CO2 injection has been used to improve oil recovery for the last 4 decades. In recent years, CO2 injection has become more attractive because of the dual effect: injection in the subsurface (1) allows for reduction of the CO2 concentration in the atmosphere to reduce global warming and (2) improves the oil recovery. One of the screening criteria for CO2 injection as an enhanced oil recovery method is based on the measurement of CO2 minimum miscibility pressure (MMP) in a slim tube. The slim tube data are used for the purpose of field evaluation and for the tuning of the equations of state. The slim tube represents one-dimensional (1D) horizontal flow. When CO2 dissolves in the oil, the density may increase. The effect of the density increase in high-permeability reservoirs when CO2 is injected from the top has not been modeled in the past. The increase in density changes the flow path from ID to two-dimensional (2D) and three-dimensional (3D) (downward flow). As a result of this density effect, the compositional path in a reservoir can be radically different from the flow path in a slim tube. In this work, we study the density effect from CO2 dissolution in modeling of CO2 injection. We account for the increase in oil density with CO2 dissolution using the Peng-Robinson equation of state. The viscosity is modeled based on the Pedersen-Fredenslund viscosity correlation. We perform compositional simulation of CO2 injection in a 2D vertical cross-section with the density effect. Our results show that the density increase from CO2 dissolution may have a drastic effect on the CO2 flow path and recovery performance. One conclusion from this work is that there is a need to have accurate density data for CO2/oil mixtures at different CO2 concentrations to model properly CO2 injection studies. Our main conclusion is that the downward flow of the CO2 and oil mixture may not be gravity-stable, despite the widespread assumption in the literature.