Analytical Model for Post-Injection Spreading and Migration of CO$_2$ in Saline Aquifers, including Capillary Trapping, Solubility, and Leakage

In geological CO$_2$ storage, careful site selection and effective injection methods are the two primary means of maximizing reservoir ``fill'' and assessing and avoiding potential leakage paths. An accurate understanding of the subsurface spreading and migration of mobile CO$_2$ during and after injection is essential for these purposes. We present an analytical model for the post-injection spreading and migration of a plume of CO$_2$ in a saline aquifer, including the effects of gravity segregation, capillary trapping, natural groundwater flow, dissolution of CO$_2$ into groundwater, and leakage through the caprock. We account rigorously for the injection period, using the true end-of-injection plume shape as an initial condition. This comprehensive model allows us to estimate reservoir capacity for CO$_2$ storage at the basin scale, and to assess dynamically the relative importance of structural, capillary, and solution trapping mechanisms.