Abstract
We study the convergence of a combined finite volume nonconforming finite element scheme on general meshes for a partially miscible two-phase flow model in anisotropic porous media. This model includes capillary effects and exchange between the phase. The diffusion term, which can be anisotropic and heterogeneous, is discretized by piecewise linear nonconforming triangular finite elements. The other terms are discretized by means of a cell-centered finite volume scheme on a dual mesh. The relative permeability of each phase is decentred according the sign of the velocity at the dual interface. The convergence of the scheme is proved thanks to an estimate on the two pressures which allows to show estimates on the discrete time and compactness results in the case of degenerate relative permeabilities. A key point in the scheme is to use particular averaging formula for the dissolution function arising in the diffusion term. We show also a simulation of CO\(_2\) injection in a water saturated reservoir and nuclear waste management. Numerical results are obtained by in-house numerical code.
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References
Caro, F., Saad, B., Saad, M.: Study of degenerate parabolic system modeling the hydrogen displacement in a nuclear waste repository. Discrete Continuous Dyn. Syst. Ser. S 7, 191–205 (2014)
Chamoun, G., Saad, M., Talhouk, R.: Monotone combined edge finite volume-finite element scheme for anisotropic Keller-Segel model. Numer. Methods Partial Differ. Eqn. 26 (2014). doi:10.1002/num.21858
Eymard, R., Schleper, V.: Study of a numerical scheme for miscible two-phase flow in porous media. hal-00741425, version 3 (2013)
MOMAS: http://www.gdrmomas.org
Neumann, R., Bastian, P., Ippisch, O.: Modeling and simulation of two-phase two-component flow with disappearing nonwetting phase. Comput. Geosci. 17, 139–149 (2013)
Saad, B., Saad, M.: Study of full implicit petroleum engineering finite volume scheme for compressible two phase flow in porous media. Siam J. Numer. Anal. 51(1), 716–741 (2013)
Saad, B., Saad, M.: A combined finite volume-nonconforming finite element scheme for compressible two phase flow in porous media. Numer. Math. (in revision) (2014)
Acknowledgments
This work was partially supported by the Saudi Basic Industries Corporation “SABIC”.
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Saad, B., Saad, M. (2014). Convergence Analysis of a FV-FE Scheme for Partially Miscible Two-Phase Flow in Anisotropic Porous Media. In: Fuhrmann, J., Ohlberger, M., Rohde, C. (eds) Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems. Springer Proceedings in Mathematics & Statistics, vol 78. Springer, Cham. https://doi.org/10.1007/978-3-319-05591-6_71
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DOI: https://doi.org/10.1007/978-3-319-05591-6_71
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