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A mathematical model of the footprint of the CO[subscript 2] plume during and after injection in deep saline aquifer systems

We present a sharp-interface mathematical model of CO2 migration in saline aquifers, which accounts for gravity override, capillary trapping, natural groundwater flow, and the shape of the plume during the injection period. The model leads to a nonlinear advection–diffusion equation, where the diffusive term is due to buoyancy forces, not physical diffusion. For the case of interest in geological CO2 storage, in which the mobility ratio is very unfavorable, the mathematical model can be simplified to a hyperbolic equation. We present a complete analytical solution to the hyperbolic model. The main outcome is a closed-form expression that predicts the ultimate footprint on the CO2 plume, and the time scale required for complete trapping. The capillary trapping coefficient emerges as the key parameter in the assessment of CO2 storage in saline aquifers. The expressions derived here have immediate applicability to the risk assessment and capacity estimates of CO2 sequestration at the basin scale. In a companion paper [Szulczewski and Juanes, GHGT-9, Paper 463 (2008)] we apply the model to specific geologic basins. © 2008 Elsevier Ltd. All rights reserved