Three-phase compressible flow in porous media: Total Differential Compatible interpolation of relative permeabilities
Schäfer, Gerhard; Chavent, Guy; di Chiara Roupert, Raphaël (2010), Three-phase compressible flow in porous media: Total Differential Compatible interpolation of relative permeabilities, Journal of Computational Physics, 229, 12, p. 4762-4780. http://dx.doi.org/10.1016/j.jcp.2010.03.013
TypeArticle accepté pour publication ou publié
Journal nameJournal of Computational Physics
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Abstract (EN)We describe the construction of Total Differential (TD) three-phase data for the implementation of the exact global pressure formulation for the modeling of three-phase compressible flow in porous media. This global formulation is preferred since it reduces the coupling between the pressure and saturation equations, compared to phase or weighted formulations. It simplifies the numerical analysis of the problem and boosts its computational efficiency. However, this global pressure approach exists only for three-phase data (relative permeabilities, capillary pressures) which satisfy a TD condition. Such TD three-phase data are determined by the choice of a global capillary pressure function and a global mobility function, which take both saturations and global pressure level as argument. Boundary conditions for global capillary pressure and global mobility are given such that the corresponding three-phase data are consistent with a given set of three two-phase data. The numerical construction of global capillary pressure and global mobility functions by C1 and C0 finite element is then performed using bi-Laplacian and Laplacian interpolation. Examples of the corresponding TD three-phase data are given for a compressible and an incompressible case.
Subjects / KeywordsMultiphase flow; Porous media; Compressible flow; Global pressure; Mathematical modeling; Biharmonic equation
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Construction of three-phase data to model multiphase flow in porous media: Comparing an optimization approach to the finite element approach di Chiara Roupert, Raphaël; Schäfer, Gerhard; Ackerer, Philippe; Quintard, Michel; Chavent, Guy (2010) Article accepté pour publication ou publié