Correspondence Between One- and Two-Equation Models for Solute Transport in Two-Region Heterogeneous Porous Media

Handle URI:
http://hdl.handle.net/10754/597886
Title:
Correspondence Between One- and Two-Equation Models for Solute Transport in Two-Region Heterogeneous Porous Media
Authors:
Davit, Y.; Wood, B. D.; Debenest, G.; Quintard, M.
Abstract:
In this work, we study the transient behavior of homogenized models for solute transport in two-region porous media. We focus on the following three models: (1) a time non-local, two-equation model (2eq-nlt). This model does not rely on time constraints and, therefore, is particularly useful in the short-time regime, when the timescale of interest (t) is smaller than the characteristic time (τ 1) for the relaxation of the effective macroscale parameters (i. e., when t ≤ τ 1); (2) a time local, two-equation model (2eq). This model can be adopted when (t) is significantly larger than (τ 1) (i.e., when t≫τ 1); and (3) a one-equation, time-asymptotic formulation (1eq ∞). This model can be adopted when (t) is significantly larger than the timescale (τ 2) associated with exchange processes between the two regions (i. e., when t≫τ 2). In order to obtain insight into this transient behavior, we combine a theoretical approach based on the analysis of spatial moments with numerical and analytical results in several simple cases. The main result of this paper is to show that there is only a weak asymptotic convergence of the solution of (2eq) towards the solution of (1eq ∞) in terms of standardized moments but, interestingly, not in terms of centered moments. The physical interpretation of this result is that deviations from the Fickian situation persist in the limit of long times but that the spreading of the solute is eventually dominating these higher order effects. © 2012 Springer Science+Business Media B.V.
Citation:
Davit Y, Wood BD, Debenest G, Quintard M (2012) Correspondence Between One- and Two-Equation Models for Solute Transport in Two-Region Heterogeneous Porous Media. Transport in Porous Media 95: 213–238. Available: http://dx.doi.org/10.1007/s11242-012-0040-y.
Publisher:
Springer Nature
Journal:
Transport in Porous Media
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
26-Jul-2012
DOI:
10.1007/s11242-012-0040-y
Type:
Article
ISSN:
0169-3913; 1573-1634
Sponsors:
Support from CNRS/GdR 2990 is gratefully acknowledged. The second author (BDW) was supported in part by the Office of Science (BER), U.S. Department of Energy, Grant No. DE-FG02-07ER64417. This publication was based on work supported in part by Award No KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorDavit, Y.en
dc.contributor.authorWood, B. D.en
dc.contributor.authorDebenest, G.en
dc.contributor.authorQuintard, M.en
dc.date.accessioned2016-02-25T12:58:21Zen
dc.date.available2016-02-25T12:58:21Zen
dc.date.issued2012-07-26en
dc.identifier.citationDavit Y, Wood BD, Debenest G, Quintard M (2012) Correspondence Between One- and Two-Equation Models for Solute Transport in Two-Region Heterogeneous Porous Media. Transport in Porous Media 95: 213–238. Available: http://dx.doi.org/10.1007/s11242-012-0040-y.en
dc.identifier.issn0169-3913en
dc.identifier.issn1573-1634en
dc.identifier.doi10.1007/s11242-012-0040-yen
dc.identifier.urihttp://hdl.handle.net/10754/597886en
dc.description.abstractIn this work, we study the transient behavior of homogenized models for solute transport in two-region porous media. We focus on the following three models: (1) a time non-local, two-equation model (2eq-nlt). This model does not rely on time constraints and, therefore, is particularly useful in the short-time regime, when the timescale of interest (t) is smaller than the characteristic time (τ 1) for the relaxation of the effective macroscale parameters (i. e., when t ≤ τ 1); (2) a time local, two-equation model (2eq). This model can be adopted when (t) is significantly larger than (τ 1) (i.e., when t≫τ 1); and (3) a one-equation, time-asymptotic formulation (1eq ∞). This model can be adopted when (t) is significantly larger than the timescale (τ 2) associated with exchange processes between the two regions (i. e., when t≫τ 2). In order to obtain insight into this transient behavior, we combine a theoretical approach based on the analysis of spatial moments with numerical and analytical results in several simple cases. The main result of this paper is to show that there is only a weak asymptotic convergence of the solution of (2eq) towards the solution of (1eq ∞) in terms of standardized moments but, interestingly, not in terms of centered moments. The physical interpretation of this result is that deviations from the Fickian situation persist in the limit of long times but that the spreading of the solute is eventually dominating these higher order effects. © 2012 Springer Science+Business Media B.V.en
dc.description.sponsorshipSupport from CNRS/GdR 2990 is gratefully acknowledged. The second author (BDW) was supported in part by the Office of Science (BER), U.S. Department of Energy, Grant No. DE-FG02-07ER64417. This publication was based on work supported in part by Award No KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).en
dc.publisherSpringer Natureen
dc.subjectDispersionen
dc.subjectHomogenizationen
dc.subjectPorous mediaen
dc.subjectSpatial momentsen
dc.subjectVolume averagingen
dc.titleCorrespondence Between One- and Two-Equation Models for Solute Transport in Two-Region Heterogeneous Porous Mediaen
dc.typeArticleen
dc.identifier.journalTransport in Porous Mediaen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
dc.contributor.institutionOregon State University, Corvallis, United Statesen
dc.contributor.institutionUniversite de Toulouse, Toulouse, Franceen
dc.contributor.institutionIMFT Institut de Mecaniques des Fluides, Toulouse, Franceen
kaust.grant.numberKUK-C1-013-04en
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.