A numerical upscaling procedure to estimate effective plane wave and shear moduli in heterogeneous fluid-saturated poroelastic media

Autores
Santos, Juan Enrique; Rubino, Jorge German; Ravazzoli, Claudia Leonor
Año de publicación
2009
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
An important loss effect in heterogeneous poroelastic Biot media is the dissipation mechanism due to wave-induced fluid flow caused by mesoscopic scale heterogeneities, which are larger than the pore size but much smaller than the predominant wavelengths of the fast compressional and shear waves. These heterogeneities can be due to local variations in lithological properties or to patches of immiscible fluids. For example, a fast compressional wave traveling across a porous rock saturated with water and patchesof gas induces a smaller fluid-pressure in the gas patches than in the water-saturated parts of the material. This in turn generates fluid flow and slow Biot waves which diffuse away from the gas­water interfaces generating significant energy losses and velocity dispersion. To perform numerical simulations using Biot´s equations of motion, it would be necessary to employ extremely fine meshes to properly represent these mesoscopic heterogeneities and their attenuation effects on the fast waves. An alternative approach to model wave propagation in these type of Biot media is to employ a numerical upscaling procedure to determine effective complex P-wave and shear moduli defining locally a viscoelastic medium having in the average the same properties than the original Biot medium. In this work the complex P-wave and shear moduli in heterogeneous fluid-saturated porous media are obtained using numerical gedanken experiments in a Monte Carlo fashion. The experiments are defined as local boundary value problems on a reference representative volume of bulk material containing stochastic heterogeneities characterized by their statistical properties. These boundary value problems represent compressibility and shear tests needed to determine these moduli for a given realization. The average and variance of the phase velocities and quality factors associated with these moduli are obtained by averaging over realizations of the stochastic parameters. The Monte Carlo realizations were stopped when the variance of the computed quantities stabilized at an almost constant value. The approximate solution of the local boundary value problems was obtained using a Galerkin finite element procedure, and the method was validated by reproducing known solutions in the case of periodic layered media. For the spatial discretization, standard bilinear finite element spaces are employed for the solid phase, while for the fluid phase the vector part of the Raviart­Thomas­Nedelec mixed finite element space of order zero was used. Results on the uniqueness of the continuous and discrete problems as well as optimal a priori error esti-mates for the Galerkin finite element procedure are derived. Numerical experiments showing the implementation of the procedure to estimate the average and variance of the fast compressional and shear phase velocities and inverse quality factors in these kind of highly heterogeneous fluid-saturated porous media are presented.
Fil: Santos, Juan Enrique. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Purdue University; Estados Unidos. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentina
Fil: Rubino, Jorge German. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentina
Fil: Ravazzoli, Claudia Leonor. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
ATTENUATION AND DISPERSION
POROELASTICITY
VISCOELASTICITY
FINITE ELEMENT METHODS
MONTE CARLO METHOD
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/244038

id CONICETDig_052bb24ee5e0a6e4774311036f3919db
oai_identifier_str oai:ri.conicet.gov.ar:11336/244038
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling A numerical upscaling procedure to estimate effective plane wave and shear moduli in heterogeneous fluid-saturated poroelastic mediaSantos, Juan EnriqueRubino, Jorge GermanRavazzoli, Claudia LeonorATTENUATION AND DISPERSIONPOROELASTICITYVISCOELASTICITYFINITE ELEMENT METHODSMONTE CARLO METHODhttps://purl.org/becyt/ford/1.5https://purl.org/becyt/ford/1https://purl.org/becyt/ford/2.7https://purl.org/becyt/ford/2An important loss effect in heterogeneous poroelastic Biot media is the dissipation mechanism due to wave-induced fluid flow caused by mesoscopic scale heterogeneities, which are larger than the pore size but much smaller than the predominant wavelengths of the fast compressional and shear waves. These heterogeneities can be due to local variations in lithological properties or to patches of immiscible fluids. For example, a fast compressional wave traveling across a porous rock saturated with water and patchesof gas induces a smaller fluid-pressure in the gas patches than in the water-saturated parts of the material. This in turn generates fluid flow and slow Biot waves which diffuse away from the gas­water interfaces generating significant energy losses and velocity dispersion. To perform numerical simulations using Biot´s equations of motion, it would be necessary to employ extremely fine meshes to properly represent these mesoscopic heterogeneities and their attenuation effects on the fast waves. An alternative approach to model wave propagation in these type of Biot media is to employ a numerical upscaling procedure to determine effective complex P-wave and shear moduli defining locally a viscoelastic medium having in the average the same properties than the original Biot medium. In this work the complex P-wave and shear moduli in heterogeneous fluid-saturated porous media are obtained using numerical gedanken experiments in a Monte Carlo fashion. The experiments are defined as local boundary value problems on a reference representative volume of bulk material containing stochastic heterogeneities characterized by their statistical properties. These boundary value problems represent compressibility and shear tests needed to determine these moduli for a given realization. The average and variance of the phase velocities and quality factors associated with these moduli are obtained by averaging over realizations of the stochastic parameters. The Monte Carlo realizations were stopped when the variance of the computed quantities stabilized at an almost constant value. The approximate solution of the local boundary value problems was obtained using a Galerkin finite element procedure, and the method was validated by reproducing known solutions in the case of periodic layered media. For the spatial discretization, standard bilinear finite element spaces are employed for the solid phase, while for the fluid phase the vector part of the Raviart­Thomas­Nedelec mixed finite element space of order zero was used. Results on the uniqueness of the continuous and discrete problems as well as optimal a priori error esti-mates for the Galerkin finite element procedure are derived. Numerical experiments showing the implementation of the procedure to estimate the average and variance of the fast compressional and shear phase velocities and inverse quality factors in these kind of highly heterogeneous fluid-saturated porous media are presented.Fil: Santos, Juan Enrique. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Purdue University; Estados Unidos. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas; ArgentinaFil: Rubino, Jorge German. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas; ArgentinaFil: Ravazzoli, Claudia Leonor. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaElsevier Science SA2009-05info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/244038Santos, Juan Enrique; Rubino, Jorge German; Ravazzoli, Claudia Leonor; A numerical upscaling procedure to estimate effective plane wave and shear moduli in heterogeneous fluid-saturated poroelastic media; Elsevier Science SA; Computer Methods in Applied Mechanics and Engineering; 198; 27-29; 5-2009; 2067-20770045-7825CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0045782509000668info:eu-repo/semantics/altIdentifier/doi/10.1016/j.cma.2009.02.003info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:56:16Zoai:ri.conicet.gov.ar:11336/244038instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 09:56:16.87CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A numerical upscaling procedure to estimate effective plane wave and shear moduli in heterogeneous fluid-saturated poroelastic media
title A numerical upscaling procedure to estimate effective plane wave and shear moduli in heterogeneous fluid-saturated poroelastic media
spellingShingle A numerical upscaling procedure to estimate effective plane wave and shear moduli in heterogeneous fluid-saturated poroelastic media
Santos, Juan Enrique
ATTENUATION AND DISPERSION
POROELASTICITY
VISCOELASTICITY
FINITE ELEMENT METHODS
MONTE CARLO METHOD
title_short A numerical upscaling procedure to estimate effective plane wave and shear moduli in heterogeneous fluid-saturated poroelastic media
title_full A numerical upscaling procedure to estimate effective plane wave and shear moduli in heterogeneous fluid-saturated poroelastic media
title_fullStr A numerical upscaling procedure to estimate effective plane wave and shear moduli in heterogeneous fluid-saturated poroelastic media
title_full_unstemmed A numerical upscaling procedure to estimate effective plane wave and shear moduli in heterogeneous fluid-saturated poroelastic media
title_sort A numerical upscaling procedure to estimate effective plane wave and shear moduli in heterogeneous fluid-saturated poroelastic media
dc.creator.none.fl_str_mv Santos, Juan Enrique
Rubino, Jorge German
Ravazzoli, Claudia Leonor
author Santos, Juan Enrique
author_facet Santos, Juan Enrique
Rubino, Jorge German
Ravazzoli, Claudia Leonor
author_role author
author2 Rubino, Jorge German
Ravazzoli, Claudia Leonor
author2_role author
author
dc.subject.none.fl_str_mv ATTENUATION AND DISPERSION
POROELASTICITY
VISCOELASTICITY
FINITE ELEMENT METHODS
MONTE CARLO METHOD
topic ATTENUATION AND DISPERSION
POROELASTICITY
VISCOELASTICITY
FINITE ELEMENT METHODS
MONTE CARLO METHOD
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.5
https://purl.org/becyt/ford/1
https://purl.org/becyt/ford/2.7
https://purl.org/becyt/ford/2
dc.description.none.fl_txt_mv An important loss effect in heterogeneous poroelastic Biot media is the dissipation mechanism due to wave-induced fluid flow caused by mesoscopic scale heterogeneities, which are larger than the pore size but much smaller than the predominant wavelengths of the fast compressional and shear waves. These heterogeneities can be due to local variations in lithological properties or to patches of immiscible fluids. For example, a fast compressional wave traveling across a porous rock saturated with water and patchesof gas induces a smaller fluid-pressure in the gas patches than in the water-saturated parts of the material. This in turn generates fluid flow and slow Biot waves which diffuse away from the gas­water interfaces generating significant energy losses and velocity dispersion. To perform numerical simulations using Biot´s equations of motion, it would be necessary to employ extremely fine meshes to properly represent these mesoscopic heterogeneities and their attenuation effects on the fast waves. An alternative approach to model wave propagation in these type of Biot media is to employ a numerical upscaling procedure to determine effective complex P-wave and shear moduli defining locally a viscoelastic medium having in the average the same properties than the original Biot medium. In this work the complex P-wave and shear moduli in heterogeneous fluid-saturated porous media are obtained using numerical gedanken experiments in a Monte Carlo fashion. The experiments are defined as local boundary value problems on a reference representative volume of bulk material containing stochastic heterogeneities characterized by their statistical properties. These boundary value problems represent compressibility and shear tests needed to determine these moduli for a given realization. The average and variance of the phase velocities and quality factors associated with these moduli are obtained by averaging over realizations of the stochastic parameters. The Monte Carlo realizations were stopped when the variance of the computed quantities stabilized at an almost constant value. The approximate solution of the local boundary value problems was obtained using a Galerkin finite element procedure, and the method was validated by reproducing known solutions in the case of periodic layered media. For the spatial discretization, standard bilinear finite element spaces are employed for the solid phase, while for the fluid phase the vector part of the Raviart­Thomas­Nedelec mixed finite element space of order zero was used. Results on the uniqueness of the continuous and discrete problems as well as optimal a priori error esti-mates for the Galerkin finite element procedure are derived. Numerical experiments showing the implementation of the procedure to estimate the average and variance of the fast compressional and shear phase velocities and inverse quality factors in these kind of highly heterogeneous fluid-saturated porous media are presented.
Fil: Santos, Juan Enrique. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Purdue University; Estados Unidos. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentina
Fil: Rubino, Jorge German. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentina
Fil: Ravazzoli, Claudia Leonor. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description An important loss effect in heterogeneous poroelastic Biot media is the dissipation mechanism due to wave-induced fluid flow caused by mesoscopic scale heterogeneities, which are larger than the pore size but much smaller than the predominant wavelengths of the fast compressional and shear waves. These heterogeneities can be due to local variations in lithological properties or to patches of immiscible fluids. For example, a fast compressional wave traveling across a porous rock saturated with water and patchesof gas induces a smaller fluid-pressure in the gas patches than in the water-saturated parts of the material. This in turn generates fluid flow and slow Biot waves which diffuse away from the gas­water interfaces generating significant energy losses and velocity dispersion. To perform numerical simulations using Biot´s equations of motion, it would be necessary to employ extremely fine meshes to properly represent these mesoscopic heterogeneities and their attenuation effects on the fast waves. An alternative approach to model wave propagation in these type of Biot media is to employ a numerical upscaling procedure to determine effective complex P-wave and shear moduli defining locally a viscoelastic medium having in the average the same properties than the original Biot medium. In this work the complex P-wave and shear moduli in heterogeneous fluid-saturated porous media are obtained using numerical gedanken experiments in a Monte Carlo fashion. The experiments are defined as local boundary value problems on a reference representative volume of bulk material containing stochastic heterogeneities characterized by their statistical properties. These boundary value problems represent compressibility and shear tests needed to determine these moduli for a given realization. The average and variance of the phase velocities and quality factors associated with these moduli are obtained by averaging over realizations of the stochastic parameters. The Monte Carlo realizations were stopped when the variance of the computed quantities stabilized at an almost constant value. The approximate solution of the local boundary value problems was obtained using a Galerkin finite element procedure, and the method was validated by reproducing known solutions in the case of periodic layered media. For the spatial discretization, standard bilinear finite element spaces are employed for the solid phase, while for the fluid phase the vector part of the Raviart­Thomas­Nedelec mixed finite element space of order zero was used. Results on the uniqueness of the continuous and discrete problems as well as optimal a priori error esti-mates for the Galerkin finite element procedure are derived. Numerical experiments showing the implementation of the procedure to estimate the average and variance of the fast compressional and shear phase velocities and inverse quality factors in these kind of highly heterogeneous fluid-saturated porous media are presented.
publishDate 2009
dc.date.none.fl_str_mv 2009-05
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/244038
Santos, Juan Enrique; Rubino, Jorge German; Ravazzoli, Claudia Leonor; A numerical upscaling procedure to estimate effective plane wave and shear moduli in heterogeneous fluid-saturated poroelastic media; Elsevier Science SA; Computer Methods in Applied Mechanics and Engineering; 198; 27-29; 5-2009; 2067-2077
0045-7825
CONICET Digital
CONICET
url http://hdl.handle.net/11336/244038
identifier_str_mv Santos, Juan Enrique; Rubino, Jorge German; Ravazzoli, Claudia Leonor; A numerical upscaling procedure to estimate effective plane wave and shear moduli in heterogeneous fluid-saturated poroelastic media; Elsevier Science SA; Computer Methods in Applied Mechanics and Engineering; 198; 27-29; 5-2009; 2067-2077
0045-7825
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0045782509000668
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.cma.2009.02.003
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier Science SA
publisher.none.fl_str_mv Elsevier Science SA
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
_version_ 1844613691747598336
score 13.070432