In this paper, we conduct a thorough mathematical analysis of the unified formulation advocated by Lauser et al. [Adv. Water Res. 34 (2011) 957–966] for compositional multiphase flows in porous media. The interest of this formulation lies in its potential to automatically handle the appearance and disappearance of phases. However, its practical implementation turned out to be not always robust for realistic fugacity laws associated with cubic equations of state, as shown by Ben Gharbia and Flauraud [Oil Gas Sci. Technol. 74 (2019) 43]. By focusing on the subproblem of phase equilibrium, we derive sufficient conditions for the existence of the corresponding system of equations. We trace back the difficulty of cubic laws to a deficiency of the Gibbs functions that comes into play due to the ``unifying’’ feature of the new formulation. We propose a partial remedy for this problem by extending the domain of definition of these functions in a natural way. Besides, we highlight the crucial but seemingly unknown fact that the unified formulation encapsulates all the properties known to physicists on phase equilibrium, such as the tangent plane criterion and the minimization of the Gibbs energy of the mixture.
Accepté le :
Publié le :
DOI : 10.1051/m2an/2021075
Keywords: Complementarity condition, unified formulation, phase equilibrium, Gibbs energy function, cubic EOS
@article{M2AN_2021__55_6_2981_0,
author = {Ben Gharbia, Ibtihel and Haddou, Mounir and Tran, Quang Huy and Vu, Duc Thach Son},
title = {An analysis of the unified formulation for the equilibrium problem of compositional multiphase mixtures},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {2981--3016},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
number = {6},
doi = {10.1051/m2an/2021075},
mrnumber = {4347302},
zbl = {1491.76083},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2021075/}
}
TY - JOUR AU - Ben Gharbia, Ibtihel AU - Haddou, Mounir AU - Tran, Quang Huy AU - Vu, Duc Thach Son TI - An analysis of the unified formulation for the equilibrium problem of compositional multiphase mixtures JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2021 SP - 2981 EP - 3016 VL - 55 IS - 6 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2021075/ DO - 10.1051/m2an/2021075 LA - en ID - M2AN_2021__55_6_2981_0 ER -
%0 Journal Article %A Ben Gharbia, Ibtihel %A Haddou, Mounir %A Tran, Quang Huy %A Vu, Duc Thach Son %T An analysis of the unified formulation for the equilibrium problem of compositional multiphase mixtures %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2021 %P 2981-3016 %V 55 %N 6 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/m2an/2021075/ %R 10.1051/m2an/2021075 %G en %F M2AN_2021__55_6_2981_0
Ben Gharbia, Ibtihel; Haddou, Mounir; Tran, Quang Huy; Vu, Duc Thach Son. An analysis of the unified formulation for the equilibrium problem of compositional multiphase mixtures. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 55 (2021) no. 6, pp. 2981-3016. doi: 10.1051/m2an/2021075
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