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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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