A Mixed Discretization Scheme for CO
2Sequestration in Fractured
Porous Media
Rafid Al-Khoury* and Mojtaba Talebian†
*
Computational Mechanics Chair
Faculty of Civil Engineering and Geosciences, Delft University of Technology, The Netherlands e-mail: r.i.n.alkhoury@tudelft.nl
†
Computational Mechanics Chair
Faculty of Civil Engineering and Geosciences, Delft University of Technology, The Netherlands e-mail: m.talebian@tudelft.nl
ABSTRACT
In this contribution, a finite element model for simulating coupled hydromechanic and electrokinetic flow in a multiphase domain is introduced. Emphasis is placed on modelling CO2 flow in a deformed, unsaturated fractured geological formation and its associated
streaming potential flow. The governing field equations are derived based on the averaging theory and the double porosity model, and solved numerically based on a mixed discretization scheme. This scheme is formulated on the basis of the standard Galerkin finite element method (SG), the extended finite element method (XFEM), the level-set method (LS) and the Petrov–Galerkin method (PG). This technique is suitable for advective dominant flow, typically existing in fractured domains. 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 and the Petrov-Galerkin method, is utilized to discretize the advective dominant field equations [1]. The level-set method and the Petrov-Galerkin method are employed to trace the CO2 plume front,
and the extended finite element method is employed to model the high gradient in the saturation field front. The novel aspect of the proposed model is in the choice of the highly advective balance equation for XFEM discretization, while treating other equations by standard procedures. The mixed discretization scheme leads to a convergent system, giving a stable and effectively mesh-independent model. The capability of the proposed model is illustrated by several numerical examples. They demonstrate the capability of the proposed SG–XFEM–LS model to simulate challenging problems comprising coupled solid deformation, multiphase flow and electrokinetic flow in unsaturated fractured porous media. It will be shown that the proposed model is capable of solving these kinds of problems, which typically involve several state variables with different transient nature, using relatively coarse meshes.
REFERENCES
[1] Talebian, M., Al-khoury, R. & Sluys, L.J.: A computational model for coupled multiphysics processes of CO2 sequestration in fractured porous media. Advances in Water Resources 59 (2013), 238-255.
