Two-phase inertial flow in homogeneous porous media: A theoretical derivation of a macroscopic model
Article dans une revue avec comité de lecture
Date
2008Journal
Transport in Porous MediaRésumé
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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Communication sans acteLASSEUX, Didier; AHMADI-SENICHAULT, Azita; ABBASIAN ARANI, Ali Akbar (2010)This work focuses on the stationary one-phase Newtonian flow in a class of homogeneous porous media at large enough flow rates leading to a non-linear relationship between the filtration velocity and the pressure gradient. ...
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Communication avec acteLASSEUX, Didier; ABBASIAN ARANI, Ali Akbar; AHMADI-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, ...
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Communication avec acteABBASIAN ARANI, Ali Akbar; LASSEUX, Didier; AHMADI-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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Communication sans acteLASSEUX, Didier; AHMADI-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 ...
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Communication sans acteABBASIAN ARANI, Ali Akbar; LASSEUX, Didier; AHMADI-SENICHAULT, Azita (2009)The purpose of this work is to propose a derivation of a macroscopic model for a certain class of inertial two-phase, incompressible, Newtonian fluid flow through homogenous porous media. The starting point of the procedure ...