Résolution numérique de l’écoulement diphasique en milieu poreux hétérogène incluant les effets inertiels

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 semi analytique 1D de type Buckley-Leverett. Des résultats obtenus dans différentes configurations homogène et hétérogènes 1D et 2D mettent en évidence l'importance des termes inertiels en fonction d'un nombre de Reynolds de l'écoulement

Analysis of the role of structural disorder on the inertial correction to Darcy’s Law

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. A numerical analysis of the non linear -inertialcorrection to Darcy's law is carried out for model periodic structures made of arrays of square-section cylinders. The global aim is to determine and analyze the effective properties appearing in the macroscopic model resulting from the volume averaging of the mass and momentum (Navier-Stokes) equations at the pore scal

One-phase flow in porous media: is the Forchheimer correction relevant?

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 analysis is the averaged flow model operating at Darcy's scale. It shows that the inertial correction to Darcy's law involves a second order tensor that can be determined from the solution of the associated closure problem requiring the microscopic (pore-scale) velocity field. Numerical solutions achieved on 2D model structures are presented. The accent is laid upon the role of the Reynolds number, pressure gradient orientation and structural parameters such as porosity and structural disorder. The Forchheimer type of correction, exhibiting a quadratic dependence upon the filtration velocity, is discussed in different situations

An investigation of inertial one-phase flow in homogeneous model porous media

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, this implies a nonlinear correction to Darcy's law i.e. a nonlinear between the filtration velocity and the pressure gradient. The objective here is to analyze the nonlinear correction on some periodic models of porous media with respect to the Reynolds number and the pressure gradients orientation relative to the principal axes of the periodic unit cell

An investigation of inertial one-phase flow in homogeneous model porous media

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, this implies a nonlinear correction to Darcy's law i.e. a nonlinear between the filtration velocity and the pressure gradient. The objective here is to analyze the nonlinear correction on some periodic models of porous media with respect to the Reynolds number and the pressure gradients orientation relative to the principal axes of the periodic unit cell

Sur quelques aspects des écoulements inertiels mono- et diphasique en milieux poreux

Le contexte du travail est l'écoulement inertiel en milieu poreux, les applications étant dans le domaine de la récupération pétrolière, du génie chimique ... Tout d'abord, un modèle macroscopique d’écoulement monophasique inertiel en milieu poreux homogène obtenu par une méthode de prise moyenne volumique est utilisé. A partir de la résolution numérique des équations de Navier-Stokes à l’échelle microscopique, le comportement de la correction à la loi de Darcy est étudié en fonction du nombre de Reynolds, de l’orientation du gradient de pression, de la porosité et du désordre structural. Le changement d'échelle pour l’écoulement diphasique inertiel est ensuite abordé du point de vue théorique. Un modèle a l'échelle de Darcy est obtenu et les problèmes de fermeture permettant d’obtenir les propriétés macroscopiques correspondantes sont fournis. Enfin un simulateur 3D d'écoulement diphasique inertiel en milieu hétérogène est élaboré. Après une validation en comparaison avec des résultats de type Buckley-Leverett, des exemples de résultats sont présentés sur des structures homogènes et hétérogènes.The context of this work is the inertial flow in porous media, applications being in the field of oil recovery and chemical engineering... First, a result for the macroscopic inertial one-phase flow in homogeneous porous media obtained from the volume averaging method is used requiring the solution of the Navier-Stokes equation at the micro-scale. From the numerical resolution of the Navier-Stokes equation, the dependence of the correction to Darcy’s law on Reynolds number, pressure gradient orientation, and structural parameters such as porosity and disorder is studied. Secondly, up-scaling of inertial two-phase flow in homogeneous porous media is performed theoretically using the volume averaging method. A macroscopic model is obtained and closure problems allowing the computation of macroscopic properties are provided. Finally a 3D numerical simulator for inertial two-phase flow in heterogeneous porous media is developed. The model is validated with semi-analytical solutions of the Buckley-Leverett type and examples of results for homogeneous and heterogeneous configurations are presented

THE RELATIONSHIP BETWEEN WOMEN’S EDUCATION AND HUMAN DEVELOPMENT

The main purpose of this paper is to study the relationship between Women’s Education in primary, secondary and higher education and human development level. This relationship is studied in three groups of countries with high, medium and low human development during the period 2000-2009. The results, based on panel data model estimates show that in countries with high human development, higher educated women have more effective role in human development index. However, in countries with medium human development, secondary education of women has led to increased human development index. In countries with low human development level, all levels of education are conductive to improve the level of human development

THE RELATIONSHIP BETWEEN WOMEN’S EDUCATION AND HUMAN DEVELOPMENT

The main purpose of this paper is to study the relationship between Women’s Education in primary, secondary and higher education and human development level. This relationship is studied in three groups of countries with high, medium and low human development during the period 2000-2009. The results, based on panel data model estimates show that in countries with high human development, higher educated women have more effective role in human development index. However, in countries with medium human development, secondary education of women has led to increased human development index. In countries with low human development level, all levels of education are conductive to improve the level of human development

Surface-initiated Atom Transfer Radical Polymerization and Solution Intercalation Methods for Preparation of Cellulose-G-PS-G-PAN/MMT Bionanocomposite

Cellulose was modified by polystyrene (PS) and polyacrylonitrile (PAN) via free radical and living radical polymerization, and then cellulose was used as the matrix in the preparation of polymer/clay nanocomposite, through a solution intercalation method. For this purpose, first, the graft polymerization of styrene (St) onto cellulose fibers was performed by using suspension polymerization and the free-radical polymerization technique in the presence of potassium persulfate (PPS). Second, the synthesized cellulose-graft-polystyrene was brominated by N-bromosuccinimide (NBS) to obtain polymers with bromine a group. Third, the brominated cellulose fibers were used as macroinitiators in the atom transfer radical polymerization (ATRP) of acrylonitrile (AN) in the presence of CuCl / 2, 2’-bipyridine (Bpy) catalyst system in THF solvent at 90˚C to prepare the cellulose-graft-polystyrene–graft–polyacrylonitrile. Forth, for preparing the modified clay, Na-MMT was mixed with hexadecyl trimethyl ammonium chloride salt. Finally, cellulose-graft-polystyrene–graft–polyacrylonitrile/organoclay bionanocomposite was prepared in CCl4 by a solution intercalation method. Then, the structure of the obtained terpolymer was investigated by FT-IR, DSC, TGA, XRD, and SEM techniques. Moreover, the structure of the bionanocomposite was probed by XRD, SEM, and TEM images