Untangling flow and mass transport in aquifers is essential for effective water management and protection. However, understanding the mechanisms underlying such phenomena is challenging, particularly in highly heterogeneous natural aquifers. Past research has been limited by the lack of dense data series and experimental models that provide precise knowledge of such aquifer characteristics. To bridge this gap and advance our current understanding, we present the findings of a pioneering experimental investigation that characterizes a unique, strongly heterogeneous, laboratory-constructed phreatic aquifer at an intermediate scale under radial flow conditions. This strong heterogeneity was achieved by randomly distributing 2527 cells across 7 layers, each filled with one of 12 different soil mixtures, with their textural characteristics, porosity, and saturated hydraulic conductivity measured in the laboratory. We placed 37 fully penetrating piezometers radially at varying distances from the central pumping well, allowing for an extensive pumping test campaign to obtain saturated hydraulic conductivity values for each piezometer location and scaling laws along eight directions. Results reveal that the aquifer’s strong heterogeneity led to significant vertical and directional anisotropy in saturated hydraulic conductivity. Furthermore, we experimentally demonstrated for the first time that the porous medium tends toward homogeneity when transitioning from the scale of heterogeneity to the scale of investigation. These novel findings, obtained on a uniquely highly heterogeneous aquifer, contribute to the field and provide valuable insights for researchers studying flow and mass transport phenomena. The comprehensive dataset obtained will serve as a foundation for future research and as a tool to validate findings from previous studies on strongly heterogeneous aquifers.

Steady flow toward a fully penetrating well takes place in a natural porous formation, where the erratic spatial variations, and the raising uncertainty, of the hydraulic conductivity K are modeled within a stochastic framework which regards the log-conductivity, ln K, as a Gaussian, stationary, random field. The study provides second order moments of the flow variables by regarding the variance of the log-conductivity as a perturbation parameter. Unlike similar studies on the topic, moments are expressed in a quite general (valid for any autocorrelation function of ln K) and very simple (from the computational stand point) form. It is shown that the (cross)variances, unlike the case of mean uniform flows, are not anymore stationary due to the dependence of the mean velocity upon the distance from the well. In particular, they vanish at the well because of the condition of given head along the well's axis, whereas away from it they behave like those pertaining to a uniform flow. Then, theoretical results are applied to a couple (one serving for calibration and the other used for validation purposes) of pumping tests to illustrate how they can be used to determine the hydraulic properties of the aquifers. In particular, the concept of head-factor is shown to be the key-parameter to identify the statistical moments of the random field K.

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 (D2O) 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.

Steady well-type flow was monitored in an aquifer that was artificially packed in order to reproduce a given, highly heterogeneous, statistical distribution of the log-conductivity Y. In particular, we focus on pumping tests carried out at 10 volumetric flow rates. The experimental arrangement was composed by a pumping well and several surrounding observation piezometers. The unique feature of this experimental study is that the high heterogeneity structure of Y is known fairly well. Thus, the study lends itself as a valuable tool to corroborate theoretical findings about flows driven by sources through porous formations, where the variance sigma(2)(Y) (in the present study equal to 3.79) of Y is large. Besides discussing experimental findings, we tackle the crucial issue of upscaling the hydraulic conductivity in a well-flow configuration. In particular, we deal with the equivalent conductivity (EC) as that pertaining to a homogeneous (fictitious) medium which conveys the same volumetric flow rate of the real one, under the same boundary conditions. Hence, the EC can be identified straightforwardly by means of head measurements. Even if we show that the EC is a proper parameter to reproduce measurements, it is experimentally shown (in line with the theoretical results) to be position-dependent, and therefore, it cannot be regarded (unlike groundwater-type flow) as a formation's property. This implies that the EC applies only to the configuration at stake. Then, we show that the EC, combined with a recent model of effective conductivity in well-flows through highly heterogeneous porous formation, leads to a reasonably reliable estimate of sigma(2)(Y), some limitations and approximations, notwithstanding. It is hoped that the present experimental study will be useful for other researchers who are engaged with similar research-topics.

At a channel (reach) scale, braided channels are fluvial, geomorphological, complex systems that are characterized by a shift of bars during flood events. In such events water flows are channeled in multiple and mobile channels across a gravel floodplain that remain in unmodified conditions. From a geometrical point of view, braided patterns of the active hydraulic channels are characterized by multicursal nature with structures that are spatially developed by either simple- and multi-scaling behavior. Since current studies do not take into account a general procedure concerning scale measurements, the latter behavior is still not well understood. The aim of our investigation is to analyze directly, through a general procedure, the scaling behavior of hydraulically active channels per transect and per reach analyzed. Our generalized stochastic approach is based on Taylor’s law, and the theory of exponential dispersion distributions. In particular, we make use of a power law, based on the variance and mean of the active channel fluctuations. In this way we demonstrate that the number of such fluctuations with respect to the unicursal behavior of the braided rivers, follows a jump-process of Poisson and compound Poisson–Gamma distributions. Furthermore, a correlation is also provided between the scaling fractal exponents obtained by Taylor’s law and the Hurst exponents.

This paper presents the experimental investigation results from the modalities of variation of the hydraulic conductivity scaling law for a confined aquifer, varying the porous medium that constitutes it. In four subsequent stages, different confined aquifers were built up, each with a different typological configuration of a porous medium. For each of the aquifers considered, various hydraulic conductivity ( K ) measurements were performed by slug tests. The effective porosity ( n e ) was set as a scale parameter, therefore the scaling laws K = K(n e ) , already determined and reported in previous studies, were taken into consideration for each of the four artificial aquifers considered. The same variation law of K vs n e was also determined by means of some of the well-known empirical and semi-empirical relationships. The latter are based on the particle size distribution and are suitable for application to the porous media considered here, which can be classified as coarse sand. The comparison between the different scaling laws mentioned above allowed us to discuss, through graphical analysis, the reliability of the models considered here. This will facilitate researchers and practitioners working in the field, in the methodological choice of the most appropriate model that should be used for this type of porous media.

Groundwater management or remediation requires the knowledge of the main hydrodynamic parameters of the hydrological system. The aim of the study focused on the investigation of the reliability of the methods used for the estimation of these important parameters. Several pumping and slug tests were performed in the Hydraulics Laboratory of University of Calabria, where a high controlled experimental apparatus was designed and constructed. The data collected during the experiments have been used to estimate the hydraulic conductivity and the storage coefficient of the porous medium. The analysis was carried out both through classical analytical methods and by the development of an ad hoc three-dimensional finite element model of the apparatus working in transient conditions. An extreme variability in the results was observed but the estimates obtained by the inverse numerical modelling were the ones returning, on average, the best outcomes among all the characterisation methods.

The most common reactive material used for the construction of a permeable reactive barrier (PRB) is zero valent iron (ZVI), however, its processing can generate corrosive effects that reduce the efficiency of the barrier. The present study makes a major contribution to understanding new reactive materials as natural and synthetic, easy to obtain, economical and environmentally friendly as possible substitutes for the traditional ZHV to be used as filters in the removal of three transition metals (Zn, Cu, Cd). To assess the ability to remove these pollutants, a series of batch and column tests were carried out at laboratory scale with these materials. Through BACH tests, four of seven substances with a removal percentage higher than 99% were prioritized (cabuya, natural clinoptilolite zeolites, sodium mordenite and mordenite). From this group of substances, column tests were performed where it is evidenced that cabuya fiber presents the lowest absorption time (≈189 h) while natural zeolite mordenite shows the highest time (≈833 h). The latter being the best option for the PRB design. The experimental values were also reproduced by the RETRASO code; through this program, the trend between the observed and simulated values with respect to the best reactive substance was corroborated.

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.

We consider the problem of steady pumping of water from a line drain on the surface of a wet ground. Unlike the classical formulation, which regards the conductivity parameter K as uniformly distributed in the domain, the problem here is solved within a stochastic framework in order to account for the irregular (random), and more realistic, spatial variability of K. Due to the linearity of the problem at stake, we focus on the derivation of the mean Green function G. This is computed by means of an asymptotic expansion. The fundamental result is an analytical (closed form) expression of G which generalizes the classical solution. Based on this, we develop an equivalent conductivity K-eq which enables one to tackle the problem similarly to the classical one. In particular, it is shown that the equivalent conductivity grows monotonically with the radial distance r from the drain, and it lies within the range K-eq(0) <= K-eq(r) <= K-eq(infinity) < infinity. (C) 2020 Elsevier Inc. All rights reserved.

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.

An accurate measurement campaign, carried out on a confined porous aquifer, expressly reproduced in laboratory, allowed the determining of hydraulic conductivity values by performing a series of slug tests. This was done for four porous medium configurations with different granulometric compositions. At the scale considered, intermediate between those of the laboratory and the field, the scalar behaviors of the hydraulic conductivity and the effective porosity was verified, determining the respective scaling laws. Moreover, assuming the effective porosity as scale parameter, the scaling laws of the hydraulic conductivity were determined for the different injection volumes of the slug test, determining a new relationship, valid for coarse-grained porous media. The results obtained allow the influence that the differences among the characteristics of the porous media considered exerted on the scaling laws obtained to be highlighted. Finally, a comparison was made with the results obtained in a previous investigation carried out at the field scale.

Groundwater flow and contaminant transport are strongly influenced by the aquifer’s heterogeneity (Chao et al., 2000; Fernàndez-Garcia et al., 2004). Generally, the flow (and transport) variables, such as the effective conductivity Keff, can be modelled as random space functions (RSFs) and determined by means of a self-consistent approximation (Severino, 2018). In particular, we aim at estimating the effective conductivity Keff of a highly heterogeneous aquifer made of 12 different porous materials, whose K-values were experimentally measured. A heterogeneous phreatic aquifer was built in the GMI Laboratory of the Department of Civil Engineering of the University of Calabria, inside a metal box (2 m x 2 m x 1 m). The thickness (0.35 m) of the aquifer was built by overlapping 7 different layers of 0.05 m, each consisting of 361 cells (19 x 19), with dimensions equal to 0.1 m x 0.1 m x 0.05 m. For each layer, each cell was filled with one of the 12 porous materials previously characterized in the lab, making the choice randomly. A central (pumping) well and 37 piezometers were located at different distances from the first according to a radial configuration. A pumping test was carried out by a constant flow rate of 70 L/hour. The hydraulic head data, evaluated by using the Neuman method and verified in compliance with the boundary conditions, allowed an effective hydraulic conductivity value Keff to be obtained. Afterwards, this value was compared with K values measured in laboratory by permeameter for each of the 12 porous media used to build the heterogeneous aquifer considered here and with the main statistical parameters related to them. We found the Keff value in a very good agreement with the expression obtained by the self-consistent approximation (Severino, 2018). References Chao C.-H., Rajaram H. and Illangasekare T. H. (2000). Intermediatescale experiments and numerical simulations of transport under radial flow in a two-dimensional heterogeneous porous medium, Water Resour. Res., 36(10), 2869– 2884. Fernàndez-Garcia D., Illangasekare T. H. and Rajaram H. (2004). Conservative and sorptive forced-gradient and uniform flow tracer tests in a three-dimensional laboratory test aquifer. Water Resour. Res., Vol. 40, W10103, doi:10.1029/2004WR003112. Severino G., 2018. Effective conductivity in steady well-type flows through porous formations. Stochastic Environmental Research and Risk Assessment, Vol. 5, https://doi.org/10.1007/s00477-018-1639-5.

We deal with the spatial distribution of the hydraulic conductivity K within heterogeneous porous formations where a radial flow (typical of pumping and slug tests) is taking place. In particular, the study provides a wide data-set which is instrumental to corroborate theoretical findings about the stochastic behavior of K in the above flow configuration. Here, K-data pertain to a series of slug tests conducted within a large caisson which was densely instrumented in order to capture the transitional behavior of the conductivity from the near field (close to the pumping well) to the far field (away from the pumping well). For the experiments at stake, it is shown that the apparent conductivity  $$K_{\mathrm{app}}$$ is a very robust property. In fact, with the exception of a very tiny annulus surrounding the pumping well, $$K_{\mathrm{app}}$$ can be used to solve flow (and transport) problems in close analogy to the effective theory approach adopted for a groundwater-type flow. It is hoped that the data-set exploited in the present study will be useful for other researchers who are engaged with similar studies.

A filtering analysis of hydraulic head data deduced from slug tests injected in a confined aquifer with different porous media is proposed. Experimental laboratory tests were conducted in a large-scale physical model developed at the University of Calabria. The hydraulic head data were deduced from the records of a pressure sensor arranged in the injection well and subjected to a processing operation to filter the high-frequency noise. The involved smoothing techniques are the Fourier transform and two types of wavelet transform. The performances of the filtered hydraulic heads were examined for different slug volumes and four model layouts in terms of optimal fitting of the Cooper's analytical solution. The hydraulic head variations in the confined aquifer were analyzed using wavelet transform in order to discover their energy contributions and frequency oscillations. Finally, the raw and smoothed hydraulic heads were adopted to calculate the hydraulic conductivity of the aquifer.

Abstract The importance of a law that, for an assigned porous medium, gives the variability of the hydraulic conductivity with the effective porosity is well known. Commonly this variability is represented by a power law at different scales, especially those of laboratory and field. Often it can be useful to have a scaling law valid for a single scale range, comprising both those of laboratory and field. Therefore investigation about the reliability of the laws representing the scaling behavior in the various intervals to which reference was made could be suitable. The purpose of this study is to provide evidence about the reliability of the scaling laws for laboratory, field and global (laboratory plus field) scaling ranges, verifying consistency with the expected proportionality between hydraulic conductivity and effective porosity for each of these. This verification was carried out using power-type scaling laws to two and four parameters respectively, and performing suitable moving averages of original data sets, in an attempt to reduce the inevitable measurement uncertainties. The experimental results, obtained with reference to the confined aquifer of Montalto Uffugo test field, show that there are no significant differences between the scaling laws considered and highlight the need to reduce the measurement uncertainties, which weigh heavily on the reliability of scaling laws. Keywords: Scaling law; Hydraulic conductivity; Effective porosity; Laboratory measurement, Field measurement. INFLUENCIA DE LA AMPLITUD DEL INTERVALO DE ESCALA EN LA DETERMINACIÓN DE LA CONDUCTIVIDAD HIDRÁULICA Y LA POROSIDAD EFECTIVA. EL CASO DE UN ACUÍFERO POROSA DEL SUR DE ITALIA La importancia de una ley que, para un dado medio poroso, describa la variabilidad de la conductividad hidráulica en función de la porosidad efectiva es bien conocida. Frecuentemente esta variabilidad está representada por una ley de potencia a diferentes escalas, especialmente las de laboratorio y de campo. A menudo es útil tener una ley de escalamiento válida para un cierto rango de escala incluyendo los de laboratorio y campo. Por esta razón, es oportuno investigar la confiabilidad de las leyes que representan este comportamiento de escalamiento en los diferentes intervalos a los cuales típicamente se hace referencia. El propósito de este estudio es proporcionar evidencia sobre la confiabilidad de las leyes de escalamiento para intervalos de escala válidos para laboratorio, campo y globales (laboratorio + campo), verificando la consistencia con la proporcionalidad esperada entre la conductividad hidráulica y la porosidad efectiva para cada uno de estos. Esta verificación se llevó a cabo utilizando leyes de escalamiento de potencia para dos y cuatro parámetros respectivamente, y tratando de reducir las inevitables incertidumbres de medición. Los resultados experimentales obtenidos con referencia al acuífero confinado del campo de prueba Montalto Uffugo, muestran que no hay diferencias significativas entre las leyes de escalamiento consideradas y se destaca la necesidad de reducir las incertidumbres de medición, las cuales tienen un alto peso sobre la fiabilidad de las leyes de escala. Palabras clave: ley de escalamiento; Conductividad hidráulica; porosidad efectiva; mediciones de laboratorio, medición de campo.

A series of experimental batch tests has been carried out with the aim of improving the knowledge of fundamental processes related to the fate and behavior of heavy metals that can be of environmental concern in groundwater. The analysis of contaminants (i.e., Cu, Zn, Cd and Pb) dynamics in different environmental compartments is specifically addressed by comparing the removal efficiencies of different types of reactive materials, three natural (i.e., vegetal fibers, natural limestone and natural zeolite) and one synthetic (i.e., synthetic zeolite). Results stemming from these reactive media has been compared with the outcomes related to the same test performed using zero valent iron which is the reactant usually employed for heavy metals remediation. All tested reactants exhibited important removal percentages, even larger than 90% in most cases, achieved in a contact time ranging between about 12 h and slightly longer than a day (i.e., 30 h). Maximum adsorption percentages are observed for pH ranging between 4 and 8 for all tested materials and contaminants. Our findings provided relevant evidence, to both researchers and technicians, on the competitiveness of the explored alternative mediums with respect to the classical reactants usually employed for heavy metals remediation.

The dependence of the soil water content theta upon thematric potential psi is studied within a fractal approach that regards the water retention curve as a sequence of well defined fractal regimes. Each of such regimes accounts for a given functional dependence theta equivalent to theta(psi), which in turn is characterized by a fractal dimension. The difference between the double fractal (observed into sandy soils) and multifractal (observed into clay soils) regime is explained by recalling that, for a sandy soil, the transition from saturated to dry conditions is driven by a steep reduction of psi. To the contrary, for a clay (where the change from the highest water contents to the smallest ones is characterized by a large range of thematric potential), the multifractal behaviour is observed. These results are also confirmed by the analysis of experimental data. In particular, we show that the intermediate regime, generally accounting for the fractal multimodality, is due to the sandy nature of the soil at stake, practically immaterial. Finally, we demonstrate that our model can be also regarded as the straightforward generalization of that of Millan and Gonzalez-Posada (2005).