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Coupling of a Two Phase Gas Liquid Compositional 3D Darcy Flow with a 1D Compositional Free Gas Flow

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Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 78))

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Abstract

A model coupling a three dimensional gas liquid compositional Darcy flow and a one dimensional compositional free gas flow is presented. The coupling conditions at the interface between the gallery and the porous media account for the molar normal fluxes continuity for each component, the gas liquid thermodynamical equilibrium, the gas pressure continuity and the gas and liquid molar fractions continuity. This model is applied to the simulation of the mass exchanges at the interface between the repository and the ventilation excavated gallery in a nuclear waste geological repository. The convergence of the Vertex Approximate Gradient discretization is analysed for a simplified model coupling the Richards approximation in the porous media and the gas pressure equation in the gallery.

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References

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  4. Mosthaf, K., Baber, K., Flemisch, B., Helmig, R., Leijnse, A., Rybak, I., Wohlmuth, B.: A coupling concept for two-phase compositional porous-medium and single-phase compositional free flow. Water Resour. Res. 47(10), 16 (2011)

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Acknowledgments

The authors would like to thank Andra for its financial support.

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Authors and Affiliations

  1. Laboratoire de Mathématiques J.A. Dieudonné UMR CNRS 7251 and Team Coffee, Université Nice Sophia Antipolis, CNRS and INRIA Sophia Antipolis Méditerranée, Parc Valrose, 06108, Nice, France

    Konstantin Brenner, Roland Masson & Yumeng Zhang

  2. Andra, 1 rue Jean Monnet, 92290 , Chatenay-Malabry, France

    Laurent Trenty

Authors
  1. Konstantin Brenner
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  2. Roland Masson
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  3. Laurent Trenty
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  4. Yumeng Zhang
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Corresponding author

Correspondence to Roland Masson .

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Editors and Affiliations

  1. Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany

    Jürgen Fuhrmann

  2. Institute Comp. Applied Mathematics, University of Münster Center for Nonlinear Sciences (CeNoS ), Münster, Germany

    Mario Ohlberger

  3. Inst. Appl. Analysis and Num. Simulation, University of Stuttgart, Stuttgart, Germany

    Christian Rohde

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Brenner, K., Masson, R., Trenty, L., Zhang, Y. (2014). Coupling of a Two Phase Gas Liquid Compositional 3D Darcy Flow with a 1D Compositional Free Gas Flow. 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_51

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