DISPERSION IN DISORDERED POROUS MEDIA

We report results of Monte Carlo investigations of dispersion in one- and two-phase flow through disordered porous media represented by square and simple cubic networks of pores of random radii. Dispersion results from the different flow paths and consequent different transit times available to tracer particles crossing from one plane to another in a porous medium. Dispersion is found to be diffusive for the process simulated, i.e., a concentration front of solute particles can be described macroscopically by a convective diffusion equation. Dispersivity in the direction of mean flow, i.e., longitudinal dispersivity, is round to be an order of magnitude larger than dispersivity transverse to the direction of mean flow. In two-phase flow, longitudinal dispersivity in a given phase increases greatly as the saturation of that phase approaches its percolation threshold; transverse dispersivity also increases, but more slowly. As the percolation threshold is neared, the backbone of the sublattice occupied by the phase becomes increasingly tortuous, with numerous subloops which provide alternate particle paths that are evidently highly effeetive in dispersing a concentration front of tracer particles.