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Numerical modeling of three-phase dissolution of underground cavities using a diffuse interface model

Luo, Haishan and Laouafa, Farid and Guo, Jianwei and Quintard, Michel Numerical modeling of three-phase dissolution of underground cavities using a diffuse interface model. (2014) International Journal for Numerical and Analytical Methods in Geomechanics. ISSN 0363-9061

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Official URL: http://dx.doi.org/10.1002/nag.2274

Abstract

Natural evaporite dissolution in the subsurface can lead to cavities having critical dimensions in the sense of mechanical stability. Geomechanical effects may be significant for people and infrastructures because the underground dissolution may lead to subsidence or collapse (sinkholes). The knowledge of the cavity evolution in space and time is thus crucial in many cases. In this paper, we describe the use of a local nonequilibrium diffuse interface model for solving dissolution problems involving multimoving interfaces within three phases, that is, solid–liquid–gas as found in superficial aquifers and karsts. This paper generalizes developments achieved in the fluid–solid case, that is, the saturated case [1]. On one hand, a local nonequilibrium dissolution porous medium theory allows to describe the solid–liquid interface as a diffuse layer characterized by the evolution of a phase indicator (e.g., porosity). On the other hand, the liquid–gas interface evolution is computed using a classical porous medium two-phase flow model involving a phase saturation, that is, generalized Darcy’s laws. Such a diffuse interface model formulation is suitable for the implementation of a finite element or finite volume numerical model on a fixed grid without an explicit treatment of the interface movement. A numerical model has been implemented using a finite volume formulation with adaptive meshing (e.g., adaptive mesh refinement), which improves significantly the computational efficiency and accuracy because fine gridding may be attached to the dissolution front. Finally, some examples of three-phase dissolution problems including density effects are also provided to illustrate the interest of the proposed theoretical and numerical framework.

Item Type:Article
Additional Information:Thanks to Wiley editor. The definitive version is available at http://onlinelibrary.wiley.com/doi/10.1002/nag.2274/abstract;jsessionid=0B3EAC4FA00FEDEE65FEFD788ACC3C4A.f03t01
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
French research institutions > Institut National de l'Environnement Industriel et des Risques - INERIS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - INPT (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UPS (FRANCE)
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Deposited By: Jianwei GUO
Deposited On:04 Apr 2014 13:52

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