## 4 Conclusions  
Due to the high CO\({}_{2}\) mole fraction in the associated gas of CO\({}_{2}\) flooding, it is prone to the formation of hydrate blockages in pipelines. Accurately understanding the critical conditions for the hydrates' formation in production fluids of CO\({}_{2}\) flooding is crucial for  
Figure 7: Dissociation enthalpy of CO\({}_{2}\)-CH\({}_{4}\) hydrates under different CO\({}_{2}\) mole fraction in gas phase.  
preventing and controlling hydrate formation. In this study, a predictive model for the phase equilibrium conditions of CO\({}_{2}\)-CH\({}_{4}\) mixed gas hydrate formation was developed, and the following conclusions were drawn:  
1. The Chen-Guo theoretical model can accurately predict the conditions for the formation of CO\({}_{2}\)-CH\({}_{4}\) mixed gas hydrates above the freezing point of water, with an absolute average relative error of 3.05%. However, the prediction error of the model below the freezing point is large.
2. Based on the phase equilibrium data obtained from the Chen-Guo and vdW-P theoretical model, a multi-parameter empirical predictive model was established using polynomial fitting. The absolute average relative deviation of the phase equilibrium pressure calculation results of this model is 3.09%, slightly better than the theoretical models. This model has the advantages of simplicity, stability, high accuracy, and applicability to a wide range of CO\({}_{2}\) mole fractions, temperatures, and pressure. It can effectively guide the development of hydrate prevention and control technologies for CO\({}_{2}\)-driven production fluids.
3. Below the critical point, as the CO\({}_{2}\) mole fraction in gas phase increases, the formation pressure of mixed gas hydrates decreases, making hydrate formation easier. Within a certain concentration range, an increase in CO\({}_{2}\) mole fraction also leads to an increase in the dissociation enthalpy of mixed gas hydrates, resulting in a stronger thermodynamic stability of the hydrates. This poses a significant challenge for the prevention and control of hydrates in production fluids of CO\({}_{2}\) flooding. However, above the critical point, the higher the CO\({}_{2}\) mole fraction, the greater the pressure for hydrate formation.
4. As CO\({}_{2}\) and CH\({}_{4}\) coexist in gas phase, CO\({}_{2}\) molecules tend to occupy the large cages of the structure I hydrate, while CH\({}_{4}\) molecules tend to occupy the small cages, demonstrating a certain synergistic effect. The combined effect of these two factors makes the structure of hydrates more stable. In view of the prevention and control of hydrates in fluids with high CO\({}_{2}\) mole fraction, the existing prevention and control methods of natural gas hydrates need to be re-evaluated.  
Conceptualization, N.L. and J.L. ([PERSON]); methodology, H.M.; software, J.L. ([PERSON]) and Y.Z.; validation, J.K.; formal analysis, H.M.; investigation, H.M., J.L. ([PERSON]) and Y.Z.; resources, N.L.; data curation, N.L.; writing--original draft preparation, H.M.; writing--review and editing, J.L. ([PERSON]); supervision, N.L.; project administration, J.L. ([PERSON]). All authors have read and agreed to the published version of the manuscript.  
This work was supported by Natural Science Foundation of Xinjiang Uygur Autonomous Region (2022D01F62) and Karamay Science and Technology Plan Project (20212022 hjcxrc0038).  
Not applicable.  
The data that support the findings of this paper are available upon request.  
The authors declare no conflicts of interest.