Dispersion in periodic porous media. Experience versus theory for two-dimensional systems

Abstract

A method is presented for the experimental study of dispersion in saturated porous media for two-dimensional spatially periodic systems. The use of stereophotolithography laser as the basis of the porous media fabrication process made this investigation feasible. The porous media consist of a set of circular cylinders accurately positioned in an ordered (in line) or in a disordered (random) unit cell periodically reproduced in the plane of the study. For two directions of the average fluid velocity in the in-line array and one direction of the velocity vector in the disordered array, dye is injected in the form of a pulse at the entrance to the medium. The tracer concentration variations with time are measured by a video camera and are averaged over a unit cell. The measured time distributions are compared with computations using the macroscopic convection-diffusion equation in order to estimate the longitudinal dispersion coefficient. The variations of this coefficient with particulate Péclet number in the three geometries investigated are compared with the available numerical results. All the results agree, showing a significant influence of the direction of the average fluid velocity for the ordered medium. Concerning the random medium, the results appear to indicate that, in spite of its periodic character, this type of medium is capable of describing the behaviour of disordered porous media. This original technique is highly promising for the explanation of dispersion mechanisms in porous media.