We perform large-scale numerical simulations of convection in 3D porous media at Rayleigh-Darcy numbers up to $Ra=8\times10^4$. To investigate the convective mixing of carbon dioxide (CO$_2$) in geological formations, we consider a semi-infinite domain, where the CO$_2$ concentration is constant at the top and no flux is prescribed at bottom. Convection begins with a diffusion-dominated phase, transitions to convection-driven solute finger growth, and ends with a shutdown stage as fingers reach the bottom boundary and the concentration in the system increases. For $Ra \ge 5\times10^3$, we observe a constant-flux regime with dissolution flux stabilizing at 0.019, approximately 13\% higher than in 2D estimates. Finally, we provide a simple and yet accurate physical model describing the mass of solute entering the system throughout the whole mixing process. These findings extend solutal convection insights to 3D and high-$Ra$, improving the reliability of tools predicting the long-term CO$_2$ dynamics in the subsurface.