Carbon dioxide Utilization and storage technology (CCUS) plays an important role for oil and gas field to further improve oil and gas recovery and achieve the goal of "double carbon" in recent years. Numerical simulation is an essential means for reservoir engineers to study the flow mechanism of CO2 flooding and storage, screen the CCUS technical indicators, predict the enhanced oil recovery and evaluate storage potential. This paper discusses the multiphase and multicomponent mathematical model based on the seepage theory of carbon dioxide flooding and storage, the calculation method of gas-liquid equilibrium based on EOS equation, the miscibility determination technique and two phase P-T flash calculation method. Meanwhile the CCUS numerical simulator developed based on above theoretical model and calculation method. Applying the simulator to CO2 miscible flooding in a carbonate reservoir of the Middle East, the results show that the model and software accurately describes the CO2-EOR seepage mechanism and CO2 miscible displacement process. It effectively predicts the effect of CO2 injection on EOR and the storage potential after CO2 flooding. It can provide feasible technical guidance for the optimization of CO2 utilization and storage programs.