A Mixed Discretization Scheme for CO
2Leakage Through Heterogeneous
Geological Layers
Mehdi Musivand Arzanfudi* and Rafid Al-Khoury† *, †
Faculty of Civil Engineering and Geosciences, Delft University of Technology, P.O. Box 5048, 2600 GA Delft, The Netherlands
e-mail: M.MusivandArzanfudi@tudelft.nl, e-mail: r.i.n.alkhoury@tudelft.nl ABSTRACT
A computational model for CO2 leakage in heterogeneous geological layers with different pore properties is introduced. Due to the capillary pressure effect at the boundary between layers, the saturation field is expected to exhibit a discontinuity [1]. The governing equations are derived based on the averaging theory and solved numerically using a mixed-discretization finite element scheme [2,3]. The discontinuous saturation field is discretized using the partition of unity finite element method, and the continuous pore pressure field is discretized using the standard Galerkin finite element method. The finite element mesh does not necessarily coincide with the boundary between layers. This discretization scheme provides an accurate and effectively mesh-independent solution. It allows the use of structured and geometry-independent finite element meshes. These features are illustrated in a CO2 injection numerical example, in which the CO2 is injected from the lower left corner of a two layered system consisting of an aquifer and a cap-rock layer. Computational results obtained from the standard finite element method (SG) and the proposed mixed-discretization method (MD) are presented in Figure 1 for two different mixed-discretizations. The figure shows that the standard Galerkin model, even with a relatively fine mesh, is not capable of simulating the saturation discontinuity at the interface between layers, giving a false impression about the amount of leakage. On the contrary, the proposed mixed-discretization model is capable of capturing the discontinuity in the saturation field, even with a very coarse mesh.
SG, 9 elements MD, 9 elements
SG, 400 elements MD, 400 elements
Figure 1. CO2 phase saturation distribution at t = 82 days.
REFERENCES
[1] Musivand Arzanfudi, M., Al-Khoury, R. & Sluys, L.J.: A computational model for CO2 geo-sequestration in heterogeneous layered media. Transport in Porous Media, Under review. [2] Al-Khoury, R. & Sluys, L.J.: A computational model for fracturing porous media.
International Journal for Numerical Methods in Engineering 70 (2007), 423−444.
[3] Talebian, M., Al-Khoury, R. & Sluys, L.J.: Coupled electrokinetic–hydromechanic model for CO2 sequestration in porous media. Transport in Porous Media 98 (2013) 287−321.
