The emission of greenhouse gases such as carbon dioxide CO2 is particularly concerning and has prompted the global search for new technologies to capture and store this chemical compound. Carbon Capture and Storage (CCS) is one of the promising technologies to reduce the net emission of CO2 into the atmosphere. Depending on its source, injected CO2 in a CCS project may be contaminated by other chemical components such as methane, nitrogen, water, and more. This CO2-rich mixture can create multi-phase flow phenomena, which can significantly affect the injection flow dynamics and thermal behavior. Therefore, an accurate prediction of pressure, temperature and composition during CO2 flow in wellbores can support engineering and investments decisions for a CCS project. In this chapter, a fully implicit finite volume model for single and two-phase thermal multi-component flow of CO2 mixtures within wellbores is presented. The governing equations are composed of the mass balance equations for each component, one energy equation for mixture and distinct momentum equations for each phase. In addition to the conservation laws, the thermodynamics equilibrium conditions and mole and volume fractions constraints are included to solve the governing equations. Momentum equations are based on the single pressure two-fluid model and the thermodynamic properties, phase stability and flash calculations are found by using a Cubic Equation of State. The obtained numerical solutions are in excellent agreement when compared to experimental and numerical data published in the literature. The impact of transient petroleum field operations (start-up and shut-in) on flow and thermal behavior of injected CO2 are evaluated and the numerical results discussed. Finally, the effects of surge pressure, phase change and segregation generated during start-up and shut-in of wells were qualitatively predicted by the proposed model.