Geometrical and Taylor dispersion in a fracture with random obstacles: An experimental study with fluids of different rheologies

Abstract

The miscible displacement of a Newtonian or shear‐thinning fluid by another one of same rheological properties has been studied optically in a flat transparent model fracture with a random distribution of identical cylindrical obstacles on one of the walls. At the local scale, the concentration variation on individual pixels satisfies a Gaussian convection‐dispersion relation with local transit time ( x, y ) and dispersivity l d ( x, y ). The variation of l d with the Péclet number Pe shows that it results from a combination of geometrical and Taylor dispersion, respectively dominant at low and high Pe values. Using shear‐thinning solutions instead of a Newtonian fluid enhances the velocity contrasts (and therefore geometrical dispersion) and reduces Taylor dispersion. At the global scale, the front geometry is studied from the isoconcentration lines c = 0.5 (equivalent to lines of constant ( x, y ) value): beyond a transition travel time, their width in the direction parallel to the flow reaches a constant limit varying linearly with Log ( Pe ) with a slope increasing with the shear‐thinning character of the fluid. These characteristics are compared to previous observations on other model fractures with a self‐affine roughness displaying channelization effects.