Nonlocal and localized analyses of nonreactive solute transport in bounded randomly heterogeneous porous media

Persistent Link:
http://hdl.handle.net/10150/280728
Title:
Nonlocal and localized analyses of nonreactive solute transport in bounded randomly heterogeneous porous media
Author:
Morales-Casique, Eric
Issue Date:
2004
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
Solute transport in randomly heterogeneous media is described by stochastic transport equations that are typically solved by Monte Carlo simulation. A promising alternative is to solve a corresponding system of statistical moment equations directly. The moment equations are generally integro-differential and include nonlocal parameters depending on more than one point in space-time [Neuman, 1993; Zhang and Neuman, 1996; Guadagnini and Neuman, 2001]. We present recursive approximations, and a numerical algorithm, that allow computing lead ensemble moments of non-reactive solute transport in bounded, randomly heterogeneous media. Our recursive equations are formally valid for mildly heterogeneous aquifers with σ²ᵧ < 1, where σ²ᵧ is a measure of log-hydraulic conductivity variance, or well-conditioned highly heterogeneous aquifers. Our algorithm utilizes a finite element Laplace transform method (FELT) valid for steady state velocity fields. We solved the recursive moment equations up to second order in σᵧ. We also present an iterative improvement of the recursive equations which allows reaching a solution of order higher than two in σᵧ but does not reach third order accuracy because we do not include third order moments in the computations. Computational results in two spatial dimensions conditioned on synthetic measurements of K , hydraulic conductivity, compare well with Monte Carlo results for σ²ᵧ and Peclet number (in terms of the integral scale of K) as high as 0.3 and 100 respectively for the iterative approach. As these parameters increase, the quality of our iterative moment solution deteriorates. Without conditioning the quality of the solution deteriorates more rapidly as dimensionless time increases. The recursive solution without iteration is much less accurate and deteriorates more rapidly as σ²ᵧ , Peclet number, and/or dimensionless time increase. We infer that this loss in accuracy is due to higher order moments which become important as σ²ᵧ , dimensionless time, and/or Pe increase. We also evaluate a space-localized moment equation and show that the quality of its solution is of inferior accuracy than the iterative solution. In terms of computational efficiency, the recursive and iterative methods require less CPU time than Monte Carlo transport simulations using the same numerical solution method (FELT) and without parallelization.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Hydrology.; Environmental Sciences.; Engineering, Environmental.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Hydrology and Water Resources
Degree Grantor:
University of Arizona
Advisor:
Neuman, Shlomo P.

Full metadata record

DC FieldValue Language
dc.language.isoen_USen_US
dc.titleNonlocal and localized analyses of nonreactive solute transport in bounded randomly heterogeneous porous mediaen_US
dc.creatorMorales-Casique, Ericen_US
dc.contributor.authorMorales-Casique, Ericen_US
dc.date.issued2004en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractSolute transport in randomly heterogeneous media is described by stochastic transport equations that are typically solved by Monte Carlo simulation. A promising alternative is to solve a corresponding system of statistical moment equations directly. The moment equations are generally integro-differential and include nonlocal parameters depending on more than one point in space-time [Neuman, 1993; Zhang and Neuman, 1996; Guadagnini and Neuman, 2001]. We present recursive approximations, and a numerical algorithm, that allow computing lead ensemble moments of non-reactive solute transport in bounded, randomly heterogeneous media. Our recursive equations are formally valid for mildly heterogeneous aquifers with σ²ᵧ < 1, where σ²ᵧ is a measure of log-hydraulic conductivity variance, or well-conditioned highly heterogeneous aquifers. Our algorithm utilizes a finite element Laplace transform method (FELT) valid for steady state velocity fields. We solved the recursive moment equations up to second order in σᵧ. We also present an iterative improvement of the recursive equations which allows reaching a solution of order higher than two in σᵧ but does not reach third order accuracy because we do not include third order moments in the computations. Computational results in two spatial dimensions conditioned on synthetic measurements of K , hydraulic conductivity, compare well with Monte Carlo results for σ²ᵧ and Peclet number (in terms of the integral scale of K) as high as 0.3 and 100 respectively for the iterative approach. As these parameters increase, the quality of our iterative moment solution deteriorates. Without conditioning the quality of the solution deteriorates more rapidly as dimensionless time increases. The recursive solution without iteration is much less accurate and deteriorates more rapidly as σ²ᵧ , Peclet number, and/or dimensionless time increase. We infer that this loss in accuracy is due to higher order moments which become important as σ²ᵧ , dimensionless time, and/or Pe increase. We also evaluate a space-localized moment equation and show that the quality of its solution is of inferior accuracy than the iterative solution. In terms of computational efficiency, the recursive and iterative methods require less CPU time than Monte Carlo transport simulations using the same numerical solution method (FELT) and without parallelization.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectHydrology.en_US
dc.subjectEnvironmental Sciences.en_US
dc.subjectEngineering, Environmental.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.disciplineHydrology and Water Resourcesen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorNeuman, Shlomo P.en_US
dc.identifier.proquest3158131en_US
dc.identifier.bibrecord.b48137765en_US
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