EFFECT OF LOCAL DISPERSION ON SOLUTE TRANSPORT IN RANDOMLY HETEROGENEOUS MEDIA

Recently, an exact Eulerian-Lagrangian theory of advective transport i n spacetime random velocity fields was developed by one of us. We pres ent a formal extension of this theory that accounts for anisotropic lo cal dispersion. The resultant (conditional) mean transport equation is generally nonlocal in space-time. To assess the impact of local dispe rsion on the prediction of transport under uncertainty, we adopt a fir st-order pseudo-Fickian approximation for this equation. We then solve it numerically by Galerkin finite elements for two-dimensional transp ort from an instantaneous square source in a uniform (unconditional) m ean flow field subject to isotropic local dispersion. We use a higher- order approximation to compute explicitly the standard deviation and c oefficient of variation of the predicted concentrations. Our theory sh ows (in an exact manner), and our numerical results demonstrate (under the above closure approximations), that the effect of local dispersio n on first and second concentration moments varies monotonically with the magnitude of the local dispersion coefficient. When this coefficie nt is small relative to macrodispersion, its effect on the prediction of nonreactive transport under uncertainty can, for all practical purp oses, be disregarded. This is contrary to some recent assertions in th e literature that local dispersion must always be taken into account, no matter how small.