Derivation of Vertical Equilibrium Models for $\rm{CO}_2$ Migration from Pore Scale Equations

Abstract

Equations describing flow in porous media averaged to allow for lateral spatial variability but integrated over the vertical dimension are derived from pore scale equations. Under conditions of vertical equilibrium, the equations are simplified and employed to describe migration of $\rm{CO}_2$ injected into an aquifer of variable thickness. The numerical model based on the vertical equilibrium equations is shown to agree well with a fully three-dimensional model. Trapping of $\rm{CO}_2$ in undulations at the top of the aquifer is shown to retard $\rm{CO}_2$ migration.