LASSEUX, Didier; AHMADI-SENICHAULT, Azita; ABBASIAN ARANI, Ali Akbar

doi:10.1007/s11242-008-9231-y

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LASSEUX, Didier

Transferts, écoulements, fluides, énergétique [TREFLE]

AHMADI-SENICHAULT, Azita
Transferts, écoulements, fluides, énergétique [TREFLE]

ABBASIAN ARANI, Ali Akbar

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Transport in Porous Media. 2008-05, vol. 75, n° 3, p. 371-400

Springer Verlag

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The purpose of this article is to derive a macroscopic model for a certain classof 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 onthe 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 thatare functions of flow-rates. The dominant and coupling permeability tensors K∗αα and K∗ακand the permeability and viscous drag tensors Kα and Kακ are intrinsic and are those definedin the conventional manner as in (Whitaker, Chem Eng Sci 49:765–780, 1994) and (Lasseuxet al., Transport Porous Media 24(1):107–137, 1996). All these tensors can be determinedfrom closure problems that are to be solved using a spatially periodic model of a porousmedium. The practical procedure to compute these tensors is provided.< Réduire

Mots clés en anglais

Homogeneous porous media

Two-phase flow

Inertial or non-Darcian flow

Up-scaling

Volume averaging

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

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