Origin of the inertial deviation from Darcy's law: An investigation from a microscopic flow analysis on two-dimensional model structures
Article dans une revue avec comité de lecture
Inertial flow in porous media occurs in many situations of practical relevance among which one can cite flows in column reactors, in filters, in aquifers, or near wells for hydrocarbon recovery. It is characterized by a deviation from Darcy’s law that leads to a nonlinear relationship between the pressure drop and the filtration velocity. In this work, this deviation, also known as the nonlinear, inertial, correction to Darcy’s law, which is subject to controversy upon its origin and dependence on the filtration velocity, is studied through numerical simulations. First, the microscopic flow problem was solved computationally for a wide range of Reynolds numbers up to the limit of steady flow within ordered and disordered porous structures. In a second step, the macroscopic characteristics of the porous medium and flow (permeability and inertial correction tensors) that appear in the macroscale model were computed. From these results, different flow regimes were identified: (1) the weak inertia regime where the inertial correction has a cubic dependence on the filtration velocity and (2) the strong inertia (Forchheimer) regime where the inertial correction depends on the square of the filtration velocity. However, the existence and origin of those regimes, which depend also on the microstructure and flow orientation, are still not well understood in terms of their physical interpretations, as many causes have been conjectured in the literature. In the present study, we provide an in-depth analysis of the flow structure to identify the origin of the deviation from Darcy’s law. For accuracy and clarity purposes, this is carried out on two-dimensional structures. Unlike the previous studies reported in the literature, where the origin of inertial effects is often identified on a heuristic basis, a theoretical ustification is presented in this work. Indeed, a decomposition of the convective inertial term into two components is carried out formally allowing the identification of a correlation between the flow structure and the different inertial regimes. These components correspond to the curvature of the flow streamlines weighted by the local fluid kinetic energy on the one hand and the distribution of the kinetic energy along these lines on the other hand. In addition, the role of the recirculation zones in the occurrence and in the form of the deviation from Darcy’s law was thoroughly analyzed. For the porous structures under consideration, it is shown that (1) the kinetic energy lost in the vortices is insignificant even at high filtration velocities and (2) the shape of the flow streamlines induced by the recirculation zones plays an important role in the variation of the flow structure, which is correlated itself to the different flow regimes.
Cette publication figure dans le(s) laboratoire(s) suivant(s)
Visualiser des documents liés par titre, auteur, créateur et sujet.
Communication avec acteAGNAOU, Mehrez; LASSEUX, Didier; AHMADI-SENICHAULT, Azita (2013)The aim of this work is to study the correction to Darcy's law for inertial flow in porous media. In many situations encountered in industrial applications such as flow in column reactors, gas flow near wells for hydrocarbon ...
From steady to unsteady laminar flow in model porous structures: an investigation of the first Hopf bifurcation Article dans une revue avec comité de lectureAGNAOU, Mehrez; LASSEUX, Didier; AHMADI-SENICHAULT, Azita (Elsevier, 2016)This work focuses on the occurrence of the first Hopf bifurcation, corresponding to the transition from steady to unsteady flow conditions, on 2D periodic ordered and disordered non-deformable porous structures. The ...
Numerical porosimetry: Evaluation and comparison of yield stress fluids method, mercury intrusion porosimetry and pore network modelling approaches Article dans une revue avec comité de lectureRODRIGUEZ DE CASTRO, Antonio; AGNAOU, Mehrez; AHMADI-SENICHAULT, Azita; OMARI, Abdelaziz (Elsevier BV, 2020)Mercury Intrusion Porosimetry (MIP) is still today the reference porosimetry technique despite its environmental health and safety concerns. As a safe alternative, the Yield Stress fluids Method (YSM) consists in computing ...
Application of Non-toxic Yield Stress Fluids Porosimetry Method and Pore-Network Modelling to Characterize the Pore Size Distribution of Packs of Spherical Beads Article dans une revue avec comité de lectureRODRIGUEZ DE CASTRO, Antonio; AGNAOU, Mehrez; AHMADI-SENICHAULT, Azita; OMARI, Abdelaziz (Springer Science and Business Media LLC, 2019)With X-ray computed tomography still being flawed as a result of limitations in terms of spatial resolution and cost, toxic mercury intrusion porosimetry (MIP) is nowadays the prevailing technique to determine PSDs of most ...
Numerical investigation of Herschel–Bulkley fluid flows in 2D porous media: Yielding behaviour and tortuosity Article dans une revue avec comité de lectureRODRIGUEZ DE CASTRO, Antonio; AGNAOU, Mehrez; AHMADI-SENICHAULT, Azita; OMARI, Abdelaziz (Elsevier BV, 2020)Hydraulic tortuosity is commonly used as an input to macroscopic flow models in porous media, accounting for the sinuosity of the streamlines. It is well known that hydraulic tortuosity does not depend on the applied ...