Numerical simulations have been carried out to evaluate the rate at which a plume of CO2 moves upward through the subsurface, and the amounts of dissolution and phase trapping that occur along the way. A quantity of CO2 is injected into a 1000-m deep, 100-m thick layer saturated with saline water, where it forms an immiscible supercritical fluid phase and partially dissolves in the aqueous phase. As the supercritical CO2 moves upward, it smoothly transitions into a gas. Between the injection interval and the ground surface the medium (the overburden ) is assumed to be homogeneous, but anisotropic, with a ratio of vertical to horizontal permeability of 1:2. 1000-year simulations are conducted for overburden vertical permeabilities of 100 md, 10 md, and 1 md, using a version of the TOUGH2 numerical simulator that incorporates hysteretic relative permeability and capillary pressure functions. For each permeability, simulations are carried out for a range of maximum residual gas saturations (Sgrmax), because this parameter plays a key role in phase trapping and is poorly known for aqueous/CO2 systems. The time required for the CO2 plume to reach the surface increases with decreasing overburden permeability and increasing Sgrmax. CO2 reaches the surface within 1000 years only for the highest overburden permeability (100 md), with times ranging from 775 years for the large values of Sgrmax commonly used in the petroleum industry to 2.2 years for small values of Sgrmax. Additional simulations including a high-permeability conduit in an otherwise low-permeability overburden provide insights into the effects of geologic heterogeneity.