In this work, we investigate numerically the injection of supercritical carbon dioxide into a deep saline reservoir from a single well. We analyze systematically the sharp-interface evolution in different flow regimes. The flow regimes can be parameterized by two dimensionless numbers, the gravity number, Gamma and the mobility ratio, lambda. Numerical simulations are performed using the volume of fluid method, and the results are compared with the solutions of the self-similarity equation established in previous works, which describes the evolution of the sharp interface. We show that these theoretical solutions are in very good agreement with the results from the numerical simulations presented over the different flow regimes, thereby showing that the theoretical and simulation models predict consistently the spreading and migration of the created CO2 plume under complex flow behavior in porous media. Furthermore, we compare the numerical results with known analytic approximations in order to assess their applicability and accuracy over the investigated parametric space. The present study indicates that the self-similar solutions parameterized by the dimensionless numbers lambda, Gamma are significant for examining effectively injection scenarios, as these numbers control the shape of the interface and migration of the CO2 plume. This finding is essential in assessing the storage capacity of saline aquifers.