Upscaling of Capillary Trapping Under Gravity Override:Application to CO2 Sequestration in Aquifers

摘要

We present a sharp-interface mathematical model of CO2 migration in saline aquifers, which accounts for gravity override and capillary trapping. The major differences with respect to previous investigations is that we model the shape of the plume during the injection period, we account for regional groundwater flow during the post-injection period, and we introduce rigorously the reduction in water mobility due to trapping of the CO2. The model leads to a nonlinear advection-diffusion equation, in which the diffusive term is due to buoyancy forces, not physical diffusion. The three key dimensionless groups are the mobility ratio between the injected and initial fluids (M), the gravity number (Ng), and a newly defened trapping coefficient (Γ). For the case of interest in geological CO2 storage, in which the mobility ratio is much smaller than 1, the solution is largely insensitive to the value of the gravity number. Under these conditions, the mathematical model can be simplifi to a hyperbolic model. We present a complete analytical solution to the hyperbolic model that includes the injection, early post-injection, and late post-injection periods. Despite the fact that the solution involves the interaction of a sharp imbibition front with a drainage rarefaction front, it admits a closed-form expression. The main outcome of the analytical developments presented here is a formula that predicts the ultimate footprint on the CO2 plume, and the time scale required for complete trapping. Both quantities depend strongly on the shape of the plume at the end of the injection period, which must-therefore-be modeled. A second application of the analytical solution is a formulation for upscaling the capillary trapping coefficient from the lab- oratory scale to the basin scale. Explicit expressions are given for the megascopic and gridblock-effective trapping coefficients, as functions of the local trapping coefficient, the mobility ratio, and the grid resolution. Although the expressions derived are based on a one-dimensional sharp-interface model, we anticipate that they will have broader applicability to injection scenarios with unfavorable mobility ratio and dominated by gravity override.