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In recent years, CO₂ flooding has become an important technical measure for oil and gas field enterprises to further improve oil and gas recovery and achieve the goal of “dual carbon”. It is also one of the concrete application forms of CCUS. Numerical simulation based on CO₂-EOR plays an indispensable role in the study of the mechanism of CO₂ flooding and buried percolation, allowing for technical indicators to be selected and EOR/EGR prediction to be improved for reservoir engineers. This paper discusses the numerical simulation techniques related to CO₂ flooding and storage, including mathematical models and solving algorithms. A multiphase and multicomponent mathematical model is developed to describe the flow mechanism of hydrocarbon components–CO₂–water underground and to simulate the phase diagram of the components. The two-phase P-T flash calculation with SSI (+DEM) and the Newton method is adopted to obtain the gas–liquid phase equilibrium parameters. The extreme value judgment of the TPD function is used to form the phase stability test and miscibility identification model. A tailor-made multistage preconditioner is built to solve the linear equation of the strong-coupled, multiphase, multicomponent reservoir simulation, which includes the variables of pressure, saturation, and composition. The multistage preconditioner improves the computational efficiency significantly. A numerical simulation of CO₂ injection in a carbonate reservoir in the Middle East shows that it is effective for researching the recovery factor and storage quantity of CO₂ flooding based on the above numerical simulation techniques. Full article