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Two-phase inertial flow in homogeneous porous media: A theoretical derivation of a macroscopic model

Article dans une revue avec comité de lecture
Auteur
LASSEUX, Didier
ccAHMADI-SENICHAULT, Azita
ABBASIAN ARANI, Ali Akbar

URI
http://hdl.handle.net/10985/9745
DOI
10.1007/s11242-008-9231-y
Date
2008
Journal
Transport in Porous Media

Résumé

The purpose of this article is to derive a macroscopic model for a certain class of inertial two-phase, incompressible, Newtonian fluid flow through homogenous porous media. Starting from the continuity and Navier–Stokes equations in each phase β and γ , the method of volume averaging is employed subjected to constraints that are explicitly provided to obtain the macroscopic mass and momentum balance equations. These constraints are on the length- and time-scales, as well as, on some quantities involving capillary, Weber and Reynolds numbers that define the class of two-phase flow under consideration. The resulting macroscopic momentum equation relates the phase-averaged pressure gradient ∇ pα α to the filtration or Darcy velocity vα in a coupled nonlinear form explicitly given by : (equations) In these equations, Fαα and Fακ are the inertial and coupling inertial correction tensors that are functions of flow-rates. The dominant and coupling permeability tensors K∗αα and K∗ακ and the permeability and viscous drag tensors Kα and Kακ are intrinsic and are those defined the conventional manner as in (Whitaker, Chem Eng Sci 49:765–780, 1994) and (Lasseux et al., Transport Porous Media 24(1):107–137, 1996). All these tensors can be determined from closure problems that are to be solved using a spatially periodic model of a porous medium. The practical procedure to compute these tensors is provided.

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  • Institut de Mécanique et d’Ingénierie de Bordeaux (I2M)

Documents liés

Visualiser des documents liés par titre, auteur, créateur et sujet.

  • Two-phase non-Darcy flow in heterogeneous porous media: A numerical investigation 
    Conférence invitée
    ccAHMADI-SENICHAULT, Azita; ABBASIAN ARANI, Ali Akbar; LASSEUX, Didier (2010)
    Significant inertial effects are observed for many applications such as flow in the near-wellbore region, in very permeable reservoirs or in packed-bed reactors. In these cases, the classical description of two-phase flow ...
  • An investigation of inertial one-phase flow in homogeneous model porous media 
    Communication avec acte
    LASSEUX, Didier; ABBASIAN ARANI, Ali Akbar; ccAHMADI-SENICHAULT, Azita (2009)
    Our interest in this work is the stationary one-phase Newtonian flow in a class of homogeneous porous media at large enough flow rates requiring the introduction of the inertial forces at the pore-scale. At the macroscale, ...
  • Numerical simulation of two-phase inertial flow in heterogeneous porous media 
    Article dans une revue avec comité de lecture
    ccAHMADI-SENICHAULT, Azita; ABBASIAN ARANI, Ali Akbar; LASSEUX, Didier (Springer Verlag, 2010)
    In this study, non-Darcy inertial two-phase incompressible and non-stationary flow in heterogeneous porous media is analyzed using numerical simulations. For the purpose, a 3D numerical tool was fully developed using a ...
  • One-phase flow in porous media: is the Forchheimer correction relevant? 
    Communication sans acte
    LASSEUX, Didier; ccAHMADI-SENICHAULT, Azita; ABBASIAN ARANI, Ali Akbar (2012)
    Our interest in this work is dedicated to the dependence upon the filtration velocity (or Reynolds number) of the inertial correction to Darcy's law for one-phase flow in homogeneous porous media. The starting point of our ...
  • Résolution numérique de l’écoulement diphasique en milieu poreux hétérogène incluant les effets inertiels 
    Communication avec acte
    ABBASIAN ARANI, Ali Akbar; LASSEUX, Didier; ccAHMADI-SENICHAULT, Azita (2007)
    La mise en place d'un outil numérique 3D de simulation d'écoulement diphasique hors régime de Darcy basé sur le modèle de Darcy-Forchheimer généralisé est présentée. L'outil est tout d’abord validé à l’aide d'une solution ...

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