ON CHARACTERIZATION OF ANOMALOUS-DISPERSION IN POROUS AND FRACTURED MEDIA

A key characterization of dispersion inaquifers and other porous media has been to map the effects of inhomogeneous velocity fields onto a F ickian dispersion term (D) within the context of the conventional adve ction-dispersion equation (ADE), Recent compilations of data have reve aled, however, that the effective D coefficient is not constant but va ries systematically with the length or timescale over which transport occurs. A natural strategy to encompass this ''anomalous'' behavior in to the context of the conventional ADE is to make D time dependent. Th is approach, to use D(t) to handle the same anomalous dispersion pheno mena, has also been common in the field of electronic transport in dis ordered materials. In this paper we discuss the intrinsic inadequacy o f considering a time-dependent dispersivity in the conventional ADE co ntext, and show that the D = D(t) generalization leads to quantifiably incorrect solutions. In the course of proving this result we discuss the nature of anomalous dispersion and provide physical insight into t his important Problem in hydrogeology via analysis of a class of kinet ic approaches. Particular emphasis is placed on the effects of a distr ibution of solute ''delay times'' with a diverging mean time, which we relate to configurations of preferential pathways in heterogeneous me dia.