## 3 Results and Discussions
### Dissociation Enthalpy of CO\({}_{2}\)-CH\({}_{4}\) Gas Hydrate  
The magnitude of dissociation enthalpy can reflect the thermodynamic stability of hydrates. Due to the difficulty of forming hydrates with mixed gases above the critical point, the calculation of enthalpy values in this section is only applicable to CO\({}_{2}\)-CH\({}_{4}\) hydrates below the freezing point and within the temperature range of 0-10 \({}^{\circ}\)C. Figure 6 shows the relationship between the natural logarithm (In \(P\)) of the equilibrium pressure of CO\({}_{2}\)-CH\({}_{4}\) hydrates under different CO\({}_{2}\) mole fractions (\(y_{\text{CO}2}\)) and the reciprocal (\(1/T\)) of the corresponding equilibrium temperature. From the figure, it can be seen that there is a clear linear relationship between In \(P\) and \(1/T\) under different CO\({}_{2}\) mole fractions. The slope can be obtained through linear regression, and then the decomposition enthalpy of CO\({}_{2}\)-CH\({}_{4}\) mixed gas hydrates under different compositions can be calculated. Moreover, the slope of the fitted line is different under conditions below and above the freezing point. Figure 7 shows the change in dissociation enthalpy of CO\({}_{2}\)-CH\({}_{4}\) gas hydrate with different CO\({}_{2}\) mole fractions above the freezing point of water. As shown in the figure, it can be seen that as the CO\({}_{2}\) mole fraction increases, the dissociation enthalpy of CO\({}_{2}\)-CH\({}_{4}\) gas hydrates increases rapidly in the range of \(y=0\) to 0.4, increases slowly in the range of \(y=0.4\) to 0.8, and decreases slowly in the range of \(y=0.8\) to 1.0. Overall, there is a trend of increasing followed by decreasing. When \(y_{\text{CO}2}\) increases from 0 (pure methane hydrate) to 0.8, the dissociation enthalpy of CO\({}_{2}\)-CH\({}_{4}\) gas hydrates gradually increases from 62.22 kJ/mol to 64.67 kJ/mol, and the increasing trend gradually slows down. This result indicates that within a certain range of CO\({}_{2}\) mole fraction, the presence of CO\({}_{2}\) increases the thermodynamic stability of mixed gas hydrates, making their dissociation more difficult. The energy consumption required to remove hydrate blockages using heating methods is also higher, which is one of the challenges in preventing and controlling hydrates in production fluids with high CO\({}_{2}\) mole fraction. Additionally, when CO\({}_{2}\) mole fraction increases from 0.8 to 1 (pure CO\({}_{2}\) hydrate), the dissociation enthalpy of hydrates slightly decreases from 64.67 kJ/mol to 64.53 kJ/mol, indicating that the thermodynamic stability of pure CO\({}_{2}\) hydrates is slightly weaker than that of hydrates formed by high CO\({}_{2}\) mixed gases. Figure 6: Clausius-Clapeyron relationship of CO\({}_{2}\)-CH\({}_{4}\) hydrates under different CO\({}_{2}\) mole fraction. The cause of the above phenomenon is related to the sizes of CO\({}_{2}\) and CH\({}_{4}\) molecules and the occupation of hydrate cages. Since CO\({}_{2}\) molecules are larger than methane molecules, the size of CO\({}_{2}\) matches better with the large cages in the structure I hydrates, while the size of methane matches better with the small cages. As the CO\({}_{2}\) mole fraction in the gas increases, CO\({}_{2}\) molecules tend to occupy the large cages of the structure I hydrate, while methane molecules tend to occupy the small cages. The combined effect of these two factors makes the structure of hydrates more stable, resulting in an increase in the dissociation enthalpy of hydrates with increasing CO\({}_{2}\) mole fraction in the gas. However, when the CO\({}_{2}\) mole fraction in the gas further increases, the small cages in the hydrates are gradually occupied by the larger CO\({}_{2}\) molecules, leading to a decrease in the stability of the hydrate structure. Therefore, when the CO\({}_{2}\) mole fraction in the gas reaches a certain value, the dissociation enthalpy of hydrates gradually decreases. Figure 7 also shows the dissociation enthalpy of mixed gas hydrates below the freezing point.