in the early stage. After a certain period of gas flooding, some pore throats were opened, and water redistributed. Numerous gas channels (Figure 6a,b) were formed in the pores between sand grains, which reduced the gas flow resistance. Therefore, the reduction of pressure differences slowed down later.  
However, the water-ice phase transition also occurred in the pores, because of the expansion of the water volume during freezing, and the pore spacing between sand grains was enlarged, which would undoubtedly reduce the flow resistance of gas. The coupling of the water-ice phase transition and displacement reduced the pressure differences gradually. This reduction phenomenon of pressure  
Figure 5: Pressure difference between two ends of the freezing model during natural cold gas injection ((**a**) Experiment 1, (**b**) Experiment 2, (**c**) Experiment 3, and (**d**) Experiment 4).  
Figure 6: Gas channels. (**a**) Gas channels in the outlet after injection, (**b**) Diagram of gas channels in pores.  
difference can decrease the difficulty of natural cold gas injection, which is beneficial to the actual artificial freezing construction.  
AGF can not only improve the strength of soil, but also block groundwater flow. Freezing of the water-bearing sand will undoubtedly increase the strength of soil; however, when groundwater outside the frozen area flows in, water will change into ice under the effect of the subcooled environment, and then the flow passage will be blocked [27]. Meanwhile, after displacement by the gas flow, the gas phase saturation in the pores would increase, and the block effect on groundwater flow will be improved with the aid of the gas resistance [28; 29].