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

Breakthrough curves of a conservative tracer in a heterogeneous two-dimensional aquifer are analyzed by means of their temporal moments. The average velocity and the longitudinal macrodispersion coefficient of the equivalent one-dimensional aquifer obtained through cross-sectional averaging of concentration can be defined from the first and second central moments of a breakthrough curve integrated over the outflow boundary of the domain. On the basis of an integrated breakthrough curve, one cannot distinguish between actual solute dilution, which involves concentration reduction, and variability of arrival times among parts of the plume at different cross-sectional positions. 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 seepage velocity v(a) and an apparent dispersivity of mixing alpha(a) can be derived. For short travel distances, alpha(a) equals the local-scale longitudinal dispersivity. It increases with the travel distance but much more slowly than the macrodispersivity. At the large-distance limit, alpha(a) may eventually reach the level of macrodispersivity. Lenses of high conductivity where groundwater flow converges are identified as regions of preferential enhanced mixing. The spatial distribution of these regions causes a high degree of variability of alpha(a) within a domain, indicating a high degree of uncertainty in the quantification of dilution at early stages. In an accompanying paper [Cirpka and Kitanidis, this issue] the results of conservative tracer transport are utilized for the study of mixing-controlled reactive transport.