Documents published in 2020 : Scipedia

Bayesian estimation of the transmissivity spatial structure from pumping test data
M. Demir, N. Copty, P. Trinchero, X. Sánchez-Vila

Advances in Water Resources (2017). Vol. 104, pp. 174-182 (Preprint)

Abstract
Estimating the statistical parameters (mean, variance, and integral scale) that define the spatial structure of the transmissivity or hydraulic conductivity fields is a fundamental step for the accurate prediction of subsurface flow and contaminant transport. In practice, the determination of the spatial structure is a challenge because of spatial heterogeneity and data scarcity. In this paper, we describe a novel approach that uses time drawdown data from multiple pumping tests to determine the transmissivity statistical spatial structure. The method builds on the pumping test interpretation procedure of Copty et al. (2011) (Continuous Derivation method, CD), which uses the time-drawdown data and its time derivative to estimate apparent transmissivity values as a function of radial distance from the pumping well. A Bayesian approach is then used to infer the statistical parameters of the transmissivity field by combining prior information about the parameters and the likelihood function expressed in terms of radially-dependent apparent transmissivities determined from pumping tests. A major advantage of the proposed Bayesian approach is that the likelihood function is readily determined from randomly generated multiple realizations of the transmissivity field, without the need to solve the groundwater flow equation. Applying the method to synthetically-generated pumping test data, we demonstrate that, through a relatively simple procedure, information on the spatial structure of the transmissivity may be inferred from pumping tests data. It is also shown that the prior parameter distribution has a significant influence on the estimation procedure, given the non-uniqueness of the estimation procedure. Results also indicate that the reliability of the estimated transmissivity statistical parameters increases with the number of available pumping tests.
Abstract
Estimating the statistical parameters (mean, variance, and integral scale) that define the spatial structure of the transmissivity or hydraulic [...]
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Interaction between physical heterogeneity and microbial processes in subsurface sediments: a laboratory-scale column experiment
N. Perujo, X. Sánchez-Vila, L. Proia, A. Romaní

Environmental science and technology (2017). Vol. 51 (11), pp. 6110-6119 (Preprint)

Abstract
Physical heterogeneity determines interstitial fluxes in porous media. Nutrients and organic matter distribution in depth influence physicochemical and microbial processes occurring in subsurface. Columns 50 cm long were filled with sterile silica sand following five different setups combining fine and coarse sands or a mixture of both mimicking potential water treatment barriers. Water was supplied continuously to all columns during 33 days. Hydraulic conductivity, nutrients and organic matter, biofilm biomass, and activity were analyzed in order to study the effect of spatial grain size heterogeneity on physicochemical and microbial processes and their mutual interaction. Coarse sediments showed higher biomass and activity in deeper areas compared to the others; however, they resulted in incomplete denitrification, large proportion of dead bacteria in depth, and low functional diversity. Treatments with fine sediment in the upper 20 cm of the columns showed high phosphorus retention. However, low hydraulic conductivity values reported in these sediments seemed to constraint biofilm activity and biomass. On the other hand, sudden transition from coarse-to-fine grain sizes promoted a hot-spot of organic matter degradation and biomass growth at the interface. Our results reinforce the idea that grain-size disposition in subsurface sandy sediments drives the interstitial fluxes, influencing microbial processes. This document is the unedited Author’s version of a Submitted Work that was subsequently accepted for publication in Environmental science and technology
Abstract
Physical heterogeneity determines interstitial fluxes in porous media. Nutrients and organic matter distribution in depth influence physicochemical and microbial processes [...]
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Improving degradation of emerging organic compounds by applying chaotic advection in Managed Aquifer Recharge in randomly heterogeneous porous media
P. Rodríguez-Escales, D. Fernàndez-García, J. Drechsel, A. Folch, X. Sánchez-Vila

Water Resources Research (2017). Vol. 53 (5), pp. 4376-4392

Abstract
Improving degradation rates of emerging organic compounds (EOCs) in groundwater is still a challenge. Although their degradation is not fully understood, it has been observed that some substances are preferably degraded under specific redox conditions. The coupling of Managed Aquifer Recharge with soil aquifer remediation treatment, by placing a reactive layer containing organic matter at the bottom of the infiltration pond, is a promising technology to improve the rate of degradation of EOCs. Its success is based on assuming that recharged water and groundwater get well mixed, which is not always true. It has been demonstrated that mixing can be enhanced by inducing chaotic advection through extraction-injection-engineering. In this work, we analyze how chaotic advection might enhance the spreading of redox conditions with the final aim of improving degradation of a mix of benzotriazoles: benzotriazole, 5-methyl-benzotriazole, and 5-chloro-benzotriazole. The degradation of the first two compounds was fastest under aerobic conditions whereas the third compound was best degraded under denitrification conditions. We developed a reactive transport model that describes how a recharged water rich in organic matter mixes with groundwater, how this organic matter is oxidized by different electron acceptors, and how the benzotriazoles are degraded attending for the redox state. The model was tested in different scenarios of recharge, both in homogenous and in heterogenous media. It was found that chaotic flow increases the spreading of the plume of recharged water. Consequently, different redox conditions coexist at a given time, facilitating the degradation of EOCs.
Abstract
Improving degradation rates of emerging organic compounds (EOCs) in groundwater is still a challenge. Although their degradation is not fully understood, it has been observed [...]
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Stochastic estimation of hydraulic transmissivity fields using flow connectivity indicator data
G. Freixas, D. Fernàndez-García, X. Sánchez-Vila

Water Resources Research (2017). Vol. 53 (1), pp. 602-618 (Preprint)

Abstract
Most methods for hydraulic test interpretation rely on a number of simplified assumptions regarding the homogeneity and isotropy of the underlying porous media. This way, the actual heterogeneity of any natural parameter, such as transmissivity ( math formula), is transferred to the corresponding estimates in a way heavily dependent on the interpretation method used. An example is a long-term pumping test interpreted by means of the Cooper-Jacob method, which implicitly assumes a homogeneous isotropic confined aquifer. The estimates obtained from this method are not local values, but still have a clear physical meaning; the estimated math formula represents a regional-scale effective value, while the log-ratio of the normalized estimated storage coefficient, indicated by math formula, is an indicator of flow connectivity, representative of the scale given by the distance between the pumping and the observation wells. In this work we propose a methodology to use math formula, together with sampled local measurements of transmissivity at selected points, to map the expected value of local math formula values using a technique based on cokriging. Since the interpolation involves two variables measured at different support scales, a critical point is the estimation of the covariance and crosscovariance matrices. The method is applied to a synthetic field displaying statistical anisotropy, showing that the inclusion of connectivity indicators in the estimation method provide maps that effectively display preferential flow pathways, with direct consequences in solute transport.
Abstract
Most methods for hydraulic test interpretation rely on a number of simplified assumptions regarding the homogeneity and isotropy of the underlying porous media. This way, [...]
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A mechanistic model (BCC-PSSICO) to predict changes in the hydraulic properties for bio-amended variably saturated soils
A. Carles-Brangari, X. Sánchez-Vila, A. Freixa, A. Romaní, S. Rubol, D. Fernàndez-García

Water Resources Research (2017). Vol. 53 (1), pp. 93-109 (Preprint)

Abstract
The accumulation of biofilms in porous media is likely to influence the overall hydraulic properties and, consequently, a sound understanding of the process is required for the proper design and management of many technological applications. In order to bring some light into this phenomenon we present a mechanistic model to study the variably saturated hydraulic properties of bio-amended soils. Special emphasis is laid on the distribution of phases at pore-scale and the mechanisms to retain and let water flow through, providing valuable insights into phenomena behind bioclogging. Our approach consists in modeling the porous media as an ensemble of capillary tubes, obtained from the biofilm-free water retention curve. This methodology is extended by the incorporation of a biofilm composed of bacterial cells and extracellular polymeric substances (EPS). Moreover, such a microbial consortium displays a channeled geometry that shrinks/swells with suction. Analytical equations for the volumetric water content and the relative permeability can then be derived by assuming that biomass reshapes the pore space following specific geometrical patterns. The model is discussed by using data from laboratory studies and other approaches already existing in the literature. It can reproduce (i) displacements of the retention curve toward higher saturations and (ii) permeability reductions of distinct orders of magnitude. Our findings also illustrate how even very small amounts of biofilm may lead to significant changes in the hydraulic properties. We, therefore, state the importance of accounting for the hydraulic characteristics of biofilms and for a complex/more realistic geometry of colonies at the pore-scale.
Abstract
The accumulation of biofilms in porous media is likely to influence the overall hydraulic properties and, consequently, a sound understanding of the process is required for [...]
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The role of advection and dispersion in the rock matrix on the transport of leaking CO2-saturated brine along a fractured zone
N. Ahmad, A. Wörman, X. Sánchez-Vila, A. Bottacin-Busolin

Advances in Water Resources (2016). Vol. 98, pp. 132-146 (Preprint)

Abstract
CO2 that is injected into a geological storage reservoir can leak in dissolved form because of brine displacement from the reservoir, which is caused by large-scale groundwater motion. Simulations of the reactive transport of leaking CO2aq along a conducting fracture in a clay-rich caprock are conducted to analyze the effect of various physical and geochemical processes. Whilst several modeling transport studies along rock fractures have considered diffusion as the only transport process in the surrounding rock matrix (diffusive transport), this study analyzes the combined role of advection and dispersion in the rock matrix in addition to diffusion (advection-dominated transport) on the migration of CO2aq along a leakage pathway and its conversion in geochemical reactions. A sensitivity analysis is performed to quantify the effect of fluid velocity and dispersivity. Variations in the porosity and permeability of the medium are found in response to calcite dissolution and precipitation along the leakage pathway. We observe that advection and dispersion in the rock matrix play a significant role in the overall transport process. For the parameters that were used in this study, advection-dominated transport increased the leakage of CO2aq from the reservoir by nearly 305%, caused faster transport and increased the mass conversion of CO2aq in geochemical reactions along the transport pathway by approximately 12.20% compared to diffusive transport.
Abstract
CO2 that is injected into a geological storage reservoir can leak in dissolved form because of brine displacement from the reservoir, which is caused by large-scale groundwater [...]
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Debates—Stochastic subsurface hydrology from theory to practice: why stochastic modeling has not yet permeated into practitioners?
X. Sánchez-Vila, D. Fernàndez-García

Water Resources Research (2016). Vol. 52 (12), pp. 9246-9258

Abstract
We address modern topics of stochastic hydrogeology from their potential relevance to real modeling efforts at the field scale. While the topics of stochastic hydrogeology and numerical modeling have become routine in hydrogeological studies, nondeterministic models have not yet permeated into practitioners. We point out a number of limitations of stochastic modeling when applied to real applications and comment on the reasons why stochastic models fail to become an attractive alternative for practitioners. We specifically separate issues corresponding to flow, conservative transport, and reactive transport. The different topics addressed are emphasis on process modeling, need for upscaling parameters and governing equations, relevance of properly accounting for detailed geological architecture in hydrogeological modeling, and specific challenges of reactive transport. We end up by concluding that the main responsible for nondeterministic models having not yet permeated in industry can be fully attributed to researchers in stochastic hydrogeology.
Abstract
We address modern topics of stochastic hydrogeology from their potential relevance to real modeling efforts at the field scale. While the topics of stochastic hydrogeology [...]
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Fate of sulfamethoxazole in groundwater: Conceptualizing and modeling metabolite formation under different redox conditions
P. Rodríguez-Escales, X. Sánchez-Vila

Water Research (Oxford) (2016). Vol. 105, pp. 540-550 (Preprint)

Abstract
Degradation of emerging organic compounds in saturated porous media is usually postulated as following simple low-order models. This is a strongly oversimplified, and in some cases plainly incorrect model, that does not consider the fate of the different metabolites. Furthermore, it does not account for the reversibility in the reaction observed in a few emerging organic compounds, where the parent is recovered from the metabolite. One such compound is the antibiotic sulfamethoxazole (SMX). In this paper, we first compile existing experimental data to formulate a complete model for the degradation of SMX in aquifers subject to varying redox conditions, ranging from aerobic to iron reducing. SMX degrades reversibly or irreversibly to a number of metabolites that are specific of the redox state. Reactions are in all cases biologically mediated. We then propose a mathematical model that reproduces the full fate of dissolved SMX subject to anaerobic conditions and that can be used as a first step in emerging compound degradation modeling efforts. The model presented is tested against the results of the batch experiments of Barbieri et al. (2012) and Nödler et al. (2012) displaying a non-monotonic concentration of SMX as a function of time under denitrification conditions, as well as those of Mohatt et al. (2011), under iron reducing conditions.
Abstract
Degradation of emerging organic compounds in saturated porous media is usually postulated as following simple low-order models. This is a strongly oversimplified, and in some [...]
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Injection of CO2-saturated brine in geological reservoir: a way to enhanced storage safety
N. Ahmad, A. Wörman, X. Sánchez-Vila, J. Jarsjö, A. Borracin-Busolin, H. Hellevang

International Journal of Greenhouse Gas Control (2016). Vol. 54 (1), pp. 129-144 (Preprint)

Abstract
Injection of free-phase supercritical CO2 into deep geological reservoirs is associated with risk of considerable return flows towards the land surface due to the buoyancy of CO2, which is lighter than the resident brine in the reservoir. Such upward movements can be avoided if CO2 is injected in the dissolved phase (CO2aq). In this work, injection of CO2-saturated brine in a subsurface carbonate reservoir was modelled. Physical and geochemical interactions of injected low-pH CO2-saturated brine with the carbonate minerals (calcite, dolomite and siderite) were investigated in the reactive transport modelling. CO2-saturated brine, being low in pH, showed high reactivity with the reservoir minerals, resulting in a significant mineral dissolution and CO2 conversion in reactions. Over the injection period of 10 yr, up to 16% of the injected CO2 was found consumed in geochemical reactions. Sorption included in the transport analysis resulted in additional quantities of CO2 mass stored. However, for the considered carbonate minerals, the consumption of injected CO2aq was found mainly in the form of ionic trapping.
Abstract
Injection of free-phase supercritical CO2 into deep geological reservoirs is associated with risk of considerable return flows towards the land surface due to the buoyancy [...]
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Modeling long term Enhanced in situ Biodenitrification and induced heterogeneity in column experiments under different feeding strategies
P. Rodríguez-Escales, A. Folch, B. Breukelen, G. Vidal-Gavilan, X. Sánchez-Vila

Journal of Hydrology (2016). Vol. 538, pp. 127-137 (Preprint)

Abstract
Enhanced In situ Biodenitrification (EIB) is a capable technology for nitrate removal in subsurface water resources. Optimizing the performance of EIB implies devising an appropriate feeding strategy involving two design parameters: carbon injection frequency and C:N ratio of the organic substrate nitrate mixture. Here we model data on the spatial and temporal evolution of nitrate (up to 1.2 mM), organic carbon (ethanol), and biomass measured during a 342 day-long laboratory column experiment (published in Vidal-Gavilan et al., 2014). Effective porosity was 3% lower and dispersivity had a sevenfold increase at the end of the experiment as compared to those at the beginning. These changes in transport parameters were attributed to the development of a biofilm. A reactive transport model explored the EIB performance in response to daily and weekly feeding strategies. The latter resulted in significant temporal variation in nitrate and ethanol concentrations at the outlet of the column. On the contrary, a daily feeding strategy resulted in quite stable and low concentrations at the outlet and complete denitrification. At intermediate times (six months of experiment), it was possible to reduce the carbon load and consequently the C:N ratio (from 2.5 to 1), partly because biomass decay acted as endogenous carbon to respiration, keeping the denitrification rates, and partly due to the induced dispersivity caused by the well developed biofilm, resulting in enhancement of mixing between the ethanol and nitrate and the corresponding improvement of denitrification rates. The inclusion of a dual-domain model improved the fit at the last days of the experiment as well as in the tracer test performed at day 342, demonstrating a potential transition to anomalous transport that may be caused by the development of biofilm. This modeling work is a step forward to devising optimal injection conditions and substrate rates to enhance EIB performance by minimizing the overall supply of electron donor, and thus the cost of the remediation strategy.
Abstract
Enhanced In situ Biodenitrification (EIB) is a capable technology for nitrate removal in subsurface water resources. Optimizing the performance of EIB implies devising an [...]
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Scale dependence of the hydraulic properties of a fractured aquifer estimated using transfer functions
D. Pedretti, A. Russian, X. Sánchez-Vila, M. Dentz

Water Resources Research (2016). (preprint) Vol. 52 (7), pp. 5008-5024

Abstract
We present an investigation of the scale dependence of hydraulic parameters in fractured media based on the concept of transfer functions (TF). TF methods provide an inexpensive way to perform aquifer parameter estimation, as they relate the fluctuations of an observation time series (hydraulic head fluctuations) to an input function (aquifer recharge) in frequency domain. Fractured media are specially sensitive to this approach as hydraulic parameters are strongly scale-dependent, involving nonstationary statistical distributions. Our study is based on an extensive data set, involving up to 130 measurement points with periodic head measurements that in some cases extend for more than 30 years. For each point, we use a single-porosity and dual-continuum TF formulation to obtain a distribution of transmissivities and storativities in both mobile and immobile domains. Single-porosity TF estimates are compared with data obtained from the interpretation of over 60 hydraulic tests (slug and pumping tests). Results show that the TF is able to estimate the scale dependence of the hydraulic parameters, and it is consistent with the behavior of estimates from traditional hydraulic tests. In addition, the TF approach seems to provide an estimation of the system variance and the extension of the ergodic behavior of the aquifer (estimated in approximately 500 m in the analyzed aquifer). The scale dependence of transmissivity seems to be independent from the adopted formulation (single or dual-continuum), while storativity is more sensitive to the presence of multiple continua.
Abstract
We present an investigation of the scale dependence of hydraulic parameters in fractured media based on the concept of transfer functions (TF). TF methods provide an inexpensive [...]
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A locally adaptive kernel regression method for facies delineation
D. Fernàndez-García, M. Barahona-Palomo, C. Henri, X. Sánchez-Vila

Journal of Hydrology (2015). Vol. 531 (Part 1), pp. 62-72 (Preprint)

Abstract
Facies delineation is defined as the separation of geological units with distinct intrinsic characteristics (grain size, hydraulic conductivity, mineralogical composition). A major challenge in this area stems from the fact that only a few scattered pieces of hydrogeological information are available to delineate geological facies. Several methods to delineate facies are available in the literature, ranging from those based only on existing hard data, to those including secondary data or external knowledge about sedimentological patterns. This paper describes a methodology to use kernel regression methods as an effective tool for facies delineation. The method uses both the spatial and the actual sampled values to produce, for each individual hard data point, a locally adaptive steering kernel function, self-adjusting the principal directions of the local anisotropic kernels to the direction of highest local spatial correlation. The method is shown to outperform the nearest neighbor classification method in a number of synthetic aquifers whenever the available number of hard data is small and randomly distributed in space. In the case of exhaustive sampling, the steering kernel regression method converges to the true solution. Simulations ran in a suite of synthetic examples are used to explore the selection of kernel parameters in typical field settings. It is shown that, in practice, a rule of thumb can be used to obtain suboptimal results. The performance of the method is demonstrated to significantly improve when external information regarding facies proportions is incorporated. Remarkably, the method allows for a reasonable reconstruction of the facies connectivity patterns, shown in terms of breakthrough curves performance.
Abstract
Facies delineation is defined as the separation of geological units with distinct intrinsic characteristics (grain size, hydraulic conductivity, mineralogical composition). [...]
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Do we really need a large number of particles to simulate bimolecular reactive transport with random walk methods? A kernel density estimation approach
M. Rahbaralam, D. Fernàndez-García, X. Sánchez-Vila

Journal of computational physics (2015). Vol. 303, pp. 95-104

Abstract
Random walk particle tracking methods are a computationally efficient family of methods to solve reactive transport problems. While the number of particles in most realistic applications is in the order of 106–109106–109, the number of reactive molecules even in diluted systems might be in the order of fractions of the Avogadro number. Thus, each particle actually represents a group of potentially reactive molecules. The use of a low number of particles may result not only in loss of accuracy, but also may lead to an improper reproduction of the mixing process, limited by diffusion. Recent works have used this effect as a proxy to model incomplete mixing in porous media. In this work, we propose using a Kernel Density Estimation (KDE) of the concentrations that allows getting the expected results for a well-mixed solution with a limited number of particles. The idea consists of treating each particle as a sample drawn from the pool of molecules that it represents; this way, the actual location of a tracked particle is seen as a sample drawn from the density function of the location of molecules represented by that given particle, rigorously represented by a kernel density function. The probability of reaction can be obtained by combining the kernels associated to two potentially reactive particles. We demonstrate that the observed deviation in the reaction vs time curves in numerical experiments reported in the literature could be attributed to the statistical method used to reconstruct concentrations (fixed particle support) from discrete particle distributions, and not to the occurrence of true incomplete mixing. We further explore the evolution of the kernel size with time, linking it to the diffusion process. Our results show that KDEs are powerful tools to improve computational efficiency and robustness in reactive transport simulations, and indicates that incomplete mixing in diluted systems should be modeled based on alternative mechanistic models and not on a limited number of particles.
Abstract
Random walk particle tracking methods are a computationally efficient family of methods to solve reactive transport problems. While the number of particles in most realistic [...]
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Reactive transport modeling of leaking CO2-saturated brine along a fractured pathway
N. Ahmad, A. Wörman, A. Bottacin-Busolin, X. Sánchez-Vila

International Journal of Greenhouse Gas Control (2015). Vol. 42, pp. 672-689 (preprint)

Abstract
One concern regarding the underground storage of carbon dioxide (CO2) is its potential leakage from reservoirs. Over short period of time, the leakage risk is related mainly to CO2 as a separate supercritical fluid phase. However, over longer periods upon complete dissolution of injected CO2 in the fluid, the leakage risk is associated with dissolved phase CO2. Over the geological time scales, large-scale groundwater motion may cause displacement of brine containing dissolved CO2 along the conducting pathways. In this paper, we present a comprehensive modeling framework that describes the reactive transport of CO2-saturated brine along a fracture in the clay caprock based on the future, hypothetical leakage of the dissolved phase CO2. This study shows that the transport of leaked dissolved CO2 is significantly retarded by a combination of various physical and geochemical processes, such as mass exchange between conducting fracture and the neighboring rock matrix through molecular diffusion, sorption and calcite dissolution in the rock matrix. Mass stored in aqueous and adsorbed states in the rock matrix caused retention of dissolved CO2 along the leakage pathway. Calcite dissolution reaction in the rock matrix resulted in consumption of leaking dissolved CO2 and reduced its mass along the leakage pathway. Consumption and retention of dissolved CO2 along the leakage pathway have important implications for analyzing the potential reduction of CO2 fluxes from storage reservoirs over large periods and long travel pathways.
Abstract
One concern regarding the underground storage of carbon dioxide (CO2) is its potential leakage from reservoirs. Over short period of time, the leakage risk is related mainly [...]
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Vadose zone oxygen (O2) dynamics during drying and wetting cycles: An artificial recharge laboratory experiment
T. Dutta, A. Carles-Brangari, D. Fernàndez-García, S. Rubol, J. Tirado-Conde, X. Sánchez-Vila

Journal of Hydrology (2015). Vol. 527, pp. 151-159 (Preprint)

Abstract
Vadose zone oxygen dynamics control all subsurface redox reactions and play a decisive role in maintaining groundwater quality. Although drying and wetting events are common in artificial recharge, their effects on subsurface oxygen distribution are poorly documented. We monitored oxygen concentration in the unsaturated zone in a mid-scale (1 m high) laboratory soil lysimeter, which was subjected to short wetting and drying cycles that simulated a highly permeable shallow aquifer recharged by river water. Ten cycles of varying duration were performed for a period of 85 days. Measurements of oxygen in the liquid and the gas phases were recorded every 20 s using non-invasive optical fibers (PreSens). The results provided high-resolution (in time) oxygen concentration maps. The infiltration rate revealed a decreasing trend during wetting cycles associated with biological clogging. Such a decrease with time was accompanied by a depletion of O2 concentration, occurring within the first few hours of the infiltration. During drying, O2 concentrations recovered rapidly at all depths owing to air flushing, resulting in a stratified vertical profile consistent with the biological consumption of O2 along the air infiltration path. Furthermore, drying periods caused a potential recovery of the infiltration capacity while preserving the soil biological activity. Scraping also led to the recovery of the infiltration capacity of the soil but was less effective than drying. Our experiment suggests that the small-scale heterogeneity played a key role in accurately mapping pore-scale O2 concentrations and should be considered in modeling O2 fluxes of unsaturated soils under natural or managed recharge conditions.
Abstract
Vadose zone oxygen dynamics control all subsurface redox reactions and play a decisive role in maintaining groundwater quality. Although drying and wetting events are common [...]
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Improving the accuracy of risk prediction from particle-based breakthrough curves reconstructed with kernel density estimators
E. Siirila-Woodburn, D. Fernàndez-García, X. Sánchez-Vila

Water Resources Research (2015). Vol. 51 (6), pp. 4574-4591

Abstract
While particle tracking techniques are often used in risk frameworks, the number of particles needed to properly derive risk metrics such as average concentration for a given exposure duration is often unknown. If too few particles are used, error may propagate into the risk estimate. In this work, we provide a less error‐prone methodology for the direct reconstruction of exposure duration averaged concentration versus time breakthrough curves from particle arrival times at a compliance surface. The approach is based on obtaining a suboptimal kernel density estimator that is applied to the sampled particle arrival times. The corresponding estimates of risk metrics obtained with this method largely outperform those by means of traditional methods (reconstruction of the breakthrough curve followed by the integration of concentration in time over the exposure duration). This is particularly true when the number of particles used in the numerical simulation is small ( 105), and for small exposure times. Percent error in the peak of averaged breakthrough curves is approximately zero for all scenarios and all methods tested when the number of particles is 105. Our results illustrate that obtaining a representative average exposure concentration is reliant on the information contained in each individual tracked particle, more so when the number of particles is small. They further illustrate the usefulness of defining problem‐specific kernel density estimators to properly reconstruct the observables of interest in a particle tracking framework without relying on the use of an extremely large number of particles.
Abstract
While particle tracking techniques are often used in risk frameworks, the number of particles needed to properly derive risk metrics such as average concentration for a given [...]
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Mathematical equivalence between time-dependent single-rate and multirate mass transfer models
D. Fernàndez-García, X. Sánchez-Vila

Water Resources Research (2015). Vol. 51 (4), pp. 3166-3180

Abstract
The often observed tailing of tracer breakthrough curves is caused by a multitude of mass transfer processes taking place over multiple scales. Yet, in some cases, it is convenient to fit a transport model with a single-rate mass transfer coefficient that lumps all the non-Fickian observed behavior. Since mass transfer processes take place at all characteristic times, the single-rate mass transfer coefficient derived from measurements in the laboratory or in the field vary with time w(t). The literature review and tracer experiments compiled by Haggerty et al. (2004) from a number of sites worldwide suggest that the characteristic mass transfer time, which is proportional to w(t)^-1, scales as a power law of the advective and experiment duration. This paper studies the mathematical equivalence between the multirate mass transfer model (MRMT) and a time-dependent single-rate mass transfer model (t-SRMT). In doing this, we provide new insights into the previously observed scale-dependence of mass transfer coefficients. The memory function, g(t), which is the most salient feature of the MRMT model, determines the influence of the past values of concentrations on its present state. We found that the t-SRMT model can also be expressed by means of a memory function \phi(t,\tau). In this case, though the memory function is nonstationary, meaning that in general it cannot be written as \phi(t-\tau). Nevertheless, the full behavior of the concentrations using a single time-dependent rate w(t) is approximately analogous to that of the MRMT model provided that the equality w(t) = -dlng(t)/dt holds and the field capacity is properly chosen. This relationship suggests that when the memory function is a power law, g(t) \approx t^{1-k}, the equivalent mass transfer coefficient scales as w(t) \approx t^-1, nicely fitting without calibration the estimated mass transfer coefficients compiled by Haggerty et al. (2004).
Abstract
The often observed tailing of tracer breakthrough curves is caused by a multitude of mass transfer processes taking place over multiple scales. Yet, in some cases, it is convenient [...]
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A noise reduction method for forklift based on numerical separation and spectrum analysis of main noise sources
E. Zhang, L. Hou, J. Zhuo, G. Tao

Rev. int. métodos numér. cálc. diseño ing. (2020). Vol. 36, (4), 47

Abstract
'''The key to an acoustic signal lies in its frequency spectrum characteristics, and the primary premise of noise reduction is the identification of main noise sources. In this paper, an approach to noise source identification is introduced based on the improved fast independent component analysis (FastCA) algorithm for blind source signals to correct the uncertainty of traditional FastICA. Taking the measured noise signals radiated from a forklift at idle speed as an application case, two obvious estimated independent components (EICs) and their corresponding frequency spectrums were obtained. In addition, the result of numerical identification of sound sources is verified by scaning and paint system (SPS) and the error is less than 5%. Base on the spectral characteristics analysis, the improvement measurement of the target forklift was performed, and the results indicated that the sound power level of radiated noise from the whole vehicle is effectively reduced by 1.75dB, and meets the domestic industry requirement.
Abstract
'''The key to an acoustic signal lies in its frequency spectrum characteristics, and the primary premise of noise reduction is the identification of main noise [...]
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The effects of sediment depth and oxygen concentration on the use of organic matter: an experimental study using an infiltration sediment tank
A. Freixa, S. Rubol, A. Carles-Brangari, A. Butturini, X. Sánchez-Vila, A. Romaní

Science of the total environmental (2015). Vol. 540, pp. 20-31 (preprint)

Abstract
Water flowing through hyporheic river sediments or artificial recharge facilities promotes the development of microbial communities with sediment depth. We performed an 83-day mesocosm infiltration experment, to study howmicrobial functions (e.g., extracellular enzyme activities and carbon substrate utilization) are affected by sediment depth (up to 50 cm) and different oxygen concentrations. Results indicated that surface sediment layers were mainly colonized bymicroorganisms capable of using awide range of substrates (although they preferred to degrade carbon polymeric compounds, as indicated by the higher ß-glucosidase activity). In contrast, at a depth of 50 cm, the microbial community became specialized in using fewer carbon substrates, showing decreased functional richness and diversity. At this depth, microorganisms picked nitrogenous compounds, including amino acids and carboxyl acids. After the 83-day experiment, the sediment at the bottomof the tank became anoxic, inhibiting phosphatase activity. Coexistence of aerobic and anaerobic communities, promoted by greater physicochemical heterogeneity, was also observed in deeper sediments. The presence of specific metabolic fingerprints under oxic and anoxic conditions indicated that the microbial community was adapted to use organic matter under different oxygen conditions. Overall the heterogeneity of oxygen concentrations with depth and in time would influence organic matter metabolism in the sediment tank.
Abstract
Water flowing through hyporheic river sediments or artificial recharge facilities promotes the development of microbial communities with sediment depth. We performed an 83-day [...]
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On the formation of multiple local peaks in breakthrough curves
E. Siirila-Woodburn, X. Sánchez-Vila, D. Fernàdez-García

Water Resources Research (2015). Vol. 51 (4), pp. 2128-2152

Abstract
The analysis of breakthrough curves (BTCs) is of interest in hydrogeology as a way to parameterize and explain processes related to anomalous transport. Classical BTCs assume the presence of a single peak in the curve, where the location and size of the peak and the slope of the receding limb has been of particular interest. As more information is incorporated into BTCs (for example, with high-frequency data collection, supercomputing efforts), it is likely that classical definitions of BTC shapes will no longer be adequate descriptors for contaminant transport problems. We contend that individual BTCs may display multiple local peaks depending on the hydrogeologic conditions and the solute travel distance. In such cases, classical definitions should be reconsidered. In this work, the presence of local peaks in BTCs is quantified from high-resolution numerical simulations in synthetic fields with a particle tracking technique and a kernel density estimator to avoid either overly jagged or smoothed curves that could mask the results. Individual BTCs from three-dimensional heterogeneous hydraulic conductivity fields with varying combinations of statistical anisotropy, heterogeneity models, and local dispersivity are assessed as a function of travel distance. The number of local peaks, their corresponding slopes, and a transport connectivity index are shown to strongly depend on statistical anisotropy and travel distance. Results show that the choice of heterogeneity model also affects the frequency of local peaks, but the slope is less sensitive to model selection. We also discuss how solute shearing and rerouting can be determined from local peak quantification.
Abstract
The analysis of breakthrough curves (BTCs) is of interest in hydrogeology as a way to parameterize and explain processes related to anomalous transport. Classical BTCs assume [...]
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An approach to aquifer vulnerability including uncertainty in a spatial random function framework
S. Armengol, X. Sánchez-Vila, A. Folch

Journal of Hydrology (2014). Vol. 517, pp. 889-900

Abstract
We introduce a methodology to include uncertainty into DRASTIC (Aller et al., 1987), the most commonly used method to define aquifer vulnerability. For this purpose, we explore separately all seven DRASTIC indices, and analyze how uncertainty can be introduced into each one of them, by proposing a simple decision tree to select the most appropriate geostatistical methods depending on the amount and type of available data. We further analyzed the implications of introducing the concept of degree of confidence, based on the estimated point variances, into the estimates of some of the indices. The methodology is illustrated by mapping the DRASTIC indices in an aquifer located in northeast Spain. It is concluded that the final vulnerability index may vary substantially depending on the degree of confidence accepted in the analysis, indicating the possibility of extending the deterministic version of DRASTIC to a stochastic one, where uncertainty is directly accounted for.
Abstract
We introduce a methodology to include uncertainty into DRASTIC (Aller et al., 1987), the most commonly used method to define aquifer vulnerability. For this purpose, [...]
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GIS-based hydrogeochemical analysis tools (QUIMET)
V. Velasco, I. Tubau, D. Gaitanaru, E. Vázquez-Suñé, R. Gogu, M. Alcaraz, A. Serrano-Juan, D. Fernàndez-García, T. Garrido, J. Fraile, X. Sánchez-Vila

Computers & Geosciences (2014). Vol. 70, pp. 164-180

Abstract
A software platform (QUIMET) was developed to improve the sorting, analysis, calculations, visualizations, and interpretations of hydrogeochemical data in a GIS environment. QUIMET is composed of a geospatial database plus a set of tools specially designed for graphical and statistical analysis of hydrogeochemical data. The geospatial database has been designed to include organic and inorganic chemical records, as well as relevant physical parameters (temperature, Eh, electrical conductivity). The instruments for analysis cover a wide range of methodologies for querying, interpreting, and comparing groundwater quality data. They include, among others, chemical time-series analysis, ionic balance calculations, correlation of chemical parameters, and calculation of various common hydrogeochemical diagrams (Salinity, Schoeller-Berkaloff, Piper, and Stiff). The GIS platform allows the generation of maps of the spatial distribution of parameters and diagrams. Moreover, it allows performing a complete statistical analysis of the data including descriptive statistic univariate and bivariate analysis, the latter including generation of correlation matrices and graphics. Finally, QUIMET offers interoperability with other external platforms. The platform is illustrated with a geochemical data set from the city of Badalona, located on the Mediterranean coast in NE Spain.
Abstract
A software platform (QUIMET) was developed to improve the sorting, analysis, calculations, visualizations, and interpretations of hydrogeochemical data in a GIS environment. [...]
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Estimation of spatial covariance of log conductivity from particle size data
M. Riva, X. Sánchez-Vila, A. Guadagnini

Water Resources Research (2014). Vol. 50 (6), pp. 5298-5308

Abstract
We derive analytical relationships between the spatial covariance of the (natural) logarithm of hydraulic conductivity (K) and that of representative soil particle sizes and porosity. The latter quantities can be directly measured during routine sedimentological analyses of soil samples and provide a way of incorporating K estimates into groundwater flow models at a relatively modest experimental cost. Here we rely on widely used empirical formulations requiring measurements of representative particle diameters and, in some cases, of medium porosity. We derive exact formulations relating the spatial covariance of these quantities and K and present workable approximations on the basis of perturbation methods. Our formulations provide a direct link between key geostatistical descriptors of sedimentological and hydraulic parameters of heterogeneous aquifers which can be employed in classical estimation and simulation procedures. The approach and theoretical results are tested on an extensive data set comprising 411 particle size curves collected at 12 boreholes in a small-scale alluvial aquifer.
Abstract
We derive analytical relationships between the spatial covariance of the (natural) logarithm of hydraulic conductivity (K) and that of representative soil particle sizes and [...]
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Apparent directional mass-transfer capacity coefficients in three-dimensional anisotropic heterogeneous aquifers under radial convergent transport
D. Pedretti, D. Fernàndez-García, X. Sánchez-Vila, D. Bolster, D. Benson

Water Resources Research (2014). Vol. 50 (2), pp. 1205-1224

Abstract
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.
Abstract
Aquifer hydraulic properties such as hydraulic conductivity (K) are ubiquitously heterogeneous and typically only a statistical [...]
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Geochemical modeling of arsenic release from a deep natural solid matrix under alternated redox conditions
A. Molinari, C. Ayora, M. Marcaccio, L. Guadagnini, X. Sánchez-Vila, A. Guadagnini

Environmental science and pollution research (2014). Vol. 21 (3), pp. 1628-1637

Abstract
Dissolved arsenic (As) concentrations detected in groundwater bodies of the Emilia-Romagna Region (Italy) exhibit values which are above the regulation limit and could be related to the natural composition of the host porous matrix. To support this hypothesis, we present the results of a geochemical modeling study reproducing the main trends of the dynamics of As, Fe, and Mn concentrations as well as redox potential and pH observed during batch tests performed under alternating redox conditions. The tests were performed on a natural matrix extracted from a deep aquifer located in the Emilia-Romagna Region (Italy). The solid phases implemented in the model were selected from the results of selective sequential extractions performed on the tested matrix. The calibrated model showed that large As concentrations have to be expected in the solution for low crystallinity phases subject to dissolution. The role of Mn oxides on As concentration dynamics appears significant in strongly reducing environments, particularly for large water-solid matrix interaction times. Modeled data evidenced that As is released firstly from the outer surface of Fe oxihydroxides minerals exhibiting large concentrations in water when persistent reducing conditions trigger the dissolution of the crystalline structure of the binding minerals. The presence of organic matter was found to strongly affect pH and redox conditions, thus influencing As mobility.
Abstract
Dissolved arsenic (As) concentrations detected in groundwater bodies of the Emilia-Romagna Region (Italy) exhibit values which are above the regulation limit and could be [...]
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Dynamic interactions between hydrogeological and exposure parameters in daily dose prediction under uncertainty and temporal variability
V. Kumar, F. Barros, M. Schuhmacher, D. Fernàndez-García, X. Sánchez-Vila

Journal of hazardous materials (2013). Vol. 263 (1), pp. 197-206

Abstract
We study the time dependent interaction between hydrogeological and exposure parameters in daily dose predictions due to exposure of humans to groundwater contamination. Dose predictions are treated stochastically to account for an incomplete hydrogeological and geochemical field characterization, and an incomplete knowledge of the physiological response. We used a nested Monte Carlo framework to account for uncertainty and variability arising from both hydrogeological and exposure variables. Our interest is in the temporal dynamics of the total dose and their effects on parametric uncertainty reduction. We illustrate the approach to a HCH (lindane) pollution problem at the Ebro River, Spain. The temporal distribution of lindane in the river water can have a strong impact in the evaluation of risk. The total dose displays a non-linear effect on different population cohorts, indicating the need to account for population variability. We then expand the concept of Comparative Information Yield Curves developed earlier (see de Barros et al. [29]) to evaluate parametric uncertainty reduction under temporally variable exposure dose. Results show that the importance of parametric uncertainty reduction varies according to the temporal dynamics of the lindane plume. The approach could be used for any chemical to aid decision makers to better allocate resources towards reducing uncertainty.
Abstract
We study the time dependent interaction between hydrogeological and exposure parameters in daily dose predictions due to exposure of humans [...]
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On the formation of breakthrough curves tailing during convergent flow tracer tests in three-dimensional heterogeneous aquifers
D. Pedretti, D. Fernàndez-García, D. Bolster, X. Sánchez-Vila

Water Resources Research (2013). Vol. 49 (7), pp. 4157-4173

Abstract
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
Anomalous transport in advection-dominated convergent flow tracer tests can occurs due to small-scale heterogeneities in aquifer hydraulic properties. These result in fluctuations [...]
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Controlling scaling metrics for improved characterization of well-head protection regions
F. Barros, A. Guadagnini, D. Fernàndez-García, M. Riva, X. Sánchez-Vila

Journal of Hydrology (2013). Vol. 494 (28), pp. 107-115

Abstract
We addressed the value of hydrogeological information on the assessment of the risk that an operating pumping well is polluted. The work considered a heterogeneous aquifer and focused on the statistical characterization of the contaminant mass fraction from a diffused source recovered at the well and the solute arrival times. We explored the role of the key length scales that characterize and control the well capture region and its probabilistic delineation with respect to the contaminant source location and size. The impact of augmenting the data-base of hydraulic information on the reduction of uncertainty associated with the environmental scenario analyzed was then investigated. It was found that obtaining a robust characterization of the target Environmental Performance Metrics (EPMs) depends on the length scale considered. For the sampling scheme considered, the importance of conditioning on the probability distributions of solute mass fraction and travel times is strongly affected by the location of the contaminant source within the probabilistic well catchment. With reference to the characterization of the travel time distribution associated with the recovery of a given mass fraction, the worth of augmenting the hydraulic parameter data-sets tends to decrease with decreasing solute residence time within the well catchment
Abstract
We addressed the value of hydrogeological information on the assessment of the risk that an operating pumping well is polluted. The work considered a heterogeneous aquifer and [...]
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Review of new flow friction equations: Constructing Colebrook’s explicit correlations accurately
P. Praks, D. Brkić

Rev. int. métodos numér. cálc. diseño ing. (2020). Vol. 36, (3), 41

Abstract
Using only a limited number of computationally expensive functions, we show a way how to construct accurate and computationally efficient approximations of the Colebrook equation for flow friction based on the asymptotic series expansion of the Wright ω-function and on symbolic regression. The results are verified with 8 million of Quasi-Monte Carlo points covering the domain of interest for engineers. In comparison with the built-in “wrightOmega” feature of Matlab R2016a, the herein introduced related approximations of the Wright ω-function significantly accelerate the explicit solution of the Colebrook equation. Such balance between speed and accuracy could be achieved only using symbolic regression, a computational intelligence approach that can find optimal coefficients and the best structure of the equation. The presented numerical experiments show that the novel symbolic regression approximation reduced the maximal relative error from 0.045% to 0.00337%, i.e. more than 13 times, even the complexity remains almost unchanged. Moreover, we also provide a novel highly precise symbolic regression approximation (max. relative error 0.000024%), which, for the same speed as asymptotic expansion, reduces the relative error by factor 219. This research is motivated by estimation of flow rate using electrical parameters of pumps where direct measurement is not always possible such as in offshore underwater pipelines.
Abstract
Using only a limited number of computationally expensive functions, we show a way how to construct accurate and computationally efficient approximations of the Colebrook equation [...]
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Siphon pipe Parameter Optimization of the Toilet Using CFD-DEM Coupling Method
Z. Li, X. Ge, K. Li, X. Tong

Siphon pipe Parameter Optimization of the Toilet Using CFD-DEM Coupling Method (2020). 1

Abstract
The computational fluid dynamics (CFD) and discrete element method (DEM) coupling method is used to simulate the flushing process of the toilet and this paper analyzes the influence of different structural parameters of siphon pipe on the flushing performance of the toilet. And through the adjusted-parameters toilet, tlushing experments were carried out to verify the simulations. Meanwhile the orthogonal test of different structural parameters of siphon pipes were conducted to study the flushing Performance. The research results show that the CFD-DEM coupling method can be used to study the regularity of the toilet flushing performance. The toilet can get the better flushing performance when the tilt angle of the angle of inclination is 50°, the curvature width and length are 50 mm and 220 mm, the width and height of the secondary water seal are 100 mm and 25 mm and pipe diameter is 53 mm. The method in this paper can provide a new idea for the study and design of the flushing performance of the toilet. '''Keyword:''' CFD-DEM, flushing performance, structural parameters, coupling method, adjusted-parameters toilet
Abstract
The computational fluid dynamics (CFD) and discrete element method (DEM) coupling method is used to simulate the flushing process of the toilet and this paper analyzes the [...]
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Mobility and Interaction of Heavy Metals in a Natural Soil
E. Janetti, I. Dror, M. Riva, A. Guadagnini, X. Sánchez-Vila

Transport in Porous Media (2013). Vol. 97 (3), pp. 295-315

Abstract
We study the mobility and interaction under competing conditions observed for copper ( Cu2+ Cu2+) and zinc ( Zn2+ Zn2+) ions in the context of laboratory-scale experiments performed in natural soil columns. The experiments focus on the analysis of solute breakthrough curves (BTCs) obtained after injection of an aqueous solution containing similar concentrations of the two metal ions into a soil column fully saturated with double deionized water. Transport of the competing ions is tested for the same soil under aerobic and anaerobic conditions. Measurements show that the species with lower affinity for the soil, Zn2+ Zn2+, migrates occupying all available adsorption sites, and is then progressively replaced by the ion with higher affinity, Cu2+ Cu2+. The two ions are displaced in the system with different effective retardation. The slowest species replaces the sorbed ions, resulting in observed Zn2+ Zn2+ concentrations that display a non-monotonic behavior in time and which, for a certain period, are larger than the concentration supplied continuously at the inlet. In the absence of a complete geochemical characterization of the system, we show that the measured concentrations of both metals can be interpreted through simple models based on a set of coupled partial differential and algebraic equations, involving a small subset of aqueous and adsorbed species that are present in the system. Depending on the model considered, the relationship between aqueous and adsorbed ion concentrations is described at equilibrium by a Gaines–Thomas (GT) formulation, a competitive Sheindorf–Rebhun–Sheintuch (SRS) isotherm, or an Extended Langmuir (EL) isotherm, respectively. The GT formulation provides the best interpretation of the observed behavior among the models tested. We find that employing these simple models, which account only for the main governing reactive processes, allows reasonable estimation of the observed BTCs in experiments where only partial geochemical datasets are available.
Abstract
We study the mobility and interaction under competing conditions observed for copper ( Cu2+ Cu2+) and zinc ( Zn2+ Zn2+) ions in the context of laboratory-scale [...]
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A risk‐based probabilistic framework to estimate the endpoint of remediation: Concentration rebound by rate‐limited mass transfer
F. Barros, D. Fernàndez-García, D. Bolster, X. Sánchez-Vila

Water Resources Research (2013). Vol. 49 (4), pp. 1929-1942

Abstract
Aquifer remediation is a challenging problem with environmental, social, and economic implications. As a general rule, pumping proceeds until the concentration of the target substance within the pumped water lies below a prespecified value. In this paper we estimate the a priori potential failure of the endpoint of remediation due to a rebound of concentrations driven by back diffusion. In many cases, it has been observed that once pumping ceases, a rebound in the concentration at the well takes place. For this reason, administrative approaches are rather conservative, and pumping is forced to last much longer than initially expected. While a number of physical and chemical processes might account for the presence of rebounding, we focus here on diffusion from low water mobility into high mobility zones. In this work we look specifically at the concentration rebound when pumping is discontinued while accounting for multiple mass transfer processes occurring at different time scales and parametric uncertainty. We aim to develop a risk‐based optimal operation methodology that is capable of estimating the endpoint of remediation based on aquifer parameters characterizing the heterogeneous medium as well as pumping rate and initial size of the polluted area.
Abstract
Aquifer remediation is a challenging problem with environmental, social, and economic implications. As a general rule, pumping proceeds until the concentration of the target [...]
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An analytical solution to study substrate-microbial dynamics in soils
X. Sánchez-Vila, S. Rubol, A. Carles-Brangari, D. García

Advances in Water Resources (2013). Vol. 54, pp. 181-190

Abstract
We provide an approximate analytical solution for the substrate-microbial dynamics of the organic carbon cycle in natural soils under hydro-climatic variable forcing conditions. The model involves mass balance in two carbon pools: substrate and biomass. The analytical solution is based on a perturbative solution of concentrations, and can properly reproduce the numerical solutions for the full non-linear problem in a system evolving towards a steady state regime governed by the amount of labile carbon supplied to the system. The substrate and the biomass pools exhibit two distinct behaviors depending on whether the amount of carbon supplied is below or above a given threshold. In the latter case, the concentration versus time curves are always monotonic. Contrarily, in the former case the C-pool concentrations present oscillations, allowing the reproduction of non-monotonic small-scale biomass concentration data in a natural soil, observed so far only in short-term experiments in the rhizosphere. Our results illustrate the theoretical dependence of oscillations from soil moisture and temperature and how they may be masked at intermediate scales due to the superposition of solutions with spatially variable parameters.
Abstract
We provide an approximate analytical solution for the substrate-microbial dynamics of the organic carbon cycle in natural soils under hydro-climatic variable forcing conditions. [...]
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Arsenic release from deep natural solid matrices under experimentally controlled redox conditions
A. Molinari, A. Guadagnini, M. Marcaccio, S. Straface, X. Sánchez-Vila, L. Guadagnini

Science of the total environment (2013). Vol. 444, pp. 231-240

Abstract
We investigated the role of iron (Fe) on arsenic (As) release from two samples of a natural deep soil collected in an aquifer body in the Emilia-Romagna Region, Italy. Each sample is representative of a different solid matrix, i.e., sand and vegetal matter. Batch experiments were performed by applying alternating aerobic/anaerobic conditions to the samples under a range of redox and pH conditions, consistent with the corresponding values measured in the field. Arsenic mobilization was triggered by abrupt and rapid changes in redox conditions and displayed a clear correlation with oxidation/reduction potential for both solid matrices. Vegetal matter showed high binding capacity and large As concentration release. Arsenic release was also correlated with Fe released from the solid matrices. Our results suggest that the environmentally critical As concentrations detected in some aquifers in the Emilia-Romagna Region are consistent with (a) the occurrence of high natural As content in the component of the host porous medium associated with vegetal matter and (b) the effect of possible sharp localized (and temporally oscillating) variations in redox conditions.
Abstract
We investigated the role of iron (Fe) on arsenic (As) release from two samples of a natural deep soil collected in an aquifer body in the Emilia-Romagna Region, Italy. Each [...]
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Formation of diclofenac and sulfamethoxazole reversible transformation products in aquifer material under denitrifying conditions: Batch experiments
M. Barbieri, J. Carrera, C. Ayora, X. Sánchez-Vila, T. Licha, K. Nödler, V. Osorio, S. Pérez, M. Köck-Schulmeyer, M. Alda, D. Barceló

Science of the Total Environment (2012). Vol. 426, pp. 265-263

Abstract
Soil-aquifer processes have proven to work as a natural treatment for the attenuation of numerous contaminants during artificial recharge of groundwater. Nowadays, significant scientific effort is being devoted to understanding the fate of pharmaceuticals in subsurface environments, and to verify if such semipersistent organic micropollutants could also be efficiently removed from water. In this context we carried out a series of batch experiments involving aquifer material, selected drugs (initial concentration of 1 μg/L and 1 mg/L), and denitrifying conditions. Diclofenac and sulfamethoxazole exhibited an unreported and peculiar behavior. Their concentrations consistently dropped in the middle of the tests but recovered toward the end, which suggest a complex effect of denitrifying conditions on aromatic amines. The transformation products Nitro-Diclofenac and 4-Nitro-Sulfamethoxazole were detected in the biotic experiments, while nitrite was present in the water. Their concentrations developed almost opposite to those of their respective parent compounds. We conjecture that this temporal and reversible effect of denitrifying conditions on the studied aromatic amines could have significant environmental implications, and could explain at least partially the wide range of removals in subsurface environments reported in literature for DCF and SMX, as well as some apparent discrepancies on SMX behavior.
Abstract
Soil-aquifer processes have proven to work as a natural treatment for the attenuation of numerous contaminants during artificial recharge [...]
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Assessing and forecasting the impacts of global change on Mediterranean rivers. The SCARCE Consolider project on Iberian basins
A. Navarro-Ortega, V. Acuña, R. Batalla, J. Blasco, C. Conde, F. Elorza, A. Elosegi, F. Francés, F. La-Roca, I. Muñoz, M. Petrovic, Y. Picó, S. Sabater, X. Sánchez-Vila, M. Schuhmacher, D. Barceló

Evironmental Science and Pollution Research (2012). Vol. 19 (4), pp. 918-933

Abstract
Introduction The Consolider-Ingenio 2010 project SCARCE, with the full title “Assessing and predicting effects on water quantity and quality in Iberian Rivers caused by global change” aims to examine and predict the relevance of global change on water availability, water quality, and ecosystem services in Mediterranean river basins of the Iberian Peninsula, as well as their socio-economic impacts. Starting in December 2009, it brought together a multidisciplinary team of 11 partner Spanish institutions, as well as the active involvement of water authorities, river basin managers, and other relevant agents as stakeholders. Methods The study areas are the Llobregat, Ebro, Jucar, and Guadalquivir river basins. These basins have been included in previous studies and projects, the majority of whom considered some of the aspects included in SCARCE but individually. Historical data will be used as a starting point of the project but also to obtain longer time series. The main added value of SCARCE project is the inclusion of scientific disciplines ranging from hydrology, geomorphology, ecology, chemistry, and ecotoxicology, to engineering, modeling, and economy, in an unprecedented effort in the Mediterranean area. The project performs data mining, field, and lab research as well as modeling and upscaling of the findings to apply them to the entire river basin. Results Scales ranging from the laboratory to river basins are addressed with the potential to help improve river basin management. The project emphasizes, thus, linking basic research and management practices in a single framework. In fact, one of the main objectives of SCARCE is to act as a bridge between the scientific and the management and to transform research results on management keys and tools for improving the River Basin Management Plans. Here, we outline the general structure of the project and the activities conducted within the ten Work Packages of SCARCE.
Abstract
Introduction The Consolider-Ingenio 2010 project SCARCE, with the full title “Assessing and predicting effects on water quantity and quality in Iberian Rivers caused [...]
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A quick and inexpensive method to quantify spatially variable infiltration capacity for artificial recharge ponds using photographic images
D. Pedretti, M. Barahona-Palomo, D. Bolster, X. Sánchez-Vila, D. Fernàdez-García

Journal of Hydrology (2012). Vol. 430-431, pp. 118-126

Abstract
The efficiency of artificial surface ponds (SPs) for managed aquifer recharge (MAR) is mostly controlled by the topmost portion of the soil. The most significant soil property controlling recharge is the infiltration capacity (Ic), which is highly variable in space. Assessing its spatial distribution in detail is prohibitive in practice due to high costs, time effort, and limited site accessibility. We present an alternative method for a quick and low-cost quantitative estimation of the spatial distribution of Ic based on satellite images. The fact that hydraulic properties of topsoils and color intensities of digital images depend on some common factors such as moisture content, nature and organization of grains, proportion of iron, and organic and clay content among others, allow us to infer infiltration capacities from color intensities. The relationship between these two variables is site specific and requires calibration. A pilot SP site in Catalonia (Spain) is used as an application example. Two high-resolution digital images of the site are provided at no cost by the local cartographic institute as well as from a popular Internet-based map server. An initial set of local infiltration experiments, randomly located, were found to correlate to color intensities of the digital images. This relationship was then validated against additional independent measurements. The resulting maps of infiltration were then used to estimate the total maximum infiltration of the artificial pond area, the results being consistent with an independent flooding test performed at the site.
Abstract
The efficiency of artificial surface ponds (SPs) for managed aquifer recharge (MAR) is mostly controlled by the topmost portion of the soil. The most significant soil property [...]
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A Bayesian approach to integrate temporal data into probabilistic risk analysis of monitored NAPL remediation
D. Fernàndez-García, D. Bolster, X. Sánchez-Vila, D. Tartakovsky

Advances in Water Resources (2012). Vol. 36, pp. 108-120

Abstract
Upon their release into the subsurface, non-aqueous phase liquids (NAPLs) dissolve slowly in groundwater and/or volatilize in the vadose zone threatening the environment and public health over extended periods of time. The failure of a treatment technology at any given site is often due to the unnoticed presence of dissolved NAPL trapped in low permeability areas and/or the remaining presence of substantial amounts of pure phase NAPL after remediation efforts. The design of remediation strategies and the determination of remediation endpoints are traditionally carried out without quantifying risks associated with the failure of such efforts. We conduct a probabilistic risk analysis (PRA) to estimate the likelihood of failure of an on-site NAPL treatment technology. The PRA integrates all aspects of the problem (causes, pathways, and receptors) without resorting to extensive modeling. It accounts for a combination of multiple mechanisms of failure of a monitoring system, such as bypassing, insufficient sampling frequency and malfunctioning of the observation wells. We use a Bayesian framework to update the likelihood of failure of the treatment technology with observed measurements of concentrations at nearby monitoring wells
Abstract
Upon their release into the subsurface, non-aqueous phase liquids (NAPLs) dissolve slowly in groundwater and/or volatilize in the vadose zone threatening the environment and [...]
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Probabilistic analysis of maintenance and operation of artificial recharge ponds
D. Pedretti, M. Barahona-Palomo, D. Bolster, D. Fernàndez-García, X. Sánchez-Vila, D. Tartakovsky

Advances in Water Resources (2012). Vol. 36, pp. 23-35

Abstract
Aquifer artificial recharge from surface infiltration ponds is often conducted to replenish depleted aquifers in arid and semi-arid zones. Physical and bio-geochemical clogging decreases the host soil’s infiltration capacity, which has to be restored with periodic maintenance activities. We develop a probabilistic modeling framework that quantifies the risk of a pond’s infiltration capacity falling below its target value due to soil heterogeneity and clogging. This framework can act as a tool to aid managers in optimally selecting and designing maintenance strategies. Our model enables one to account for a variety of maintenance strategies that target different clogging mechanisms. The framework is applied to an existing pond in Barcelona, Spain as well as to several synthetic infiltration ponds with varying statistical distributions of initial infiltration capacity. We find that physical clogging mechanisms induce the greatest uncertainty and that maintenance targeted at these can yield optimal results. However, considering the fundamental role of the spatial variability in the initial properties, we conclude that an adequate initial characterization of the surface infiltration ponds is crucial to determining the degree of uncertainty of different maintenance solutions and thus to making cost-effective and reliable decisions.
Abstract
Aquifer artificial recharge from surface infiltration ponds is often conducted to replenish depleted aquifers in arid and semi-arid zones. [...]
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Probabilistic analysis of groundwater-related risks at subsurface excavation sites
A. Jurado, F. Gaspari, V. Vilarrasa, D. Bolster, X. Sánchez-Vila, D. Fernàndez-García, D. Tartakovsky

Engineering geology (2012). Vol. 125, pp. 35-44

Abstract
Construction of underground structures (e.g., subway lines, railways and highway tunnels) is inherently hazardous, posing risks to both workers and machinery at the site and to surrounding buildings. The presence of groundwater may increase these risks. We develop a general probabilistic risk assessment (PRA) framework to quantify risks driven by groundwater to the safety of underground constructions. The proposed approach is fully compatible with standard PRA practices, employing well-developed risk analysis tools based on the fault tree analysis method. The novelty and computational challenges of the proposed approach stem from the reliance on a combination of approaches including extracting information from databases, solving stochastic differential equations, or relying on expert judgment to compute probabilities of basic events. The general framework is presented in a case study and used to estimate and minimize risks at a construction site of an underground station for a new subway line in the Barcelona metropolitan area.
Abstract
Construction of underground structures (e.g., subway lines, railways and highway tunnels) is inherently hazardous, posing risks to both [...]
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Fate of β-blockers in aquifer material under nitrate reducing conditions: Batch experiments
M. Barbieri, T. Licha, K. Nödler, J. Carrera, C. Ayora, X. Sánchez-Vila

Chemosphere (2012). Vol. 89 (11), pp. 1272-1277

Abstract
The fate of the three environmentally relevant β-blockers atenolol, metoprolol and propranolol has been studied in batch experiments involving aquifer material and nitrate reducing conditions. Results from the about 90 d long tests indicate that abiotic processes, most likely sorption, jointly with biotransformation to atenololic acid were responsible for the 65% overall removal observed for atenolol. Zero order kinetics, typical of enzyme-limited reactions, controlled the transformation of this beta blocker to its corresponding carboxylic acid. The mass balance evidences that no mineralization of atenolol occurs in the biotic experiment and that atenololic acid is more stable than its parent compound under the studied conditions. This finding stresses the importance of considering atenololic acid as target compound in the environmental studies on the fate of atenolol. For metoprolol and propranolol the results from the experiment suggest a slower sorption to be the dominant removal process, which led to final decreases in concentrations of 25–30% and 40–45%, respectively. Overall, the removals observed in the experiments suggest that subsurface processes potentially constitute an alternative water treatment for the target beta-blockers, when compared to the removals reported for conventional wastewater treatment plants.
Abstract
The fate of the three environmentally relevant β-blockers atenolol, metoprolol and propranolol has been studied in batch experiments [...]
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Microcosm experiments to control anaerobic redox conditions when studying the fate of organic micropollutants in aquifer material
M. Barbieri, J. Carrera, X. Sánchez-Vila, C. Ayora, J. Cama, M. Köck-Schulmeyer, M. Alda, D. Barceló, J. Brunet, M. García

Journal of Contaminant Hydrology (2011). Vol. 126 (3-4), pp. 330-345

Abstract
The natural processes occurring in subsurface environments have proven to effectively remove a number of organic pollutants from water. The predominant redox conditions revealed to be one of the controlling factors. However, in the case of organic micropollutants the knowledge on this potential redox-dependent behavior is still limited. Motivated by managed aquifer recharge practices microcosm experiments involving aquifer material, settings potentially feasible in field applications, and organic micropollutants at environmental concentrations were carried out. Different anaerobic redox conditions were promoted and sustained in each set of microcosms by adding adequate quantities of electron donors and acceptors. Whereas denitrification and sulfate-reducing conditions are easily achieved and maintained, Fe- and Mn-reduction are strongly constrained by the slower dissolution of the solid phases commonly present in aquifers. The thorough description and numerical modeling of the evolution of the experiments, including major and trace solutes and dissolution/precipitation of solid phases, have been proven necessary to the understanding of the processes and closing the mass balance. As an example of micropollutant results, the ubiquitous beta-blocker atenolol is completely removed in the experiments, the removal occurring faster under more advanced redox conditions. This suggests that aquifers constitute a potentially efficient alternative water treatment for atenolol, especially if adequate redox conditions are promoted during recharge and long enough residence times are ensured.
Abstract
The natural processes occurring in subsurface environments have proven to effectively remove a number of organic pollutants from water. [...]
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Assessing preferential flow through an unsaturated waste rock pile using spectral analysis
P. Trinchero, R. Beckie, X. Sánchez-Vila, C. Nichol

Water Resources Research (2011). Vol. 47 (W07532), pp. 1-11

Abstract
Waste rock piles are an outcome of open pit and underground mining operations. Unprocessed low‐grade rock is disposed of in piles from several meters high to 100 m+ high. Waste rock piles may still contain sufficient concentrations of metals to be a potential source of pollution. The evaluation of the potential risk involves properly characterizing flow through these piles under unsaturated conditions. The main flow characteristic of the piles is the presence of a large range of grain and pore sizes. Based on data from an instrumented rock pile located in Saskatchewan Canada, unsaturated flow through the pile is modeled as a linear system after separating a fast and a slow component. Water reaching the base of the pile is monitored by 16 contiguous zero‐tension lysimeters. The fast component, flowing through macropores, is assumed to be released instantaneously, while the slow component is simulated using a linear‐reservoir model that assumes the presence of an interconnected porous matrix. An empirical transfer function (TF) is computed as the ratio of the spectra of signals between the output (basal outflow) and the input (rainfall time series). Determination of a parametric transfer function model provides information on the characteristic time of water storage in the matrix and on the fraction of the water within each subsection of the experimental pile that is channeled through the macropores. An analysis of the output signal at different support scales is performed, indicating the nonlinearity of the macropore fraction scaling processes
Abstract
Waste rock piles are an outcome of open pit and underground mining operations. Unprocessed low‐grade rock is disposed of in piles from several meters high to 100 m+ high. [...]
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Combining physical-based models and satellite images for the spatio-temporal assessment of soil infiltration capacity
D. Pedretti, D. Fernàndez-García, X. Sánchez-Vila, M. Barahona-Palomo, D. Bolster

Stochastic environmental research and risk assessment (2011). Vol. 25 (8), pp. 1065-1075

Abstract
The performance of managed artificial recharge (MAR) facilities by means of surface ponds (SP) is controlled by the temporal evolution of the global infiltration capacity Ic of topsoils. Cost-effective maintenance operations that aim to maintain controlled infiltration values during the activity of the SP require the full knowledge of the spatio-temporal variability of Ic. This task is deemed uncertain. The natural reduction in time of Ic depends on complex physical, biological and chemical reactions that clog the soil pores and has been observed to decay exponentially to an asymptotic non-zero value. Moreover, the relative influence of single clogging processes depend on some initial parameters of the soil, such as the initial infiltration capacity (Ic,0). This property is also uncertain, as aquifers are typically heterogeneous and scarcely characterized in practical situations. We suggest a method to obtain maps of Ic using a geostatistical approach, which is suitable to be extended to engineering risk assessment concerning management of SP facilities. We propose to combine geostatistical inference and a temporally-lumped physical model to reproduce non-uniform clogging in topsoils of a SP, using field campaigns of local and large scale tests and additionally by means of satellite images as secondary information. We then postulate a power-law relationship between the parameter of the exponential law, k, and Ic,0. It is found that calibrating the two parameters of the power law model it is possible to fit the temporal evolution of total infiltration rate at the pond scale in a MAR test facility. The results can be used to design appropriate measures to selectively limit clogging during operation, extending the life of the infiltration pond. The performance of managed artificial recharge (MAR) facilities by means of surface ponds (SP) is controlled by the temporal evolution of the global infiltration capacity Ic of topsoils. Cost-effective maintenance operations that aim to maintain controlled infiltration values during the activity of the SP require the full knowledge of the spatio-temporal variability of Ic. This task is deemed uncertain. The natural reduction in time of Ic depends on complex physical, biological and chemical reactions that clog the soil pores and has been observed to decay exponentially to an asymptotic non-zero value. Moreover, the relative influence of single clogging processes depend on some initial parameters of the soil, such as the initial infiltration capacity (Ic,0). This property is also uncertain, as aquifers are typically heterogeneous and scarcely characterized in practical situations. We suggest a method to obtain maps of Ic using a geostatistical approach, which is suitable to be extended to engineering risk assessment concerning management of SP facilities. We propose to combine geostatistical inference and a temporally-lumped physical model to reproduce non-uniform clogging in topsoils of a SP, using field campaigns of local and large scale tests and additionally by means of satellite images as secondary information. We then postulate a power-law relationship between the parameter of the exponential law, ¿, and Ic,0. It is found that calibrating the two parameters of the power law model it is possible to fit the temporal evolution of total infiltration rate at the pond scale in a MAR test facility. The results can be used to design appropriate measures to selectively limit clogging during operation, extending the life of the infiltration pond
Abstract
The performance of managed artificial recharge (MAR) facilities by means of surface ponds (SP) is controlled by the temporal evolution of the global infiltration capacity [...]
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A divide and conquer approach to cope with uncertainty, human health risk, and decision making in contaminant hydrology
F. Pereira, D. Bolster, X. Sánchez-Vila, W. Nowak

Water Resources Research (2011). Vol. 47 (W05508), pp. 1-13

Abstract
Assessing health risk in hydrological systems is an interdisciplinary field. It relies on the expertise in the fields of hydrology and public health and needs powerful translation concepts to provide decision support and policy making. Reliable health risk estimates need to account for the uncertainties and variabilities present in hydrological, physiological, and human behavioral parameters. Despite significant theoretical advancements in stochastic hydrology, there is still a dire need to further propagate these concepts to practical problems and to society in general. Following a recent line of work, we use fault trees to address the task of probabilistic risk analysis and to support related decision and management problems. Fault trees allow us to decompose the assessment of health risk into individual manageable modules, thus tackling a complex system by a structural divide and conquer approach. The complexity within each module can be chosen individually according to data availability, parsimony, relative importance, and stage of analysis. Three differences are highlighted in this paper when compared to previous works: (1) The fault tree proposed here accounts for the uncertainty in both hydrological and health components, (2) system failure within the fault tree is defined in terms of risk being above a threshold value, whereas previous studies that used fault trees used auxiliary events such as exceedance of critical concentration levels, and (3) we introduce a new form of stochastic fault tree that allows us to weaken the assumption of independent subsystems that is required by a classical fault tree approach. We illustrate our concept in a simple groundwater‐related setting
Abstract
Assessing health risk in hydrological systems is an interdisciplinary field. It relies on the expertise in the fields of hydrology and public health and needs powerful translation [...]
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Quantitative comparison of impeller-flowmeter and particle-size-distribution techniques for the characterization of hydraulic conductivity variability
M. Barahona-Palomo, M. Riva, X. Sánchez-Vila, E. Vázquez-Suñé, A. Guadagnini

Hydrogeology Journal (2011). Vol. 19 (3), pp. 603-612

Abstract
Hydraulic conductivities associated with measurement scale of the order of 10–1 m and collected during an extensive field campaign near Tübingen, Germany, are analyzed. Estimates are provided at coinciding locations in the system using: (1) the empirical Kozeny-Carman formulation, providing conductivity values, K GS, based on particle-size distribution, and (2) borehole impeller-type flowmeter tests, which infer conductivity, K FM, from measurements of vertical flows within a borehole. Correlation between the two sets of estimates is virtually absent. However, statistics of the natural logarithm of K GS and K FM at the site are similar in terms of mean values (averages of ln K GS being slightly smaller) and differ in terms of variogram ranges and sample variances. This is consistent with the fact that the two types of estimates can be associated with different (albeit comparable) measurement (support) scales. It also matches published results on interpretations of variability of geostatistical descriptors of hydraulic parameters on multiple observation scales. The analysis strengthens the idea that hydraulic conductivity values and associated key geostatistical descriptors inferred from different methodologies and at similar observation scales (of the order of tens of cm) are not readily comparable and should not be embedded blindly into a flow (and eventually transport) prediction model.
Abstract
Hydraulic conductivities associated with measurement scale of the order of 10–1 m and collected during an extensive field campaign near Tübingen, Germany, [...]
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Inferring spatial distribution of the radially integrated transmissivity from pumping tests in heterogeneous confined aquifers
N. Copty, P. Trinchero, X. Sánchez-Vila

Water Resources Research (2011). vol. 47 (W05526), pp. 1-11

Abstract
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
Hydrologists routinely analyze pumping test data using conventional interpretation methods that are based on the assumption of homogeneity and that, consequently, yield single [...]
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Optimal reconstruction of concentrations, gradients and reaction rates from particle distributions
D. Fernàndez-García, X. Sánchez-Vila

Journal of Contaminant Hydrology (2011). Vol. 120-121 (c), pp. 99-114

Abstract
Random walk particle tracking methodologies to simulate solute transport of conservative species constitute an attractive alternative for their computational efficiency and absence of numerical dispersion. Yet, problems stemming from the reconstruction of concentrations from particle distributions have typically prevented its use in reactive transport problems. The numerical problem mainly arises from the need to first reconstruct the concentrations of species/components from a discrete number of particles, which is an error prone process, and then computing a spatial functional of the concentrations and/or its derivatives (either spatial or temporal). Errors are then propagated, so that common strategies to reconstruct this functional require an unfeasible amount of particles when dealing with nonlinear reactive transport problems. In this context, this article presents a methodology to directly reconstruct this functional based on kernel density estimators. The methodology mitigates the error propagation in the evaluation of the functional by avoiding the prior estimation of the actual concentrations of species. The multivariate kernel associated with the corresponding functional depends on the size of the support volume, which defines the area over which a given particle can influence the functional. The shape of the kernel functions and the size of the support volume determines the degree of smoothing, which is optimized to obtain the best unbiased predictor of the functional using an iterative plug-in support volume selector. We applied the methodology to directly reconstruct the reaction rates of a precipitation/dissolution problem involving the mixing of two different waters carrying two aqueous species in chemical equilibrium and moving through a randomly heterogeneous porous medium
Abstract
Random walk particle tracking methodologies to simulate solute transport of conservative species constitute an attractive alternative for their computational efficiency [...]
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Interpretation of column experiments of transport of solutes undergoing an irreversible bimolecular reaction using a continuum approximation
X. Sánchez-Vila, D. Fernàndez-García, A. Guadagnini

Water Resources Research (2010). Vol. 46 (w12510), pp. 1-7

Abstract
We provide a quantitative interpretation of the column experiment reported by Gramling et al. (2002). The experiment involves advection‐dominated transport in porous media of three dissolved species, i.e., two reactants undergoing a fast irreversible reaction and the resulting product. The authors found that their observations could not be properly fitted with a model based on an advection‐dispersion‐reaction equation (ADRE) assuming the reaction was instantaneous, the actual measured total reaction product being lower than predictions for all times. The data have been recently well reproduced by Edery et al. (2009, 2010) by means of a particle tracking approach in a continuous time random walk framework. These and other authors have questioned the use of partial differential equation (PDE)–based approaches to quantify reactive transport because of the difficulty in capturing local‐scale mixing and reaction. We take precisely this approach and interpret the experiments mentioned by means of a continuum‐scale model based on the ADRE. Our approach differs from previous modeling attempts in that we imbue effects of incomplete mixing at the pore scale in a time‐dependent kinetic reaction term and show that this model allows quantitative interpretation of the experiments in terms of both reaction product profiles and time‐dependent global production rate. The time dependence of the kinetic term presented accounts for the progressive effects of incomplete mixing due to pore‐scale rate‐limited mass transfer, and follows a power law, which is consistent with the compilation of existing experiments reported by Haggerty et al. (2004). Our interpretation can form the basis for further research to assess the potential use of PDE approaches for the interpretation of reactive transport problems in moderately heterogeneous media
Abstract
We provide a quantitative interpretation of the column experiment reported by Gramling et al. (2002). The experiment involves advection‐dominated transport in porous media [...]
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A solution for multicomponent reactive transport under equilibrium and kinetic reactions
X. Sánchez-Vila, L. Donado, A. Guadagnini, J. Carrera

Water Resources Research (2010). Vol. 46 (7), pp. 1-13

Abstract
Analysis of the space‐time evolution of reactive solutes in porous systems is complex owing to the presence of different types of chemical reactions. The complete description of a reactive transport scenario entails calculating the spatial and temporal distribution of species concentrations and reaction rates. Here we develop an exact explicit expression for the space‐time distribution of reaction rates for a scenario where the geochemical system can be described by an arbitrary number of equilibrium (fast) reactions and one kinetic (slow) reaction, in the absence of non‐constant‐activity immobile species. The key result is that the equilibrium reaction rate is the sum of two terms representing the availability of reactants. One term involves diffusion and dispersion and represents the contribution of mixing. The other term includes the contribution of the kinetic reaction. The approach also yields the local concentrations of all dissolved species. Yet the latter are not needed for the direct computation of equilibrium reaction rates. We illustrate the approach by means of a simple reactive transport scenario, involving a common ion effect in the presence of a kinetic and an equilibrium reaction leading to precipitation and dissolution processes within a one‐dimensional fully saturated porous medium. The example highlights the highly nonlinear and nonmonotonic response of the system to the controlling input parameters
Abstract
Analysis of the space‐time evolution of reactive solutes in porous systems is complex owing to the presence of different types of chemical reactions. The complete description [...]
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Coupling of mass transfer and reactive transport for nonlinear reactions in heterogeneous media
M. Willmann, J. Carrera, X. Sánchez-Vila, O. Silva, M. Dentz

Water Resources Research (2010). Vol. 46 (w07515), pp. 1-15

Abstract
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
Fast chemical reactions are driven by mixing‐induced chemical disequilibrium. Mixing is poorly represented by the advection‐dispersion equation. Instead, effective dynamics [...]
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An approach to identify urban groundwater recharge
E. Vázquez-Suñé, J. Carrera, I. Tubau, X. Sánchez-Vila, A. Soler

Hydrology and Earth system sciences (2010). Vol. 14 (10), pp. 2085-2097

Abstract
Evaluating the proportion in which waters from different origins are mixed in a given water sample is relevant for many hydrogeological problems, such as quantifying total recharge, assessing groundwater pollution risks, or managing water resources. Our work is motivated by urban hydrogeology, where waters with different chemical signature can be identified (losses from water supply and sewage networks, infiltration from surface runoff and other water bodies, lateral aquifers inflows, ...). The relative contribution of different sources to total recharge can be quantified by means of solute mass balances, but application is hindered by the large number of potential origins. Hence, the need to incorporate data from a large number of conservative species, the uncertainty in sources concentrations and measurement errors. We present a methodology to compute mixing ratios and end-members composition, which consists of (i) Identification of potential recharge sources, (ii) Selection of tracers, (iii) Characterization of the hydrochemical composition of potential recharge sources and mixed water samples, and (iv) Computation of mixing ratios and reevaluation of end-members. The analysis performed in a data set from samples of the Barcelona city aquifers suggests that the main contributors to total recharge are the water supply network losses (22%), the sewage network losses (30%), rainfall, concentrated in the non-urbanized areas (17%), from runoff infiltration (20%), and the Besòs River (11%). Regarding species, halogens (chloride, fluoride and bromide), sulfate, total nitrogen, and stable isotopes (18O, 2H, and 34S) behaved quite conservatively. Boron, residual alkalinity, EDTA and Zn did not. Yet, including these species in the computations did not affect significantly the proportion estimations.
Abstract
Evaluating the proportion in which waters from different origins are mixed in a given water sample is relevant for many hydrogeological problems, such as quantifying total [...]
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Conditional stochastic mapping of transport connectivity
D. Fernàndez-García, P. Trinchero, X. Sánchez-Vila

Water Resources Research (2010). Vol. 46 (10), pp. 1-14

Abstract
We present a method for the stochastic simulation of point‐to‐point transport connectivity honoring data from three types of information: (1) travel time estimates obtained from field tracer tests; (2) estimates of flow connectivity indicators obtained from the relatively fast or slow flow response that is observed at a point location given the flow impulse at another location, and (3) measurements of transmissivity at a local scale. The method thus efficiently integrates data obtained from different hydraulic tests, each sampling different areas within the aquifer. To achieve this, we first extend the concept of point‐to‐point flow connectivity and transport connectivity, mathematically formulated by Trinchero et al. (2008) for pumping conditions, to support a more general flow configuration. Interestingly, point‐to‐point flow connectivity can be generally seen as a weighted integral of transmissivity over the entire domain, the weighting function being proportional to the sensitivity of heads with respect to the natural log of transmissivity per unit of aquifer volume. On the contrary, point‐to‐point transport connectivity is a weighted integral along the particle path of the solute mass that involves two variables: transmissivity and flow connectivity. Each variable has its own distinct weighting function. The weighting function of transmissivity is inversely proportional to both the homogeneous travel time and the point velocity sampled along the travel path. On this basis, we show how to generate conditional point‐to‐point transport connectivity maps. The method avoids the inference of cross‐covariance functions between variables measured over different scales and sampled areas (which cannot be otherwise estimated with a few data measurements) by expressing them as a function of the local transmissivity covariance function. An example of the method is provided to evaluate the worth of including tracer data to delineate capture zones of abstraction wells originally defined from local transmissivity measurements. Monte Carlo simulations reveal that the impact of including tracer data is a maximum when the travel time data are obtained at a location different than that of transmissivity measurements. The reason is that weighting functions give larger weights to the injection location, so introducing tracer test data at points where transmissivity is already known is somewhat redundant
Abstract
We present a method for the stochastic simulation of point‐to‐point transport connectivity honoring data from three types of information: (1) travel time estimates obtained [...]
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An analytical approach to transient homovalent cation exchange problems
X. Sánchez-Vila, D. Bolster

Journal of Hydrology (2009). Vol. 378 (3-4), pp. 281-289

Abstract
Cation exchange in groundwater is one of the dominant surface reactions that occurs in nature and it carries with it many important environmental implications. The mass transfer of cation exchanging pollutants in groundwater can be described by a series of coupled partial differential equations, involving both aqueous and adsorbed species. The resulting system is mathematically challenging due to the complex nonlinearities that arise, which in turn complicates analytical approaches. While some analytical solutions for simplified problems exist, these typically lack the mechanisms that allow the waters to change their global chemical signature (in terms of total cations present in aqueous form) over time. We propose a methodology to solve the problem of exchanging two homovalent cations by deriving the driving equation for one of the aqueous species. This equation incorporates explicitly a retardation factor and a decay term, both with parameters that can vary in space and time. While the full solution can only be obtained numerically, we provide a solution in terms of a perturbative approach, where the leading terms can be obtained explicitly. The resulting solution provides physical explanations for the possible existence of non-monotonic concentrations for a range of parameters governing cation exchange processes
Abstract
Cation exchange in groundwater is one of the dominant surface reactions that occurs in nature and it carries with it many important environmental implications. The mass transfer [...]
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Effect of sorption heterogeneity on moments of solute residence time in convergent flows
M. Riva, A. Guadagnini, X. Sánchez-Vila

Mathematical geosciences (2009). Vol. 41 (8), pp. 835-853

Abstract
In this paper, we analyze the impact of physical and chemical heterogeneity on solute travel time to a pumping well. We consider a solute undergoing reversible linear instantaneous equilibrium sorption. Both the distribution coefficient, K d , and the transmissivity field, T, are considered spatially variable, and are modeled as partially correlated spatial random functions. Groundwater flow and solute transport are then solved within the context of a numerical Monte Carlo framework. The results are analyzed on the basis of dimensional analysis techniques. Simple and compact expressions characterizing the dependence of the target travel time moments on relevant dimensionless groups are proposed. The functional form of these expressions is inspired by, and is consistent with, the previous works of Sanchez-Vila and Rubin (Water Resour. Res. 39(4):1086, 2003) and Riva et al. (J. Contam. Hydrol. 82:23–43, 2006) A key result is that the effects of the chemical and physical heterogeneities on the mean travel time can be decoupled consistently with existing analytical results. The relative role of physical and geochemical heterogeneities in travel time variance is more complex, and such a decoupling is not observed. Potential uses of this work include the assessment of aquifer reclamation time by means of a single pumping well
Abstract
In this paper, we analyze the impact of physical and chemical heterogeneity on solute travel time to a pumping well. We consider a solute undergoing reversible linear instantaneous [...]
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Probabilistic risk analysis of groundwater remediation strategies
D. Bolster, M. Barahona, M. Dentz, D. Fernàndez-García, X. Sánchez-Vila, P. Trinchero, C. Valhondo, D. Tartakovsky

Water Resources Research (2009). Vol. 45 (6), pp. 1-10

Abstract
Heterogeneity of subsurface environments and insufficient site characterization are some of the reasons why decisions about groundwater exploitation and remediation have to be made under uncertainty. A typical decision maker chooses between several alternative remediation strategies by balancing their respective costs with the probability of their success or failure. We conduct a probabilistic risk assessment (PRA) to determine the likelihood of the success of a permeable reactive barrier, one of the leading approaches to groundwater remediation. While PRA is used extensively in many engineering fields, its applications in hydrogeology are scarce. This is because rigorous PRA requires one to quantify structural and parametric uncertainties inherent in predictions of subsurface flow and transport. We demonstrate how PRA can facilitate a comprehensive uncertainty quantification for complex subsurface phenomena by identifying key transport processes contributing to a barrier's failure, each of which is amenable to uncertainty analysis. Probability of failure of a remediation strategy is computed by combining independent and conditional probabilities of failure of each process. Individual probabilities can be evaluated either analytically or numerically or, barring both, can be inferred from expert opinion
Abstract
Heterogeneity of subsurface environments and insufficient site characterization are some of the reasons why decisions about groundwater exploitation and remediation have to [...]
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Characterization of mixing and spreading in a bounded stratified medium
V. Zavala-Sánchez, M. Dentz, X. Sánchez-Vila

Advances in Water Resources (2008). Vol. 32 (5), pp. 635-648

Abstract
Matheron and de Marsily [Matheron M, de Marsily G. Is the transport in porous media always diffusive? A counter-example. Water Resour Res 1980;16:901–17] studied transport in a perfectly stratified infinite medium as an idealized aquifer model. They observed superdiffusive solute spreading quantified by anomalous increase of the apparent longitudinal dispersion coefficient with the square root of time. Here, we investigate solute transport in a vertically bounded stratified random medium. Unlike for the infinite medium at asymptotically long times, disorder-induced mixing and spreading is uniquely quantified by a constant Taylor dispersion coefficient. Using a stochastic modeling approach we study the effective mixing and spreading dynamics at pre-asymptotic times in terms of effective average transport coefficients. The latter are defined on the basis of local moments, i.e., moments of the transport Green function. We investigate the impact of the position of the initial plume and the initial plume size on the (highly anomalous) pre-asymptotic effective spreading and mixing dynamics for single realizations and in average. Effectively, the system “remembers” its initial state, the effective transport coefficients show so-called memory effects, which disappear after the solute has sampled the full vertical extent of the medium. We study the impact of the intrinsic non-ergodicity of the confined medium on the validity of the stochastic modeling approach and study in this context the transition from the finite to the infinite medium
Abstract
Matheron and de Marsily [Matheron M, de Marsily G. Is the transport in porous media always diffusive? A counter-example. Water Resour Res 1980;16:901–17] studied transport [...]
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Application of a mixing-ratios based formulation to model mixing-driven dissolution experiments
A. Guadagnini, X. Sánchez-Vila, M. Saaltink, M. Bussini, B. Berkowitz

Advances in Water Resources (2009). Vol. 32 (5), pp. 756-766

Abstract
We address the question of how one can combine theoretical and numerical modeling approaches with limited measurements from laboratory flow cell experiments to realistically quantify salient features of complex mixing-driven multicomponent reactive transport problems in porous media. Flow cells are commonly used to examine processes affecting reactive transport through porous media, under controlled conditions. An advantage of flow cells is their suitability for relatively fast and reliable experiments, although measuring spatial distributions of a state variable within the cell is often difficult. In general, fluid is sampled only at the flow cell outlet, and concentration measurements are usually interpreted in terms of integrated reaction rates. In reactive transport problems, however, the spatial distribution of the reaction rates within the cell might be more important than the bulk integrated value. Recent advances in theoretical and numerical modeling of complex reactive transport problems [De Simoni M, Carrera J, Sanchez-Vila X, Guadagnini A. A procedure for the solution of multicomponent reactive transport problems. Water Resour Res 2005;41:W11410. doi: 10.1029/2005WR004056, De Simoni M, Sanchez-Vila X, Carrera J, Saaltink MW. A mixing ratios-based formulation for multicomponent reactive transport. Water Resour Res 2007;43:W07419. doi: 10.1029/2006WR005256] result in a methodology conducive to a simple exact expression for the space–time distribution of reaction rates in the presence of homogeneous or heterogeneous reactions in chemical equilibrium. The key points of the methodology are that a general reactive transport problem, involving a relatively high number of chemical species, can be formulated in terms of a set of decoupled partial differential equations, and the amount of reactants evolving into products depends on the rate at which solutions mix. The main objective of the current study is to show how this methodology can be used in conjunction with laboratory experiments to properly describe the key processes that occur in a complex, geochemically-active system under chemical equilibrium conditions. We model three CaCO3 dissolution experiments reported in Singurindy et al. [Singurindy O, Berkowitz B, Lowell RP. Carbonate dissolution and precipitation in coastal environments: Laboratory analysis and theoretical consideration. Water Resour Res 2004;40:W04401. doi: 10.1029/2003WR002651, Singurindy O, Berkowitz B, Lowell RP. Correction to Carbonate dissolution and precipitation in coastal environments: laboratory analysis and theoretical consideration. Water Resour Res 2005;41:W11701. doi: 10.1029/2005WR004433], in which saltwater and freshwater were mixed in different proportions. The integrated reaction rate within the cell estimated from the experiments are modeled independently by means of (a) a state-of-the-art reactive transport code, and (b) the uncoupled methodology of [12, 13], both of which use dispersivity as a single, adjustable parameter. The good agreement between the results from both methodologies demonstrates the feasibility of using simple solutions to design and analyze laboratory experiments involving complex geochemical problems
Abstract
We address the question of how one can combine theoretical and numerical modeling approaches with limited measurements from laboratory flow cell experiments to realistically [...]
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Multicomponent reactive transport in multicontinuum media
L. Donado, X. Sánchez-Vila, M. Dentz, J. Carrera

Water Resources Research (2009). Vol. 45 (W11402), pp. 1-11

Abstract
Multicomponent reactive transport in aquifers is a highly complex process, owing to a combination of variability in the processes involved and the inherent heterogeneity of nature. To date, the most common approach is to model reactive transport by incorporating reaction terms into advection-dispersion equations (ADEs). Over the last several years, a large body of literature has emerged criticizing the validity of the ADE for transport in real media, and alternative models have been presented. One such approach is that of multirate mass transfer (MRMT). In this work, we propose a model that introduces reactive terms into the MRMT governing equations for conservative species. This model conceptualizes the medium as a multiple continuum of one mobile region and multiple immobile regions, which are related by kinetic mass transfer processes. Reactants in both the mobile and immobile regions are assumed to always be in chemical equilibrium. However, the combination of local dispersion in the mobile region and the various mass transfer rates induce a global chemical nonequilibrium. Assuming this model properly accounts for transport of reactive species, we derive explicit expressions for the reaction rates in the mobile and immobile regions, and we study the impact of mass transfer on reactive transport. Within this framework, we observe that the resulting reaction rates can be very different from those that arise in a system governed by an ADE-type equation.
Abstract
Multicomponent reactive transport in aquifers is a highly complex process, owing to a combination of variability in the processes involved and the inherent heterogeneity of [...]
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Transport upscaling in heterogeneous aquifers: What physical parameters control memory functions?
M. Willmann, J. Carrera, X. Sánchez-Vila

Water Resources Research (2008). Vol. 44 (12), pp. 1-13

Abstract
Power law tailing is often observed in the breakthrough curves (BTCs) of tracer tests. Tailing is attributed to heterogeneity of aquifer properties and cannot be properly modeled by means of the homogeneous advection‐dispersion equation. Mass transfer models (e.g., continuous time random walk method, multirate mass transfer, or fractional‐order advection‐dispersion equations) using memory have been widely applied for reproducing observed tails. The relationship between memory parameters obtained from BTC fitting and the parameters characterizing the heterogeneity of hydraulic properties is still unclear. Here we investigate the conditions under which heterogeneity produces the type of tailing observed in the field and how memory functions are influenced by measurable heterogeneity parameters (e.g., variance, variogram, or integral scale of the underlying transmissivity field). We find that the slope of a BTC in a log‐log plot is mainly influenced by the connectivity of the underlying permeability field but is insensitive to its variance. The slope BTC reaches asymptotically 2 as connectivity increases. We conclude that an appropriate choice of the memory function allows reproducing the spreading caused by hydraulic heterogeneity but not necessarily the rate of mixing.
Abstract
Power law tailing is often observed in the breakthrough curves (BTCs) of tracer tests. Tailing is attributed to heterogeneity of aquifer properties and cannot be properly [...]
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Point-to-point connectivity, an abstract concept or a key issue for risk assessment studies?
P. Trinchero, X. Sánchez-Vila, D. Fernàndez-García

Advances in Water Resources (2008). Vol. 31 (12), pp. 1742-1753

Abstract
Connectivity of high/low-permeability areas has been recognized to significantly impact groundwater flow and solute transport. The task of defining a rigorous quantitative measure of connectivity for continuous variables has failed so far, and thus there exist a suite of connectivity indicators which are dependent on the specific hydrodynamic processes and the interpretation method. Amongst the many existing indicators, we concentrate on those characterizing connectivity between the points involved in a hydraulic or tracer test. The flow connectivity indicator used here is based on the time elapsed for hydraulic response in a pumping test (e.g., the storage coefficient estimated by the Cooper–Jacob method, Sest). Regarding transport, we select the estimated porosity from the breakthrough curve (ϕest). According to Knudby and Carrera [Knudby C, Carrera J. On the relationship between indicators of geostatistical, flow and transport connectivity. Adv Water Resour 2005;28(4):405–21] these two indicators measure connectivity differently, and are poorly correlated. Here, we use perturbation theory to analytically investigate the intrinsic relationship between Sest and ϕest. We find that ϕest can be expressed as a weighted line integral along the particle trajectory involving two parameters: the transmissivity point values, T, and the estimated values of Sest along the particle path. The weighting function is linear with the distance from the pumping well, thus the influence of the weighting function is maximum at the injection area, whereas the hydraulic information close to the pumping well becomes redundant (null weight). The relative importance of these two factors is explored using numerical simulations in a given synthetic aquifer and tested against intermediate-scale laboratory tracer experiments. We conclude that the degree of connectivity between two points of an aquifer (point-to-point connectivity) is a key issue for risk assessment studies aimed at predicting the travel time of a potential contaminant.
Abstract
Connectivity of high/low-permeability areas has been recognized to significantly impact groundwater flow and solute transport. The task of defining a rigorous quantitative [...]
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Influence of heterogeneity on the interpretation of pumping test data in leaky aquifers
N. Copty, P. Trinchero, X. Sánchez-Vila, M. Sarioglu, A. Findikakis

Water Resources Research (2008). Vol. 44 (11), 1-15

Abstract
Pumping tests are routinely interpreted from the analysis of drawdown data and their derivatives. These interpretations result in a small number of apparent parameter values which lump the underlying heterogeneous structure of the aquifer. Key questions in such interpretations are (1) what is the physical meaning of those lumped parameters and (2) whether it is possible to infer some information about the spatial variability of the hydraulic parameters. The system analyzed in this paper consists of an aquifer separated from a second recharging aquifer by means of an aquitard. The natural log transforms of the transmissivity, ln T, and the vertical conductance of the aquitard, ln C, are modeled as two independent second‐order stationary spatial random functions (SRFs). The Monte Carlo approach is used to simulate the time‐dependent drawdown at a suite of observation points for different values of the statistical parameters defining the SRFs. Drawdown data at each observation point are independently used to estimate hydraulic parameters using three existing methods: (1) the inflection‐point method, (2) curve‐fitting, and (3) the double inflection‐point method. The resulting estimated parameters are shown to be space dependent and vary with the interpretation method since each method gives different emphasis to different parts of the time‐drawdown data. Moreover, the heterogeneity in the pumped aquifer or the aquitard influences the estimates in distinct manners. Finally, we show that, by combining the parameter estimates obtained from the different analysis procedures, information about the heterogeneity of the leaky aquifer system may be inferred
Abstract
Pumping tests are routinely interpreted from the analysis of drawdown data and their derivatives. These interpretations result in a small number of apparent parameter values [...]
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Relative importance of geostatistical and transport models in describing heavily tailed breakthrough curves at the Lauswiesen site
M. Riva, A. Guadagnini, D. Fernàndez-García, X. Sánchez-Vila, T. Ptak

Journal of Contaminant Hydrology (2008). Vol. 101 (1-4), pp. 1-13

Abstract
We analyze the relative importance of the selection of (1) the geostatistical model depicting the structural heterogeneity of an aquifer, and (2) the basic processes to be included in the conceptual model, to describe the main aspects of solute transport at an experimental site. We focus on the results of a forced-gradient tracer test performed at the “Lauswiesen” experimental site, near Tübingen, Germany. In the experiment, NaBr is injected into a well located 52 m from a pumping well. Multilevel breakthrough curves (BTCs) are measured in the latter. We conceptualize the aquifer as a three-dimensional, doubly stochastic composite medium, where distributions of geomaterials and attributes, e.g., hydraulic conductivity (K) and porosity (ϕ), can be uncertain. Several alternative transport processes are considered: advection, advection–dispersion and/or mass-transfer between mobile and immobile regions. Flow and transport are tackled within a stochastic Monte Carlo framework to describe key features of the experimental BTCs, such as temporal moments, peak time, and pronounced tailing. We find that, regardless the complexity of the conceptual transport model adopted, an adequate description of heterogeneity is crucial for generating alternative equally likely realizations of the system that are consistent with (a) the statistical description of the heterogeneous system, as inferred from the data, and (b) salient features of the depth-averaged breakthrough curve, including preferential paths, slow release of mass particles, and anomalous spreading. While the available geostatistical characterization of heterogeneity can explain most of the integrated behavior of transport (depth-averaged breakthrough curve), not all multilevel BTCs are described with equal success. This suggests that transport models simply based on integrated measurements may not ensure an accurate representation of many of the important features required in three-dimensional transport models.
Abstract
We analyze the relative importance of the selection of (1) the geostatistical model depicting the structural heterogeneity of an aquifer, and (2) the basic processes [...]
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Reaction rates and effective parameters in stratified aquifers
D. Fernàndez-García, X. Sánchez-Vila, A. Guadagnini

Advances in Water Resources (2008). Vol. 31 (10), pp. 1364-1376

Abstract
Chemical species are advected by water and undergo mixing processes due to effects of local diffusion and/or dispersion. In turn, mixing causes reactions to take place so that the system can locally equilibrate. In general, a multicomponent reactive transport problem is described through a system of coupled non-linear partial differential equations. Under instantaneous chemical equilibrium, a complex geochemical problem can be highly simplified by fully defining the system in terms of conservative quantities, termed master species or components, and the space–time distribution of reaction rates. We investigate the parameters controlling reaction rates in a heterogeneous aquifer at short distances from the source. Hydraulic conductivity at this scale is modeled as a random process with highly anisotropic correlation structure. In the limit for very large horizontal integral scales, the medium can be considered as stratified. Upon modeling transport by means of an ADE (Advection Dispersion Equation), we derive closed-form analytical solutions for statistical moments of reaction rates for the particular case of negligible transverse dispersion. This allows obtaining an expression for an effective hydraulic conductivity, , as a representative parameter describing the mean behavior of the reactive system. The resulting is significantly smaller than the effective conductivity representative of the flow problem. Finally, we analyze numerically the effect of accounting for transverse local dispersion. We show that transverse dispersion causes no variation in the distribution of (ensemble) moments of local reaction rates at very short travel times, while it becomes the dominant effect for intermediate to large travel times.
Abstract
Chemical species are advected by water and undergo mixing processes due to effects of local diffusion and/or dispersion. In turn, mixing causes reactions to take place so [...]
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Conditional probability density functions of concentrations for mixing-controlled reactive transport in heterogeneous aquifers
X. Sánchez-Vila, A. Guadagnini, D. Fernández-García

Mathematical geosciences (2008). Vol. 41 (3), pp. 323-351

Abstract
This paper presents an approach conducive to an evaluation of the probability density function (pdf) of spatio-temporal distributions of concentrations of reactive solutes (and associated reaction rates) evolving in a randomly heterogeneous aquifer. Most existing approaches to solute transport in heterogeneous media focus on providing expressions for space–time moments of concentrations. In general, only low order moments (unconditional or conditional mean and covariance) are computed. In some cases, this allows for obtaining a confidence interval associated with predictions of local concentrations. Common applications, such as risk assessment and vulnerability practices, require the assessment of extreme (low or high) concentration values. We start from the well-known approach of deconstructing the reactive transport problem into the analysis of a conservative transport process followed by speciation to (a) provide a partial differential equation (PDE) for the (conditional) pdf of conservative aqueous species, and (b) derive expressions for the pdf of reactive species and the associated reaction rate. When transport at the local scale is described by an Advection Dispersion Equation (ADE), the equation satisfied by the pdf of conservative species is non-local in space and time. It is similar to an ADE and includes an additional source term. The latter involves the contribution of dilution effects that counteract dispersive fluxes. In general, the PDE we provide must be solved numerically, in a Monte Carlo framework. In some cases, an approximation can be obtained through suitable localization of the governing equation. We illustrate the methodology to depict key features of transport in randomly stratified media in the absence of transverse dispersion effects. In this case, all the pdfs can be explicitly obtained, and their evolution with space and time is discussed.
Abstract
This paper presents an approach conducive to an evaluation of the probability density function (pdf) of spatio-temporal distributions of concentrations of reactive solutes [...]
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A New Method for the Interpretation of Pumping Tests in Leaky Aquifers
P. Trinchero, X. Sánchez-Vila, N. Copty, A. Findikakis

Ground water (2008). Vol. 46 (1), pp. 133-143

Abstract
A novel methodology for the interpretation of pumping tests in leaky aquifer systems, referred to as the double inflection point (DIP) method, is presented. The method is based on the analysis of the first and second derivatives of the drawdown with respect to log time for the estimation of the flow parameters. Like commonly used analysis procedures, such as the type‐curve approach developed by Walton (1962) and the inflection point method developed by Hantush (1956), the mathematical development of the DIP method is based on the assumption of homogeneity of the leaky aquifer layers. However, contrary to the two methods developed by Hantush and Walton, the new method does not need any fitting process. In homogeneous media, the two classic methods and the one proposed here provide exact results for transmissivity, storativity, and leakage factor when aquifer storage is neglected and the recharging aquifer is unperturbed. The real advantage of the DIP method comes when applying all methods independently to a test in a heterogeneous aquifer, where each method yields parameter values that are weighted differently, and thus each method provides different information about the heterogeneity distribution. Therefore, the methods are complementary and not competitive. In particular, the combination of the DIP method and Hantush method is shown to lead to the identification of contrasts between the local transmissivity in the vicinity of the well and the equivalent transmissivity of the perturbed aquifer volume.
Abstract
A novel methodology for the interpretation of pumping tests in leaky aquifer systems, referred to as the double inflection point (DIP) method, is presented. The method is [...]
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Gestión de los recursos hídricos: los modelos hidrogeológicos como herramienta auxiliar
X. Sánchez-Vila, D. Fernández

Enseñaza de las ciencias de la Tierra (2007). Vol. 15 (3), pp. 250-255

Abstract
Water is scarce, and thus must be managed adequately in order to satisfy the global demand within a water resources integral planning. Management can act either on offer or demand. Proper management implies an accountability system capable both of reproducing the existing situation and quantifying the effect of management scenarios upon resources quantity and quality. The need for quantification makes indispensable numerical models in general, and hydrogeological models in particular. We present some of the elements that are included in a hydrogeological model, including the need for managing huge amounts of data and some technical aspects on discretization and calibration of numerical models. Hydrogeological models must be included into management models that account for conjunctive use of all available resources.
Abstract
Water is scarce, and thus must be managed adequately in order to satisfy the global demand within a water resources integral planning. Management can act either on offer or [...]
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On the meaning of the transmissivity values obtained from recovery tests
M. Willmann, J. Carrera, X. Sánchez-Vila, E. Vázquez-Suñé

Hydrogeology Journal (2007). Vol. 15 (5), pp. 833-842

Abstract
Recovery tests are based on estimating transmissivity, T, from the heads that rebound after pumping has stopped. Recovery tests can be performed in wells where conventional constant-rate pumping tests would not be possible. Test interpretation is based on the simple Theis recovery method, related to late time drawdown in an infinite homogeneous aquifer. Yet, field data often cannot be explained by the homogeneous theory. Because T is heterogeneous over an evolving range of scales, it is important to evaluate the support scale of hydraulic tests. Numerical simulations are performed to show that heterogeneity in T can explain these field observations. It is also shown that the local T value around the well can be inferred from early time-recovery data, assuming ideal conditions, whereas late time data yield a large-scale (regional) representative value. Even when recovery is observed for a short time, indirect information about the regional value can also be obtained. A method for the interpretation of recovery tests is proposed based on the Theis recovery method that takes into account the heterogeneity of aquifers. Finally, some guidelines are provided for best test performance depending on the scale of the problem.
Abstract
Recovery tests are based on estimating transmissivity, T, from the heads that rebound after pumping has stopped. Recovery tests [...]
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A mixing ratios‐based formulation for multicomponent reactive transport
M. Simoni, X. Sánchez-Vila, M. Saaltink

Water Resources Research (2007). Vol. 43 (7), pp. 1-10

Abstract
Chemical reactions are driven by disequilibrium, which is often caused by mixing. Therefore quantification of the mixing rate is essential for evaluating the fate of solutes in natural systems, such as rivers, lakes, and aquifers. We propose a novel mixing ratios‐based formulation to evaluate solute concentrations and reaction rates when equilibrium aqueous reactions and precipitation/dissolution of minerals are driven by mixing of different end‐members. Each end‐member corresponds to a water from a given source with a specific chemical signature. The approach decouples the solute transport and chemical speciation problems, so that mixing ratios can be first obtained from the solution of conservative transport and then be used in general speciation codes to obtain the concentration of reacting species. One key finding is a general expression for reaction rates which demonstrates that the amount of reactants evolving into products depends on the rate at which solutions mix. Our formulation constitutes a general framework according to which one can design and interpret experimental analyses devoted to study mixing‐driven reactive processes and obtain transverse dispersion coefficients. The formulation is also proposed as a useful tool to derive analytical solutions of reactive transport problems and may result computationally advantageous when compared to previous approaches to reactive transport modeling. We apply the developed formulation to provide an analytical solution of the reactive transport process resulting from mixing different CaCO3‐saturated waters in a two‐dimensional setup
Abstract
Chemical reactions are driven by disequilibrium, which is often caused by mixing. Therefore quantification of the mixing rate is essential for evaluating the fate of solutes [...]
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Quasi-horizontal circulation cells in 3D seawater intrusion
E. Abarca, J. Carrera, X. Sánchez-Vila, C. Voss

Journal of Hydrology (2007). Vol. 339 (3-4), pp. 118-129

Abstract
The seawater intrusion process is characterized by the difference in freshwater and seawater density that causes freshwater to float on seawater. Many confined aquifers have a large horizontal extension with respect to thickness. In these cases, while buoyancy acts in the vertical direction, flow is confined between the upper and bottom boundaries and the effect of gravity is controlled by variations of aquifer elevation. Therefore, the effective gravity is controlled by the slope and the shape of the aquifer boundaries. Variability in the topography of the aquifer boundaries is one case where 3D analysis is necessary. In this work, density-dependent flow processes caused by 3D aquifer geometry are studied numerically and specifically, considering a lateral slope of the aquifer boundaries. Sub-horizontal circulation cells are formed in the saltwater entering the aquifer. The penetration of the saltwater can be quantified by a dimensionless buoyancy number that measures the lateral slope of the aquifer relative to freshwater flux. The penetration of the seawater intrusion wedge is controlled more by this slope than by the aquifer thickness and dispersivity. Thus, the slope must be taken into account in order to accurately evaluate seawater intrusion.
Abstract
The seawater intrusion process is characterized by the difference in freshwater and seawater density that causes freshwater to float on seawater. Many confined aquifers have [...]
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Transport‐controlled reaction rates under local non‐equilibrium conditions
X. Sánchez-Vila, M. Dentz, L. Donado

Geophysical research letters (2007). Vol. 34 (10), pp. 10404

Abstract
Chemical reactions are driven by non‐equilibrium and can be fully described by the spatio‐temporal distribution of the reaction rate. We present an analytical approach for the computation of reaction rates under local non‐equilibrium conditions for a precipitation/dissolution problem. We derive an original non‐linear partial differential equation for the reaction rate r and present a series expansion of r for large Damköhler numbers, i.e., fast local scale reactions. The impact of local scale non‐equilibrium conditions on the transport‐controlled reaction rate is studied for reactive transport in a column.
Abstract
Chemical reactions are driven by non‐equilibrium and can be fully described by the spatio‐temporal distribution of the reaction rate. We present an analytical approach [...]
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Anisotropic dispersive Henry problem
E. Abarca, J. Carrera, X. Sánchez-Vila, M. Dentz

Advances in Water Resources (2007). Vol. 30 (4), pp. 913-926

Abstract
The Henry problem has played a key role in our understanding of seawater intrusion into coastal aquifers and in benchmarking density dependent flow codes. This paper seeks to modify Henry’s problem to ensure sensitivity to density variations and vertical salinity profiles that resemble field observations. In the proposed problem, the “dispersive Henry problem”, mixing is represented by means of the traditional Scheidegger dispersion tensor (dispersivity times water flux). Anisotropy in the hydraulic conductivity is acknowledged and Henry’s seaside boundary condition of prescribed salt concentration is replaced by a flux dependent boundary condition, which represents more realistically salt transport across the seaside boundary. This problem turns out to be very sensitive to density variations and its solution gets closer to reality. However, an improvement in the traditional Henry problem (gain in sensitivity and realism) can be also achieved if the value of the Peclet number is significantly reduced. Although the dispersive problem lacks an analytical solution, it can shed light on flow in coastal aquifers. It provides significant information about the factors controlling seawater penetration, width of the mixing zone and influx of seawater. The width of the mixing zone depends basically on dispersion with longitudinal and transverse dispersion controlling different parts of the mixing zone but displaying similar overall effects. Toe penetration is mainly controlled by the horizontal permeability and by the geometric mean of the dispersivities. Finally, transverse dispersivity and the geometric mean of the hydraulic conductivity are the leading parameters controlling the amount of saltwater that enters the aquifer
Abstract
The Henry problem has played a key role in our understanding of seawater intrusion into coastal aquifers and in benchmarking density dependent flow codes. [...]
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Ergodicity of pumping tests
X. Sánchez-Vila, D. Tartakovsky

Water Resources Research (2007). Vol. 43 (3), pp. 1-5

Abstract
Standard interpretations of pumping tests in heterogeneous formations rely on effective representations of porous media, which replace spatially varying hydraulic properties with their constant counterparts averaged over the support volume of a test. Rigorous approaches for deriving representative (effective, apparent, upscaled, etc.) parameters employ either ensemble or spatial averaging. We derive a set of conditions under which these two paradigms yield identical results. We refer to them as conditions for the ergodicity of pumping tests. This allows one to use stochastic approaches to estimate the statistics of the spatial variability of hydraulic parameters on scales smaller than the support volume of a pumping test.
Abstract
Standard interpretations of pumping tests in heterogeneous formations rely on effective representations of porous media, which replace spatially varying hydraulic properties [...]
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Ensemble based optimization for electric demand forecast: Genetic programming and heuristic algorithms
J. Garcia, D. Alvarez, S. Rivera

Rev. int. métodos numér. cálc. diseño ing. (2020). Vol. 36, (3), 36

Abstract
Power generation using renewable energy such as wind and solar energy depend on weather behavior. An accurate weather forecast improves the operation management of a Smart Grid. However, the environmental conditions vary with both time and space and, depending on the location have different classifications. The environmental conditions vary with time and depending on the country, also the changes between standard, local and summer time can result in days of 23 h, to obtain days of 24 h; the two adjacent hours are used to calculate the missing hour. In this paper is addressed a nonlinear symbolic regression (RS by its acronym in Spanish) model is used to make annual demand forecasts. This algorithm is assessment with real measurements creating models that conform to the load forecasting of 28 weather stations. The learning variables are loads of demand and temperatures; that are grouped by hours for a two-year time interval. The RS-DEEPSO algorithm is proposed to improve the forecast. This is used due to its evolutionary, self-adaptive qualities and the possibility of exploring new scenarios in search of optimum. The forecast obtained using the new hybrid RS-DEEPSO has an average error per day less than 3.9% and per hour is less than 5.62% during a period of 1 year.
Abstract
Power generation using renewable energy such as wind and solar energy depend on weather behavior. An accurate weather forecast improves the operation management of a Smart [...]
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Effective dispersion in a chemically heterogeneous medium under temporally fluctuating flow conditions
V. Zavala-Sánchez, M. Dentz, X. Sánchez-Vila

Advances in Water Resources (2007). Vol. 30 (5), pp. 1342-1354

Abstract
We investigate effective solute transport in a chemically heterogeneous medium subject to temporal fluctuations of the flow conditions. Focusing on spatial variations in the equilibrium adsorption properties, the corresponding fluctuating retardation factor is modeled as a stationary random space function. The temporal variability of the flow is represented by a stationary temporal random process. Solute spreading is quantified by effective dispersion coefficients, which are derived from the ensemble average of the second centered moments of the normalized solute distribution in a single disorder realization. Using first-order expansions in the variances of the respective random fields, we derive explicit compact expressions for the time behavior of the disorder induced contributions to the effective dispersion coefficients. Focusing on the contributions due to chemical heterogeneity and temporal fluctuations, we find enhanced transverse spreading characterized by a transverse effective dispersion coefficient that, in contrast to transport in steady flow fields, evolves to a disorder-induced macroscopic value (i.e., independent of local dispersion). At the same time, the asymptotic longitudinal dispersion coefficient can decrease. Under certain conditions the contribution to the longitudinal effective dispersion coefficient shows superdiffusive behavior, similar to that observed for transport in s stratified porous medium, before it decreases to its asymptotic value. The presented compact and easy to use expressions for the longitudinal and transverse effective dispersion coefficients can be used for the quantification of effective spreading and mixing in the context of the groundwater remediation based on hydraulic manipulation and for the effective modeling of reactive transport in heterogeneous media in general.
Abstract
We investigate effective solute transport in a chemically heterogeneous medium subject to temporal fluctuations of the flow conditions. Focusing on spatial variations in the [...]
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Variable density flow in porous media
M. Dentz, D. Tartakovsky, E. Abarca, A. Guadagnini, X. Sánchez-Vila, J. Carrera

Journal of Fluid Mechanics (2006). Vol. 561, pp. 209-235

Abstract
We review the state of the art in modeling of variable-density flow and transport in porous media, including conceptual models for convection systems, governing balance equations, phenomenological laws, constitutive relations for fluid density and viscosity, and numerical methods for solving the resulting nonlinear multifield problems. The discussion of numerical methods addresses strategies for solving the coupled spatio-temporal convection process, consistent velocity approximation, and error-based mesh adaptation techniques. As numerical models for those nonlinear systems must be carefully verified in appropriate tests, we discuss weaknesses and inconsistencies of current model-verification methods as well as benchmark solutions. We give examples of field-related applications to illustrate specific challenges of further research, where heterogeneities and large scales are important.
Abstract
We review the state of the art in modeling of variable-density flow and transport in porous media, including conceptual models for convection systems, governing balance equations, [...]
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Representative hydraulic conductivities in saturated groundwater flow
X. Sánchez-Vila, A. Guadagnini, J. Carrera

Reviews of geophysics (2006). Vol. 44 (3), pp. 1-46

Abstract
Heterogeneity is the single most salient feature of hydrogeology. An enormous amount of work has been devoted during the last 30 years to addressing this issue. Our objective is to synthesize and to offer a critical appraisal of results related to the problem of finding representative hydraulic conductivities. By representative hydraulic conductivity we mean a parameter controlling the average behavior of groundwater flow within an aquifer at a given scale. Three related concepts are defined: effective hydraulic conductivity, which relates the ensemble averages of flux and head gradient; equivalent conductivity, which relates the spatial averages of flux and head gradient within a given volume of an aquifer; and interpreted conductivity, which is the one derived from interpretation of field data. Most theoretical results are related to effective conductivity, and their application to real world scenarios relies on ergodic assumptions. Fortunately, a number of results are available suggesting that conventional hydraulic test interpretations yield (interpreted) hydraulic conductivity values that can be closely linked to equivalent and/or effective hydraulic conductivities. Complex spatial distributions of geologic hydrofacies and flow conditions have a strong impact upon the existence and the actual values of representative parameters. Therefore it is not surprising that a large body of literature provides particular solutions for simplified boundary conditions and geological settings, which are, nevertheless, useful for many practical applications. Still, frequent observations of scale effects imply that efforts should be directed at characterizing well‐connected stochastic random fields and at evaluating the corresponding representative hydraulic conductivities
Abstract
Heterogeneity is the single most salient feature of hydrogeology. An enormous amount of work has been devoted during the last 30 years to addressing this issue. Our objective [...]
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Travel time and trajectory moments of conservative solutes in two-dimensional convergent flows
M. Riva, X. Sánchez-Vila, A. Guadagnini, M. Willmann, M. Simoni

Journal of Contaminant Hydrology (2006). Vol. 82 (1-2), pp. 23-43

Abstract
We address advective transport of a solute traveling toward a single pumping well in a two-dimensional randomly heterogeneous aquifer. The two random variables of interest are the trajectory followed by an individual particle from the injection point to the well location and the particle travel time under steady-state conditions. Our main objective is to derive the predictors of trajectory and travel time and the associated uncertainty, in terms of their first two statistical moments (mean and variance). We consider a solute that undergoes mass transfer between a mobile and an immobile zone. Based on Lawrence et al. [Lawrence, A.E., Sánchez-Vila, X., Rubin, Y., 2002. Conditional moments of the breakthrough curves of kinetically sorbing solute in heterogeneous porous media using multirate mass transfer models for sorption and desorption. Water Resour. Res. 38 (11), 1248, doi:10.1029/2001WR001006.], travel time moments can be written in terms of those of a conservative solute times a deterministic quantity. Moreover, the moments of solute particles trajectory do not depend on mass transfer processes. The resulting mean and variance of travel time and trajectory for a conservative species can be written as functions of the first, second moments and cross-moments of trajectory and velocity components. The equations are developed from a consistent second order expansion in σY (standard deviation of the natural logarithm of hydraulic conductivity). Our solution can be completely integrated with the moment equations of groundwater flow of Guadagnini and Neuman [Guadagnini, A., Neuman, S.P., 1999a. Nonlocal and localized analyses of conditional mean steady state flow in bounded, randomly non uniform domains 1. Theory and computational approach. Water Resour. Res. 35(10), 2999–3018.,Guadagnini, A., Neuman, S.P., 1999b. Nonlocal and localized analyses of conditional mean steady state flow in bounded, randomly non uniform domains 2. Computational examples. Water Resour. Res. 35(10), 3019–3039.], it is free of distributional assumptions regarding the log conductivity field, and formally includes conditioning. We present analytical expressions for the unconditional case by making use of the results of Riva et al. [Riva, M., Guadagnini, A., Neuman, S.P., Franzetti, S., 2001. Radial flow in a bounded randomly heterogeneous aquifer. Transport in Porous Media 45, 139–193.]. The quality of the solution is supported by numerical Monte Carlo simulations. Potential uses of this work include the determination of aquifer reclamation time by means of a single pumping well, and the demarcation of the region potentially affected by the presence of a contaminant in the proximity of a well, whenever the aquifer is very thin and Dupuit–Forchheimer assumption holds.
Abstract
We address advective transport of a solute traveling toward a single pumping well in a two-dimensional randomly heterogeneous aquifer. The two random variables [...]
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A procedure for the solution of multicomponent reactive transport problems
J. Carrera, M. Simoni, X. Sánchez-Vila, A. Guadagnini

Water Resources Research (2005). Vol. 41 (W11410), pp. 1-16

Abstract
Modeling transport of reactive solutes is a challenging problem, necessary for understanding the fate of pollutants and geochemical processes occurring in aquifers, rivers, estuaries, and oceans. Geochemical processes involving multiple reactive species are generally analyzed using advanced numerical codes. The resulting complexity has inhibited the development of analytical solutions for multicomponent heterogeneous reactions such as precipitation/dissolution. We present a procedure to solve groundwater reactive transport in the case of homogeneous and classical heterogeneous equilibrium reactions induced by mixing different waters. The methodology consists of four steps: (1) defining conservative components to decouple the solution of chemical equilibrium equations from species mass balances, (2) solving the transport equations for the conservative components, (3) performing speciation calculations to obtain concentrations of aqueous species, and (4) substituting the latter into the transport equations to evaluate reaction rates. We then obtain the space‐time distribution of concentrations and reaction rates. The key result is that when the equilibrium constant does not vary in space or time, the reaction rate is proportional to the rate of mixing, ∇TuD ∇u, where u is the vector of conservative components concentrations and D is the dispersion tensor. The methodology can be used to test numerical codes by setting benchmark problems but also to derive closed‐form analytical solutions whenever steps 2 and 3 are simple, as illustrated by the application to a binary system. This application clearly elucidates that in a three‐dimensional problem both chemical and transport parameters are equally important in controlling the process.
Abstract
Modeling transport of reactive solutes is a challenging problem, necessary for understanding the fate of pollutants and geochemical processes occurring in aquifers, rivers, [...]
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Travel time and trajectory moments of conservative solutes in three dimensional heterogeneous porous media under mean uniform flow
X. Sánchez-Vila, A. Guadagnini

Advances in Water Resources (2005). Vol. 28 (5), pp. 429-439

Abstract
We present expressions satisfied by the first statistical moments (mean and variance–covariance) of travel time and trajectory of conservative solute particles advected in a three-dimensional heterogeneous aquifer under uniform in the mean flow conditions. Closure of the model is obtained by means of a consistent second-order expansion in σY (standard deviation of the log hydraulic conductivity) of (statistical) moments of quantities of interest. As such, the results obtained are nominally limited to mildly non-uniform fields, with σY < 1. Resulting mean and variance of particles travel time and trajectory are functions of first and second moments and cross-moments of trajectory and velocity components. Our solution is applicable to infinite domains and is free of distributional assumptions. As an important application of the methodology we obtain closed-form expressions for the unconditional mean and variance of travel time and particle trajectory for isotropic log-conductivity domain characterized by an exponential variogram. This allows us to recover the non linear behavior of mean travel time versus distance, in agreement with numerical results published in the literature, as well as a non-linear effect in the mean trajectory. The analysis of trajectory variance allows recovering some known results regarding transverse macro-dispersion, evidencing some limitations typical of perturbation theory.
Abstract
We present expressions satisfied by the first statistical moments (mean and variance–covariance) of travel time and trajectory of conservative solute particles advected [...]
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A methodolgy to compute mixing ratios with uncertain end-members
J. Carrera, E. Vázquez-Suñé, X. Sánchez-Vila

Water Resources Research (2004). Vol. 40 (W12101), pp. 1-11

Abstract
Mixing calculations involve computing the ratios in which two or more end‐members are mixed in a sample. Mixing calculations are useful for a number of tasks in hydrology, such as hydrograph separation, water or solute mass balances, and identification of groundwater recharge sources. Most methods available for computing mixing ratios are based on assuming that end‐member concentrations are perfectly known, which is rarely the case. Often, end‐members cannot be sampled, and their concentrations vary in time and space. Still, much information about them is contained in the mixtures. To take advantage of this information, we present here a maximum likelihood method to estimate mixing ratios, while acknowledging uncertainty in end‐member concentrations. Maximizing the likelihood of concentration measurements with respect to both mixing ratios and end‐member concentrations leads to a general constrained optimization problem. An algorithm for solving this problem is presented and applied to two synthetic examples of water mixing problems. Results allow us to conclude that the method outperforms traditional approaches, such as least squares or linear mixing, in the computation of mixing ratios. The method also yields improved estimates of end‐member concentrations, thus enlarging the potential of mixing calculations. The method requires defining the reliability of measurements, but results are quite robust with respect to the assumed standard deviations. A nice feature of the method is that it allows for improving the quality of computations by increasing the number of samples and/or analyzed species.
Abstract
Mixing calculations involve computing the ratios in which two or more end‐members are mixed in a sample. Mixing calculations are useful for a number of tasks in hydrology, [...]
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Introductory review of specific factors influencing urban groundwater, an emerging branch of hydrogeology, with reference to Barcelona, Spain
E. Vázquez-Suñé, X. Sánchez-Vila, J. Carrera

Hydrogeology Journal (2005). Vol. 13, pp. 522-533

Abstract
A number of specific factors must be considered when dealing with groundwater in urban areas. Urbanization significantly affects the natural water cycle, both in terms of quantity and quality. In particular, the main contributors to recharge and discharge clearly differ from those in natural systems. Moreover, water can affect underground structures and infrastructure characteristics of cities such as basements, public transport services (trains, underground railways, etc.), and utility conduits. As a result, urban groundwater is emerging as a distinct branch of hydrogeology. The objective of this paper is to review some of the topics that are specific to urban groundwater. These include (1) fluctuations in groundwater levels caused by changes in land and water uses; (2) pollution problems caused by point or non-point sources in urban areas; (3) characterization and quantification of the components contributing to groundwater recharge and discharge; (4) specific characteristics of groundwater flow and solute transport models in urban areas; and (5) integration of data for sustainable urban water management. Some of these issues are illustrated for the particular case of Barcelona, where a comprehensive hydrogeological study has been carried out during the last few years by both the public and the private sectors.
Abstract
A number of specific factors must be considered when dealing with groundwater in urban areas. Urbanization significantly affects the natural water cycle, both in terms of [...]
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On the striking similarity between the moments of breakthrough curves for a heterogeneous medium and a homogeneous medium with a matrix diffusion term
X. Sánchez-Vila, J. Carrera

Journal of Hydrology (2004). Vol. 294 (1-3), pp. 164-175

Abstract
A usual method to obtain aquifer parameters is to analyze the moments of the breakthrough curves (BTCs) in tracer tests. The parameters to be estimated in this analysis would depend on the conceptual model adopted. Intuitively, if different processes were considered, the shape of the BTCs should be quite different, and one would tend to think that the time and space evolution of the temporal moments should also be quite different. Contrarily, in this paper, we show that two very different conceptual models of solute transport lead to virtually identical moments of the BTC. The two models selected for this study are the classical advection–dispersion equation with a Fickian macrodispersive term and a homogeneous medium advection model with mass-transfer between mobile and immobile matrix phases, for three different models of matrix shape. In both models, the first three moments are linear with travel distance, while the fourth moment is a second order polynomial. This agreement allows us to choose parameters yielding the same moments in the two models. As we consider two fitting parameters, we select them to match the second and third moment. Match in the first moment is obtained from physical arguments. It turns out that the resulting leading term of the fourth moment is identical for both models. As a direct consequence of this work, it follows that for large travel distances it would not be possible to discriminate between conceptual models using data from a single BTC.
Abstract
A usual method to obtain aquifer parameters is to analyze the moments of the breakthrough curves (BTCs) in tracer tests. The parameters to be estimated [...]
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A perturbation solution to the transient Henry problem for seawater intrusion
D. Tartakovsky, A. Guadagnini, X. Sánchez-Vila, M. Dentz, J. Carrera

Development in Water Science (2004). Vol. 55 (2), pp. 1573-1581

Abstract
Henry's formulation of seawater intrusion in coastal aquifers consists of a fully coupled system of flow and transport equations with variable density. While the Henry problem often serves as a benchmark for numerical codes, the accuracy of the existing analytical solutions is hard to gauge. We use a perturbation expansion in a small parameter, the ratio between the densities of seawater and freshwater, to derive an analytical solution for the transient Henry problem, which describes the saline intrusion caused by a sudden change in fresh groundwater discharge. This approach is effective for other variable density flow scenarios, since it allows one to decouple the flow and transport equations.
Abstract
Henry's formulation of seawater intrusion in coastal aquifers consists of a fully coupled system of flow and transport equations with variable density. While the Henry [...]
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Sobre la no identificabilidad de los momentos estadísticos del tiempo de llegada de un soluto en un medio heterogéneo
X. Sánchez-Vila, J. Carrera

Boletín geológico y minero (2003). Vol. 114 (3), pp. 287-298

Abstract
El análisis de las curvas de llegada procedentes de ensayos de trazadores es una de las metodologías habituales para la obtención de parámetros hidráulicos. En cualquier interpretación de un ensayo, loe parámetros estimados dependerán del modelo conceptual adoptado. Intuitivamente, la inclusión conceptual de diferentes modelos debería dar lugar a curvas con una apariencia muy distinta, lo que a su vez supondría unos momentos estadísticos de la curva de llegada muy distintos. Por el contrarío, en este articulo se muestra que la utilización de algunos modelos conceptuales habituales y en apariencia muy distintos dan lugar e momentos estadísticos virtualmente idénticos en cuanto e su variación con respecto e la distancia o el tiempo recorrido por el soluto. Loe modelos presentados corresponden a: (1) la ecuación de advección dispersión clásica IADEI con un término macrodispersivo de tipo Fickiano: 121 un medio homogéneo con un término de transferencia de masa entre la fase móvil y la matriz rocosa (fase inmóvil) dentro de la cual el soluto presenta transporte difusivo; y 131 el transporte de un soluto que experimente reacciones de adsorción con cinética de equilibrio. En los tres modelos estudiados loe primeros tres momentos de la curva de llegada son lineales con la distancia, mientras que el término dominante del momento de cuarto orden es cuadrático. Este similar comportamiento permite encontrar pare cede modelo conceptual un conjunto de parámetros de modo que reproduzcan de manera similar une curva de llegada concrete. Esto supone un problema importante de identificabilidad de parámetros cuando se usen datos procedentes de une única curve de llegada, puesto que por le apariencia de le curve no seré posible deducir cuáles han sido los procesos dominantes o, por lo menos, descartar alguno de loe procesos posibles. En cualquier ejemplo real será necesario recurrir e información externa pera identificar loe procesos relevantes que han dedo forme e le curva de llegada
Abstract
El análisis de las curvas de llegada procedentes de ensayos de trazadores es una de las metodologías habituales para la obtención de parámetros [...]
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Mean travel time of conservative solutes in randomly heterogeneous unbounded domains under mean uniform flow
A. Guadagnini, X. Sánchez-Vila, M. Riva, M. Simoni

Water Resources Research (2003). Vol. 39 (3), pp. 1-5

Abstract
We derive a closed‐form expression for mean travel time of a conservative solute migrating under uniform in the mean flow conditions within an infinite stationary field with simple exponential correlation of the natural logarithm of hydraulic conductivity. Our expression is developed from a consistent second‐order expansion in σY (standard deviation of the log hydraulic conductivity) of the equations for moments of travel time and trajectories of conservative solutes in two‐dimensional randomly nonuniform flows of Guadagnini et al. [2001]. As such, it is nominally valid for moderately heterogeneous fields, with σY2 < 1. Its validity for larger heterogeneity degrees is tested against numerical Monte Carlo simulations. Our results clarify the nonlinear effect in the mean travel time with respect to distance that has been observed numerically (and modeled empirically) in the literature.
Abstract
We derive a closed‐form expression for mean travel time of a conservative solute migrating under uniform in the mean flow conditions within an infinite stationary field [...]
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Travel time moments for sorbing solutes in heterogeneous domains under nonuniform flow conditions
X. Sánchez-Vila, Y. Rubin

Water Resources Research (2003). Vol. 39 (4), pp. 1-13

Abstract
A methodology for evaluating the unconditional and conditional moments of travel time for a sorbing solute is presented. The approach is applicable for any flow configuration and for a wide range of mass transfer rate‐limited linear processes. The methodology is applicable to the general case of spatially variable hydrological and chemical parameters. The sorption model used to derive the temporal moments is that of a continuous distribution of mass rate coefficients [Haggerty and Gorelick, 1998]. Models such as instantaneous equilibrium, first‐order and two‐site sorption kinetics, among others, can be considered as particular cases of this general model. Using a deterministic approach, the low‐order moments of the breakthrough curves for reactive solutes can be obtained as a function of those for conservative tracers. Using a stochastic approach, the unconditional low‐order statistics of the travel time moments can be obtained. These moments depend on the statistics of two Lagrangian functions, the travel time for a conservative solute, and an integral of the variations of the chemical parameters weighted by the inverse local velocity along the trajectory. Finally, conditional temporal moments are derived. Moments can be conditioned to any type of information, hard or soft, hydraulic or geochemical. Conditioning is found to reduce uncertainty, characterized by a reduction in the variance of the travel time. The general results are particularized for both uniform in the mean and convergent flow conditions and for simple sorption models such as linear instantaneous equilibrium and first‐order kinetics. In all such cases, close‐form results, based on small perturbations expansions, are presented for the travel time moments.
Abstract
A methodology for evaluating the unconditional and conditional moments of travel time for a sorbing solute is presented. The approach is applicable for any flow configuration [...]
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Conditional moments of the breakthrough curves of kinetically sorbing solute in heterogeneous porous media using multirate mass transfer models for sorption and desorption
A. Lawrence, X. Sánchez-Vila, Y. Rubin

Water resources research (2002). Vol. 38 (11), pp. 1-12

Abstract
A methodology is presented for evaluating the temporal moments of solutes undergoing linear rate‐limited mass transfer processes based on a Lagrangian approach to solute transport in heterogeneous media. The temporal moments of sorbing solutes are written as a function of those of conservative tracers. The general continuous diffusion rate model that has recently appeared in the hydrologic literature is used to model the rate‐limited mass transfer processes. The methodology is also applied to desorption from an initially uniformly contaminated aquifer, and the concentration expected value and variance are found quasi‐analytically. The conditional temporal moments of sorbing solutes can be written as a function of the conditional moments of conservative tracers. Conditioning results in a reduction of the variance of travel time. The amount of reduction depends on the chemical model selected
Abstract
A methodology is presented for evaluating the temporal moments of solutes undergoing linear rate‐limited mass transfer processes based on a Lagrangian approach to solute [...]
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Using Geostatistical Analysis to Evaluate the Presence of Rotylenchulus reniformis in Cotton Crops in Brazil: Economic Implications.
P. Farias, X. Sánchez-Vila, J. Barbosa, S. Vieira, L. Ferraz, J. Delfín

Journal of nematology (2002). Vol. 34 (3), pp. 232-238

Abstract
In recent years, the productivity of cotton in Brazil has been progressively decreasing, often the result of the reniform nematode Rotylenchulus reniformis. This species can reduce crop productivity by up to 40%. Nematodes can be controlled by nematicides but, because of expense and toxicity, application of nematicides to large crop areas may be undesirable. In this work, a methodology using geostatistics for quantifying the risk of nematicide application to small crop areas is proposed. This risk, in economic terms, can be compared to nematicide cost to develop an optimal strategy for Precision Farming. Soil (300 cm(3)) was sampled in a regular network from a R. reniformis-infested area that was a cotton monoculture for 20 years. The number of nematodes in each sample was counted. The nematode number per volume of soil was characterized using geostatistics, and 100 conditional simulations were conducted. Based on the simulations, risk maps were plotted showing the areas where nematicide should be applied in a Precision Farming context. The methodology developed can be applied to farming in countries that are highly dependent on agriculture, with useful economic implications.
Abstract
In recent years, the productivity of cotton in Brazil has been progressively decreasing, often the result of the reniform nematode Rotylenchulus reniformis. This species can [...]
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Convergent-flow tracer tests in heterogeneous media: combined experimental–numerical analysis for determination of equivalent transport parameters
D. Fernàndez-García, X. Sánchez, T. Illangasekare

Journal of Contaminant Hydrology (2002). Vol. 57 (1-2), pp. 129-145

Abstract
In modeling transport within naturally heterogeneous aquifers, it is usually assumed that the transport equations valid at local scales can also be applied at larger scales. At larger scales, the heterogeneous domain is represented by an equivalent homogeneous medium. Convergent-flow tracer tests constitute one of the most frequently used field tests to estimate effective input parameters of equivalent homogeneous aquifers. Traditionally, statistical approaches applied to groundwater flow and solute transport have provided tools to estimate these equivalent parameters. These approaches are based on a number of simplifications including the assumption that the point transmissivity values follow a multilog-normal random function. Several investigators have found that this assumption may not be valid in many field cases. In order to study the applicability of the equivalent homogeneous formulation in a nontraditional stochastic field, a number of experimental and numerical studies were conducted. The results are used to determine the apparent values of porosity and dispersivity that would be obtained if convergent-flow tracer tests were conducted in a deterministically generated heterogeneous transmissivity field displaying anisotropy in the correlation structure. It is shown that in this particular heterogeneous media, apparent porosity strongly depends on connectivity rather than on transmissivity. This dependence on connectivity questions the theoretical results obtained in continuum equivalent fields to estimate effective porosity.
Abstract
In modeling transport within naturally heterogeneous aquifers, it is usually assumed that the transport equations valid at local scales can also be applied at larger [...]
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Simulation of Gas Dipole Tests in Fractures at the Intermediate Scale Using a New Upscaling Method
H. Ramajo, S. Olivella, J. Carrera, X. Sánchez-Vila

Transport in porous media (2002). Vol. 46 (2-3), pp. 269-284

Abstract
A high-level radioactive waste disposal site may lead to gas generation by different physical mechanisms. As these sites are to be located in areas with low water flow, any small amount of gas can lead to relative high gas pressures, so that multiphase flow analysis becomes relevant. The movement of gas and water through the system has two important implications. Firstly, water flow takes place in unsaturated conditions, and thus travel times of the radioactive particles transported are affected; and secondly, gas can also carry radioactive particles. Therefore, one of the key points in such studies is the time when gas would break through the biosphere under a number of different flow conditions. In fractured zones, gas would flow preferentially through the most conductive features. We consider a two-dimensional system representing an isolated fracture. In each point we assign a local porosity and permeability and a local pressure-saturation relationship. A dipole (injector-producer) gas flow system is generated and the variation in water saturation is studied. A simple method is proposed for obtaining upscaled values for several parameters involved in two-phase flow. It is based on numerical simulation on a block scale assuming steady-state conditions and absence of capillary pressure gradients. The proposed method of upscaling is applied to simulate a dipole test using a coarser grid than that of the reference field. The comparison between the results in both scales shows an encouraging agreement
Abstract
A high-level radioactive waste disposal site may lead to gas generation by different physical mechanisms. As these sites are to be located in areas with low water flow, any [...]
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Geostatistical analysis of the spatial distribution of Rotylenchulus reniformis on cotton cultivated under crop rotation
P. Farias, J. Barbosa, S. Vieira, X. Sánchez-Vila

Russian Journal of Nematology (2002). Vol. 10 (9), pp. 1-9

Abstract
The spatial distribution of Rotylenchulus reniformis on cotton cultivated in crop rotation with sorghum-peanut-velvetbean was studied using geostatistics. The experimental field, which had been continuously cropped with cotton during 20 years, comprised two 32 x 48 m-grids, each divided in sixty-four 4 x 6 m sampling plots. For all crops, 300 cm 3 of soil samples were taken at the center of each plot at crop germination (Pi) and again at harvest (Pf), from which the numbers of nematodes were determined. The results revealedthat the spatial distribution of R. reniformis was highly aggregated and with the aid of the geostatistical techniques the nematode intensities were mapped and the risk areas accurately identified. Consequently, geostatistics is here considered a useful tool for planning nematode control strategies, particularly in Precision Agriculture.
Abstract
The spatial distribution of Rotylenchulus reniformis on cotton cultivated in crop rotation with sorghum-peanut-velvetbean was studied using geostatistics. The experimental [...]
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Solute transport in heterogeneous media: the impact of anisotropy and non-ergodicity in risk assessment
J. Delfín, X. Sánchez-Vila

Stochastic environmental research and risk assessment (1999). Vol. 13 (5), pp. 365-379

Abstract
Conceptual model selection is a key issue in risk assessment studies. We analyze the effect of a number of conceptual aspects related to solute transport in two-dimensional heterogeneous media. The main issues addressed are non-ergodicity, anisotropy in the correlation structure of the transmissivity field, and dispersion at the local scale. In particular, we study the development of a solute plume when mean flow is oriented at an angle with respect to the principal directions of anisotropy. The study is carried out in a Lagrangian framework using Monte Carlo analysis. Of special interest is the evolution of individual plumes. A number of aspects are analyzed, namely the location of the center of mass for each plume and the different ways to compute the angles that the main axes of the plume develop with respect to the direction of the mean flow. Stochastic theories based upon ergodicity conclude that the plume gets oriented in the mean flow direction. In our non-ergodic simulations, the mean of the offset angles, for each individual plume in each particular realization, is offset from the mean flow direction towards the direction of maximum anisotropy. If, instead, the analysis is performed on the ensemble plume (superposition of all different simulations), it is then found oriented closer to the direction of the mean flow than the average offset angle for the different plumes considered separately. This last result adds an extra word of caution to the use of ensemble averaged values in solute transport studies. Serious implications for risk assessment follow from the conceptual model adopted. First, in any single realization there will a large uncertainty in locating the plume at any given time; second, real dilution would be less than what would be expected if the macrodispersion values obtained for ergodic conditions were applied; third, the volume that is affected by a non-zero concentration is smaller than that predicted from macrodispersion concepts; fourth, the orientation of the plume does not correspond to that of the mean flow; and fifth, accounting for local dispersion helps reducing uncertainty.
Abstract
Conceptual model selection is a key issue in risk assessment studies. We analyze the effect of a number of conceptual aspects related to solute transport in two-dimensional [...]
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Sobre la interpretación de ensayos hidráulicos en acuíferos no homogéneos
P. Meier, X. Sánchez-Vila, J. Carrera

Boletín geológico y minero (2000). Vol. 111 (4), pp. 69-82

Abstract
La obtención de parámetros hidráulicos de un acuífero suele realizarse a partir de la interpretación de ensayos hidráulicos con condiciones de flujo radial convergente. El objetivo de este artículo es ver como las fórmulas habituales de la hidráulica de pozos se pueden extender para incluir explícitamente la heterogeneidad del medio, y más importante, que los valores que se obtienen de la interpretación de ensayos en medios heterogéneos son valores representativos del medio y con un claro significado e interés hidrogeológico. Para ello es preciso relacionar la transmisividad deducida de ensayos de bombeo con la heterogeneidad natural. Esto se ha realizado analítica y numéricamente. El resultado, que coincide con las observaciones de campo, es que cuando existen varios puntos de observación, la transmisividad (T) deducida por el método de Jacob tiende a ser la misma para todos los puntos de observación. Más importante, dicha transmisividad es, bajo condiciones muy generales, igual a la T efectiva, es decir, a la que controla el flujo natural bajo condiciones de gradiente uniforme. Esto apoya la metodología que han venido usando tradicionalmente los hidrogeólogos
Abstract
La obtención de parámetros hidráulicos de un acuífero suele realizarse a partir de la interpretación de ensayos hidráulicos con condiciones [...]
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Gestión de las aguas subterráneas en zonas urbanas. conceptualización y modelización: aplicación a barcelona (españa)
E. Vázquez-Suñé, X. Sánchez-Vila, J. Carrera

Series de correlación geológica (1999). pp. 41-49

Abstract
Availability and quality of groundwater resources is seriously affected by urbanization in many large cities. This leads to significant social, environmental, economical, and political implications. Any urban hydrology study requires a detailed analysis of water fluxes flowing in and out of the system, including their magnitude and relative importance. Analyzing the quality of the resources is another key issue. In any real case study one has to face at least three aspects: (1) process identification, (2) aquifer characterization, and (3) water resources management. This methodology has been applied to the city of Barcelona. The outcome is a groundwater model that allows defining, characterizing, and quantifying the potential risk of aquifers, both on urban structures, and upon population. In this sense, it may become a management tool. This is an important step towards convincing city managers to consider groundwater as one of the topics to be taken into account in city planning.
Abstract
Availability and quality of groundwater resources is seriously affected by urbanization in many large cities. This leads to significant social, environmental, economical, [...]
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A Numerical Study on the Relationship Between Transmissivity and Specific Capacity in Heterogeneous Aquifers
P. Meier, J. Carrera, X. Sánchez-Vila

Ground water (1999). Vol. 37 (4), pp. 611-617

Abstract
Specific capacity (Q/s) data are usually much more abundant than transmissivity (T) data. Theories which assume uniform transmissivity predict a nearly linear relationship between T and Q/s. However, linear dependence is seldom observed in field studies. Since hydrogeologic studies usually require T data, many hydrogeologists use linear regression analysis of T versus Q/s data to estimate T values where only Q/s data are available. In this paper we use numerical models to investigate the effects of aquifer heterogeneity on the relationship between Q/s and T estimates. The simulations of hydraulic tests in heterogeneous media show that estimates of T derived using Jacob's method tend to their late‐time effective value much faster than Q/s values. The latter are found to be more dependent upon local transmissivities near the well. This explains why the regression parameters for T versus Q/s data depend on heterogeneity and the‘lateness’of the test period analyzed. Since this effect is more marked in high T zones than in low T zones, we conclude that natural aquifer heterogeneity can explain the convex deviation from linearity often observed in the field. A further result is that the geometric mean of T estimates, obtained from short and intermediate time pumping tests, seems to systematically underestimate effective T (Teff) of heterogeneous aquifers. In the studied simulation cases, the median of the T values or the arithmetic mean yield better estimates for Teff
Abstract
Specific capacity (Q/s) data are usually much more abundant than transmissivity (T) data. Theories which assume uniform transmissivity predict a nearly linear relationship [...]
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Pumping tests in heterogeneous aquifers: An analytical study of what can be obtained from their interpretation using Jacob's Method
X. Sánchez-Vila, P. Meier, J. Carrera

Water Resources Research (1999). Vol. 35 (4), pp. 943-952

Abstract
Interpretation of pumping tests to estimate hydraulic parameter values is typically based on the assumption of aquifer homogeneity. The applicability of the traditional methods of interpretation in real aquifers can be questioned, since the evaluation of the drawdown curves observed at different locations in a single test may not result in one consistent set of hydraulic parameters. Thus most hydrogeologists tend to look at estimated transmissivities (T) as some average property of the medium, while estimated storativities (S) are disregarded in some cases, particularly when they are obtained from data measured at the pumping well. An analytical study of drawdown under radially convergent flow toward a single point in heterogeneous aquifers shows that large time drawdown values form a straight line on a drawdown versus log time plot. Jacob's method consists of obtaining estimates for T and S from the slope and intercept of this line. We find that even in a heterogeneous field, these estimates provide valuable information about the aquifer. Estimated T values for different observation points tend to converge to a single value, which corresponds to the effective T derived under parallel flow conditions. Estimated storativities, however, display higher variability, but the geometric mean of the Sest values can be used as an unbiased estimator of the actual S. Thus it appears that although Jacob's method was originally derived for homogeneous media, it can provide valuable information in real aquifers
Abstract
Interpretation of pumping tests to estimate hydraulic parameter values is typically based on the assumption of aquifer homogeneity. The applicability of the traditional [...]
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Upscaling transmissivity under radially convergent flow in heterogeneous media
X. Sánchez-Vila, C. Axness, J. Carrera

Water Resources Research (1999). Vol. 104 (3), pp. 613-621

Abstract
Most field methods used to estimate transmissivity values rely on the analysis of drawdown under convergent flow conditions. For a single well in a homogeneous and isotropic aquifer and under steady state flow conditions, drawdown s is directly related to the pumping rate Q through transmissivity T. In real, nonhomogeneous aquifers, s and Q are still directly related, now through a value called equivalent transmissivity Teq. In this context, Teq is defined as the value that best fits Thiem's equation and would, for example, be the transmissivity assigned to the well location in the classical interpretation of a steady state pumping test. This equivalent or upscaled transmissivity is clearly not a local value but is some representative value of a certain area surrounding the well. In this paper we present an analytical solution for upscaling transmissivities under radially convergent steady state flow conditions produced by constant pumping from a well of radius rw in a heterogeneous aquifer based upon an extension of Thiem's equation. Using a perturbation expansion, we derive a second‐order expression for Teq given as a weighted average of the fluctuations in log T throughout the domain. This expression is compared to other averaging formulae from the literature, and differences are pointed out. Teq depends upon an infinite series which may be expressed in terms of coefficients of the finite Fourier transform of the log transmissivity function. Sufficient conditions for convergence of this series are examined. Finally, we show that our solution agrees with existing analytical ones to second order and test the solution with a numerical example
Abstract
Most field methods used to estimate transmissivity values rely on the analysis of drawdown under convergent flow conditions. For a single well in a homogeneous and isotropic [...]
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An evaluation of Jacob's Method for the interpretation of pumping tests in heterogeneous formations
P. Meier, J. Carrera, X. Sánchez-Vila

Water Resources Research (1995). Vol. 34 (5), pp. 1011-1025

Abstract
Most pumping tests are interpreted using the classical Theis assumption of large‐scale homogeneity with various corrections to account for early time behavior of drawdown curves. When drawdowns are plotted versus log time, late time data often delineate a straight line, which is consistent with Jacob's approximation of Theis' solution but may seem surprising in view of the heterogeneity of natural media. The aim of our work is to show that Jacob's method leads to a good approximation of the effective transmissivity of heterogeneous media when constrained to late time data. A review of several multiwell pumping tests demonstrates that when drawdown curves from each observation well are interpreted separately, they produce very similar transmissivity T estimates. However, the corresponding estimates for storativity span a broad range. This behavior is verified numerically for several models of formation heterogeneity. A very significant finding of the numerical investigation is that T values estimated using simulated drawdown from individual observation wells are all very close to the effective T value for parallel flow. This was observed even in nonmultiGaussian T fields, where high T zones are well connected and where the effective T is larger than the geometric average of point values. This implies that Jacob's method can be used for estimating effective T values in many, if not most, formations.
Abstract
Most pumping tests are interpreted using the classical Theis assumption of large‐scale homogeneity with various corrections to account for early time behavior of drawdown [...]
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On matrix diffusion: formulations, solution methods and qualitative effects
J. Carrera, X. Sánchez-Vila, I. Benet, A. Medina, G. Galarza, J. Guimerà

Journal of Hydrology (1997). Vol. 6, pp. 178-190

Abstract
Matrix diffusion has become widely recognized as an important transport mechanism. Unfortunately, accounting for matrix diffusion complicates solute-transport simulations. This problem has led to simplified formulations, partly motivated by the solution method. As a result, some confusion has been generated about how to properly pose the problem. One of the objectives of this work is to find some unity among existing formulations and solution methods. In doing so, some asymptotic properties of matrix diffusion are derived. Specifically, early-time behavior (short tests) depends only on φ m 2 R m D m / L m 2, whereas late-time behavior (long tracer tests) depends only on φ m R m , and not on matrix diffusion coefficient or block size and shape. The latter is always true for mean arrival time. These properties help in: (a) analyzing the qualitative behavior of matrix diffusion; (b) explaining one paradox of solute transport through fractured rocks (the apparent dependence of porosity on travel time); (c) discriminating between matrix diffusion and other problems (such as kinetic sorption or heterogeneity); and (d) describing identifiability problems and ways to overcome them.
Abstract
Matrix diffusion has become widely recognized as an important transport mechanism. Unfortunately, accounting for matrix diffusion complicates solute-transport simulations. [...]
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