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

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

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

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

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

Analysis of Magnetic Field Effects on Distributed Heat Sources in a Nanofluid-Filled Enclosure by Natural Convection

This paper studies the effect of magnetic field on the flow field and heat transfer of nanofluid with variable properties in the square enclosure with two arrangements of heat sources. Based upon numerical predictions, the effects of pertinent parameters such as the Rayleigh number (103, 104 and 105), the Hartmann number (0, 25, 50, 75 and 100) and the solid volume fraction (0 to 4%) on the flow and temperature fields and the heat transfer performance of the enclosure are examined. For the numerical solution of conservation equations, finite volume method and SIMPLER algorithm was used. The results show that the heat transfer rate influenced by district heat sources and it increases with distributing heat sources on the side walls and it increases with an increase of the Rayleigh number and volume fraction, but decreases with an increase of Hartmann number

Numerical Investigation of Forced Convection of Nanofluid Flow in Microchannels: Effect of Adding Micromixer

In the present study, forced convection of CuO–water nanofluid in a two dimensional parallel plate microchannel with and without micromixers has been investigated numerically. Two horizontal hot baffles were inserted between the adiabatic plates and three vertical baffles, which were attached on the plates, worked as micromixers in order to improve the cooling process. The effect of Reynolds number, Re = 10, 30, 60, 100, and 150 and nanoparticles volume fraction, from 0 to 4%, were examined on flow field and heat transfer. Different geometrical configurations for the arrangement of the hot baffles were tested. A FORTRAN code based on finite volume method was developed to solve the governing equations and SIMPLER algorithm was used for handling the pressure-velocity coupling. Simulations showed that the presence of micromixers and increasing the Reynolds number as well as nanoparticles volume fraction, increase the average Nusselt number. In order to achieve maximum heat transfer, best arrangements for the baffles were reported. It was also observed that the size of recirculation zones, which are created behind the micromixer baffles, increases with increasing Reynolds number and leads to better cooling

A numerical analysis of the inertial correction to Darcy's law

Our interest in this work is the stationary one-phase Newtonian flow in a class of homogeneous porous media at large enough flow rates so that the relationship between the filtration velocity and the pressure gradient is no longer linear. The non linear -inertial- correction to Darcy's law is investigated from a numerical point of view on model periodic structures made of regular arrays of cylinders. The starting point of the analysis is the macroscopic model resulting from the volume averaging of the mass and momentum (Navier-Stokes) equations at the pore scale. Identification of the macroscopic properties in this model is made by first solving the microscopic flow as well as the closure problem resulting from the upscaling. From these solutions, the inertial correction is computed and analyzed with respect to the Reynolds number and the pressure gradient orientation relative to the principal axes of the periodic unit cell

A numerical approach of two-phase non-Darcy flow in heterogeneous porous media

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 in porous media by the generalized Darcy's law is no longer valid. Due to the lack of a formalized theoretical model confirmed experimentally, our study is based on a generalized Darcy-Forchheimer approach for modelling two-phase incompressible inertial flow in porous media. Using a finite volume formulation, an IMPES (IMplicit for Pressures, Explicit for Saturations) scheme and a Fixed Point method for the treatment of non-linearities caused by inertia, a 3D numerical tool has been developed. For 1D flow in a homogeneous porous medium, comparison of saturation profiles obtained numerically at different times to those obtained semi-analytically using an “Inertial Buckley-Leverett model” allows a validation of the tool. The influence of inertial effects on the saturation profiles and therefore on the breakthrough curves for homogeneous media is analysed for different Reynolds numbers, thus emphasizing the necessity of taking into account this additional energy loss when necessary. For 1D heterogeneous configurations, a thorough analysis of the saturation fronts as well as the saturation jumps at the interface between two media of contrasted properties highlights the influence of inertial effects for different Reynolds and capillary numbers. In 2D heterogeneous configurations, saturation distributions are strongly affected by inertial effects. In particular, capillary trapping of the displaced fluid observed for the Darcy regime in certain regions can completely disappears when inertial effects become dominant