Geological storage of carbon dioxide (CO₂) is a promising technology for reducing atmospheric emissions. The large discrepancy in the time- and length-scales between up-dip migration of buoyant supercritical CO₂ and the sinking fingers of dissolved CO₂ poses a challenge for numerical simulations aimed at describing the fate of the plume. Hence, several investigators have suggested methods to simplify the problem, but to date there has been no reference solution with which these simplified models can be compared. We investigate the full problem of Darcy-based two-phase flow with gravity-current propagation and miscible convective mixing, using high-resolution numerical simulations. We build on recent developments of the Automatic Differentiation - General Purpose Research Simulator (AD-GPRS) at Stanford. The results show a CO₂ plume that travels for 5000 years reaching a final distance of 14 km up-dip from the injection site. It takes another 2000 years before the CO₂ is completely trapped as residual (40%) and dissolved (60%) CO₂. Dissolution causes a significant reduction of the plume speed. While fingers of dissolved CO₂ appear under the propagating gravity current, the resident brine does not become fully saturated with CO₂ anywhere under the plume. The overall mass transfer of CO₂ into the brine under the plume remains practically constant for several thousands of years. These results can be used as a benchmark for verification, or improvements, of simplified (reduced-dimensionality, upscaled) models. Our results indicate that simplified models need to account for: (i) reduced dissolution due to interaction with the plume, and (ii) gradual reduction of the local dissolution rate after the fingers begin to interact with the bottom of the aquifer.