The rate of buoyant migration of CO is of fundamental importance in storage in deep saline formations, and is known to be strongly affected by local heterogeneity. Using a simple model of heterogeneity consisting of a random distribution of impermeable barriers to represent a reservoir containing shale barriers, theoretical predictions of the time to reach the top of the formation (the breakthrough time) are presented for both two and three dimensions. For two dimensions, the breakthrough time is predicted to scale as , where , the number of barriers in the vertical direction, scales linearly with reservoir height . In three dimensions, the theoretical model predicts that the breakthrough time scales as for elliptical barriers, where depending on the barrier geometry. The predicted breakthrough time is compared with the results of numerical simulations in two dimensions, with reasonable agreement observed in most cases.