Daniele Pedretti

Apparent directional mass-transfer capacity coefficients in three-dimensional anisotropic heterogeneous aquifers under radial convergent transport

Aquifer hydraulic properties such as hydraulic conductivity (K) are ubiquitously heterogeneous and typically only a statistical characterization can be sought. Additionally, statistical anisotropy at typical characterization scales is the rule. Thus, regardless of the processes governing solute transport at the local (pore) scale, transport becomes non-Fickian. Mass-transfer models provide an efficient tool that reproduces observed anomalous transport; in some cases though, these models lack predictability as model parameters cannot readily be connected to the physical properties of aquifers. In this study, we focus on a multirate mass-transfer model (MRMT), and in particular the apparent capacity coefficient (β), which is a strong indicator of the potential of immobile zones to capture moving solute. We aim to find if the choice of an apparent β can be phenomenologically related to measures of statistical anisotropy. We analyzed an ensemble of random simulations of three-dimensional log-transformed multi-Gaussian permeability fields with stationary anisotropic correlation under convergent flow conditions. It was found that apparent β also displays an anisotropic behavior, physically controlled by the aquifer directional connectivity, which in turn is controlled by the anisotropic correlation model. A high hydraulic connectivity results in large β values. These results provide new insights into the practical use of mass-transfer models for predictive purposes.

Analysis of convergent flow tracer tests in a heterogeneous sandy box with connected gravel channels

We analyzed the behavior of convergent flow tracer tests performed in a 3-D heterogeneous sandbox in presence of connected gravel channels under laboratory-controlled conditions. We focused on the evaluation of connectivity metrics based on characteristic times calculated from experimental breakthrough curves (BTCs), and the selection of upscaling model parameters related to connectivity. A conservative compound was injected from several piezometers in the box, and depth-integrated BTCs were measured at the central pumping well. Results show that transport was largely affected by the presence of gravel channels, which generate anomalous transport behavior such as BTC tailing and double peaks. Connectivity indicators based on BTC peak times provided better information about the presence of connected gravel channels in the box. One of these indicators, β, was defined as the relative temporal separation of the BTCs peaks from the BTCs centers of mass. The mathematical equivalence between β and the capacity coefficient adopted in mass transfer-based formulations suggests how connectivity metrics could be directly embedded in mass transfer formulations. This finding is in line with previous theoretical studies and was corroborated by reproducing a few representative experimental BTCs using a 1-D semianalytical bimodal solution embedding a mass transfer term. Model results show a good agreement with experimental BTCs when the capacity coefficient was constrained by measured β. Models that do not embed adequate connectivity metrics or do not adequately reproduce connectivity showed poor matching with observed BTCs.

Geological entropy and solute transport in heterogeneous porous media

We propose a novel approach to link solute transport behavior to the physical heterogeneity of the aquifer, which we fully characterize with two measurable parameters: the variance of the log K values ( math formula), and a new indicator (HR) that integrates multiple properties of the K field into a global measure of spatial disorder or geological entropy. From the results of a detailed numerical experiment considering solute transport in K fields representing realistic distributions of hydrofacies in alluvial aquifers, we identify empirical relationship between the two parameters and the first three central moments of the distributions of arrival times of solute particles at a selected control plane. The analysis of experimental data indicates that the mean and the variance of the solutes arrival times tend to increase with spatial disorder (i.e., HR increasing), while highly skewed distributions are observed in more orderly structures (i.e., HR decreasing) or at higher math formula. We found that simple closed-form empirical expressions of the bivariate dependency of skewness on HR and math formula can be used to predict the emergence of non-Fickian transport in K fields considering a range of structures and heterogeneity levels, some of which based on documented real aquifers. The accuracy of these predictions and in general the results from this study indicate that a description of the global variability and structure of the K field in terms of variance and geological entropy offers a valid and broadly applicable approach for the interpretation and prediction of transport in heterogeneous porous media.

Impact of a Storm-Water Infiltration Basin on the Recharge Dynamics in a Highly Permeable Aquifer

Infiltration basins are increasingly used worldwide to both mitigate flood risk in urban areas and artificially recharge shallow aquifers. Understanding recharge dynamics controlling the quantity and quality of infiltrating water is required to correctly design and maintain these facilities. In this paper, we focus on quantitative aspects and analyze in detail the temporal evolution of infiltration rates in basins overlying highly permeable aquifers. In these settings, recharge is a complex process due to high recharge rate and volume, undetected soil hydraulic heterogeneity and topsoil clogging. A 16-ha infiltration basin in Northern Italy has been intensively characterized and monitored for over four years. Field and laboratory tests were performed to characterize soil hydraulic properties. An unsaturated-saturated numerical model was implemented to obtain additional quantitative information supporting experimental data. Results show a strong impact of the infiltration basin on natural recharge patterns. When properly maintained (no clogging of topsoil), estimated infiltration rates from the bottom of the basin are about fifty times higher than recharge under natural conditions in the same area. When the infiltration basin is not properly maintained, bioclogging progressively diminishes the infiltration capacity of the basin, which turns to have no impact on aquifer recharge. Recharge patterns are highly erratic and difficult to predict. We observed natural recharge rates of the order of 1 m/h and a poor correlation between recharge times and maximum intensity of rainfall events. Due to the complex behavior of the recharge, the numerical model (based on the classical Richards equation) is able to explain many but not all the observed recharge events. Macropores flow and Lisse effects on piezometric measurements may be responsible for the disagreement between model predictions and observations.

Scale dependence of the hydraulic properties of a fractured aquifer estimated using transfer functions

This is the peer reviewed version of the following article: [Pedretti, D., A. Russian, X. Sanchez-Vila, and M. Dentz (2016), Scale dependence of the hydraulic properties of a fractured aquifer estimated using transfer functions, Water Resour. Res., 52, 5008–5024, doi:10.1002/2016WR018660. ], which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/2016WR018660/abstract. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.

Stochastic evaluation of simple pairing approaches to reconstruct incomplete rainfall time series

Two-station pairing approaches are routinely used to infill missing information in incomplete rainfall databases. We evaluated the performance of three simple methodologies to reconstruct incomplete time series in presence of variable nonlinear correlation between data pairs. Nonlinearity stems from the statistics describing the marginal peak-over-threshold (POT) values of rainfall events. A Monte Carlo analysis was developed to quantitatively assess expected errors from the use of chronological pairing (CP) with linear and nonlinear regression and frequency pairing (FP). CP is based on a priori selection of regression functions, while FP is based on matching the probability of non-exceedance of an event from one time series with the probability of non-exceedance of a similar event from another time series. We adopted a generalized Pareto (GP) model to describe POT events, and a t-copula algorithm to generate reference nonlinearly correlated pairs of random temporal distributions distributed according with the GP model. The results suggest that the optimal methodology strongly depends on GP statistics. In general, CP seems to provide the lowest errors when GP statistics were similar and correlation became linear; we found that a power-2 function performs well for the selected statistics when the number of missing points is limited. FP outperforms the other methods when POT statistics are different and variables are markedly nonlinearly correlated. Ensemble-based results seem to be supported by the analysis of observed precipitation at two real-world gauge stations.

Evaluation of single- and dual-porosity models for reproducing the release of external and internal tracers from heterogeneous waste-rock piles

Accurate predictions of solute release from waste-rock piles (WRPs) are paramount for decision making in mining-related environmental processes. Tracers provide information that can be used to estimate effective transport parameters and understand mechanisms controlling the hydraulic and geochemical behavior of WRPs. It is shown that internal tracers (i.e. initially present) together with external (i.e. applied) tracers provide complementary and quantitative information to identify transport mechanisms. The analysis focuses on two experimental WRPs, Piles 4 and Pile 5 at the Antamina Mine site (Peru), where both an internal chloride tracer and externally applied bromide tracer were monitored in discharge over three years. The results suggest that external tracers provide insight into transport associated with relatively fast flow regions that are activated during higher-rate recharge events. In contrast, internal tracers provide insight into mechanisms controlling solutes release from lower-permeability zones within the piles. Rate-limited diffusive processes, which can be mimicked by nonlocal mass-transfer models, affect both internal and external tracers. The sensitivity of the mass-transfer parameters to heterogeneity is higher for external tracers than for internal tracers, as indicated by the different mean residence times characterizing the flow paths associated with each tracer. The joint use of internal and external tracers provides a more comprehensive understanding of the transport mechanisms in WRPs. In particular, the tracer tests support the notion that a multi-porosity conceptualization of WRPs is more adequate for capturing key mechanisms than a dual-porosity conceptualization.