Anthropogenic emissions of CO₂ have increased atmospheric concentration of CO₂ by about 35 percent during the past 200 years. The current concentration, at about 385 ppm, represents the highest CO₂ concentration in the last 500,000 years. Projected future emissions will lead to doubling of preindustrial CO₂ concentration within the next 50 years. If this relentless increase of atmospheric CO₂ is to be reduced, or reversed, technological solutions must be implemented on a massive scale. While many options are being considered, one attractive approach is carbon capture and storage, or CCS.

The "geological storage" version of CCS involves capture of CO₂ before it is emitted into the atmosphere and subsequent injection of the CO₂ into deep geological formations. Injection of CO₂ into deep formations leads to a multiphase flow problem that may involve important mass exchange between phases, nonisothermal effects, and complex geochemical reactions. In addition, because enormous quantities of CO₂ must be injected to have any significant impact on the atmospheric carbon problem, the spatial scale of the problem becomes very large.

Broad questions involving the fate of the injected CO₂, including possible leakage of CO₂ out of the formation, as well as the fate of displaced fluids like resident brines, lead to very challenging modeling and analysis problems. Because important leakage pathways can be very localized, and their properties can be highly uncertain, an overall analysis of the system requires resolution of multiple length scales in the context of a probabilistic approach. These requirements render standard numerical simulators ineffective due to excessive computational demands. A series of simplifying assumptions may be proposed to provide more efficient numerical calculations, even to the point of allowing for analytical or semianalytical solutions.