Concentration fluctuations in aquifer transport: a rigorous first-order solution and applications

Fiori, Aldo; Dagan, Gédéon

doi:10.1016/s0169-7722(00)00123-6

Cited by 131 publications

(233 citation statements)

References 15 publications

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“…(47)). We also note that (30) is the time derivative of the relation (15) of Fiori and Dagan [12], which, together with Remarks 4.1 and 4.2, proves the equivalence of Eulerian expressions for the ensemble and effective dispersion coefficients of Dentz et al [7,8] and the Lagragian expressions derived by Fiori and Dagan [12] and by Vanderborght [31] for the corresponding variances. We note here that the Eulerian approach has the important advantage of providing first-order approximations of the concentration fields (e.g., Eq.…”

Section: Explicit First-order Results For Transport In Aquiferssupporting

confidence: 72%

“…The opposite Fourier transform convention and the same homogeneity condition as in (22) change ik 1 U t into −ik 1 U t and let −k 2 Dt unchanged (see Remark 3). This is the case in the derivation of the variance Σ jj by Fiori and Dagan [12] (Eq. (14)), which is exactly the integral of (25) from above, with ik 1 U t replaced by −ik 1 U t .…”

Section: Explicit First-order Results For Transport In Aquifersmentioning

confidence: 94%

“…(14)), which is exactly the integral of (25) from above, with ik 1 U t replaced by −ik 1 U t . Dentz et al [7] used the same conventions as Fiori and Dagan [12], (i.e. Eqs.…”

Section: Explicit First-order Results For Transport In Aquifersmentioning

confidence: 99%

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Solute transport in aquifers with evolving scale heterogeneity

Suciu

Attinger

Radu

et al. 2015

Analele Universitatii "Ovidius" Constanta - Seria Matematica

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Transport processes in groundwater systems with spatially heterogeneous properties often exhibit anomalous behavior. Using first-order approximations in velocity fluctuations we show that anomalous superdiffusive behavior may result if velocity fields are modeled as superpositions of random space functions with correlation structures consisting of linear combinations of short-range correlations. In particular, this corresponds to the superposition of independent random velocity fields with increasing integral scales proposed as model for evolving scale heterogeneity of natural porous media [Gelhar, L. W. Water Resour. Res. 22 (1986), 135S-145S]. Monte Carlo simulations of transport in such multi-scale fields support the theoretical results and demonstrate the approach to superdiffusive behavior as the number of superposed scales increases. Lagrangian and Eulerian representations of diffusion in random velocity fieldsLet {X i,t = X i (t), i = 1, 2, 3, t ≥ 0} be the advection-dispersion process with a space variable drift V(x), sample of a statistically homogeneous random

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Section: Explicit First-order Results For Transport In Aquiferssupporting

confidence: 72%

Section: Explicit First-order Results For Transport In Aquifersmentioning

confidence: 94%

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Solute transport in aquifers with evolving scale heterogeneity

Suciu

Attinger

Radu

et al. 2015

Analele Universitatii "Ovidius" Constanta - Seria Matematica

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“…Starting from the work of Dagan (1989), several analytical solutions have been proposed rendering space-time distributions of (ensemble) mean and variance-covariance of concentrations or trajectories and time-of-residence of conservative solutes in multidimensional porous systems (Cvetkovic et al 1992;Kapoor and Gelhar 1994;Kapoor and Kitanidis 1998;Fiori and Dagan 2000;Vanderborght 2001;Guadagnini et al 2003;Sanchez-Vila and Guadagnini 2005;Riva et al 2006). All of these solutions rely on (different flavors of) the perturbation theory to provide approximations of governing equations and associated solutions.…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, the assessment of the state of an aquifer, based only on low order (statistical) moments, provides a picture which is at best incomplete in the context of risk and/or vulnerability assessment. In particular, Kapoor and Kitanidis (1998) and Fiori and Dagan (2000) showed that in unbounded formations under uniform mean flow conditions the coefficient of variation of the solute concentration is a non-monotonic function of travel time and reaches a maximum at a time linked with the time scale of processes characterizing pore-scale dispersion. In this sense, the interest lays in the knowledge of the extreme values where quantities such as concentration, travel time and/or trajectories can attain in a region of investigation.…”

Section: Introductionmentioning

confidence: 99%

Conditional Probability Density Functions of Concentrations for Mixing-Controlled Reactive Transport in Heterogeneous Aquifers

2008

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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 Math Geosci 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.

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First-order based cumulative distribution function for solute concentration in heterogeneous aquifers: Theoretical analysis and implications for human health risk assessment

Barros

Fiori

2014

Water Resour. Res.

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Quantifying the uncertainty of solute concentration in heterogeneous aquifers is an important step in both human health and ecological risk analysis. The need for a probabilistic representation of transport is justified by the incomplete characterization of the subsurface. We derive the one-point concentration cumulative distribution function (CDF) while taking into account the spatial statistical structure of the hydraulic conductivity, space dimensionality, the injection source size, the Peclet number, and the sampling volume at the monitoring location. The CDF is application oriented and derived at first order in the logconductivity variance. We illustrate how several key parameters control the shape of the concentration CDF. The CDF shape is important since it reflects both uncertainty and the dilution state of the plume. The transition from a bimodal to a unimodal CDF is examined and results are further supported by analyzing the concentration coefficient of variation. Results indicate the significance of the statistical anisotropy ratio (i.e., the ratio between the hydraulic conductivity correlation scales) in determining the CDF shape. The importance of the sampling volume in the tails of the concentration CDF and a comparison between the proposed model with the b-CDF approach (i.e., beta distribution) are also shown. Finally, we illustrate how the framework could be used in applications by evaluating the human health risk CDF. Our results are formally valid for low to moderate heterogeneous aquifers and source sizes small as compared to the hydraulic conductivity correlation length. The proposed approach can serve as a benchmark tool for other methods.

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Concentration fluctuations in aquifer transport: a rigorous first-order solution and applications

Cited by 131 publications

References 15 publications

Solute transport in aquifers with evolving scale heterogeneity

Solute transport in aquifers with evolving scale heterogeneity

Conditional Probability Density Functions of Concentrations for Mixing-Controlled Reactive Transport in Heterogeneous Aquifers

First-order based cumulative distribution function for solute concentration in heterogeneous aquifers: Theoretical analysis and implications for human health risk assessment

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