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Convergence Analysis of a FV-FE Scheme for Partially Miscible Two-Phase Flow in Anisotropic Porous Media

  • Bilal SaadEmail author
  • Mazen Saad
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 78)

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.

Keywords

Porous Medium Capillary Pressure Relative Permeability Finite Volume Scheme Anisotropic Porous Medium 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

This work was partially supported by the Saudi Basic Industries Corporation “SABIC”.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Division of Computer, Electrical and Mathematical Sciences and EngineeringKing Abdullah University of Science and TechnologyThuwalKingdom of Saudi Arabia
  2. 2.Ecole Centrale de NantesNantesFrance

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