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.
Accepté le :
DOI : 10.1051/m2an/2015091
Mots clés : Finite volume scheme, compositional Darcy flows, two phase Darcy flows, coupling free and Darcy flows, Convergence analysis
@article{M2AN_2016__50_5_1491_0,
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},
publisher = {EDP-Sciences},
volume = {50},
number = {5},
year = {2016},
doi = {10.1051/m2an/2015091},
zbl = {1456.65082},
mrnumber = {3554550},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2015091/}
}
TY - JOUR AU - Brenner, K. AU - Masson, R. AU - Trenty, L. AU - Zhang, Y. TI - Coupling of a two phase gas liquid compositional 3D Darcy flow with a 1D compositional free gas flow JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2016 SP - 1491 EP - 1522 VL - 50 IS - 5 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2015091/ DO - 10.1051/m2an/2015091 LA - en ID - M2AN_2016__50_5_1491_0 ER -
%0 Journal Article %A Brenner, K. %A Masson, R. %A Trenty, L. %A Zhang, Y. %T Coupling of a two phase gas liquid compositional 3D Darcy flow with a 1D compositional free gas flow %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2016 %P 1491-1522 %V 50 %N 5 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2015091/ %R 10.1051/m2an/2015091 %G en %F M2AN_2016__50_5_1491_0
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. http://www.numdam.org/articles/10.1051/m2an/2015091/
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