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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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