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Assessment of uncertainty associated with the estimation of well catchments by moment equations
No full textNon-local stochastic moment equations are used successfully to analyze groundwater flow in randomly heterogeneous media.
Here we present a moment equations-based approach to quantify the uncertainty associated with the estimation of well catchments.
Our approach is based on the development of a complete second order formalism which allows obtaining the first statistical moments of the trajectories of conservative solute particles advected in a generally non-uniform groundwater flow. Approximate equations of moments of particles trajectories are then derived on the basis of a second order expansion in terms of the standard deviation of the aquifer log hydraulic conductivity. Analytical expressions are then obtained for the predictors of locations of mean stagnation points, together with their associated uncertainties. We implement our approach on heterogeneous media in bounded two-dimensional domains, with and without including the effect of conditioning on hydraulic conductivity information. The impact of domain size, boundary conditions, heterogeneity and non-stationarity of hydraulic conductivity on the prediction of a well catchment is explored. The results are compared against Monte Carlo simulations and semi-analytical solutions available in the literature. The methodology is applicable to both infinite and bounded domains and is free of distributional assumptions (and so applies to both Gaussian and non-Gaussian log hydraulic conductivity fields) and formally includes the effect of conditioning on available information
Impact of the choice of the variogram model on flow and travel time predictors in radial flows
No full textPrediction of hydraulic head, flux and contaminant travel time/trajectories in natural aquifers is uncertain due to the geologic media complexity and lack of information. Hence it is appropriate to cast the equations that govern groundwater flow and contaminant transport within a stochastic framework. The latter is oriented towards rendering ensemble moments of the analyzed quantities. In this view the spatial variable transmissivity is usually modeled as a Stochastic Continuum, characterized by a set of parameters (covariance shape, geometric mean, variance and correlation length). These are generally assumed to be known with certainty even though they are usually derived using a limited amount of experimental data, which are often not enough for a complete characterization.
Full-Bayesian approaches (e.g. Woodbury and Rubin 2000; Woodbury and Ulrych 2000) take into account the uncertainty in the knowledge of the variogram parameters (geometric mean, variance and correlation length). Feyen et al. (2002) illustrate an application of these methodologies to determine the uncertainty asso-ciated with the delineation of well capture zones. Hendricks Franssen et al. (2002) investigate the impact of the uncertainty of variogram parameters on the same topic using sequential Gaussian simulation (Gómez-Hernández and Journel 1993) to generate transmissivity fields and the sequential self-calibrated method for in-verse conditioning. In all these works the shape of the correlation structure of the natural logarithm of transmissivity is fixed and assumed known without uncertainty. Salandin and Rinaldo (1989) analyze the influence of the form of the log-conductivity covariance on dispersion coefficients in random permeability fields under mean uniform flow conditions.
Here, we focus on the impact of the choice of the functional form for the log-transmissivity variogram on (ensemble) moments of hydraulic head and contami-nant residence time under convergent flow conditions, such as those created by a single pumping well.
Although of high relevance in practical applications, problems associated to contaminant transport in the vicinity of extraction wells in heterogeneous media have been tackled only recently (e.g. Guadagnini and Franzetti 1999, Riva et al. 1999, Dagan and Indelman 1999, van Leeuwen et al. 2000, Feyen et al. 2002).
We perform a numerical Monte Carlo analysis of (a) the predictors of hydraulic head and residence time (rendered by their means) for conservative solute particles injected at various radial distances from the well, and (b) the associated prediction errors (rendered by the variance of the state variables investigated).
The natural logarithm of aquifer transmissivity, Y, is modeled as a statistically homogeneous Gaussian random field. Three functional forms of the variogram (namely Exponential, Gaussian and Spherical), chosen amongst the most common models used in the literature, are considered. The impact of the choice of the variogram model on flow and travel time predictors is analyzed for different domain sizes in terms of correlation scale of Y (i.e. extent of the aquifer within which the effects of pumping are not negligible) and degrees of heterogeneity (in terms of the variance of Y )
Support Vector Machines for delineation of geologic facies from poorly differentiated data
No full textA procedure for the solution of multicomponent reactive transport problems
No full textModeling 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. 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
Mean travel time of conservative solutes in randomly heterogeneous unbounded domains under mean uniform flow
No full textWe 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 sY (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 sY < 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
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Utilizzo di dati idrogeologici per la stima dell’incertezza associata a zone di cattura di pozzi di estrazione.
No full textUna soluzione analitica del trasporto di soluti in presenza di reazioni di precipitazione/dissoluzione in acquiferi bi-dimensionali omogenei
No full textTravel time and trajectory moments of conservative solutes in two-dimensional convergent flows
No full textWe 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., Sanchez-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 sY (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
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