Study of tracer dispersion in self-affine fractures using lattice–gas automata

This paper studies the problem of hydrodynamic dispersion of a tracer in a fluid flowing through a two-dimensional rough channel bounded by self-affine surfaces. Changing the surface roughness exponent H, rough walls having different microstructure are obtained. In order to simulate hydrodynamics, a lattice–gas automata modified to introduce two different species of particles is used. In the studied range of Péclet numbers (20–50), the concentration profiles along the channel are well described by Gaussian-type dispersion. A clear enhancement of the dispersion due to roughness is observed. For the studied regime of Péclet numbers, a simple approach is proposed which allows us to interpret the dispersion enhancement in terms of surface roughness. It is shown that the dispersion enhancement in the rough channel is due to the presence of two characteristic lengths, the hydraulic diameter δH which determines the velocity in the channel and the average aperture δav which determines the transverse diffusion length; next shown is that the dispersion in the rough channel varies as D∥∼(δav/δH)2. The values of δH obtained from the dispersion results are compared with those obtained from permeability measures and a good agreement is observed. In the studied domain of Péclet numbers, the roughness exponent H has only a weak influence on the dispersion.