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

Abstract

We present a sharp-interface mathematical model of CO[subscript 2] 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 CO[subscript 2] 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 CO[subscript 2] plume, and the time scale required for complete trapping. The capillary trapping coefficient emerges as the key parameter in the assessment of CO[subscript 2] storage in saline aquifers. The expressions derived here have immediate applicability to the risk assessment and capacity estimates of CO[subscript 2] 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.