## 3 Results and Discussions
### Prediction Results of the Chen-Guo Theoretical Model
Figure 3 shows the formation pressure of CO\({}_{2}\)-CH\({}_{4}\) hydrates at different temperatures and CO\({}_{2}\) molar fractions (in logarithmic form). In order to check whether the mixed gas is liquefied, we also plotted the dew point lines of the mixed gas at CO\({}_{2}\) molar fractions of 0.6, 0.8, 0.9, and 1.0 in Figure 3.  
From the figure, it can be observed that temperature significantly affects the formation pressure of CO\({}_{2}\)-CH\({}_{4}\) hydrates, with lower temperatures resulting in lower hydrate formation pressures. The trend of curve changes can be divided into three regions based on temperature: below freezing point (I), regions with a freezing point up to 10 \({}^{\circ}\)C (II), and above 10 \({}^{\circ}\)C (II). In the first two regions, the formation pressure of hydrates increases with the increase of temperature, and the higher the content of carbon dioxide in the mixed gas, the lower the formation pressure of hydrates. It is worth noting that within the freezing point region (I), the rate of increase in hydrate formation pressure with increasing temperature is significantly lower than in the region above the freezing point. Taking a gas mixture with a CO\({}_{2}\) mole fraction of 0.4 as an example, due to the large temperature difference between day and night in the cold region, the outdoor temperature in winter can even be below 0 \({}^{\circ}\)C. Under conditions of approximately 2 MPa, hydrates can quickly form. Furthermore, the calculation results also indicate that in region (I) and (II), as the CO\({}_{2}\) mole fraction increases, the formation pressure of hydrates gradually decreases, indicating that the presence of CO\({}_{2}\) makes hydrate formation easier, which poses greater challenges for the prevention and control of hydrates. Therefore, attention should be paid to wellhead thermal insulation and pressure regulation to keep the conditions in the wellbore under the hydrate equilibrium condition. In addition, the pressure of produced fluids needs to be reduced in the process of external transport, so there will be throttling effect. The pressure before and after throttling should be controlled based on the hydrate phase equilibrium condition to prevent the formation of hydrates in the throttling process. In the third region (temperature above 10 \({}^{\circ}\)C), when the CO\({}_{2}\) mole fraction is very high, as the temperature increases, the phase equilibrium line of the mixed gas intersects with the dew point line. After the intersection point, as the temperature rises, the mixed gas partially liquefies, and at this time, the pressure for hydrate formation increases sharply. Moreover, the higher the carbon dioxide content, the greater the increase in pressure. This is opposite to the first two regions. We call this intersection a critical point here. As the CO\({}_{2}\) mole fraction in the gas phase decreases and the methane content increases, the difficulty of liquefying the mixed gas increases. As shown in Figure 3, at the same temperature, the  
Figure 3: Equilibrium conditions of CO\({}_{2}\)-CH\({}_{4}\) gas hydrate under different CO\({}_{2}\) mole fraction. liquefaction pressure of the mixed gas increases with the increase in methane content. For pure CO\({}_{2}\), when the temperature is 12.85 \({}^{\circ}\)C, the formation pressure of hydrates reaches 28.1 MPa. However, when the CO\({}_{2}\) mole fraction decreases to 0.8 and the temperature is around 18 \({}^{\circ}\)C, the formation pressure of hydrates reaches 28.1 MPa. This indicates that above the critical point, the higher the CO\({}_{2}\) mole fraction, the more difficult it is to form hydrates. Obviously, such stringent formation conditions are difficult to achieve in normal oil and gas production processes, and under such conditions, hydrates can be considered almost non-existent.