Is Unique Scaling of Aquifer Macrodispersivity Supported by Field Data?
Monday, October 5, 2015: 10:45 AM
Alraune Zech1, Sabine Attinger1, Vladimir Cvetkovic2, Gedeon Dagan3, Peter Dietrich1, Aldo Fiori4, Yoram Rubin5 and Georg Teutsch1, (1)Helmholtz Centre for Environmental Research UFZ Leipzig, Leipzig, Germany, (2)Royal Institute of Technology, Stockholm, Sweden, (3)Tel Aviv University, Tel Aviv, Israel, (4)Universita' di Roma Tre, Dipartimento di Ingegneria, Rome, Italy, (5)University of California Berkeley, Berkeley, CA, United States
Abstract:
Transport by groundwater occurs over the different scales encountered by moving solute plumes. Spreading of plumes is often quantified by the longitudinal macrodispersivity α, which is defined as half the rate of change of the second spatial moment divided by the mean velocity. It was found that generally α is scale dependent, increasing with the travel distance L of the plume centroid, stabilizing eventually at a constant value in a Fickian regime.It was surmised in the literature that α(L) scales up with travel distance following a universal scaling law. Attempts to define the scaling law were pursued by several authors, by fitting a regression line in the log-log representation of results from an ensemble of field experiment, primarily those experiments included by the compendium of experiments summarized by Gelhar et al. [1992].
Despite concerns raised about universality of scaling laws, such relationships are being employed by practitioners for modeling multiscale transport, because they, presumably, offer a convenient prediction tool, with no need for detailed site characterization. Several attempts were made to provide theoretical justifications for the existence of a universal scaling law.
Our study revisited the concept of universal scaling through detailed analyses of field data including the most recent tracer tests reported in the literature. We conducted a thorough re-evaluation of the reliability of the reported macrodispersivity values (Figure, left). Our investigation concludes that transport, and particularly α(L), is formation-specific, and that modeling of transport cannot be relegated to a universal scaling law (Figure right). Instead, transport requires characterization of aquifer properties, e.g. spatial distribution of hydraulic conductivity, and the use of adequate models. The relevance of the findings to MADE is discussed.
Gelhar, L. W., C. Welty, and K. R. Rehfeldt (1992), A critical review of data on field-scale dispersion in aquifers, Water Resour. Res., 28 (7), 1955–1974, doi:10.1029/92WR00607.
Fig: Macrodispersivities α versus distance of observation L: (left) from 52 experiments reported by Gelhar et al. [1992] after re-evaluation, with color indicating reliability; (right) distance dependent values of α from a few selected aquifers.
