Many large aquifers consist of wide structures only confined by a horizontal cap rock with no distinct traps. By numerical simulations the distribution of injected CO2 into this type of aquifers has been analysed. The results show that the distribution of CO2 is controlled by gravity forces and the horizontal permeability just below the cap rock. The escape rate through a possible open periphery or fractures 8000 m from an injection well was simulated. Some of the injected CO2 will escape from a high permeable aquifer, but the long residence times showed that an effective storage will still be provided in a strategy to combat accumulation of atmospheric CO2.