An extended macroscopic model for solute dispersion in confined porous media

In the analysis of longitudinal dispersion data in a classical laboratory experiment, it is usually assumed that the dispersion of species undergoes Fickian behaviour with constant dispersivities. If the length and time scales of an experiment are not sufficient for a tracer to traverse the cylinder radius and sample the velocity variations, this could give rise to persisting non-Fickian transients that cannot be predicted by the conventional plug flow dispersion models. Such transients cause the deviation from the Gaussian concentration distribution predicted by the plug models. In this paper, some shortcomings of the Fickian model are examined and a more general non-Fickian macroscopic dispersion model is provided to give insight into some of the factors that contribute to the dispersion process. The analysis describes the transient development of the solute spread and some non-Fickian effects associated with it. The extended model provides a set of conditions under which the classical axial plug dispersion model can be applicable. The model results for tracer dispersion in cylindrical packed beds show that the longitudinal dispersion coefficient converges to its asymptotic value on a time-scale proportional to R2/〈DT〉 where R is the cylinder radius and 〈DT〉 represents the mean value of the radial dispersion coefficient DT(r) over the cross-section of the bed.