Numerical Simulation of Flows in Porous Media Using a Microstructural Model
This work presents numerical results of flow simulations through granular media modelled by a regular assembly of monosized cylinders. The adopted numerical approach consists in determining the unknown coefficients of the analytical solution by using leas
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M. El Yazidi, M. Hellou and J. Martinez Institut National des Sciences Appliquees, Rennes, France
ABSTRACT : This work presents numerical results of flow simulations through granular media modelled by a regular assembly of monosized cylinders. The adopted numerical approach consists in determining the unknown coefficients of the analytical solution by using least square method in order to satisfY the boundary conditions. We examine the influence of the geometry of the medium on the microscopic and macroscopic quantities which are characteristic of the flow. At the microscopic scale of the elementary cell, the results show some regions of fluid recirculations between the obstacles. The presence of these regions may favour the retention of the substance carried by the fluid. Furthermore by means of a homogenization technique we have determined the macroscopic permeability and analysed its evolution for several assembly configurations.
1. INTRODUCTION Several microstructural models of porous media can be found in the literature which are differentiated either by the shape of obstacles or cavities. The principal families are formed . by capillary channels or by separated fibers assemblies. Several shapes of fibers (cylindrical, elliptical. .. ) which simulate the solid matrix are used. Recently a model constituted by an array of rectangular fibers has been introduced by Wang (1996). Other authors have simulated porous media by one or two rows of cylinders (Moreau and al., 1998).
A. Cividini (ed.), Application of Numerical Methods to Geotechnical Problems © Springer-Verlag Wien 1998
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M. El Yazidi, M. Hellou and J. Martinez
Bruschke and Advani (1993) have selected two-dimensional media consisting of periodic lattices of cylindrical fibers in order to examine the effect of lattice geometries (square or hexagonal) on the permeability. The theoretical study of Caltagirone and Arquis (1986) concerning the Stokes flow through a network of identical cylinders has shown that for some values of the geometrical parameters some recirculating flows between two cylinders have been observed. In the present paper, our goal is to simulate the flow in porous media by slow flows around circular obstacles. The porous media model chosen is composed of a regular array of cylinders whose centers form isoceles or equilateral triangles. First, our efforts are devoted to the microscopic analysis of the flow structure in order to detect the dead regions and to estimate their extent. Furthermore, by means of a homogenization method we determine the permeability of the model. The calculations are carried out for different porosities values.
2. FORMULATION
2.1. Models and boundary conditions This work concerns the study of plane flow through a porous media model composed of a regular assembly of circular cylinders which allows to approximate a real porous media with high tortuosities. This model is defined by two geometrical parameters 2x., and 2yo which correspond to the distance between the centers of cylinders along the x-direction a
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