Advection-diffusion in spatially random flows: Formulation of concentration covariance

Kapoor, Vivek; Kitanidis, Peter K.

doi:10.1007/bf02427926

Cited by 21 publications

(11 citation statements)

References 21 publications

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“…Since this pdf is positively skewed along the mean flow direction, a higher variance results in the upstream position. This loss of symmetry is not evidenced from Eulerian analyses (e.g., Kapoor and Kitanidis, 1997).…”

Section: Non-linear Analysismentioning

confidence: 91%

Analysis of Concentration as Sampled in

Caroni¹,

Fiorotto²

2005

Transp Porous Med

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The aim of this paper is to analyze the statistical properties of solute concentration in natural aquifers as sampled in observation wells, having a small diameter in comparison with the characteristic size of the heterogeneity in hydraulic properties. The analysis, in Langragian framework, takes advantage of the ''reverse formulation'', where, instead of considering the destination of the injected particles, the origin of the particle being sampled is sought. In the case of small values of the log-conductivity variance ' 2 Y , it allows the derivation of an analytical expression for concentration mean, variance and pdf, while for aquifer characterized by high value in ' 2 Y , a numerical analysis based on a Monte Carlo approach using a reverse scheme is developed and applied for values of ' 2 Y up to 2. In this case, the use of a Beta function to fit the concentration pdf proves valid for practical applications. The comparison between the numerical and the analytical results defines the range of validity of the analytical ones. The relative role of large-scale dispersion processes and pore-scale effects is analyzed in terms of global variance in order to point out limits and accuracy of the Eulerian scheme in comparison with the Lagrangian one.

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Section: Non-linear Analysismentioning

confidence: 91%

Analysis of Concentration as Sampled in

Caroni¹,

Fiorotto²

2005

Transp Porous Med

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“…This clearly limits the applicability of stochastic methods in subsurface hydrology (Ginn 2004;Sirin 2006). Thus, the analysis of the associated non-stationary random field through the transformation into stationarity is a key point in this context (Kapoor and Kitanidis 1997;Kabala 1997).…”

Section: Introductionmentioning

confidence: 98%

On the non-reducibility of non-stationary correlation functions to stationary ones under a class of mean-operator transformations

Porcu

Matkowski

Mateu

2009

Stoch Environ Res Risk Assess

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Some special functional equations involving means and related to a problem of reducibility of some classes of correlation functions are considered. We show some characterizations of the reducibility problem under several choices of the mean operators and different weak regularity assumptions imposed on the involving functions. We find that mean-generated correlation functions are completely irreducible, in the sense that, for this broad class of correlation functions, there does not exist a nontrivial solution associated to the Perrin-Senoussi problem.

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“…Theoretical studies on the field-scale nonreactive solute transport process have been carried out within the Eulerian framework (e.g. Gelhar and Axness, 1983;Neuman et al, 1987;Graham and McLaughlin, 1989;Vomvoris and Gelhar, 1990;Rehfeldt and Gelhar, 1992;Neuman, 1993;Kabala and Sposito, 1994;Kappor and Gelhar, 1994;Rajaram and Gelhar, 1995;Kapoor and Kitanidis, 1997;Guadagnini and Neuman, 1999a;Neuweiler et al, 2001;Cirpka andAttinger, 2003, Attinger et al, 2004;Morales-Casique et al, 2006;Chang and Yeh, 2007;Schwede et al, 2008).…”

Section: Introductionmentioning

confidence: 99%

Stochastic analysis of field-scale heat advection in heterogeneous aquifers

Chang

Yeh

2012

Hydrol. Earth Syst. Sci.

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Abstract. Owing to the analogy between the solute and heat transport processes, it can be expected that the rate of growth of the spatial second moments of the heat flux in a heterogeneous aquifer over relatively large space scales is greater than that predicted by applying the classical heat transport model. The motivation of stochastic analysis of heat transport at the field scale is therefore to quantify the enhanced growth of the field-scale second moments caused by the spatially varying specific discharge field. Within the framework of stochastic theory, an effective advection-dispersion equation containing effective parameters (namely, the macrodispersion coefficients) is developed to model the mean temperature field. The rate of growth of the field-scale spatial second moments of the mean temperature field in the principal coordinate directions is described by the macrodispersion coefficient. The variance of the temperature field is also developed to characterize the reliability to be anticipated in applying the mean heat transport model. It is found that the heterogeneity of the medium and the correlation length of the log hydraulic conductivity are important in enhancing the field-scale heat advection, while the effective thermal conductivity plays the role in reducing the field-scale heat advection.

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Advection-diffusion in spatially random flows: Formulation of concentration covariance

Cited by 21 publications

References 21 publications

Analysis of Concentration as Sampled in

Analysis of Concentration as Sampled in

On the non-reducibility of non-stationary correlation functions to stationary ones under a class of mean-operator transformations

Stochastic analysis of field-scale heat advection in heterogeneous aquifers

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