## 1 Introduction  
In 2020, China proposed the goal of peaking carbon emissions by 2030 and achieving carbon neutrality by 2060. Carbon capture, utilization, and storage (CCUS) technology is a key means to achieve these \"dual carbon\" goals [1; 2; 3]. Major oil fields in China are actively developing CO\({}_{2}\) flooding in low-permeability reservoirs to achieve both emission reduction and enhanced oil recovery [4; 5; 6]. However, with the large-scale promotion and application of CO\({}_{2}\) flooding, more and more engineering problems have emerged. One of the challenges in oil and gas field development is the formation of hydrate blockages in the production fluid [7]. Gas hydrate refers to the ice-like crystal structure material formed between water molecules and guest molecules (such as CO\({}_{2}\), N\({}_{2}\), CH\({}_{4}\), H\({}_{2}\)S, etc.) at low temperature and high pressure, in which the guest molecules are wrapped in cage-shaped holes through hydrogen bonding between water molecules, and the guest molecules play a role in stabilizing the lattice [8]. The structure of hydrate formation also differs with the size of the guest molecules. At present, gas hydrate mainly has the following three structures: type I, type II, and type H. The degree of difficulty of hydrate formation, as well as the thermodynamic stability, is different for different gas molecules. The current research on gas hydrate is mainly based on three aspects: energy, flow assurance, and gas separation and storage. In terms of energy, the exploration and development of natural gas hydrate is the main focus [9], while flow assurance is mainly studied on the prevention and treatment of hydrate formation and blockage in pipelines [10; 11; 12; 13]. Hydrate-based separation and storage technologies include low-boiling-point gas separation, seawater desalination, solid state storage and transportation of natural gas, CO\({}_{2}\) capture and storage, and so on [14; 15; 16]. High pressure and low wellhead temperature in winter, combined with the throttling effect on the production fluid at the surface, provide ideal temperature and pressure conditions for hydrate formation [17]. Therefore, hydrate blockages in CO\({}_{2}\) flooding production fluid pipelines occur frequently, severely affecting normal production activities and causing significant economic losses. It is of great significance to conduct research on relevant prevention and control technologies for hydrate blockages in CO\({}_{2}\) flooding production fluid for the safe and efficient development of oil and gas resources and for assuring the flow of pipeline transportation. Traditional hydrate prevention and control technologies mainly include system dehydration, pipeline heating, pressure control, and injection of thermodynamic inhibitors (alcohols), which change the thermodynamic conditions of the system to prevent hydrate formation [18; 19; 20]. Therefore, it is crucial to understand the phase equilibrium conditions for hydrate formation in production fluids. Due to the high CO\({}_{2}\) mole fraction in the associated gas of CO\({}_{2}\) flooding and the presence of small hydrocarbon gases such as CH\({}_{4}\), the hydrate formation conditions differ significantly from those of natural gas hydrates. Although there have been many studies on hydrate blockages in natural gas pipelines, there are fewer studies on hydrate blockages caused by high CO\({}_{2}\) mole fraction in gas. Additionally, as the production process progresses, the composition of the produced gas changes gradually, requiring the establishment of phase equilibrium conditions for hydrate formation under a wide range of CO\({}_{2}\) mole fractions to address the issue of hydrate blockages in CO\({}_{2}\) flooding production fluids. The phase equilibrium conditions of hydrates can be obtained through a combination of experiments and modeling.