We present an experimental study aiming at the identification of the hydraulic conductivity in an aquifer which was packed according to four different configurations. The conductivity was estimated by means of slug tests, whereas the other parameters were determined by the grain size analysis. Prior to the fractal we considered the dependence of the conductivity upon the porosity through a power (scaling) law which was found in a very good agreement within the range from the laboratory to the meso-scale. The dependence of the conductivity through the porosity was investigated by identifying the proper fractal model. Results obtained provide valuable indications about the behavior, among the others, of the tortuosity, a parameter playing a crucial role in the dispersion phenomena taking place in the aquifers.

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Many hydrological applications, such as pumping tests or the set up of in situ remediation protocols, depend to a great extent upon the spatial variability (generically referred as heterogeneity) of the aquifer's hydraulic properties (Rubin, 2003). In particular, it is a common tenet to regard the heterogeneity of the hydraulic conductivity K as the controlling parameter of flow and transport (Dagan, 1989). The variability of K implies that the flow variables are affected by a spatial uncertainty, and therefore developing efficient and reliable methodologies to quantify the K-heterogeneity becomes of paramount importance. This is particularly relevant for strongly heterogeneous formations, where the difference with the homogeneous formation is not evident, sometimes counterintuitive (see, e.g., Janković et al., 2006, and references therein).Among the plethora of methods used to identify the hydraulic conductivity (a comprehensive critical review can be found in Cardiff et al., 2013), pumping tests are (thanks to their minimal equipment's requirement, and ease of implementation), by far, the most prominent tools. Owing to several (mainly economic and logistic) limitations, most of the efforts have focused on the identification of average properties (Copty et al., 2008(Copty et al., , 2011Desbarats, 1994;Zech et al., 2012). However, this is not satisfactory at all, especially to achieve meaningful predictions on solute transport (Dagan, 1989;Rubin, 2003). For this reason, recently it was suggested to carry out measurements over dense borehole spacings in order to achieve accurate three dimensional estimates for mildly heterogeneous aquifers (Cardiff et al., 2013). In line with this trend, the natural question here is whether pumping tests enable one to identify efficiently the heterogeneity structure of the conductivity even in strongly heterogeneous formations. In fact, with the exception of a single pumping test carried out as part of the well known MADE-experiment (Bohling et al., 2012), other experimental investigations under similar conditions limit to deal with "mildly heterogeneous formations" (see, e.g., Fernández-Garcia et al., 2004;Cardiff et al., 2013). Thus, from the experimental point of view, very little has been done when the degree of the formation's heterogeneity is high, and the present study constitutes an attempt to (partially) fill the gap.

The spatial variability of the aquifers' hydraulic properties can be satisfactorily described by means of scaling laws. The latter enable one to relate the small (typically laboratory) scale to the larger (typically formation/regional) ones, therefore leading de facto to an upscaling procedure. In the present study, we are concerned with the spatial variability of the hydraulic conductivity K into a strongly heterogeneous porous formation. A strategy, allowing one to identify correctly the single/multiple scaling of K, is applied for the first time to a large caisson, where the medium was packed. In particular, we show how to identify the various scaling ranges with special emphasis on the determination of the related cut-off limits. Finally, we illustrate how the heterogeneity enhances with the increasing scale of observation, by identifying the proper law accounting for the transition from the laboratory to the field scale. Results of the present study are of paramount utility for the proper design of pumping tests in formations where the degree of spatial variability of the hydraulic conductivity does not allow regarding them as “weakly heterogeneous”, as well as for the study of dispersion mechanisms.

<p>Anomalous transport processes are frequently observed in radial flow to wells in highly heterogeneous aquifers. This is generally related to the presence of preferential flow pathways that bypass the sediment matrix, thus leading to the formation of fast flow channels, whose magnitude depends on the geological entropy of the system. Tracer tests can be effectively combined with laboratory or field-scale experimental campaigns to understand better the interlinkage between heterogeneity and preferential flow, and to distinguish hydraulically active and inactive regions. Despite considerable past research efforts, these mechanisms are only partially understood. To advance the current understanding, we study transport processes in a laboratory-built highly heterogeneous aquifer under radial flow conditions. The experimental device (200 x 200 x 100 cm) consists of 2527 randomly distributed cells (10 x 10 x 5 cm) of 12 different porous mixtures assembled in 7 layers to form a 35 cm-deep aquifer. This particularly design is intended to maximize the geological entropy of the aquifer, which is equipped with 37 piezometers placed in a radial configuration at different distances from the central (pumping) well. Multiple conservative tracer tests were conducted by injecting a mixture of deuterated water (D<sub>2</sub>O) and Potassium Bromide (KBr) into different piezometers, and then by analysing the resulting Breakthrough Curves (BTCs) at the central pumping well. BTCs reveals features peculiar of anomalous transport, such as non-symmetry, early peaks and tailing, which depend on the injecting location. This, jointly with the incomplete mass recovery after 48 hours, suggests the simultaneous presence of fast flow in highly conductive regions, which exchange mass with quasi-immobile portions of the aquifer. By dealing with tests individually, it is seen that curves for the two tracers have a similar trend, with almost perfect overlap in the part before the peaks. Differences in the tailing of the BTCs between the two tracers, that exhibit different molecular diffusion coefficients, indicate the importance of diffusion mechanism taking place in the porous matrix.</p>