Scaling analysis for a 3-D CO2 plume in a sloping aquifer at a late stage of injection

We investigate supercritical CO${}_2$ injection into a sloping saline aquifer and propose a simple relationship to estimate the maximum gas migration distance in the updip direction. The estimate is derived from the system of governing equations for immiscible flow of gas and formation brine. By writing the equations in non-dimensional form, we guess the scaling law for the migration distance at a late stage of CO${}_2$ injection. Then, we verify the scaling law by means of 3-D reservoir simulations of miscible CO${}_2$ injection with account for the residual and solubility trapping. We derive an estimate that relates the maximum migration distance with the dip angle, the porosity, the anisotropic permeability, and the end-points of saturation functions. We show that the estimate is rather accurate for different reservoir temperatures and brine salinity and in the case of a flue gas injection. The proposed scaling is useful for a quick assessment of the risk of CO${}_2$ reaching a potential leakage site in a large regional aquifer. It can also be applied to estimate the propagation of the uncertainties of reservoir parameters to the uncertainty of the migration distance.