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\subsubsection{Flow simulation}  In recent years, vertical-equilibrium (VE) models have been extensively used to study gravity-driven \ce{CO2} migration \citep{Nordbotten2011}. Using an analytical description for the vertical fluid distribution not only reduces the dimensions of the problem but also lessens the coupling and increases the time constants of the dynamic model \citep{Nilsen2014}. VE models are attractive means to increase resolution while saving computational cost, computational,  thus particularly appropriate for an iterative history-match loop where many flow simulation steps are required. For the purpose of this study, we used the VE solvers included in the Matlab Reservoir Simulation Toolbox (MRST) \citep{Lie_2011}, to model the CO$_2$ injection.