Injection of CO2 deep underground into porous rocks, such as saline aquifers, appears to be a promising tool for reducing CO2 emissions and the consequent climate change. During this process CO2 displaces brine from individual pores and the sequence in which this happens determines the efficiency with which the rock is filled with CO2 at the large scale. At the pore scale, displacements are controlled by the balance of capillary, viscous and inertial forces. We simulate this process by a numerical technique, multi-GPU Lattice Boltzmann, using X-ray images of the rock pores. The simulations show the three types of fluid displacement patterns, at the larger scale, that have been previously observed in both experiments and simulations: viscous fingering, capillary fingering and stable displacement. Here we examine the impact of the patterns on storage efficiency and then focus on slow flows, where displacements at the pore scale typically happen by sudden jumps in the position of the interface between brine and CO2, Haines jumps. During these jumps, the fluid in surrounding pores can rearrange in a way that prevent later displacements in nearby pores, potentially reducing the efficiency with which the CO2 fills the total available volume in the rock.