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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.

Abstract: This paper presents a methodology to predict the shape of solute breakthrough curves in heterogeneous aquifers at early times and/or under high degrees of heterogeneity, both cases in which the classical macrodispersion theory may not be applicable. The methodology relies on the observation that breakthrough curves in heterogeneous media are generally well described by lognormal distributions, and mean breakthrough times can be predicted analytically. The log‐variance of solute arrival is thus sufficient to completely specify the breakthrough curves, and this is calibrated as a function of aquifer heterogeneity and dimensionless distance from a source plane by means of Monte Carlo analysis and statistical regression. Using the ensemble of simulated groundwater flow and solute transport realizations employed to calibrate the predictive regression, reliability estimates for the prediction are also developed. Additional theoretical contributions include heuristics for the time until an effective macrodispersion coefficient becomes applicable, and also an expression for its magnitude that applies in highly heterogeneous systems. It is seen that the results here represent a way to derive continuous time random walk transition distributions from physical considerations rather than from empirical field calibration. [ABSTRACT FROM AUTHOR]

The spatial heterogeneity of hydraulic conductivity ( K) exerts a major control on groundwater flow and solute transport. The heterogeneous spatial distribution of K can be imaged using indirect geophysical data as long as reliable relations exist to link geophysical data to K. This paper presents a nonparametric learning machine approach to predict aquifer K from cone penetrometer tests (CPT) coupled with a soil moisture and resistivity probe (SMR) using relevance vector machines (RVMs). The learning machine approach is demonstrated with an application to a heterogeneous unconsolidated littoral aquifer in a 12 km2 subwatershed, where relations between K and multiparameters CPT/SMR soundings appear complex. Our approach involved fuzzy clustering to define hydrofacies (HF) on the basis of CPT/SMR and K data prior to the training of RVMs for HFs recognition and K prediction on the basis of CPT/SMR data alone. The learning machine was built from a colocated training data set representative of the study area that includes K data from slug tests and CPT/SMR data up-scaled at a common vertical resolution of 15 cm with K data. After training, the predictive capabilities of the learning machine were assessed through cross validation with data withheld from the training data set and with K data from flowmeter tests not used during the training process. Results show that HF and K predictions from the learning machine are consistent with hydraulic tests. The combined use of CPT/SMR data and RVM-based learning machine proved to be powerful and efficient for the characterization of high-resolution K heterogeneity for unconsolidated aquifers. [ABSTRACT FROM AUTHOR]

In a recent paper (Trefry et al., 2019, https://doi.org/10.1029/2018wr023864), we showed that the interplay of aquifer heterogeneity and poroelasticity can produce complex transport in tidally forced aquifers, with significant implications for solute transport, mixing, and reaction. However, what was unknown was how broadly these transport dynamics can arise in natural groundwater systems and how these dynamics depend upon the aquifer properties and tidal and regional flow characteristics. In this study we answer these questions through parametric studies of these governing properties. We uncover the mechanisms that govern complex transport dynamics and the bifurcations between transport structures that depend upon changes in the governing parameters, and we determine the propensity for complex dynamics to occur in natural aquifer systems. These results clearly demonstrate that complex transport structures and dynamics may arise in natural tidally forced aquifers around the world, producing solute transport and mixing behavior that is very different to that of the conventional Darcy flow picture. [ABSTRACT FROM AUTHOR]

Hydrologists routinely analyze pumping test data using conventional interpretation methods that are based on the assumption of homogeneity and that, consequently, yield single estimates of representative flow parameters. However, natural subsurface formations are intrinsically heterogeneous, and hence, the flow parameters influencing the drawdown vary as the cone of depression expands in time. In this paper a novel procedure for the analysis of pumping tests in heterogeneous confined aquifers is developed. We assume that a given heterogeneous aquifer can be represented by a homogeneous system whose flow parameters evolve in time as the pumping test progresses. At any point in time, the interpreted flow parameters are estimated using the ratio of the drawdown and its derivative observed at that particular time. The procedure is repeated for all times, yielding time-dependent estimates of transmissivity Ti( t) and storativity, Si( t). Based on the analysis of the sensitivity of drawdown to inhomogeneities in the T field, the time-dependent interpreted transmissivity values are found to be a good estimate of Tg( r), the geometric mean of the transmissivity values encompassed within a progressively increasing radius r from the well. The procedure is illustrated for Gaussian heterogeneous fields with ln( T) variances up to a value of 2. The impact of the separation distance between the pumping well and observation point on data interpretation is discussed. The results show that information about the spatial variability of the transmissivity field can be inferred from time-drawdown data collected at a single observation point. [ABSTRACT FROM AUTHOR]

We study the sensitivity of aquifer‐scale estimates of transmissivity (T) and storativity (S) to the variance and correlation length scale of aquifer heterogeneity, when such estimates are obtained by the traditional approach of analyzing pumping test data. We consider both constant‐rate and variable‐rate pumping tests, and a variety of Theis‐based solution methodologies (single‐ and multiple‐observation well methods, and interpreted single value or transient values for T and S parameters) applied in pumping test data analysis. Our results indicate that achieving reliable inference of effective T and S requires that pumping be continued until the radius of the test‐induced cone of depression exceeds a "representative length" that corresponds to ∼15 times than the correlation length scale of the aquifer heterogeneity. Independent of solution type, pumping history, correlation length scale, magnitude of the sill, and location of observation well, the estimates for T will converge toward the geometric mean. For S, the estimation uncertainty is relatively large for observation wells that are close to the pumping well, but diminishes for observation wells located beyond the representative distance, resulting in convergence to the arithmetic mean. Given that these results have practical implications for how pumping tests should be carried out, we present a simple "rule‐of‐thumb" for estimating the correlation length scale of the heterogeneity of an aquifer. Key Points: The T estimates for constant and heterogeneous S aquifers differ for every observation well; instead, the difference for S strongly depends on observation well distancePumping rate and history does not affect the inferred aquifer parameters; however, Theis‐based solution type results in different interpretationsAs a rule‐of‐thumb, temporal variability of T and S diminishes when the depression cone radius exceeds 15 times the correlation length scale plus the observation well distance [ABSTRACT FROM AUTHOR]

Heat transport in fractured aquifers is determined by the combined effects of flow velocity heterogeneity in the fracture system, and diffusive exchange between the fluid in the fractures and the rock matrix, which can be assumed as impervious. We analyze the impacts of this diffusive exchange on the response to heat transport, as opposite to the pure advective displacement, which governs solute transport. We focus on the post‐peak behavior where we observe pre‐asymptotic regimes with slopes that differ from the signature of matrix diffusion, which exhibits a decay rate of −3/2. This deviation is driven by the variability of both velocity field and fracture aperture field. We derive theoretical models that predict these pre‐asymptotic tails under three extreme cases that can be related with specific network structures, that is, networks dominated by large or small fractures, networks with highly or poorly channelized flow. These theoretical predictions are compared with results from numerical simulations in different sets of three‐dimensional discrete fracture networks. We determine that the combined observation of solute and heat transport responses allows classifying the network in terms of connectivity structure, and partially characterizing the fracture aperture variability in terms of upscaled parameters. Key Points: Heat transport in heterogeneous fractured aquifers exhibits post‐peak tails that express the characteristics of the fracture networkDFN simulations show that heat BTC transition into diffusive regime depends whether the system is dominated by large or small fracturesThe combined observation of solute and heat decay rates allows characterizing connectivity structure and fracture aperture variability [ABSTRACT FROM AUTHOR]

Tidal and barometric water‐level responses in wells have been widely used to calculate the hydraulic properties of aquifer systems. The effect of anisotropy induced by shale content on such responses has not received significant attention. In this study, we examine how the presence of shale (anisotropy, extremely low porosity/permeability; approximately 10−4 to 10−3 mD), which occurs as interlayers in aquifers, affects the tidal responses of the leaky model. Our findings show that the number of wells with shale in the screened section of the study aquifer is limited. Here, we focus on the study of the limited number of wells in the North China Platform to ensure a similar geological background for each well. Calculations indicate that wells, even with a small amount of shale (≥∼5%) in the observation aquifer, may exhibit strong anisotropy and heterogeneity, deviating from the theoretical analytical solutions obtained using isotropic and homogeneous assumption models. Generally, the higher the shale content in aquifer lithology, the greater the phase shifts deviated. Thus, theoretical ideal models with isotropic and homogeneous assumptions may only obtain a rough estimation for wells with shale in aquifer lithology, suggesting that we avoid setting observation aquifers onto shale layers. Plain Language Summary: As special lithology, shale is fragile, compact, and anisotropic, and because of its extremely low porosity/permeability (10−4 to 10−3 mD), it will also induce the heterogeneity of the whole layer containing both shale and other lithology rocks. Therefore, aquifers containing shale might exhibit unique characteristics. However, there is mostly no previous research on this topic in the hydro‐geophysics region, perhaps because the number of wells with shale in aquifer lithology is very limited. Key Points: Well aquifers, even with little amount of shale (∼5%), might have strong anisotropy and heterogeneity and deviate from the ideal modelsThe more shale content in the aquifer lithology the larger the deviation occursFurther call for us to avoid setting the observation aquifers onto the shale (low permeability, friability, and anisotropy) layers [ABSTRACT FROM AUTHOR]

Steady flow generated by an injecting and a pumping well (doublet) takes place in a porous formation where the spatially variable hydraulic conductivity K is modeled as a stationary, lognormal, random field with anisotropic two‐point autocorrelation. The latter is characterized by a vertical integral scale, that is, Iv, smaller than the horizontal one, that is, I. A solute, either passive or reactive, is injected in the medium, and we aim at computing the breakthrough curve (BTC) and its moments not only at the recovery (pumping) well, but also at any location between the two wells. The strong coupling between K and the nonuniformity of the flow renders the problem very difficult. Nevertheless, a simple (analytical) solution is obtained by adopting a few assumptions: (a) wells are replaced by lines of singularity, (b) a perturbation solution which regards the variance σY2 ${\sigma }_{Y}^{2}$ of the log‐conductivity Y = ln K as a perturbation parameter is employed, (c) the study is limited to strongly anisotropic heterogeneous formations (for which the anisotropy ratio λ = Iv/I is much smaller than one), and (d) the impact of pore‐scale dispersion is neglected. Central for the computation of the BTC is the statistics of the travel time of a fluid particle released at the injecting well and reaching a control plane located at any position x1 along the distance connecting the two wells. It is shown that the spatial variability of Y acts de facto like a dispersion mechanism: it enhances spreading, especially in the early arrivals. Useful closed form expressions for moments of the travel time along the central trajectory are also obtained. Finally, the theoretical framework presented in this study is applied to two transport experiments in order to compute the second‐order (temporal) moment as function of x1, and therefore to quantify dispersion occurring in the zone delimited by the two wells. Plain Language Summary: Transport takes place between an injecting well and a pumping one through to a porous formation. The controlling parameter is the conductivity which, unlike the classical approach, here is regarded, in line with field findings, as spatially variable. This renders the problem at stake extremely difficult to solve. However, a simple solution is achieved by adopting a few simplifying assumptions, which nevertheless resemble most of the existing aquifers, and therefore it is applicable to numerous real‐world situations. It is shown that the proposed solution finds application in the identification of the aquifer's parameters as well as the quantification of efficiency of decontamination procedures. Finally, the theoretical framework is applied to a couple of transport experiments, in order to illustrate (and to quantify) how dispersion process develops in the zone delimited by the two wells. Key Points: Transport in a doublet flow is investigated by means of the breakthrough curve (BTC) and its momentsA simple solution is achieved by dealing with a strongly anisotropic heterogeneous formationResults are applied to a couple of field‐scale transport experiments [ABSTRACT FROM AUTHOR]

Numerical models of variable‐density groundwater flow and salt transport are a primary tool for predicting salinity distributions in coastal aquifers and estimating submarine groundwater discharge (SGD). Models are particularly useful to estimate the saline component of SGD, which can occur far offshore and is difficult to measure directly. Depending on the system and application, the level of geologic detail represented can range from homogeneous or layered to fully heterogeneous hydraulic conductivity fields. These features strongly affect model results, limiting understanding of subsurface salinity distributions and associated density‐driven saltwater circulation along coasts worldwide. In this study, the impact of the scale of representation of heterogeneity on salinity distributions and SGD was investigated using numerical simulations. Upscaling hydraulic conductivity can significantly modify salinity distributions and flow paths, resulting in unpredictable variations in simulated SGD, though the values for homogeneous fields with equivalent hydraulic conductivity show consistent trends. Simulated density distributions control both the rate and direction of subsurface saltwater circulation. The length of the mixing zone perimeter, a measure of salinity distribution complexity, is shown to correlate with both the rate of subsurface saltwater circulation and the amount of groundwater circulating in the reverse direction from homogeneous cases. Overall, the results demonstrate a strong dependence of salinity distributions and saltwater circulation on the scale and distribution of geologic heterogeneity represented in numerical models. This suggests that numerical models with simplified geologic structure may substantially underestimate saltwater circulation, and attempts to calibrate them using salinity distributions or SGD measurements may be problematic. Plain Language Summary: Groundwater flow and solute transport models that simulate how groundwater moves across the land‐ocean interface and seabed are important to science and engineering because these processes affect our coastal water resources as well as the chemical composition of the ocean. These models have been applied over different domain sizes, simulation grid resolutions, and geologic representations. We show that simulation results are strongly scale‐dependent, which makes it difficult to develop general conclusions that are independent of model setup. We simulated saltwater distributions and groundwater flow across a range of scales and detail of geologic representation. This work improves the understanding of scale‐dependent heterogeneity in simulations of saltwater circulation and cautions those modeling these processes to carefully consider how results relate to the model itself. Key Points: Upscaling hydraulic conductivity alters circulation direction and affects geometry of mixing zone where saltwater circulation occursFresh submarine groundwater discharge (SGD) tends to increase and saline SGD tends to decrease with upscaling; mixing zone area and perimeter do not vary systematicallyModels with simplified geologic structure may underestimate density‐driven saltwater circulation [ABSTRACT FROM AUTHOR]

Studies of coastal groundwater dynamics often assume two‐dimensional (2D) flow and transport along a shore‐perpendicular cross‐section. We show that along‐shore movement of groundwater may also be significant in heterogeneous coastal aquifers. Simulations of groundwater flow and salt transport incorporating different geologic structure show highly three‐dimensional (3D) preferential flow paths. The along‐shore movement of groundwater on average accounts for 40%–50% of the total flowpath length in both conduit‐type (e.g., volcanic) heterogeneous aquifers and statistically equivalent (e.g., deltaic) systems generated with sequential indicator simulation (SIS). Our results identify a critical role of three‐dimensionality in systems with connected high‐permeability geological features. 3D conduit features connecting land and sea cause more terrestrial groundwater flow through the inland boundary and intensify water exchange along the land‐sea interface. Therefore, conduits increase the rate of SGD compared to equivalent homogeneous, SIS and corresponding 2D models. In contrast, in SIS‐type systems, less‐connected high‐permeability features produce mixing zones and SGD nearer to shore, with comparable rates in 3D and 2D models. Onshore, 3D heterogeneous cases have longer flowpaths and travel times from recharge to discharge compared to 2D cases, but offshore travel times are much shorter, particularly for conduit‐type models in which flow is highly preferential. Flowpath lengths and travel times are also highly variable in 3D relative to 2D for all heterogeneous simulations. The results have implications for water resources management, biogeochemical reactions within coastal aquifers, and subsequent chemical fluxes to the ocean. Plain Language Summary: The findings of this study provide insight into the complex patterns of groundwater flow under the influence of geologic variability in coastal aquifers. In coastal regions, studies of solute transport processes mainly rely on an assumption of 2D groundwater flow and solute transport in the shore‐perpendicular direction. Our results reveal that groundwater does not only flow toward the sea, it also can flow along‐shore, especially in aquifers with features that connect the onshore and offshore. This affects exchange and mixing between fresh and saline groundwater, which can strongly impact delivery of contaminants and nutrients to sensitive nearshore marine ecosystems. Results highlight the importance of characterizing the geology of coastal aquifers and representing it in models of groundwater flow and contaminant transport. Key Points: Geologic heterogeneity causes substantial along‐shore movement of groundwater in coastal heterogeneous aquifersAlong‐shore groundwater flow in heterogeneous aquifers increases variability of travel length and time of groundwater prior to dischargeConnected, high‐permeability features increase the rate of SGD compared to equivalent homogeneous, SIS, and corresponding 2D models [ABSTRACT FROM AUTHOR]

Airborne electromagnetic (AEM) data can be inverted to recover models of the electrical resistivity of the subsurface; these, in turn, can be transformed to obtain models of sediment type. AEM data were acquired in Butte and Glenn Counties, California, USA to improve the understanding of the aquifer system. Around 800 line‐kilometers of high‐quality data were acquired, imaging to a depth of ∼300 m. We developed a workflow designed to obtain, from the AEM data, information about the large‐scale structure and heterogeneity of the aquifer system to better understand the vertical connectivity. Using six different inversions incorporating various forms of available information and posterior sampling of the recovered resistivity models, we produced 6,006 resistivity models. These models were transformed to models of sediment type and estimates of percentage of sand/gravel. Exploring the model space, containing the resistivity models and the derived models, allowed us to delineate the large‐scale structure of the aquifer system in a way that captures and communicates the uncertainty in the identified sediment type. The uncertainty increased, as expected, with depth, but also served to indicate, as areas of high uncertainty in sediment type, the location of both large‐scale and small‐scale interfaces between sediment types. A plan view map of the integrated percentage of sand/gravel, when compared to existing hydrographs, revealed the extent of lateral changes in vertical connectivity within the aquifer system throughout the study area. Plain Language Summary: In studying and managing groundwater systems, it can be very difficult to get the information needed about the subsurface. The airborne electromagnetic (AEM) method uses a helicopter to move a geophysical system over the land surface to collect this needed information. In this study we acquired ∼800 line‐kilometers of high‐quality AEM data in an area of Butte and Glenn Counties in the Central Valley of California, USA. Acquisition of these data allowed us to obtain three‐dimensional (3D) resistivity models covering the region from the ground surface to a depth of about 300 m. Working with descriptions from wells, we were able to transform the 3D resistivity models into 3D sediment‐type models. These models allowed us to map out the large‐scale structure of the groundwater system and better understand the vertical connectivity within the system. Because of fundamental limitations in the AEM method, we obtained many different resistivity models and corresponding sediment‐type models. Exploring these models allowed us to quantify the uncertainty in our interpretation of the data. This not only assisted in our interpretation, but it also communicated, to the local water agency, our confidence in our interpretation. Key Points: By incorporating various forms of available information in the inversion of airborne electromagnetic data, we designed a workflow that reduces and quantifies uncertainty in the derived sediment‐type modelsModels of sediment type reveal the large‐scale architecture of the aquifer systemModels of the percentage of sand/gravel, when combined with hydrographs, provide information about the lateral variability in vertical connectivity within the aquifer system [ABSTRACT FROM AUTHOR]

Preferential flow can result in rapid contamination of groundwater resources. This is particularly true in aquifers with connected, high permeability geologic structures and in coastal systems where the oceanic source of contamination is ubiquitous. We consider saltwater intrusion due to pumping in volcanic aquifers with lava tubes represented as connected high‐K structures and compare salinization responses to those of heterogeneous aquifers with different structure and equivalent homogeneous systems. Three‐dimensional simulations of variable‐density groundwater flow and salt transport show that conduits formed by lava flows create preferential groundwater flow in volcanic aquifers. These conduits allow fresh groundwater to extend further offshore than in other systems. However, onshore pumping causes saltwater to migrate landward quickly through the conduits relative to the other models, resulting in more severe saltwater intrusion, particularly at shallow depths. The geometry of geologic heterogeneity in volcanic aquifers leads to increased risk of salinization of fresh groundwater as well as substantial uncertainty due to significant spatial variation in saltwater intrusion. The findings illustrate the importance of considering geologic heterogeneity in assessing the vulnerability of coastal freshwater resources in volcanic and other aquifers with connected high‐permeability geologic structures. Plain Language Summary: The findings of this study provide insight into vulnerability of volcanic coastal aquifers to salinization due to groundwater pumping. Our results reveal significant landward movement of saltwater due to onshore pumping, which has important implications for vulnerability of coastal freshwater resources in volcanic and other aquifers with connected geologic structures. In coastal regions, the control of saltwater intrusion often relies on salinity detection in monitoring wells located near the shoreline. Our results demonstrate significant spatial variations in saltwater intrusion along the coastline that are strongly correlated to geologic heterogeneity. These variations are difficult to predict; thus, intrusion may easily bypass monitoring wells. These results highlight the importance of considering geologic heterogeneity in studies of saltwater intrusion in volcanic and other heterogeneous aquifers. Key Points: Nearshore groundwater pumping induces greater saltwater intrusion in volcanic aquifers compared to other aquifer typesPattern of saltwater intrusion is controlled by spatial distribution of geologically connected high‐permeability conduitsAdequate representation of connected structure is essential to capture saltwater intrusion dynamics in highly heterogeneous aquifers [ABSTRACT FROM AUTHOR]

Nonpoint source (NPS) groundwater contamination in sedimentary basin aquifers with overlying agricultural activities increasingly threatens groundwater supplies. The role of aquifer heterogeneity has not been well understood in the assessment of NPS and in linking pollution sources to impacts in water supply wells. A typical well taps into and mixes groundwater varying in age by decades or even centuries. This study investigates the joint impact of aquifer heterogeneity and pumping well characteristics (well depth, pumping rate, and screen length) on expected values of and uncertainty about key management metrics: (1) travel time of a NPS contaminant to a production well, (2) spatiotemporal characteristics of the source area, and (3) contaminant compliance at production wells. A stochastic approach is employed using Monte Carlo simulation of flow and nonreactive transport in 3‐D highly heterogeneous alluvial aquifer systems. Well design is shown to dominate the distribution of travel time mixing and the overall location and spread of the source area. Larger extraction intensity and closer proximity to the land surface are shown to significantly suppress effects of large aquifer heterogeneity on uncertainty on all metrics. Deep wells and wells with lower pumping rates have more uncertain source areas. Long‐term NPS contaminants with high source concentration (>10 times compliance level) will be exceeded in most wells within decades, while low‐intensity source concentrations (2–4 times compliance level, typical for nitrate and salinity) have large uncertainty about time to exceedance suggesting wide variability among a set of wells with similar well design subject to the same NPS pollution. Key Points: Management metrics for nonpoint source (NPS) pollution of large production wells are assessed stochasticallyWell characteristics (pumping rate and depth) significantly impact statistics and uncertaintyExtraction intensity and proximity to the NPS suppress the potential for heterogeneity to generate uncertainty [ABSTRACT FROM AUTHOR]

Abstract: Solute mixing, spreading, and fast chemical reactions in aquifers are strongly influenced by spatial variability of the hydraulic properties, temporal flow fluctuations, and fluid density differences. We study the coupling of heterogeneity, transient forcing, and density‐driven flow on mixing and chemical reactions between two fluids of different density under a stable stratification. We consider the reaction of the fast dissolution of calcite. We find that temporal fluctuations and heterogeneity cause strong local enhancement of the mixing and reaction rates and this impact increases with the degree of connectivity of hydraulic conductivity. The global mixing and reactivity, however, are on the order of or smaller than their homogeneous counterparts due to heterogeneity‐induced fluid segregation. The local maxima of the mixing and reaction rates are found to be located around strongly stretched regions corresponding to high velocity zones where dispersive mass transfer mechanisms are increased by dispersion. We also find that density variations compress the interface, which in turn emphasizes local maxima in mixing and reaction rates. Numerical results provide evidence that the stretching of the interface induced by spatial heterogeneity and transient effects coupled with density variations lead to the formation of complex patterns of reactive hotspots, zones of enhanced reaction efficiency, and that its distribution is directly linked to the deformation properties and topology of the flow field. These results provide new insights into the role of spatial and temporal variability on the mixing and reaction efficiency as well as the formation of reactive geochemical patterns in actual environmental systems. [ABSTRACT FROM AUTHOR]

Abstract: The presence of unsaturated zones at the river‐aquifer interface has large implications on numerous hydraulic and chemical processes. However, the hydrological and geological controls that influence the development of unsaturated zones have so far only been analyzed with simplified conceptualizations of flow processes, or homogeneous conceptualizations of the hydraulic conductivity in either the aquifer or the riverbed. We systematically investigated the influence of heterogeneous structures in both the riverbed and the aquifer on the development of unsaturated zones. A stochastic 1‐D criterion that takes both riverbed and aquifer heterogeneity into account was developed using a Monte Carlo sampling technique. The approach allows the reliable estimation of the upper bound of the spatial extent of unsaturated areas underneath a riverbed. Through systematic numerical modeling experiments, we furthermore show that horizontal capillary forces can reduce the spatial extent of unsaturated zones under clogged areas. This analysis shows how the spatial structure of clogging layers and aquifers influence the propensity for unsaturated zones to develop: In riverbeds where clogged areas are made up of many small, spatially disconnected patches with a diameter in the order of 1 m, unsaturated areas are less likely to develop compared to riverbeds where large clogged areas exist adjacent to unclogged areas. A combination of the stochastic 1‐D criterion with an analysis of the spatial structure of the clogging layers and the potential for resaturation can help develop an appropriate conceptual model and inform the choice of a suitable numerical simulator for river‐aquifer systems. [ABSTRACT FROM AUTHOR]

A framework for interpreting transient pumping tests in heterogeneous transmissivity fields is developed to infer the overall geostatistical parameters of the medium without reconstructing the specific heterogeneous structure point wise. The methodology of Radial Coarse Graining is applied to deduce an effective radial description of multi-Gaussian transmissivity. It was used to derive an Effective Well Flow Solution for transient flow conditions including not only the storativity, but also the geometric mean, the variance, and the correlation length of log-transmissivity. This solution is shown to be appropriate to characterize the pumping test drawdown behavior in heterogeneous transmissivity fields making use of ensembles of simulated pumping tests with multiple combinations of statistical parameters. Based on the Effective Well Flow Solution, a method is developed for inferring heterogeneity parameters from transient pumping test drawdown data by inverse estimation. Thereby, the impact of statistical parameters on the drawdown is analyzed, allowing to determine the dependence of reliability of parameter estimates on location and number of measurements. It is shown, that the number of measurements can be reduced compared to steady state pumping tests. Finally, a sampling strategy for single aquifer analysis is developed, which allows to estimate the statistical parameters, in particular variance and correlation length for individual heterogeneous transmissivity fields making use of transient pumping test measurements at multiple locations. [ABSTRACT FROM AUTHOR]

We analyze the probability distribution of the hazard attenuation factor for a noncarcinogenic reactive compound captured by a well in heterogeneous porous formations. The hazard attenuation factor is defined as the ratio between the hazard index HI at a detection well and at the source. Heterogeneity of the aquifer is represented through the multi-indicator model (a collection of blocks of independent permeability) while flow and transport are solved by the means of the self-consistent approach that is able to deal with any degree of heterogeneity. Due to formation heterogeneity, HI is a random variable and similar for hazard attenuation index. The latter can be fully characterized by its cumulative distribution function (CDF), which in turn can be related to the statistics of the travel time of solute particles, from the source to the detection well. The approach is applied to the case of a solute which undergoes decay and a well with a screen much smaller than the correlation scale of hydraulic conductivity. The results show that the probability of exceeding a given acceptable threshold of the hazard index is significantly affected by the level of heterogeneity comparable to the one observed for the MADE site, and the distance between the source and the well. [ABSTRACT FROM AUTHOR]

Although aquifers are naturally heterogeneous, the interpretation of pumping tests is commonly performed under the assumption of aquifer homogeneity. This yields interpreted hydraulic parameters averaged over a domain of uncertain extent which disguises their relation to the underlying heterogeneity. In this study, we numerically investigate the sensitivity of the transient drawdown at the pumping well, to nonuniform distributions of transmissivity in confined aquifers. Frechet kernels and their time derivative are used to estimate two spatially averaged transmissivities, denoted the equivalent and interpreted transmissivity, Teq and Tin, respectively, for the case of single-well pumping tests. Interrelating Teq and Tin is achieved by modeling Tin in terms of a distance dependent, radially heterogeneous field. In weakly heterogeneous aquifers, Teq approximates TPW, the local transmissivity at the pumped well. With increasing degree of heterogeneity, Teq deviates from TPW as pumping propagates. Tin starts at TPW, approaching the spatial geometric mean of transmissivity during late pumping times. Limits of the proposed spatial weighting functions are investigated by treating the interpreted storativity, Sest, as an indicator for flow connectivity. It is shown numerically that the spatial weights for Teq and Tin agree well to the underlying heterogeneity if . Finally, implications for applying the concepts of Teq and Tin to heterogeneous domains, and, for real world applications are discussed. It is found that time-dependent spatial averages of Tin agree well with estimates of the interpreted transmissivity from the Continuous-Derivation method. [ABSTRACT FROM AUTHOR]

Stochastic realizations of lithofacies assemblage based on lithological data from a relatively small number of boreholes were used to simulate solute transport at the well-known Macrodispersion Experiment (MADE) site in Mississippi (USA). With sharp vertical contrasts and lateral connectivity explicitly accounted for in the corresponding hydraulic conductivity fields, experimental results from a large-scale tracer experiment were adequately reproduced with a relatively simple model based on advection and local dispersion. The geologically based model of physical heterogeneity shows that one well-interconnected lithofacies, with a significantly higher hydraulic conductivity and accounting for 12% of the total aquifer volume, may be responsible for the observed non-Fickian transport behavior indicated by the asymmetric shape of the plumes and by variations of the dispersion rate in both space and time. This analysis provides a lithological basis to the hypothesis that transport at MADE site is controlled by a network of high-conductivity sediments embedded in a less permeable matrix. It also explains the calibrated value of the ratio of mobile to total porosities used in previous modeling studies based on the dual-domain mass transfer approach. The results of this study underscore the importance of geologically plausible conceptualizations of the subsurface for making accurate predictions of the fate and transport of contaminants in highly heterogeneous aquifers. These conceptualizations may be developed through integration of raw geological data with expert knowledge, interpretation, and appropriate geostatistical methods. [ABSTRACT FROM AUTHOR]

We study the combined effect of heterogeneity in the hydraulic conductivity field and tidal oscillations on the three-dimensional dynamics of seawater intrusion in coastal aquifers. We focus on the quantification of its impact on solute mixing and spreading of the freshwater-seawater interface. Three-dimensional Monte Carlo realizations of log-normally distributed permeability fields were performed, and for each realization, numerical variable density flow and solute transport simulations were conducted. Mixing is characterized by the spatial moments of concentration. The enhanced solute mixing is quantified by an effective dispersion coefficient. The simulations show that heterogeneity produces an inland movement of the toe location along with a significant widening of the transition zone, which is linearly proportional to the product of the arithmetic mean of the correlation lengths in the three spatial dimensions ( λa) and the permeability field variance ( [ABSTRACT FROM AUTHOR]

A primary concern for geologic carbon storage is the potential for leakage of stored carbon dioxide (CO2) into the shallow subsurface where it could degrade the quality of groundwater and surface water. In order to predict and mitigate the potentially negative impacts of CO2 leakage, it is important to understand the physical processes that CO2 will undergo as it moves through naturally heterogeneous porous media formations. Previous studies have shown that heterogeneity can enhance the evolution of gas phase CO2 in some cases, but the conditions under which this occurs have not yet been quantitatively defined, nor tested through laboratory experiments. This study quantitatively investigates the effects of geologic heterogeneity on the process of gas phase CO2 evolution in shallow aquifers through an extensive set of experiments conducted in a column that was packed with layers of various test sands. Soil moisture sensors were utilized to observe the formation of gas phase near the porous media interfaces. Results indicate that the conditions under which heterogeneity controls gas phase evolution can be successfully predicted through analysis of simple parameters, including the dissolved CO2 concentration in the flowing water, the distance between the heterogeneity and the leakage location, and some fundamental properties of the porous media. Results also show that interfaces where a less permeable material overlies a more permeable material affect gas phase evolution more significantly than interfaces with the opposite layering. [ABSTRACT FROM AUTHOR]

This technical note presents a useful methodology for studying how the variance of hydraulic and/or reactive attributes of an aquifer are linked to the multiscaled and hierarchical sedimentary architecture of the aquifer. A new recursive equation is derived which quantitatively describes how the variance is related to sedimentary facies defined at all scales across an entire stratal hierarchy. As compared to prior published equations that emphasize differences in means among facies populations within a hierarchical level, it emphasizes differences across levels. Because of the hierarchical relationships among the terms of the equation, we find it to be useful for conducting a holistic analysis of the relative contributions to the variance arising from all facies types defined across all scales. The methodology is demonstrated using appropriate field data, and is shown to be useful in defining parsimonious classification systems. [ABSTRACT FROM AUTHOR]

Periodic pumping tests, in which a fluid is extracted during half a period, then reinjected, have been used historically to estimate effective aquifer properties. In this work, we suggest a modified approach to periodic pumping test analysis in which one uses several periodic pumping signals of different frequencies as stimulation, and responses are analyzed through inverse modeling using a 'steady-periodic' model formulation. We refer to this strategy as multifrequency oscillatory hydraulic imaging. Oscillating pumping tests have several advantages that have been noted, including no net water extraction during testing and robust signal measurement through signal processing. Through numerical experiments, we demonstrate additional distinct advantages that multifrequency stimulations have, including: (1) drastically reduced computational cost through use of a steady-periodic numerical model and (2) full utilization of the aquifer heterogeneity information provided by responses at different frequencies. We first perform fully transient numerical modeling for heterogeneous aquifers and show that equivalent results are obtained using a faster steady-periodic heterogeneous numerical model of the wave phasor. The sensitivities of observed signal response to aquifer heterogeneities are derived using an adjoint state-based approach, which shows that different frequency stimulations provide complementary information. Finally, we present an example 2-D application in which sinusoidal signals at multiple frequencies are used as a data source and are inverted to obtain estimates of aquifer heterogeneity. These analyses show the different heterogeneity information that can be obtained from different stimulation frequencies, and that data from several sinusoidal pumping tests can be rapidly inverted using the steady-periodic framework. [ABSTRACT FROM AUTHOR]

Anomalous transport in advection-dominated convergent flow tracer tests can occurs due to small-scale heterogeneities in aquifer hydraulic properties. These result in fluctuations of the groundwater velocity field and complex connectivity patterns between injection and extraction wells. While detailed characterization of heterogeneity is often not possible in practice, a proper understanding of what fundamental physical mechanisms can give rise to macroscopic behaviors that are measurable is essential for proper upscaling of solute transport processes. We analyze here how heavy-tailed breakthrough curves can arise in radially convergent flow to a well. The permeability fields are three-dimensional multi-Gaussian fields with varying statistical geometry and degrees of heterogeneity. We consider transport of conservative tracers from multiple injection locations by varying distance and angle from the extraction well. Anomalous power law tailing in breakthrough curves is attributed to a variety of features including the initial vertical stratification of the solute that arises due to a flux-weighted injection, the injection distance to the well relative to the depth of the aquifer, and the statistics of the heterogeneity field as defined by the correlation length and variance of the permeability. When certain conditions cooccur for a given injection, such as strong connectivity contrasts between aquifer layers, injection distances comparable to the horizontal heterogeneity integral scales, and large global variances, breakthrough curves tend to scale as a PL with unit slope at late time. These findings offer new insights to understand what physical processes must be understood to develop and choose appropriate upscaling approaches that might reproduce such anomalous transport in heterogeneous advection-dominated systems. [ABSTRACT FROM AUTHOR]

The aim of this work is to develop a theoretical framework for the analysis of groundwater head oscillations commonly observed in bores near boundaries of surface water bodies that are subject to periodic variations in stage height. Restricting attention to the linear groundwater flow equation, the dynamics of head variations induced by periodic modes acting at boundaries are governed by a complex-valued time-independent equation parameterized by the modal frequency of interest. For randomly heterogeneous aquifers the hydraulic conductivity field may be regarded as a spatial random variable. Stochastic relationships between the conductivity spectrum and the induced head oscillation spectrum are generated from a stochastic perturbation approach. Spatial correlative relationships are derived for several stochastic models incorporating up to three spatial dimensions. Explicit calculations of head oscillation autocovariances and spectral densities are parameterized by conductivity statistics, including integral scale and variance, and by modal frequency. The results show that time domain head responses to periodic boundary forcing are strongly dependent on multidimensional effects and on spatial correlation structure. Computational simulations show that the stochastic variance estimators match simulated head fluctuation variances for a range of modal frequencies and aquifer diffusivities and that joint inversion of conductivity integral scale and variance is possible with moderate numbers of sampling points. [ABSTRACT FROM AUTHOR]

In this study, the S-shaped log-log drawdown-time curve typical of pumping tests in unconfined aquifers is reinvestigated via numerical experiments. Like previous investigations, this study attributes the departure of the S shape from the drawdown-time behavior of the confined aquifer to the presence of an 'additional' source of water. Unlike previous studies, this source of water is reinvestigated by examining the temporal and spatial evolution of the rate of change in storage in an unconfined aquifer during pumping. This evolution is then related to the transition of water release mechanisms from the expansion of water and compaction of the porous medium to the drainage of water from the unsaturated zone above the initial water table and initially saturated pores as the water table falls during the pumping of the aquifer. Afterward, the 1-D vertical drainage process in a soil column is simulated. Results of the simulation show that the transition of the water release mechanisms in the 1-D vertical flow without an initial unsaturated zone can also yield the S-shaped drawdown-time curve as in an unconfined aquifer. We therefore conclude that the transition of the water release mechanisms and vertical flow in the aquifer are the cause of the S-shaped drawdown-time curve observed during pumping in an unconfined aquifer. We also find that the moisture retention characteristics of the aquifer material have greater impact than its relative permeability characteristics on the drawdown-time curve. Furthermore, influences of the spatial variability of saturated hydraulic conductivity, specific storage, and saturated moisture content on the drawdown curve in the saturated zone are found to be more significant than those of other unsaturated properties. Finally, a cross-correlation analysis reveals that the drawdown at a location in a heterogeneous unconfined aquifer is mainly affected by local heterogeneity near the pumping and observation wells. Applications of a model assuming homogeneity to the estimation of aquifer parameters as such may require a large number of observation wells to obtain representative parameter values. In conclusion, we advocate that the governing equation for variably saturated flow through heterogeneous media is a more appropriate and realistic model that explains the S-shaped drawdown-time curves observed in the field. [ABSTRACT FROM AUTHOR]

A new approach for analytic element (AE) modeling of groundwater flow is presented. The approach divides the modeled region into polygonal subdomains, each with its own analytic flow model and its own local isotropic or anisotropic aquifer parameters. This allows analytic modeling of systems where the anisotropy ratio and direction vary spatially, an AE capability not possible without subdomains. It also allows for flexible layering in a model, with more layers in the area of interest abutting fewer layers in the far field. The approach is demonstrated in a model with seven subdomains and a mix of single-layer and triple-layer areas. Checks of the model indicate that the inter-subdomain boundary conditions can be approximated well, and where the differential equation is approximated (multilayer areas and transient flow), that approximation can be quite accurate. [ABSTRACT FROM AUTHOR]

Fast chemical reactions are driven by mixing-induced chemical disequilibrium. Mixing is poorly represented by the advection-dispersion equation. Instead, effective dynamics models, such as multirate mass transfer (MRMT), have been successful in reproducing observed field-scale transport, notably, breakthrough curves (BTCs) of conservative solutes. The objective of this work is to test whether such effective models, derived from conservative transport observations, can be used to describe effective multicomponent reactive transport in heterogeneous media. We use a localized formulation of the MRMT model that allows us to solve general reactive transport problems. We test this formulation on a simple three-species mineral precipitation problem at equilibrium. We first simulate the spatial and temporal distribution of mineral precipitation rates in synthetic hydraulically heterogeneous aquifers. We then compare these reaction rates to those corresponding to an equivalent (i.e., same conservative BTC) homogenized medium with transport characterized by a nonlocal in time equation involving a memory function. We find an excellent agreement between the two models in terms of cumulative precipitated mass for a broad range of generally stationary heterogeneity structures. These results indicate that mass transfer models can be considered to represent quite accurately the large-scale effective dynamics of mixing controlled reactive transport at least for the cases tested here, where individual transport paths sample the full range of heterogeneities represented by the BTC. [ABSTRACT FROM AUTHOR]