Characterization of mixing and dilution in heterogeneous aquifers by meansof local temporal moments

Breakthrough curves of a conservative tracer in a heterogeneous two-dimensi onal aquifer are analyzed by means of their temporal moments. The average v elocity and the longitudinal macrodispersion coefficient of the equivalent one-dimensional aquifer obtained through cross-sectional averaging of conce ntration can be defined from the first and second central moments of a brea kthrough curve integrated over the outflow boundary of the domain. On the b asis of an integrated breakthrough curve, one cannot distinguish between ac tual solute dilution, which involves concentration reduction, and variabili ty of arrival times among parts of the plume at different cross-sectional p ositions. Analyzing the temporal moments of breakthrough curves at a "point " within the domain gives additional information about the dilution of the tracer. From these local first and second central moments an apparent seepa ge velocity v(a) and an apparent dispersivity of mixing alpha(a) can be der ived. For short travel distances, alpha(a) equals the local-scale longitudi nal dispersivity. It increases with the travel distance but much more slowl y than the macrodispersivity. At the large-distance limit, alpha(a) may eve ntually reach the level of macrodispersivity. Lenses of high conductivity w here groundwater flow converges are identified as regions of preferential e nhanced mixing. The spatial distribution of these regions causes a high deg ree of variability of alpha(a) within a domain, indicating a high degree of uncertainty in the quantification of dilution at early stages. In an accom panying paper [Cirpka and Kitanidis, this issue] the results of conservativ e tracer transport are utilized for the study of mixing-controlled reactive transport.