The presence of impermeable barriers in a reservoir can significantly impede the buoyant migration of injected deep into a heterogeneous geological formation. An important consequence of the presence of these impermeable barriers in terms of the long-term storage of is the residual trapping that takes place beneath the barriers, which acts to both increase the storage potential of the reservoir and improve the storage security of the . Analytical results for the total amount of trapped in a reservoir with an uncorrelated random distribution of impermeable barriers are obtained for both two and three-dimensional cases. In two dimensions, it is shown that the total amount of contained in this fashion scales as , where is the number of barriers in the vertical direction. In three dimensions, the trapped amount scales as , where depending on the aspect ratio of the barriers. The analytical two-dimensional results are compared with results of detailed numerical simulations, and good agreement is observed.