For deep injection of CO2 in thick saline formations, the movements of both the free gas phase and dissolved CO2 are sensitive to variations in vertical permeability. A simple model for vertical heterogeneity was studied, consisting of a random distribution of horizontal impermeable barriers with a given overall volume fraction and distribution of lengths. Analytical results were obtained for the distribution of values for the permeability, and compared to numerical simulations of deep CO2 injection and convection in heterogeneous formations, using multiple realizations for the permeability distribution. It is shown that for a formation of thickness H, the breakthrough times in two dimensions for deep injection scale as H (2) for moderate injection rates. In comparison to heterogeneous shale distributions, a homogeneous medium with equivalent effective vertical permeability has a longer breakthrough time for deep injection, and a longer onset time for convection.