Derivation of a macroscopic model for two-phase non-Darcy flow in homogeneous porous media using volume averaging
Communication sans acte
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 is the pore-scale boundary value problem given by the continuity and Navier–Stokes equations in each phase β and γ along with boundary conditions at interfaces. The method of volume averaging is employed subjected to a series of constraints for the development to hold. 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 development also assumes that fluctuations of the curvature of the fluid–fluid interfaces are unimportant over the unit cell representing the porous medium. Under these circumstances, the resulting macroscopic momentum equation, for the -phase (=, ) relates the gradient of the phase-averaged pressure to the filtration or Darcy velocity in a coupled nonlinear form. All tensors appearing in the macroscopic equation can be determined from closure problems that are to be solved using a spatially periodic model of a porous medium. Some indications to compute these tensors are 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. ...
Conférence invitéeAHMADI-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 ...
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 ...
Communication sans acteABBASIAN ARANI, Ali Akbar; AHMADI-SENICHAULT, Azita; LASSEUX, Didier (2009)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 ...
On the stationary macroscopic inertial effects for one phase flow in ordered and disordered porous media Article dans une revue avec comité de lectureLASSEUX, Didier; ABBASIAN ARANI, Ali Akbar; AHMADI-SENICHAULT, Azita (American Institute of Physics, 2011)We report on the controversial dependence of the inertial correction to Darcy’s law upon the filtration velocity (or Reynolds number) for one-phase Newtonian incompressible flow in model porous media. Our analysis is ...