Coupled Electrokinetic–Hydromechanic Model for $$\text{ CO}_{2}$$ Sequestration in Porous Media

Abstract

In this paper, a computational model for the simulation of coupled electrokinetic and hydromechanical flow in a multiphase domain is introduced. Particular emphasis is placed on modeling $$\text{ CO}_{2}$$ flow in a deformed, unsaturated geologic formation and its associated streaming potential. The governing field equations are derived based on the averaging theory and solved numerically based on a mixed discretization scheme. The standard Galerkin finite element method is utilized to discretize the deformation and the diffusive dominant field equations, and the extended finite element method, together with the level-set method, is utilized to discretize the advective dominant field equations. The level-set method is employed to trace the $$\text{ CO}_{2}$$ plume front, and the extended finite element method is employed to model the high gradient in the saturation field front. This mixed discretization scheme leads to a highly convergent system, giving a stable and effectively mesh-independent model; furthermore, it minimizes the number of degrees of freedom, making the numerical scheme computationally efficient. The capability of the proposed model is evaluated by verification and numerical examples. Effects of the formation stiffness on the $$\text{ CO}_{2}$$ flow and the salinity content on the streaming potential are discussed.