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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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• 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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