Concentration fluctuations and dilution in aquifers

Kapoor, Vivek; Kitanidis, Peter K.

doi:10.1029/97wr03608

Cited by 140 publications

(111 citation statements)

References 22 publications

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“…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%

“…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%

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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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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

2008

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“…One can develop an evolution equation for the productc AγcBγ , which is frequently done. [50][51][52] Although this shows that the evolution ofc AγcBγ depends upon the scalar dissipation rate, this in itself is not entirely helpful because one does not know the scalar dissipation rate a priori either. Additionally, the expression forc AγcBγ exhibits the typical hierarchy problem for nonlinear equations; thus, it is not technically possible to close and expression for this product without significant approximations.…”

Section: A Localization Of the Closure Problemsmentioning

confidence: 99%

A non-scale-invariant form for coarse-grained diffusion-reaction equations

Ostvar

Wood

2016

The Journal of Chemical Physics

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The process of mixing and reaction is a challenging problem to understand mathematically. Although there have been successes in describing the effective properties of mixing and reaction under a number of regimes, process descriptions for early times have been challenging for cases where the structure of the initial conditions is highly segregated. In this paper, we use the method of volume averaging to develop a rigorous theory for diffusive mixing with reactions from initial to asymptotic times under highly segregated initial conditions in a bounded domain. One key feature that arises in this development is that the functional form of the averaged differential mass balance equations is not, in general, scale invariant. Upon upscaling, an additional source term arises that helps to account for the initial configuration of the reacting chemical species. In this development, we derive the macroscopic parameters (a macroscale source term and an effectiveness factor modifying the reaction rate) defined in the macroscale diffusion-reaction equation and provide example applications for several initial configurations.

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“…Mixing processes in groundwater have not been investigated systematically, although their existence was noted in passing by Kitanidis [1994] and Kapoor and Kitanidis [1998a]. However, mixing phenomena, being important much earlier in the spreading of a solute plume than is dilution, create the complex plume-groundwater interface that enhances local dispersion processes [Ottino, 1991;Kitanidis, 1994;Kapoor and Kitanidis, 1998a].…”

Section: Paper Number 98wr02535mentioning

confidence: 99%

“…However, mixing phenomena, being important much earlier in the spreading of a solute plume than is dilution, create the complex plume-groundwater interface that enhances local dispersion processes [Ottino, 1991;Kitanidis, 1994;Kapoor and Kitanidis, 1998a]. In this paper we discuss basic concepts of plume mixing into groundwater, following the conceptual design of Ottino [1989, chapters 2 and 4; 1990], who considered fluid flows that were engineered to enhance mixing.…”

Section: Paper Number 98wr02535mentioning

confidence: 99%

Mixing and stretching efficiency in steady and unsteady groundwater flows

Weeks¹,

Sposito²

1998

Water Resources Research

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Abstract. Mixing is the physical process through which solute is spread into a fluid by the stretching and folding of material lines and surfaces. Mixing, as compared to dilution, is important to solute spreading by groundwater because it operates on much shorter timescales than does dilution, and it provides the increased plume boundary area and high local concentration gradients that promote effective solute dilution. In this paper, the mixing process is investigated theoretically for subsurface tracer plume movement, using as heuristic examples both steady and unsteady groundwater flows in a perfectly stratified aquifer whose properties mimic those of the sand aquifer at the Borden site. It is shown that the stretching efficiency, a parameter that characterizes the effectiveness of mixing, is largest at transitions between regions of highly contrasting hydraulic conductivity and, more broadly, that pronounced spatial variability in the hydraulic conductivity is conducive to good mixing because of the periodic resurgences in material line stretching that it causes. Unsteady groundwater flow resulting from a decrease in vertical groundwater flux with time leads to greater rates of material line stretching than do steady flows, whereas little difference from the steady flow case occurs for unsteady groundwater flow under a time-varying horizontal hydraulic head gradient. Overall, pronounced spatial variability in the hydraulic conductivity is the most important contributor to good mixing of a tracer solute plume, but highly effective mixing requires additional physical conditions that induce chaotic solute pathlines. IntroductionSolute plumes moving in aquifers are spread by two important but quite distinct physical processes. One is termed dilution, through which a plume is gradually distributed over an ever increasing volume of an aquifer to produce a reduction in solute concentration. Dilution is driven by local dispersion (i.e., dispersion processes occurring at the Darcy scale) and, secondarily, by complexity in plume shape, which serves to increase the plume boundary area through which solute mass can be transported dispersively. Kitanidis [1994]

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Concentration fluctuations and dilution in aquifers

Abstract: Abstract. The concentration of solute undergoing advection and local dispersion in a random hydraulic conductivity field is analyzed to quantify its variability and dilution.

Cited by 140 publications

References 22 publications

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

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

A non-scale-invariant form for coarse-grained diffusion-reaction equations

Mixing and stretching efficiency in steady and unsteady groundwater flows

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