Time dependence of solute dispersion in aquifers

Groundwater contamination is usually modelled using the advection-dispersion equation with a dispersivity that increases with travel distance. An alternative viewpoint is that the dispersivity is travel time dependent. The hydraulic conductivity, K, varies randomly with position so as to change the local Darcy flux throughout the aquifer. The mean movement of a passive solute is the same as the mean fluid velocity. Its spread, however, is controlled by local variations in fluid flow. Given the statistics of the Darcy flux (derived from the K statistics), it is possible to predict the macro-scale dispersion that will be experienced by a solute plume moving through the aquifer. A formula for the macro-dispersion coefficient, which is a function of the solute travel time in the aquifer, is presented. The predictions of the theory are then compared with the results of a well-controlled field experiment.