Is unique scaling of aquifer macrodispersivity supported by field data?

Abstract

Spreading of conservative solutes in groundwater due to aquifer heterogeneity is quantified by the macrodispersivity, which was found to be scale dependent. It increases with travel distance, stabilizing eventually at a constant value. However, the question of its asymptotic behavior at very large scale is still a matter of debate. It was surmised in the literature that macrodispersivity scales up following a unique scaling law. Attempts to define such a law were made by fitting a regression line in the log‐log representation of an ensemble of macrodispersivities from multiple experiments. The functional relationships differ among the authors, based on the choice of data. Our study revisits the data basis, used for inferring unique scaling, through a detailed analysis of literature marcodispersivities. In addition, values were collected from the most recent tracer tests reported in the literature. We specified a system of criteria for reliability and reevaluated the reliability of the reported values. The final collection of reliable estimates of macrodispersivity does not support a unique scaling law relationship. On the contrary, our results indicate, that the field data can be explained as a collection of macrodispersivities of aquifers with varying degree of heterogeneity where each exhibits its own constant asymptotic value. Our investigation concludes that transport, and particularly the macrodispersivity, is formation‐specific, and that modeling of transport cannot be relegated to a unique scaling law. Instead, transport requires characterization of aquifer properties, e.g., spatial distribution of hydraulic conductivity, and the use of adequate models.

Geological entropy and solute transport in heterogeneous porous media

“…The relationship between H R and the skewness is best described by a power‐law function. These results, which are valid for both high‐ K and low‐ K dominated aquifers, confirm the importance of a site specific characterization of the structure of the K field emphasized by the results of recent studies [e.g., Zech et al ., ; Bianchi and Zheng , ]. For a given degree of spatial disorder in the K field structure, the first three temporal moments of the distribution of arrival times increase with the variance . While the dependency of the variance of the arrival times is not particularly sensitive to the structure of the K field, the values of the parameters in the empirical functions describing the relationship between and the skewness differ with respect to the degree of disorder, and therefore of H R . This result confirms that structural information is not sufficient to fully predict all the different features of transport behavior [e.g., Edery et al ., ; Tyukhova and Willmann , ]. Empirical expressions relating the skewness of the BTCs to the two parameters H R and (equation ) can provide reasonable predictions of Fickian and non‐Fickian transport behavior simply from knowledge of aquifer heterogeneity without fitting parameters.…”

A Critical Analysis of Transverse Dispersivity Field Data

“…Thus, macro-dispersivities D i = α i U , i ∈ {L, T , V }, are by orders of magnitude larger than the pore scale dispersivities values based on laboratory investigations, particularly the one characterizing longitudinal spreading of solutes α L α dL (see e.g., for a recent overview Zech et al [2015]). However, dispersion at the macro-scale is not the result of pore-scale processes but related to aquifer heterogeneity.…”

“…We summarize herein the main aspects of the reliability criteria, accounting for the differences between Gelhar et al (1992) and Zech et al (2015) for longitudinal dispersivity α L , by:…”

Issues and Options in the Delineation of Well Capture Zones under Uncertainty

“…Zech et al () reanalyzed more than 50 dispersion studies from the literature in order to determine whether there is support for a unique scaling law where macrodispersivity would increase unbounded with scale. Their findings do not support the existence of such a relationship.…”

“…The authors concluded that standard transport models with dispersivities based on stochastic theories can be used to simulate transport in complex hydrogeological systems. Zech et al (2015) reanalyzed more than 50 dispersion studies from the literature in order to determine whether there is support for a unique scaling law where macrodispersivity would increase unbounded with scale. Their findings do not support the existence of such a relationship.…”