Effective dispersion coefficients for the upscaling of pore-scale mixing and reaction

We upscale reactive mixing using effective dispersion coefficients to capture the combined effect of pore-scale heterogeneity and molecular diffusion on the evolution of the mixing interface between two initially segregated dissolved species. Effective dispersion coefficients are defined in terms of...

Descripción completa

Detalles Bibliográficos
Autores: Puyguiraud, Alexandre, Pérez, Lázaro J., Hidalgo, Juan J., Dentz, Marco
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2020
País:España
Institución:Consejo Superior de Investigaciones Científicas (CSIC)
Repositorio:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/222932
Acceso en línea:http://hdl.handle.net/10261/222932
Access Level:acceso abierto
Palabra clave:Effective dispersion
Mixing
Upscaling
Incomplete mixing
Lamellar mixing
Reactive mixing
id ES_6dd3f2eb4f0a10169c9dfd5cf2c3e3b7
oai_identifier_str oai:digital.csic.es:10261/222932
network_acronym_str ES
network_name_str España
repository_id_str
spelling Effective dispersion coefficients for the upscaling of pore-scale mixing and reactionPuyguiraud, AlexandrePérez, Lázaro J.Hidalgo, Juan J.Dentz, MarcoEffective dispersionMixingUpscalingIncomplete mixingLamellar mixingReactive mixingWe upscale reactive mixing using effective dispersion coefficients to capture the combined effect of pore-scale heterogeneity and molecular diffusion on the evolution of the mixing interface between two initially segregated dissolved species. Effective dispersion coefficients are defined in terms of the average spatial variance of the solute distribution evolving from a pointlike injection, that is, the transport Green function. We numerically investigate the temporal behavior of the longitudinal effective dispersion coefficients for two porous media of different pore-scale heterogeneity as measured by the statistics of the flow speed, and different Péclet numbers. We find that the effective dispersion coefficients evolve with time, or equivalently travel distance. As the solute samples the pore-scale flow heterogeneity due to advection and transverse diffusion, the effective dispersion coefficients evolve from the value of molecular diffusion to the corresponding hydrodynamic dispersion coefficients. Thus, at times smaller than the diffusion time over a characteristic pore length, the effective dispersion coefficients can be significantly smaller than the hydrodynamic dispersion coefficients. This difference can explain frequently observed mismatches between pore-scale reactive mixing data, and predictions using Darcy scale transport descriptions based on hydrodynamic dispersion coefficients that are constant in time. This suggests that the notion of incomplete mixing on the support scale can be quantified in terms of effective pore-scale dispersion coefficients. We use effective dispersion in order to approximate the transport Green function in terms of a Gaussian-shaped distribution that is characterized by the effective variance. This is approximation is termed dispersive lamella. Based on this representation, we study reactive mixing between two initially segregated solutes. The dispersive lamella approach accurately predicts the evolution of the product mass of an instantaneous bimolecular reaction obtained from direct numerical simulations. This demonstrates that effective dispersion is an accurate measure for width of the mixing interface between the two reacting species. These results shed some new light on pore-scale mixing, the notion of incomplete mixing, and its prediction and upscaling in terms of an effective mixing model.This work has been supported by the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ ERC Grant Agreement No. 617511 (MHetScale) and the Spanish Ministry of Science and Innovation through the project HydroPore (PID2019-106887GB-C31). Juan J. Hidalgo acknowledges the support of the Spanish Ministry of Science and Innovation through the Ramon y Cajal program.Peer reviewedElsevierEuropean Research CouncilMinisterio de Ciencia e Innovación (España)Dentz, Marco [0000-0002-3940-282X]Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]202020202020info:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_6501Postprintinfo:eu-repo/semantics/acceptedVersionhttp://hdl.handle.net/10261/222932reponame:DIGITAL.CSIC. Repositorio Institucional del CSICinstname:Consejo Superior de Investigaciones Científicas (CSIC)Inglés#PLACEHOLDER_PARENT_METADATA_VALUE##PLACEHOLDER_PARENT_METADATA_VALUE#info:eu-repo/grantAgreement/EC/FP7/617511info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-106887GB-C31https://doi.org/10.1016/j.advwatres.2020.103782Síinfo:eu-repo/semantics/openAccessoai:digital.csic.es:10261/2229322026-05-22T06:33:51Z
dc.title.none.fl_str_mv Effective dispersion coefficients for the upscaling of pore-scale mixing and reaction
title Effective dispersion coefficients for the upscaling of pore-scale mixing and reaction
spellingShingle Effective dispersion coefficients for the upscaling of pore-scale mixing and reaction
Puyguiraud, Alexandre
Effective dispersion
Mixing
Upscaling
Incomplete mixing
Lamellar mixing
Reactive mixing
title_short Effective dispersion coefficients for the upscaling of pore-scale mixing and reaction
title_full Effective dispersion coefficients for the upscaling of pore-scale mixing and reaction
title_fullStr Effective dispersion coefficients for the upscaling of pore-scale mixing and reaction
title_full_unstemmed Effective dispersion coefficients for the upscaling of pore-scale mixing and reaction
title_sort Effective dispersion coefficients for the upscaling of pore-scale mixing and reaction
dc.creator.none.fl_str_mv Puyguiraud, Alexandre
Pérez, Lázaro J.
Hidalgo, Juan J.
Dentz, Marco
author Puyguiraud, Alexandre
author_facet Puyguiraud, Alexandre
Pérez, Lázaro J.
Hidalgo, Juan J.
Dentz, Marco
author_role author
author2 Pérez, Lázaro J.
Hidalgo, Juan J.
Dentz, Marco
author2_role author
author
author
dc.contributor.none.fl_str_mv European Research Council
Ministerio de Ciencia e Innovación (España)
Dentz, Marco [0000-0002-3940-282X]
Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]
dc.subject.none.fl_str_mv Effective dispersion
Mixing
Upscaling
Incomplete mixing
Lamellar mixing
Reactive mixing
topic Effective dispersion
Mixing
Upscaling
Incomplete mixing
Lamellar mixing
Reactive mixing
description We upscale reactive mixing using effective dispersion coefficients to capture the combined effect of pore-scale heterogeneity and molecular diffusion on the evolution of the mixing interface between two initially segregated dissolved species. Effective dispersion coefficients are defined in terms of the average spatial variance of the solute distribution evolving from a pointlike injection, that is, the transport Green function. We numerically investigate the temporal behavior of the longitudinal effective dispersion coefficients for two porous media of different pore-scale heterogeneity as measured by the statistics of the flow speed, and different Péclet numbers. We find that the effective dispersion coefficients evolve with time, or equivalently travel distance. As the solute samples the pore-scale flow heterogeneity due to advection and transverse diffusion, the effective dispersion coefficients evolve from the value of molecular diffusion to the corresponding hydrodynamic dispersion coefficients. Thus, at times smaller than the diffusion time over a characteristic pore length, the effective dispersion coefficients can be significantly smaller than the hydrodynamic dispersion coefficients. This difference can explain frequently observed mismatches between pore-scale reactive mixing data, and predictions using Darcy scale transport descriptions based on hydrodynamic dispersion coefficients that are constant in time. This suggests that the notion of incomplete mixing on the support scale can be quantified in terms of effective pore-scale dispersion coefficients. We use effective dispersion in order to approximate the transport Green function in terms of a Gaussian-shaped distribution that is characterized by the effective variance. This is approximation is termed dispersive lamella. Based on this representation, we study reactive mixing between two initially segregated solutes. The dispersive lamella approach accurately predicts the evolution of the product mass of an instantaneous bimolecular reaction obtained from direct numerical simulations. This demonstrates that effective dispersion is an accurate measure for width of the mixing interface between the two reacting species. These results shed some new light on pore-scale mixing, the notion of incomplete mixing, and its prediction and upscaling in terms of an effective mixing model.
publishDate 2020
dc.date.none.fl_str_mv 2020
2020
2020
dc.type.none.fl_str_mv info:eu-repo/semantics/article
http://purl.org/coar/resource_type/c_6501
Postprint
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10261/222932
url http://hdl.handle.net/10261/222932
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv #PLACEHOLDER_PARENT_METADATA_VALUE#
#PLACEHOLDER_PARENT_METADATA_VALUE#
info:eu-repo/grantAgreement/EC/FP7/617511
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-106887GB-C31
https://doi.org/10.1016/j.advwatres.2020.103782
Sí
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:DIGITAL.CSIC. Repositorio Institucional del CSIC
instname:Consejo Superior de Investigaciones Científicas (CSIC)
instname_str Consejo Superior de Investigaciones Científicas (CSIC)
reponame_str DIGITAL.CSIC. Repositorio Institucional del CSIC
collection DIGITAL.CSIC. Repositorio Institucional del CSIC
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869410380949749760
score 15,811543

Similares en LA Referencia