## 3 Results and Discussions  
### Prediction Results of the Chen-Guo Theoretical Model  
This work uses the Chen-Guo theoretical model to calculate the phase equilibrium conditions of CO\({}_{2}\)-CH\({}_{4}\) gas hydrates under certain gas compositions below and above the freezing point of water. The calculated results are compared with experimental data in the CO\({}_{2}\) mole fraction range of 0-1, the temperature range of \(-\)10.55-17.7 \({}^{\circ}\)C, and the pressure range 0.75-15 MPa [24; 27]. In these reported studies, hydrate dissociation conditions were measured by employing a temperature search in a high-pressure apparatus. A comparison was also made with the results of the vdW-P theoretical model [8], the empirical model proposed by [PERSON] et al. [24]. Figures 1 and 2 shows the comparison between the experimental values (P\({}_{\text{exp}}\)) and the models' predicted values (P\({}_{\text{cal}}\)) of hydrate formation pressure at different temperatures for different gas compositions below and above the freezing point, respectively. From Figure 1, it can be seen that the Chen-Guo theoretical model shows slightly better agreement with the experimental values compared to the vdW-P theoretical model above the freezing point. As listed in Table 2, the average absolute relative deviation (AARD) of the pressure values calculated by the Chen-Guo model is about 3.05% (compared to 3.07% for the vdW-P model). However, as shown in Figure 2 and Table 2, the accuracy of the Chen-Guo model's predictions (AARD is 6.44%) below the freezing point is significantly lower than that of the vdW model (AARD is 3.23%). The overall AARDs of the Chen-Guo and vdW-P models are 3.10% and 3.62%, respectively. [PERSON]'s model was derived from a regression of experimental data above the freezing point of water. Although it has high predictive accuracy, as shown in Table 2, its range of application is narrow (1.2-11 MPa, 0-15 \({}^{\circ}\)C). In order to obtain more accurate phase equilibrium data, this work combined the two theoretical models, namely, the formation conditions of mixed gas hydrates below the freezing point were calculated by the vdW-P model, while the data above the freezing point were provided by the Chen-Guo model. Typically, the pressure in gas pipelines is lower than 10 MPa, and the pressure at the outlet of oil and gas wells is generally far lower than 20 MPa. Therefore, this study used the theoretical models to calculate the formation pressure of CO\({}_{2}\)-CH\({}_{4}\) hydrates under the conditions of CO\({}_{2}\) molar fraction ranging from 0% to 100%, temperature ranging from \(-11.5\) to 20.85 \({}^{\circ}\)C, and pressure ranging from 0.81 MPa to 28.1 MPa, which can better meet the requirements of field applications. This temperature and pressure range essentially covers the temperature and pressure that may be involved in the transportation process of oil and gas from the wellhead to the pipeline, meeting the requirements for hydrate prevention during the oil and gas transportation process. Furthermore, from the perspective of hydrate \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Models** & **Below Ice Point** & **Above Ice Point** & **Overall** \\ \hline vdW–P & 3.23\% & 3.07\% & 3.10\% \\ Chen–Guo & 6.44\% & 3.05\% & 3.62\% \\ Adisasmito & - & 2.82\% & - \\ This work & 3.22\% & 3.07\% & 3.09\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The average absolute relative deviation (AARD) of the pressure values predicted by different models. Figure 1: Comparison of calculated results of Chen–Guo hydrate model with experimental data above the freezing point of water. Figure 2: Comparison of calculated results of Chen–Guo hydrate model with experimental data below the freezing point of water. extraction, it also covers the temperature and pressure conditions for the formation of onshore permafrost and offshore natural gas hydrates, and it can be used for applications related to CO\({}_{2}\) replacement for natural gas hydrate exploitation [15].