Geodesic
Coupling of a two phase gas liquid compositional 3D Darcy flow with a 1D compositional free gas flow
Brenner, K.1  ; Masson, R.1  ; Trenty, L.2  ; Zhang, Y.1
1 Laboratoire de Mathématiques J.A. Dieudonné, UMR 7351 CNRS, University Nice Sophia Antipolis, and team COFFEE, INRIA Sophia Antipolis Méditerranée, Parc Valrose 06108, Nice cedex 02, France.
2 Andra, 1-7 rue Jean Monnet, 92290 Chatenay-Malabry, France.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 50 (2016) no. 5, pp. 1491-1522

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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 medium 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 spatial discretization is essentially nodal and based on the vertex approximate gradient (VAG) scheme. Compared with classical nodal approaches such as the Control Volume Finite Element method, the VAG scheme has the advantage to avoid the mixture of different material properties and models in the control volumes located at the interfaces. The discrete model is validated using a quasi analytical solution for the stationary state, and the convergence of the VAG discretization is analysed for a simplified model coupling the Richards approximation in the porous medium and the gas pressure equation in the gallery.

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DOI : 10.1051/m2an/2015091
Classification : 65M08, 65M12, 76S05
Keywords: Finite volume scheme, compositional Darcy flows, two phase Darcy flows, coupling free and Darcy flows, Convergence analysis

Brenner, K. 1 ; Masson, R. 1 ; Trenty, L. 2 ; Zhang, Y. 1

1 Laboratoire de Mathématiques J.A. Dieudonné, UMR 7351 CNRS, University Nice Sophia Antipolis, and team COFFEE, INRIA Sophia Antipolis Méditerranée, Parc Valrose 06108, Nice cedex 02, France.
2 Andra, 1-7 rue Jean Monnet, 92290 Chatenay-Malabry, France. 
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     author = {Brenner, K. and Masson, R. and Trenty, L. and Zhang, Y.},
     title = {Coupling of a two phase gas liquid compositional {3D} {Darcy} flow with a {1D} compositional free gas flow},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {1491--1522},
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Brenner, K.; Masson, R.; Trenty, L.; Zhang, Y. Coupling of a two phase gas liquid compositional 3D Darcy flow with a 1D compositional free gas flow. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 50 (2016) no. 5, pp. 1491-1522. doi: 10.1051/m2an/2015091

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