We investigate the physical processes that occur during the sequestration of CO2 in liquid-saturated, brine-bearing geologic formations using the numerical simulator TOUGH2. Carbon dioxide is injected in a supercritical state that has a much lower density and viscosity than the liquid brine it displaces. In situ, the supercritical CO2 forms a gas-like phase, and also partially dissolves in the aqueous phase, creating a multiphase, multicomponent environment that shares many important features with the vadose zone. The flow and transport simulations employ an equation of state package that treats a two-phase (liquid, gas), three-component (water, salt, CO2) system. Chemical reactions between CO2 and rock minerals that could potentially contribute to mineral trapping of CO2 are not included. The geological setting considered is a fluvial/deltaic formation that is strongly heterogeneous, making preferential flow a significant effect, especially when coupled with the strong buoyancy forces acting on the gas-like CO2 plume. Key model development issues include vertical and lateral grid resolution, grid orientation effects, and the choice of characteristic curves.