Construction of three-phase data to model multiphase flow in porous media: comparing an optimization approach to the finite element approach.

Multiphase flow modelling is a major issue in the assessment of groundwater pollution. Three-phase flows are commonly governed by mathematical models that associate a pressure equation with two saturation equations. These equations involve a number of secondary variables that reflect the fluid behaviour in a porous medium. To improve the computational efficiency of multiphase flow simulators, several simplified reformulations of three-phase flow equations have been proposed. However, they require the construction of new secondary variables adapted to the reformulated flow equations. In this article, two different approaches are compared to quantify these variables. A numerical example is given for a typical fine sand.

[1]  Guy Chavent,et al.  Three-phase compressible flow in porous media: Total Differential Compatible interpolation of relative permeabilities , 2010, J. Comput. Phys..

[2]  Gerhard Schäfer,et al.  Caractérisation de zones sources de DNAPL à l'aide de traceurs bisolubles : mise en évidence d'une cinétique de partage , 2004 .

[3]  S. Jégou.  Estimation des perméabilités relatives dans des expériences de déplacements triphasiques en millieu poreux , 1997 .

[4]  D. Nayagum,et al.  Modelling Two-Phase Incompressible Flow in Porous Media Using Mixed Hybrid and Discontinuous Finite Elements , 2004 .

[5]  Robert Mosé,et al.  Approximation par les éléments finis mixtes d'une équation de diffusion non linéaire modélisant un écoulement diphasique en milieu poreux , 2001 .

[6]  G. Schäfer,et al.  Transport of a Mixture of Chlorinated Solvent Vapors in the Vadose Zone of a Sandy Aquifer: Experimental Study and Numerical Modeling , 2006 .

[7]  Jean-François Girard,et al.  Ground penetrating radar imaging and time-domain modelling of the infiltration of diesel fuel in a sandbox experiment. , 2009 .

[8]  I. Pollet,et al.  Characterisation of a DNAPL source zone in a porous aquifer using the Partitioning Interwell Tracer Test and an inverse modelling approach. , 2009, Journal of contaminant hydrology.

[9]  H. L. Stone.  Probability Model for Estimating Three-Phase Relative Permeability , 1970 .

[10]  Mladen Jurak,et al.  A new formulation of immiscible compressible two-phase flow in porous media , 2008 .

[11]  Jean-Marie Côme,et al.  Iconography : Une approche innovante pour modéliser la biodégradation des composés organochlorés volatils en aquifères poreux , 2006 .

[12]  H. L. Stone.  Estimation of Three-Phase Relative Permeability And Residual Oil Data , 1973 .

[13]  Jack C. Parker,et al.  A parametric model for constitutive properties governing multiphase flow in porous media , 1987 .

[14]  M. J. Oak,et al.  Three-phase relative permeability of Berea sandstone , 1990 .

[15]  Guy Chavent,et al.  A fully equivalent global pressure formulation for three-phases compressible flows , 2009, ArXiv.

[16]  J. Bear.  Dynamics of Fluids in Porous Media , 1975 .

[17]  Van Genuchten,et al.  A closed-form equation for predicting the hydraulic conductivity of unsaturated soils , 1980 .

[18]  Michel Bernadou,et al.  Basis functions for general Hsieh‐Clough‐Tocher triangles, complete or reduced , 1981 .

[19]  Gerhard Schäfer,et al.  Transfert du trichloréthylène en milieu poreux à partir d'un panache de vapeurs , 2003 .

[20]  R. Helmig.  Multiphase Flow and Transport Processes in the Subsurface: A Contribution to the Modeling of Hydrosystems , 2011 .

[21]  Richard E. Ewing,et al.  Comparison of Various Formulations of Three-Phase Flow in Porous Media , 1997 .

[22]  Philip John Binning,et al.  Practical implementation of the fractional flow approach to multi-phase flow simulation , 1999 .