Volume 55, Number 6, November-December 2021
|Page(s)||2981 - 3016|
|Published online||06 December 2021|
An analysis of the unified formulation for the equilibrium problem of compositional multiphase mixtures
IFP Energies nouvelles, 1 et 4 avenue de Bois Préau, 92852 Rueil-Malmaison Cedex, France
2 Univ Rennes, INSA, CNRS, IRMAR, UMR 6625, F-35000 Rennes, France
* Corresponding author: firstname.lastname@example.org
Accepted: 15 November 2021
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.
Mathematics Subject Classification: 76T99 / 80M25 / 90C33
Key words: Complementarity condition / unified formulation / phase equilibrium / Gibbs energy function / cubic EOS
© The authors. Published by EDP Sciences, SMAI 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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