CO2 miscible displacement process proved its self as a successful method for enhanced oil recovery in may oil reservoirs. Performing any gas injection process at optimum operating conditions and accurate implementation of the design are key elements to successful enhanced oil recovery. CO2 is injected in many secondary and tertiary displacement processes at supercritical conditions. Based on the definition of the supercritical conditions, along the path from the injector to the producer, CO2 will behave vapor like or liquid like. It is established that CO2 is not first contact miscible with crude oils, and miscibility develops after few contacts as a vaporizing miscibility process, this means that, even at the high pressure region around an injector, CO2 will immiscibly displace the oil for some distance before miscibility can be achieved, this displaced oil ahead of the displacement front is called oil bank with the original oil composition, and two phase flow is dominant behind the front. After miscibility is develop, the oil composition is altered and basic properties are significantly changed, particularly viscosity decreases, and the bubble point pressure increases according to the saturation pressure behavior on a Pressure-Composition plot (P-X) in a swelling test, resulting in a variable bubble point case, thus in contrast to the oil bank the new oil will remain undersaturated until at some distance where the saturation pressure is greater than the average reservoir pressure in which case gas evolves forming two phases, oil and gas, this flow behavior may occur before the miscible bank reaches the production well where pressure drop is skyrocketing and the chance of going below the new saturation pressure is high. The goal of this research is; firstly to gain a good understanding of the CO2 miscible process on the micro- and macro-scale, secondly to investigate the effect of the operating conditions especially pressure on the flow of fluids (oil, gas CO2, hydrocarbon-rich CO2, and liquid-like CO2) in a reservoir during a CO2 injection process, because performing the process at supercritical conditions can change the injected CO2 into a liquid phase and thus a fourth phase is present (liquid-like CO2). The possibility that solids deposit after extraction of light and intermediate hydrocarbons from residual oil adds a fifth phase which effects efficiency of the displacement process.