Numerical Monte Carlo analysis of the influence of pore‐scale dispersion on macrodispersion in 2‐D heterogeneous porous media
Identifieur interne : 000F96 ( Istex/Corpus ); précédent : 000F95; suivant : 000F97Numerical Monte Carlo analysis of the influence of pore‐scale dispersion on macrodispersion in 2‐D heterogeneous porous media
Auteurs : Anthony Beaudoin ; Jean-Raynald De Dreuzy ; Jocelyne ErhelSource :
- Water Resources Research [ 0043-1397 ] ; 2010-12.
Abstract
We investigate the influences of pore‐scale dispersion and of larger‐scale permeability heterogeneities on the macrodispersion without the molecular diffusion. Permeability follows a lognormal exponentially correlated distribution characterized by its correlation length λ and its lognormal variance σ2. Macrodispersion is evaluated numerically by using parallel simulations on grids of characteristic size ranging from 200λ to 1600λ. We note αL and αT the pore‐scale longitudinal and transversal dispersivities. For αL/λ < 10−2 and αT/λ < 10−3, the influence of pore‐scale dispersion on the macrodispersion is smaller than 5% of the macrodispersion due only to permeability heterogeneities. Larger dispersivities (αL/λ ≥ 10−2 or αT/λ ≥ 10−3) induce larger effects than those obtained by the semianalytical expression of Salandin and Fiorotto (1998) for σ2 > 1. The effects of local dispersion on the longitudinal macrodispersion remain limited to 25% at most of the macrodispersion due only to permeability heterogeneities. For σ2 > 1, isotropic local dispersion induces a reduction of the longitudinal macrodispersion, whereas anisotropic local dispersion lets it increase. The longitudinal and transverse local dispersions induce opposite effects on the longitudinal macrodispersion, which are respectively an increase and a reduction. The transverse macrodispersion null without local dispersion or molecular diffusion becomes strictly positive with local dispersion. Because of the velocity field heterogeneities, it is amplified by a factor of 2 to 50 from the grid scale to the macro scale. The transverse dispersion is triggered by both longitudinal and transverse local dispersions. A reduction of a factor of 2 of the transverse local dispersion at fixed longitudinal local dispersion yields only a reduction of a factor of 4 at most of the transverse macrodispersion for σ2 ≥ 2.25.
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DOI: 10.1029/2010WR009576
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Res.</title><idno type="ISSN">0043-1397</idno><idno type="eISSN">1944-7973</idno><imprint><publisher>Blackwell Publishing Ltd</publisher><date type="published" when="2010-12">2010-12</date><biblScope unit="volume">46</biblScope><biblScope unit="issue">12</biblScope><biblScope unit="page" from="/">n/a</biblScope><biblScope unit="page" to="/">n/a</biblScope></imprint><idno type="ISSN">0043-1397</idno></series><idno type="istex">CD823353B7064E4F20720FEEC391185A236627FC</idno><idno type="DOI">10.1029/2010WR009576</idno><idno type="ArticleID">2010WR009576</idno></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0043-1397</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract">We investigate the influences of pore‐scale dispersion and of larger‐scale permeability heterogeneities on the macrodispersion without the molecular diffusion. Permeability follows a lognormal exponentially correlated distribution characterized by its correlation length λ and its lognormal variance σ2. Macrodispersion is evaluated numerically by using parallel simulations on grids of characteristic size ranging from 200λ to 1600λ. We note αL and αT the pore‐scale longitudinal and transversal dispersivities. For αL/λ < 10−2 and αT/λ < 10−3, the influence of pore‐scale dispersion on the macrodispersion is smaller than 5% of the macrodispersion due only to permeability heterogeneities. Larger dispersivities (αL/λ ≥ 10−2 or αT/λ ≥ 10−3) induce larger effects than those obtained by the semianalytical expression of Salandin and Fiorotto (1998) for σ2 > 1. The effects of local dispersion on the longitudinal macrodispersion remain limited to 25% at most of the macrodispersion due only to permeability heterogeneities. For σ2 > 1, isotropic local dispersion induces a reduction of the longitudinal macrodispersion, whereas anisotropic local dispersion lets it increase. The longitudinal and transverse local dispersions induce opposite effects on the longitudinal macrodispersion, which are respectively an increase and a reduction. The transverse macrodispersion null without local dispersion or molecular diffusion becomes strictly positive with local dispersion. Because of the velocity field heterogeneities, it is amplified by a factor of 2 to 50 from the grid scale to the macro scale. The transverse dispersion is triggered by both longitudinal and transverse local dispersions. A reduction of a factor of 2 of the transverse local dispersion at fixed longitudinal local dispersion yields only a reduction of a factor of 4 at most of the transverse macrodispersion for σ2 ≥ 2.25.</div></front></TEI><istex><corpusName>wiley</corpusName><author><json:item><name>Anthony Beaudoin</name><affiliations><json:string>LOMC, Université du Havre, Le Havre, France</json:string><json:string>Institut P′, UPR 3346 CNRS, Université de Poitiers, ENSMA, SP2MI, Chasseneuil, France</json:string><json:string>E-mail: anthony.beaudoin@univ-poitiers.fr</json:string></affiliations></json:item><json:item><name>Jean‐Raynald de Dreuzy</name><affiliations><json:string>Géosciences de Rennes, UMR 6118 CNRS, Université de Rennes 1, Campus de Beaulieu, Rennes, France</json:string><json:string>Institute of Environmental Assessment and Water Research, CSIC, Barcelona, Spain</json:string></affiliations></json:item><json:item><name>Jocelyne Erhel</name><affiliations><json:string>INRIA, Campus de Beaulieu, Rennes, France</json:string></affiliations></json:item></author><subject><json:item><lang><json:string>eng</json:string></lang><value>solute transport</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>macrodispersion</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>parallel computing</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>hydrodynamic dispersion</value></json:item></subject><articleId><json:string>2010WR009576</json:string></articleId><language><json:string>eng</json:string></language><originalGenre><json:string>article</json:string></originalGenre><abstract>We investigate the influences of pore‐scale dispersion and of larger‐scale permeability heterogeneities on the macrodispersion without the molecular diffusion. Permeability follows a lognormal exponentially correlated distribution characterized by its correlation length λ and its lognormal variance σ2. Macrodispersion is evaluated numerically by using parallel simulations on grids of characteristic size ranging from 200λ to 1600λ. We note αL and αT the pore‐scale longitudinal and transversal dispersivities. For αL/λ > 10−2 and αT/λ > 10−3, the influence of pore‐scale dispersion on the macrodispersion is smaller than 5% of the macrodispersion due only to permeability heterogeneities. Larger dispersivities (αL/λ ≥ 10−2 or αT/λ ≥ 10−3) induce larger effects than those obtained by the semianalytical expression of Salandin and Fiorotto (1998) for σ2 > 1. The effects of local dispersion on the longitudinal macrodispersion remain limited to 25% at most of the macrodispersion due only to permeability heterogeneities. For σ2 > 1, isotropic local dispersion induces a reduction of the longitudinal macrodispersion, whereas anisotropic local dispersion lets it increase. The longitudinal and transverse local dispersions induce opposite effects on the longitudinal macrodispersion, which are respectively an increase and a reduction. The transverse macrodispersion null without local dispersion or molecular diffusion becomes strictly positive with local dispersion. Because of the velocity field heterogeneities, it is amplified by a factor of 2 to 50 from the grid scale to the macro scale. The transverse dispersion is triggered by both longitudinal and transverse local dispersions. 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Res.</title><idno type="pISSN">0043-1397</idno><idno type="eISSN">1944-7973</idno><idno type="DOI">10.1002/(ISSN)1944-7973</idno><imprint><publisher>Blackwell Publishing Ltd</publisher><date type="published" when="2010-12"></date><biblScope unit="volume">46</biblScope><biblScope unit="issue">12</biblScope><biblScope unit="page" from="/">n/a</biblScope><biblScope unit="page" to="/">n/a</biblScope></imprint></monogr><idno type="istex">CD823353B7064E4F20720FEEC391185A236627FC</idno><idno type="DOI">10.1029/2010WR009576</idno><idno type="ArticleID">2010WR009576</idno></biblStruct></sourceDesc></fileDesc><profileDesc><creation><date>2010</date></creation><langUsage><language ident="en">en</language></langUsage><abstract><p>We investigate the influences of pore‐scale dispersion and of larger‐scale permeability heterogeneities on the macrodispersion without the molecular diffusion. Permeability follows a lognormal exponentially correlated distribution characterized by its correlation length λ and its lognormal variance σ2. Macrodispersion is evaluated numerically by using parallel simulations on grids of characteristic size ranging from 200λ to 1600λ. We note αL and αT the pore‐scale longitudinal and transversal dispersivities. For αL/λ < 10−2 and αT/λ < 10−3, the influence of pore‐scale dispersion on the macrodispersion is smaller than 5% of the macrodispersion due only to permeability heterogeneities. Larger dispersivities (αL/λ ≥ 10−2 or αT/λ ≥ 10−3) induce larger effects than those obtained by the semianalytical expression of Salandin and Fiorotto (1998) for σ2 > 1. The effects of local dispersion on the longitudinal macrodispersion remain limited to 25% at most of the macrodispersion due only to permeability heterogeneities. For σ2 > 1, isotropic local dispersion induces a reduction of the longitudinal macrodispersion, whereas anisotropic local dispersion lets it increase. The longitudinal and transverse local dispersions induce opposite effects on the longitudinal macrodispersion, which are respectively an increase and a reduction. The transverse macrodispersion null without local dispersion or molecular diffusion becomes strictly positive with local dispersion. Because of the velocity field heterogeneities, it is amplified by a factor of 2 to 50 from the grid scale to the macro scale. The transverse dispersion is triggered by both longitudinal and transverse local dispersions. A reduction of a factor of 2 of the transverse local dispersion at fixed longitudinal local dispersion yields only a reduction of a factor of 4 at most of the transverse macrodispersion for σ2 ≥ 2.25.</p></abstract><textClass><keywords scheme="keyword"><list><head>keywords</head><item><term>solute transport</term></item><item><term>macrodispersion</term></item><item><term>parallel computing</term></item><item><term>hydrodynamic dispersion</term></item></list></keywords></textClass><textClass><keywords scheme="Journal Subject"><list><head>index-terms</head><item><term>HYDROLOGY</term></item><item><term>Groundwater transport</term></item><item><term>Modeling</term></item><item><term>Computational hydrology</term></item><item><term>INFORMATICS</term></item><item><term>Modeling</term></item></list></keywords></textClass><textClass><keywords scheme="Journal Subject"><list><head>article-category</head><item><term>Regular Article</term></item></list></keywords></textClass></profileDesc><revisionDesc><change when="2010-05-21">Received</change><change when="2010-09-20">Registration</change><change when="2010-12">Published</change></revisionDesc></teiHeader></istex:fulltextTEI><json:item><original>false</original><mimetype>text/plain</mimetype><extension>txt</extension><uri>https://api.istex.fr/document/CD823353B7064E4F20720FEEC391185A236627FC/fulltext/txt</uri></json:item></fulltext><metadata><istex:metadataXml wicri:clean="Wiley, elements deleted: body"><istex:xmlDeclaration>version="1.0" encoding="UTF-8" standalone="yes"</istex:xmlDeclaration><istex:document><component type="serialArticle" version="2.0" xml:lang="en" xml:id="wrcr12790"><header><publicationMeta level="product"><doi>10.1002/(ISSN)1944-7973</doi><issn type="print">0043-1397</issn><issn type="electronic">1944-7973</issn><idGroup><id type="product" value="WRCR"></id><id type="coden" value="WRERAQ"></id></idGroup><titleGroup><title type="main" xml:lang="en" sort="WATER RESOURCES RESEARCH">Water Resources Research</title><title type="short">Water Resour. 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Res.</journalTitle>, <vol>46</vol>, W12537, doi:<accessionId ref="info:doi/10.1029/2010WR009576">10.1029/2010WR009576</accessionId>.</citation></selfCitationGroup><linkGroup><link type="toTypesetVersion" href="file:WRCR.WRCR12790.pdf"></link></linkGroup></publicationMeta><contentMeta><countGroup><count type="wordTotal" number="7200"></count><count type="figureTotal" number="5"></count><count type="tableTotal" number="1"></count></countGroup><titleGroup><title type="main">Numerical Monte Carlo analysis of the influence of pore‐scale dispersion on macrodispersion in 2‐D heterogeneous porous media</title><title type="short">MACRODISPERSION EMERGING</title><title type="shortAuthors">Beaudoin <i>et al</i>.</title></titleGroup><creators><creator creatorRole="author" xml:id="wrcr12790-cr-0001" affiliationRef="#wrcr12790-aff-0001 #wrcr12790-aff-0002"><personName><givenNames>Anthony</givenNames> <familyName>Beaudoin</familyName></personName><contactDetails><email normalForm="anthony.beaudoin@univ-poitiers.fr">anthony.beaudoin@univ-poitiers.fr</email></contactDetails></creator><creator creatorRole="author" xml:id="wrcr12790-cr-0002" affiliationRef="#wrcr12790-aff-0003 #wrcr12790-aff-0004"><personName><givenNames>Jean‐Raynald</givenNames> <familyName>de Dreuzy</familyName></personName></creator><creator creatorRole="author" xml:id="wrcr12790-cr-0003" affiliationRef="#wrcr12790-aff-0005"><personName><givenNames>Jocelyne</givenNames> <familyName>Erhel</familyName></personName></creator></creators><affiliationGroup><affiliation countryCode="FR" type="organization" xml:id="wrcr12790-aff-0001"><orgDiv>LOMC</orgDiv><orgName>Université du Havre</orgName><address><city>Le Havre</city><country>France</country></address></affiliation><affiliation countryCode="FR" type="organization" xml:id="wrcr12790-aff-0002"><orgDiv>Institut P′, UPR 3346 CNRS</orgDiv><orgName>Université de Poitiers, ENSMA, SP2MI</orgName><address><city>Chasseneuil</city><country>France</country></address></affiliation><affiliation countryCode="FR" type="organization" xml:id="wrcr12790-aff-0003"><orgDiv>Géosciences de Rennes, UMR 6118 CNRS</orgDiv><orgName>Université de Rennes 1, Campus de Beaulieu</orgName><address><city>Rennes</city><country>France</country></address></affiliation><affiliation countryCode="ES" type="organization" xml:id="wrcr12790-aff-0004"><orgDiv>Institute of Environmental Assessment and Water Research</orgDiv><orgName>CSIC</orgName><address><city>Barcelona</city><country>Spain</country></address></affiliation><affiliation countryCode="FR" type="organization" xml:id="wrcr12790-aff-0005"><orgDiv>INRIA</orgDiv><orgName>Campus de Beaulieu</orgName><address><city>Rennes</city><country>France</country></address></affiliation></affiliationGroup><keywordGroup type="author"><keyword xml:id="wrcr12790-kwd-0001">solute transport</keyword><keyword xml:id="wrcr12790-kwd-0002">macrodispersion</keyword><keyword xml:id="wrcr12790-kwd-0003">parallel computing</keyword><keyword xml:id="wrcr12790-kwd-0004">hydrodynamic dispersion</keyword></keywordGroup><supportingInformation><supportingInfoItem><mediaResource alt="supplementary data" mimeType="text/plain" href="urn-x:wiley:00431397:media:wrcr12790:wrcr12790-sup-0001-t01"></mediaResource><caption>Tab‐delimited Table 1.</caption></supportingInfoItem></supportingInformation><abstractGroup><abstract type="main"><p xml:id="wrcr12790-para-0001" label="1">We investigate the influences of pore‐scale dispersion and of larger‐scale permeability heterogeneities on the macrodispersion without the molecular diffusion. Permeability follows a lognormal exponentially correlated distribution characterized by its correlation length <i>λ</i> and its lognormal variance <i>σ</i><sup>2</sup>. Macrodispersion is evaluated numerically by using parallel simulations on grids of characteristic size ranging from 200<i>λ</i> to 1600<i>λ</i>. We note <i>α</i><sub>L</sub> and <i>α</i><sub>T</sub> the pore‐scale longitudinal and transversal dispersivities. For <i>α</i><sub>L</sub>/<i>λ</i> < 10<sup>−2</sup> and <i>α</i><sub>T</sub>/<i>λ</i> < 10<sup>−3</sup>, the influence of pore‐scale dispersion on the macrodispersion is smaller than 5% of the macrodispersion due only to permeability heterogeneities. Larger dispersivities (<i>α</i><sub>L</sub>/<i>λ</i> ≥ 10<sup>−2</sup> or <i>α</i><sub>T</sub>/<i>λ</i> ≥ 10<sup>−3</sup>) induce larger effects than those obtained by the semianalytical expression of Salandin and Fiorotto (1998) for <i>σ</i><sup>2</sup> > 1. The effects of local dispersion on the longitudinal macrodispersion remain limited to 25% at most of the macrodispersion due only to permeability heterogeneities. For <i>σ</i><sup>2</sup> > 1, isotropic local dispersion induces a reduction of the longitudinal macrodispersion, whereas anisotropic local dispersion lets it increase. The longitudinal and transverse local dispersions induce opposite effects on the longitudinal macrodispersion, which are respectively an increase and a reduction. The transverse macrodispersion null without local dispersion or molecular diffusion becomes strictly positive with local dispersion. Because of the velocity field heterogeneities, it is amplified by a factor of 2 to 50 from the grid scale to the macro scale. The transverse dispersion is triggered by both longitudinal and transverse local dispersions. A reduction of a factor of 2 of the transverse local dispersion at fixed longitudinal local dispersion yields only a reduction of a factor of 4 at most of the transverse macrodispersion for <i>σ</i><sup>2</sup> ≥ 2.25.</p></abstract></abstractGroup></contentMeta></header></component></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Numerical Monte Carlo analysis of the influence of pore‐scale dispersion on macrodispersion in 2‐D heterogeneous porous media</title></titleInfo><titleInfo type="abbreviated" lang="en"><title>MACRODISPERSION EMERGING</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>Numerical Monte Carlo analysis of the influence of pore‐scale dispersion on macrodispersion in 2‐D heterogeneous porous media</title></titleInfo><name type="personal"><namePart type="given">Anthony</namePart><namePart type="family">Beaudoin</namePart><affiliation>LOMC, Université du Havre, Le Havre, France</affiliation><affiliation>Institut P′, UPR 3346 CNRS, Université de Poitiers, ENSMA, SP2MI, Chasseneuil, France</affiliation><affiliation>E-mail: anthony.beaudoin@univ-poitiers.fr</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Jean‐Raynald</namePart><namePart type="family">de Dreuzy</namePart><affiliation>Géosciences de Rennes, UMR 6118 CNRS, Université de Rennes 1, Campus de Beaulieu, Rennes, France</affiliation><affiliation>Institute of Environmental Assessment and Water Research, CSIC, Barcelona, Spain</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Jocelyne</namePart><namePart type="family">Erhel</namePart><affiliation>INRIA, Campus de Beaulieu, Rennes, France</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="article" displayLabel="article"></genre><originInfo><publisher>Blackwell Publishing Ltd</publisher><dateIssued encoding="w3cdtf">2010-12</dateIssued><dateCaptured encoding="w3cdtf">2010-05-21</dateCaptured><dateValid encoding="w3cdtf">2010-09-20</dateValid><edition>Beaudoin, A., J.‐R. de Dreuzyr, and J. Erhel (2010), Numerical Monte Carlo analysis of the influence of pore‐scale dispersion on macrodispersion in 2‐D heterogeneous porous media, Water Resour. Res., 46, W12537, doi:10.1029/2010WR009576.</edition><copyrightDate encoding="w3cdtf">2010</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><physicalDescription><internetMediaType>text/html</internetMediaType><extent unit="figures">5</extent><extent unit="tables">1</extent><extent unit="words">7200</extent></physicalDescription><abstract>We investigate the influences of pore‐scale dispersion and of larger‐scale permeability heterogeneities on the macrodispersion without the molecular diffusion. Permeability follows a lognormal exponentially correlated distribution characterized by its correlation length λ and its lognormal variance σ2. Macrodispersion is evaluated numerically by using parallel simulations on grids of characteristic size ranging from 200λ to 1600λ. We note αL and αT the pore‐scale longitudinal and transversal dispersivities. For αL/λ < 10−2 and αT/λ < 10−3, the influence of pore‐scale dispersion on the macrodispersion is smaller than 5% of the macrodispersion due only to permeability heterogeneities. Larger dispersivities (αL/λ ≥ 10−2 or αT/λ ≥ 10−3) induce larger effects than those obtained by the semianalytical expression of Salandin and Fiorotto (1998) for σ2 > 1. The effects of local dispersion on the longitudinal macrodispersion remain limited to 25% at most of the macrodispersion due only to permeability heterogeneities. For σ2 > 1, isotropic local dispersion induces a reduction of the longitudinal macrodispersion, whereas anisotropic local dispersion lets it increase. The longitudinal and transverse local dispersions induce opposite effects on the longitudinal macrodispersion, which are respectively an increase and a reduction. The transverse macrodispersion null without local dispersion or molecular diffusion becomes strictly positive with local dispersion. Because of the velocity field heterogeneities, it is amplified by a factor of 2 to 50 from the grid scale to the macro scale. The transverse dispersion is triggered by both longitudinal and transverse local dispersions. A reduction of a factor of 2 of the transverse local dispersion at fixed longitudinal local dispersion yields only a reduction of a factor of 4 at most of the transverse macrodispersion for σ2 ≥ 2.25.</abstract><note type="additional physical form">Tab‐delimited Table 1.</note><subject><genre>keywords</genre><topic>solute transport</topic><topic>macrodispersion</topic><topic>parallel computing</topic><topic>hydrodynamic dispersion</topic></subject><relatedItem type="host"><titleInfo><title>Water Resources Research</title></titleInfo><titleInfo type="abbreviated"><title>Water Resour. Res.</title></titleInfo><genre type="journal">journal</genre><subject><genre>index-terms</genre><topic authorityURI="http://psi.agu.org/taxonomy5/1800">HYDROLOGY</topic><topic authorityURI="http://psi.agu.org/taxonomy5/1832">Groundwater transport</topic><topic authorityURI="http://psi.agu.org/taxonomy5/1847">Modeling</topic><topic authorityURI="http://psi.agu.org/taxonomy5/1805">Computational hydrology</topic><topic authorityURI="http://psi.agu.org/taxonomy5/1900">INFORMATICS</topic><topic authorityURI="http://psi.agu.org/taxonomy5/1952">Modeling</topic></subject><subject><genre>article-category</genre><topic>Regular Article</topic></subject><identifier type="ISSN">0043-1397</identifier><identifier type="eISSN">1944-7973</identifier><identifier type="DOI">10.1002/(ISSN)1944-7973</identifier><identifier type="CODEN">WRERAQ</identifier><identifier type="PublisherID">WRCR</identifier><part><date>2010</date><detail type="volume"><caption>vol.</caption><number>46</number></detail><detail type="issue"><caption>no.</caption><number>12</number></detail><extent unit="pages"><start>n/a</start><end>n/a</end><total>9</total></extent></part></relatedItem><identifier type="istex">CD823353B7064E4F20720FEEC391185A236627FC</identifier><identifier type="DOI">10.1029/2010WR009576</identifier><identifier type="ArticleID">2010WR009576</identifier><accessCondition type="use and reproduction" contentType="copyright">Copyright 2010 by the American Geophysical Union.</accessCondition><recordInfo><recordContentSource>WILEY</recordContentSource></recordInfo></mods></metadata><enrichments><json:item><type>multicat</type><uri>https://api.istex.fr/document/CD823353B7064E4F20720FEEC391185A236627FC/enrichments/multicat</uri></json:item></enrichments><serie></serie></istex></record>Pour manipuler ce document sous Unix (Dilib)
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