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The drawdown time is important for the design and assessment of infiltration basins. This paper investigates its dependence on soil heterogeneity, and simple analytical solutions for the mean and the variance are given. The solutions are tested through Monte Carlo simulations in various realistic scenarios, using a modified Green Ampt model for layered soils and a model based on the integration of the 1‐D Richards equation. The impact of the employed approximations is assessed, and the leading role of the spatial distribution of the saturated hydraulic conductivity is emphasized. The effects of other relevant design and natural factors, including the initial water level and water content distribution, are also investigated. Plain Language Summary: Infiltration basins are receiving an increasing interest in water resources management as an alternative to surface water storage in the managed aquifer recharge and as a green infrastructure at the urban scale. One of the main parameters in the design of the infiltration basins is the drawdown time, that is, the time needed to empty the basin after it has been filled with water, for instance, after a flood event or by a managed treatment plant outlet. This work provides simple analytical solutions for the evaluation along a stochastic approach of the drawdown time, accounting for the soil heterogeneity and leading to a probabilistic design of the infiltration structure. Key Points: The time needed to empty infiltration basins, or drawdown time τ, is an important quantity for their design and assessmentThis work proposes analytical solutions for the mean and variance of τ considering the soil heterogeneitySolutions have been tested through a set of Monte Carlo numerical simulations, showing that the probability density function is lognormal and investigating the effects of design and natural factors [ABSTRACT FROM AUTHOR]

This work extends the overlay and index methods for intrinsic groundwater vulnerability, that typically involve the soil surface and the vadose zone, to groundwater (saturated) transport. The method is "hybrid" as it combines the standard overlay and index methods with a simplified process-based approach for the groundwater component. For the latter, we make use of concept and methodologies based on geomorphological analysis, employing tools that are generally implemented in Geographic Information Systems (GIS). The proposed method is based on a simple probabilistic analysis, in which the overlay and index method (that can be any) provides the probability that the contamination reaches the groundwater through the vadose zone, while the probability that the contaminant reaches a generic location in the groundwater system is determined by analyzing the groundwater streamlines. The analysis leads to the definition of the combined vulnerability index υ , that takes care of both transport in the vadose zone and the aquifer. The method is applied to a groundwater catchment in the Campania region, Southern Italy. The method is simple and effective in assessing aquifer vulnerability in a combined vadose zone—groundwater flow system, useful for preliminary, screening analysis of the intrinsic aquifer vulnerability. [ABSTRACT FROM AUTHOR]

We examine the temporal evolution of the maximum concentration of a dissolved inert solute in spatially heterogeneous subsurface flows. The maximum concentration of a given substance is at the basis of most of environmental regulatory practices where maximum tolerable levels of concentration are typically prescribed for a variety of known contaminants. Through the use of the Lagrangian framework, we elaborate over a physically based, semi-analytical model for the maximum concentration. Specifically, we address how the maximum concentration is affected by key geostatistical parameters (i.e., logconductivity variance), local-scale dispersion processes and engineering design variables such as the dimensions of the solute injection zone. The model will help in identifying the major components that determine the maximum concentration, which is important in order to better allocate resources toward site characterization and reduce uncertainty in predictions. The ultimate scope is to provide a theoretical framework that is application-oriented to estimate the maximum concentration in natural aquifers and provide some guidance in applications. It also provides an useful tool for preliminary, screening analysis and testing scenarios. We test the performance of the model against the MADE transport experiment, with reasonably good agreement. [ABSTRACT FROM AUTHOR]

Six conceptually different transport models were applied to the macrodispersion experiment (MADE)‐1 field tracer experiment as a first major attempt for model comparison. The objective was to show that complex mass distributions in heterogeneous aquifers can be predicted without calibration of transport parameters, solely making use of structural and flow data. The models differ in their conceptualization of the heterogeneous aquifer structure, computational complexity, and use of conductivity data obtained from various observation methods (direct push injection logging, DPIL, grain size analysis, pumping tests and flowmeter). They share the same underlying physical transport process of advection by the velocity field solely. Predictive capability is assessed by comparing results to observed longitudinal mass distributions of the MADE‐1 experiment. The decreasing mass recovery of the observed plume is attributed to sampling and no physical process like mass transfer is invoked by the models. Measures like peak location and strength are used in comparing the modeled and measured plume mass distribution. Comparison of models reveals that the predictions of the solute plume agree reasonably well with observations, if the models are underlain by a few parameters of close values: mean velocity, a parameter reflecting log‐conductivity variability, and a horizontal length scale related to conductivity spatial correlation. The robustness of the results implies that conservative transport models with appropriate conductivity upscaling strategies of various observation data provide reasonable predictions of plumes longitudinal mass distribution, as long as key features are taken into account. Key Points: Aquifer transport is predicted by six models of different heterogeneity conceptualization and field data inputKey model inputs are mean velocity and heterogeneity representation including spatial correlationThe macrodispersion experiment (MADE) site plume longitudinal mass distribution is a robust transport measure [ABSTRACT FROM AUTHOR]

We analyze solute transport in a radially converging 3-D flow field in a porous medium with spatially heterogeneous hydraulic conductivity ( K). The aim of the paper is to analyze the impact of heterogeneity and the mode of injection on BreakThrough Curves (BTCs) detected at a well pumping a contaminated aquifer. The aquifer is conceptualized as an ensemble of blocks of uniform but contrasting K and the analysis makes use of the travel time approach. Despite the approximations introduced, the model reproduces a laboratory experiment without calibration of transport parameters. Our results also show excellent agreement with numerical simulations for different levels of heterogeneity. We focus on the impact on the BTC of both heterogeneity in K and solute release conditions. It is shown that the injection mode matters, and the differences in the BTCs between uniform and flux-proportional injection increase with the heterogeneity of the K-field. Furthermore, we study the effect of heterogeneity and mode of injection on early and late arrivals at the well. [ABSTRACT FROM AUTHOR]

The article discusses papers presented in the AGU Chapman Conference ‘The MADE Challenge for Groundwater Transport in Highly Heterogeneous Aquifers: Insights from 30 Years of Modeling and Characterization at the Field Scale and Promising Future Directions' in Valencia, Spain in October 2015.

Heterogeneity of the hydraulic properties is one of the main causes of the seemingly random distribution of solute concentration observed in contaminated aquifers, with macrodispersivity providing a global measure of spreading. Earlier studies on transport of solutes in heterogeneous formations, either theoretical or numerical, expressed dispersivity as a function of the geostatistical properties of the hydraulic conductivity K. In most cases, K follows a second-order statistical characterization, which may not be adequate when heterogeneity is high. In this work, we adopt the Multi-Indicator Model-Self Consistent Approach (MIMSCA) to compute the longitudinal and transverse macrodispersivity. This methodology enables to model the K field by using geological inclusions of different shapes and orientation (defined here as the microstructure), while replicating the heterogeneous macrostructure obtained by the second-order statistics. The above scheme attempts to reproduce the effect on macrodispersion of different distribution and orientation of local facies, and for instance it may represent the orientation and spatial features of the layers that are often observed in aquifers. The relevant impact of the microstructure on effective conductivity, longitudinal and transverse macrodispersivities is analyzed and discussed, for both binary and lognormally distributed K fields. [ABSTRACT FROM AUTHOR]

Transport of a non-reactive solute in anisotropic bimodal porous formations is investigated through the evaluation of the breakthrough curve. The hydraulic conductivity $$K$$ structure is modelled as an ensemble of anisotropic and non-overlapping inclusions, with given hydraulic conductivity $$K_{i}$$ , randomly placed in an homogeneous matrix with hydraulic conductivity $$K_{0}$$ . The conductivity contrast $$\kappa =K_{i}/K_{0}$$ between the inclusions and the matrix represents the main source of heterogeneity. The resulting $$K$$ structure is a theoretical representation of natural porous formations where inclusions and matrix play the role of two distinct hydrofacies. Semi-analytical solutions for flow and transport are carried out in both 3D and 2D domains following a Lagrangian approach by adopting the dilute limit approximation. The procedure, formally valid for media with low inclusions-matrix relative volume fraction, is extended to dense media by a simplified formulation of the self-consistent approach. Natural porous formations are intrinsically anisotropic due to the depositional process; hence, particular emphasis is addressed to the quantification of the effects of the anisotropy on solute transport. The solution of our physically based model depends on three structural parameters: the hydraulic conductivity contrast $$\kappa $$ , the relative volume fraction $$n$$ , and the statistical anisotropy ratio $$e$$ . The procedure allows for the physical representation of high-velocity channels and stagnation zones, which can be encountered in bimodal media, and it is particular advantageous for a quick estimation of the solute breakthrough curve. Our analysis shows different transport dynamics, as function of the conductivity contrast $$\kappa =K_{i}/K_{0}$$ , leading to fast preferential flow ( $$\kappa >1$$ ) or mass retention ( $$\kappa <1$$ ), as a consequence of the lack of symmetry of the flow and transport parameters (velocity and travel time residuals). High dispersion is typically found when $$\kappa <1$$ , i.e. for low conductive inclusions, where the latter typically trap the solute particles, determining large travel times. Conversely, when $$\kappa >1$$ flow in the inclusions is constrained by the outer flow, limiting the solute velocity inside the inclusions, which results is a rather limited dispersion. Anisotropy typically enhances the solute spreading for $$\kappa <1,$$ as a consequence of the slower velocity predicted for more anisotropic inclusions, while its impact on formations with high $$\kappa $$ is rather limited. [ABSTRACT FROM AUTHOR]

Solute transport in three-dimensional aquifers, with spatially varying hydraulic conductivity of arbitrary point distribution is investigated. The basis of our study is a multiindicator model (MIM) representation of the heterogeneity, combined with a self-consistent approximation for groundwater flow and particle transport. A time-domain random walk (TDRW) approach is presented for computing the expected mass arrival along the longitudinal transport direction that is simple and honors the hydrodynamics of flow for any variability. Using hydraulic conductivity measurements at the MADE site and the MIM, it is shown that the travel time distribution for large variability, cannot be well reproduced by the common distributions used for modeling hydrological transport, such as the log-normal distribution, or the inverse-Gaussian distribution. The proposed TDRW approach directly relates to the Lagrangian trajectory formulation and is appropriate for applications where occurrence of negative flow velocities is small. These results open new possibilities for modeling solute transport in aquifers of arbitrary variability by the time-domain random walk that can readily account for a wide range of mass transfer reactions. [ABSTRACT FROM AUTHOR]

Abstract: The hydraulic conductivity K of the aquifer of the MADE transport experiment, was measured in the past at a dense three-dimensional network of sampling stations. Two methodologies were employed: initially, the flowmeter (using numerous piezometers) and recently the DPIL (direct push injection logger) method. The results for the statistical moments of the lognormal K distribution were similar for the horizontal and vertical integral scales, but quite different for the geometric mean and the variance. By using our recently developed model of transport in highly heterogeneous formations we were able to predict the observed longitudinal mass distribution spreading and to compare with measurements. We found that prediction based on DPIL parameters led to agreement, while flowmeter data resulted in discrepancy. Using our transport model, we explore here in a systematic manner the impact of the different statistical parameters upon the breakthrough curve at different distances from the injection zone. [Copyright &y& Elsevier]

Abstract: Large-scale advective transport through highly heterogeneous 3D formations is investigated using highly resolved numerical simulations and simple analytic models. Investigations are focused on impacts of two types of contaminant injection on transport through isotropic formations where flow conditions are uniform in the average. Transport is quantified by analyzing breakthrough curves for control planes at various distances from the injection zone. In flux-proportional injection mode local mass in injection zone is proportional to local groundwater flux; this setup models many practical cases such as contaminant injection through wells. In resident concentration mode local concentration in injection zone is constant. Results show that impacts of injection mode on breakthrough curves and their moments are strong and they persist for hundreds of correlation scales. The resident concentration mode leads to a fatter tails of the breakthrough curves, while the peaks are generally underpredicted. For a synthetic porous medium with logconductivity variance of 8, dispersivity computed using resident concentration mode at control plane 100 integral scales away from the injection zone was about 10 times larger than corresponding one for flux-proportional mode. Hence, injection mode impacts on transport through highly heterogeneous formations are strong and they persist for large distances from the injection zone. [ABSTRACT FROM AUTHOR]

Determination of hydraulic head, H, as a function of spatial coordinates and time, in ground water flow is the basis for aquifer management and for prediction of contaminant transport. Several computer codes are available for this purpose. Spatial distribution of the transmissivity, T( x,y), is a required input to these codes. In most aquifers, T varies in an erratic manner, and it can be characterized statistically in terms of a few moments: the expected value, the variance, and the variogram. Knowledge of these moments, combined with a few measurements, permits one to estimate T at any point using geostatistical methods. In a review of transmissivity data from 19 unconsolidated aquifers, Hoeksema and Kitanidis (1985) identified two types of the logtransmissivity Y= ln( T) variations: correlated variations with variance and correlation scale, IY, on the order of kilometers, and uncorrelated variations with variance . Direct identification of the logtransmissivity variogram, ΓY, from measurements is difficult because T data are generally scarce. However, many head measurements are commonly available. The aim of the paper is to introduce a methodology to identify the transmissivity variogram parameters ( , IY, and ) using head data in formations characterized by large logtransmissivity variance. The identification methodology uses a combination of precise numerical simulations (carried out using analytic element method) and a theoretical model. The main objective is to demonstrate the application of the methodology to a regional ground water flow in Eagle Valley basin in west-central Nevada for which abundant transmissivity and head measurements are available. [ABSTRACT FROM AUTHOR]

Abstract: One of the main assumptions that renders the stochastic theories applicable to real aquifers is the ergodic hypothesis, i.e. the possibility to exchange ensemble and spatial averages of a variable of interest. The principal aim of this paper is to elucidate the conditions that allow for an exchange between ensemble and spatially averaged second moments of concentration field (S ij ); the fulfillment of the ergodic condition underlies the applicability of the dispersion coefficients or other related quantities obtained by the stochastic theories to actual aquifers. The fulfillment of the ergodic hypothesis is assessed here by analyzing the diminishing of the variance of S ij as the initial size of the plume V 0 grows, i.e. the tendency of S ij toward its expected value 〈S ij 〉. It is shown that it is not always possible to assume ergodicity for solute plumes in heterogeneous aquifers. For the typical plume configurations encountered in applications, transverse and vertical spreading are the most problematic in this respect. In particular, satisfying the ergodic hypothesis depends largely on the initial plume configuration and size, on one hand, and the direction of the moment of interest, on the other. Numerical simulations based on the analytic element method elucidate the results. The relevance of the results is mostly felt for the inference of macrodispersive parameters, which are often derived through S ij . The work indicates that S ij may be a distorted and inadequate measure of the plume spread. This should serve as a warning against application of results based on ensemble averages to real-life plumes, particularly when estimating macrodispersion coefficient from field experiment. [Copyright &y& Elsevier]

Chiang Mai basin has an escalating population growth resulting in high demand for water consumption. Lack of surface water supply in most parts of the basin gives rise to the increasing use of groundwater which leads to a continuous decline in groundwater level in the past decades. This study is the first long-term groundwater monitoring and modeling study that aims at developing a transient, regional groundwater flow model of heterogeneous unconsolidated aquifers based on the MODFLOW program. Long-term groundwater monitoring data from 49 piezometers were used in model calibration and validation. The pilot points technique was used to account for the spatial variability of hydrogeologic parameters of heterogeneous aquifers. The simulation results and statistics showed that most sensitive and significant model parameters were spatially variable hydraulic conductivities and recharge rates. The Chiang Mai basin's unconsolidated aquifers do not have high potential. The water table and/or potentiometric surface in the southeast and southwest areas of Chiang Mai city were continuously decreasing with no sign of recovery indicating critical groundwater condition and careful management must be considered. Safe yield calculation, based on a 2-m average drawdown threshold, suggested that unconsolidated aquifers of the Chiang Mai basin can sustain overall abstraction rates up to 51.2 Mm3/y or approximately 214% of the current extraction rates. [ABSTRACT FROM AUTHOR]

We report the results of field and laboratory investigations of stream-aquifer interactions in a watershed along the California coast to assess the impact of groundwater pumping for irrigation on stream flows. The methods used include subsurface sediment sampling using direct-push drilling, laboratory permeability and particle size analyses of sediment, piezometer installation and instrumentation, stream discharge and stage monitoring, pumping tests for aquifer characterization, resistivity surveys, and long-term passive monitoring of stream stage and groundwater levels. Spectral analysis of long-term water level data was used to assess correlation between stream and groundwater level time series data. The investigations revealed the presence of a thin low permeability silt-clay aquitard unit between the main aquifer and the stream. This suggested a three layer conceptual model of the subsurface comprising unconfined and confined aquifers separated by an aquitard layer. This was broadly confirmed by resistivity surveys and pumping tests, the latter of which indicated the occurrence of leakage across the aquitard. The aquitard was determined to be 2–3 orders of magnitude less permeable than the aquifer, which is indicative of weak stream-aquifer connectivity and was confirmed by spectral analysis of stream-aquifer water level time series. The results illustrate the importance of site-specific investigations and suggest that even in systems where the stream is not in direct hydraulic contact with the producing aquifer, long-term stream depletion can occur due to leakage across low permeability units. This has implications for management of stream flows, groundwater abstraction, and water resources management during prolonged periods of drought. [ABSTRACT FROM AUTHOR]

A flow regime is influenced by the degree of hydrologic connection between surface water and groundwater. As this connection becomes more transient and the basin's runoff response more non-linear, such as for intermittent streams, the need for explicit representation of the groundwater component increases. The present study investigates the connection between Northern Etna groundwater system and the Alcantara river basin in Sicily (Italy). In particular, the upstream part of the basin, whose flow regime is essentially intermittent, is modeled through a modified version of the IHACRES rainfall-runoff model. The structure of the model includes a routing module formulated as a two-store model, with the upper store simulating the quick component of the runoff and recharging the lower store which, in turn, describes the slow component of the runoff and the groundwater extraction and losses. Both stores are conceptualized as simple linear reservoirs, with the lower one that maintains a continuous water balance account of groundwater storage volumes for the upstream basin area with respect to a control cross-section, assumed to be the stream gauging station. The model is calibrated at Moio Alcantara cross-section, where daily streamflow data are available. Model calibration and validation are carried out for the period 1980–1984 and 1986–1988, respectively. A first-order analysis is also performed to assess the sensitivity of model parameters. The adopted configuration is shown to improve model performance with respect to the original IHACRES model, with the proposed formulation able to better capture the interactions between the aquifer and the river. [ABSTRACT FROM AUTHOR]

Transport of an inert solute takes place in a heterogeneous aquifer, of random spatialdistribution of the hydraulic conductivity K(x). Steady flow is driven by a constantmean head gradient and a plume of inert solute is injected in the vertical plane x=0.Transport is quantified by the BTC (breakthrough curve) at control planes at x.The 3D structure is modeled by MIM (multi-inclusion model): an ensemble ofidentical rectangular blocks of independent K tessellating the space. The structure iscompletely characterized by the PDF (probability distribution function) of Y=lnK andthe horizontal and vertical blocks sizes. Flow and transport are solved by SCA(self-consistent approximation): the travel time in each block is derived by regarding it assubmerged in a homogeneous medium of effective conductivity Kef. Comparison withnumerical simulations for lognormal PDF with logconductivity variance σY 2 ≤ 8 hasrevealed that the MIMSCA solution is quite accurate. It was also found to be in goodagreement with findings of the MADE field experiment. MIMSCA solution can beregarded as a time domain random walk with total travel time equal to the sum ofindependent time steps associated with the blocks lying in the space between x=0 and x.We generalize MIMSCA by deriving an ADE for the BTC which is regarded as acontinuous function of x and t. The ADE generalizes the usual one satisfied by theInverse Gaussian distribution by supplementing it by an apparent mass transfer term,which is quantified by a memory function. The aim of the presentation is to analyzethe properties of the new memory function and compare it with similar processes. [ABSTRACT FROM AUTHOR]

In this Reply we further comment on the main assumptions and the results of our recent manuscript 'Advective transport in heterogeneous aquifers: Are proxy models predictive?' [ABSTRACT FROM AUTHOR]

• This setup can describe design of convergent tracer tests or containment systems. • Second-order characterization of K suffices to capture the main features of the BTC. • FOA solution provides a reasonable BTC prediction even for high heterogeneity. This paper studies the impact of the hydraulic conductivity structure on solute transport in a radially convergent heterogeneous flow field, which is generated by a well pumping a confined aquifer. The solute is injected instantaneously in a fully penetrating well at a known distance from the pumping well and the analysis is performed numerically by considering four conductivity structures sharing the same two-point statistics, but displaying widely different higher-order moments and connectivity features. The overall objective of the present work is to assess the impact of three-dimensional hydraulic conductivity structures on the Breakthrough Curve (BTC) at a pumping well as a function of a few structural parameters: the logconductivity variance the integral scales along the horizontal and vertical directions, the local-scale dispersivity and the distance of the injection well. The numerical simulations are also compared with two analytical solutions from literature based on the First Order Approximation and the Self Consistent Approximation, respectively. The results indicate that the principal features of the BTC are weakly dependent on the hydraulic conductivity structure, similar to the findings of Janković (2017) for transport in uniform flow. Also, the simple First-Order solution provides a good approximation of the BTC in most of the scenarios considered, and thus it can be a useful and effective tool for screening purposes in applications dealing with aquifers' contamination. [ABSTRACT FROM AUTHOR]

In this paper, a new analytical solution for interpreting dipole tests in heterogeneous media is derived by associating the shape of the tracer breakthrough curve with the log-conductivity variance. It is presented how the solution can be used for interpretation of dipole field test in view of geostatistical aquifer characterization on three illustrative examples. The analytical solution for the tracer breakthrough curve at the pumping well in a dipole tracer test is developed by considering a perfectly stratified formation. The analysis is carried out making use of the travel time of a generic solute particle, from the injection to the pumping well. Injection conditions are adapted to different possible field setting. Solutions are presented for resident and flux proportional injection mode as well as for an instantaneous pulse of solute and continuous solute injections. The analytical form of the solution allows a detailed investigation on the impact of heterogeneity, the tracer input conditions and ergodicity conditions at the well. The impact of heterogeneity manifests in a significant spreading of solute particles that increases the natural tendency to spreading induced by the dipole setup. Furthermore, with increasing heterogeneity the number of layers needed to reach ergodic conditions become larger. Thus, dipole test in highly heterogeneous aquifers might take place under non-ergodic conditions giving that the log-conductivity variance is underestimated. The method is a promising geostatistical analyzing tool being the first analytical solution for dipole tracer test analysis taking heterogeneity of hydraulic conductivity into account. [ABSTRACT FROM AUTHOR]