Numerical models of geologic storage of carbon dioxide (CO2) in brine-bearing formations use characteristic curves to represent the interactions of non-wetting-phase CO2 and wetting-phase brine. When a problem includes both injection of CO2 (a drainage process) and its subsequent post-injection evolution (a combination of drainage and wetting), hysteretic characteristic curves are required to correctly capture the behavior of the CO2 plume. In the hysteretic formulation, capillary pressure and relative permeability depend not only on the current grid-block saturation, but also on the history of the saturation in the grid block. For a problem that involves only drainage or only wetting, a non-hysteretic formulation, in which capillary pressure and relative permeability depend only on the current value of the grid-block saturation, is adequate. For the hysteretic formulation to be robust computationally, care must be taken to ensure the differentiability of the characteristic curves both within and beyond the turning-point saturations where transitions between branches of the curves occur. Two example problems involving geologic CO2 storage are simulated with TOUGH2, a multiphase, multicomponent code for flow and transport through geological media. Both non-hysteretic and hysteretic formulations are used, to illustrate the applicability and limitations of non-hysteretic methods. The first application considers leakage of CO2 from the storage formation to the ground surface, while the second examines the role of heterogeneity within the storage formation. Published by Elsevier Ltd.