A constitutive equation and generalized Gassmann modulus for multimineral porous media

Autores
Carcione, Jose M.; Helle, Hans B.; Santos, Juan Enrique; Ravazzoli, Claudia Leonor
Año de publicación
2005
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We derive the time-domain stress-strain relation for a porous medium composed of n - 1 solid frames and a saturating fluid. The relation holds for nonuniform porosity and can be used for numerical simulation of wave propagation. The strain-energy density can be expressed in such a way that the two phases (solid and fluid) can be mathematically equivalent. From this simplified expression of strain energy, we analogize two-, three-, and n-phase porous media and obtain the corresponding coefficients (stiffnesses). Moreover, we obtain an approx imation for the generalized Gassmann modulus. The Gassmann modulus is the bulk modulus of a saturated porous medium whose matrix (frame) is homogeneous. That is, the medium consists of two homogeneous constituents: a mineral composing the frame and a fluid. Gassmann's modulus is obtained at the low-frequency limit of Biot's theory of poroelasticity. Here, we assume that all constituents move in phase, a condition similar to the dynamic compatibility condition used by Biot, by which the P-wave velocity is equal to Gassmann's velocity at all frequencies. Our results are compared with those of the Berryman-Milton (BM) model, which provides an exact generalization of Gassmann's modulus to the three-phase case. The model is then compared to the wet-rock moduli obtained by static finite-element simulations on digitized images of microstructure and is used to fit experimental data for shaly sandstones. Finally, an example of a multimineral rock (n > 3) saturated with different fluids is given.
Fil: Carcione, Jose M.. Istituto Nazionale di Oceanografia e di Geofisica Sperimentale; Italia
Fil: Helle, Hans B.. Norsk Hydro; Noruega
Fil: Santos, Juan Enrique. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentina. Universidad de Buenos Aires. Facultad de Ingeniería. Instituto del Gas y del Petróleo; Argentina
Fil: Ravazzoli, Claudia Leonor. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentina
Materia
Gassmann
Porous media
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:11336/148916
Acceder
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling A constitutive equation and generalized Gassmann modulus for multimineral porous mediaCarcione, Jose M.Helle, Hans B.Santos, Juan EnriqueRavazzoli, Claudia LeonorGassmannPorous mediahttps://purl.org/becyt/ford/1.5https://purl.org/becyt/ford/1We derive the time-domain stress-strain relation for a porous medium composed of n - 1 solid frames and a saturating fluid. The relation holds for nonuniform porosity and can be used for numerical simulation of wave propagation. The strain-energy density can be expressed in such a way that the two phases (solid and fluid) can be mathematically equivalent. From this simplified expression of strain energy, we analogize two-, three-, and n-phase porous media and obtain the corresponding coefficients (stiffnesses). Moreover, we obtain an approx imation for the generalized Gassmann modulus. The Gassmann modulus is the bulk modulus of a saturated porous medium whose matrix (frame) is homogeneous. That is, the medium consists of two homogeneous constituents: a mineral composing the frame and a fluid. Gassmann's modulus is obtained at the low-frequency limit of Biot's theory of poroelasticity. Here, we assume that all constituents move in phase, a condition similar to the dynamic compatibility condition used by Biot, by which the P-wave velocity is equal to Gassmann's velocity at all frequencies. Our results are compared with those of the Berryman-Milton (BM) model, which provides an exact generalization of Gassmann's modulus to the three-phase case. The model is then compared to the wet-rock moduli obtained by static finite-element simulations on digitized images of microstructure and is used to fit experimental data for shaly sandstones. Finally, an example of a multimineral rock (n > 3) saturated with different fluids is given.Fil: Carcione, Jose M.. Istituto Nazionale di Oceanografia e di Geofisica Sperimentale; ItaliaFil: Helle, Hans B.. Norsk Hydro; NoruegaFil: Santos, Juan Enrique. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentina. Universidad de Buenos Aires. Facultad de Ingeniería. Instituto del Gas y del Petróleo; ArgentinaFil: Ravazzoli, Claudia Leonor. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas; ArgentinaSociety of Exploration Geophysicists2005-03-22info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/148916Carcione, Jose M.; Helle, Hans B.; Santos, Juan Enrique; Ravazzoli, Claudia Leonor; A constitutive equation and generalized Gassmann modulus for multimineral porous media; Society of Exploration Geophysicists; Geophysics; 70; 2; 22-3-2005; 17-260016-80331942-2156CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://library.seg.org/doi/10.1190/1.1897035info:eu-repo/semantics/altIdentifier/doi/10.1190/1.1897035info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2026-01-14T12:23:09Zoai:ri.conicet.gov.ar:11336/148916instacron: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:34982026-01-14 12:23:09.291CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A constitutive equation and generalized Gassmann modulus for multimineral porous media
title A constitutive equation and generalized Gassmann modulus for multimineral porous media
spellingShingle A constitutive equation and generalized Gassmann modulus for multimineral porous media
Carcione, Jose M.
Gassmann
Porous media
title_short A constitutive equation and generalized Gassmann modulus for multimineral porous media
title_full A constitutive equation and generalized Gassmann modulus for multimineral porous media
title_fullStr A constitutive equation and generalized Gassmann modulus for multimineral porous media
title_full_unstemmed A constitutive equation and generalized Gassmann modulus for multimineral porous media
title_sort A constitutive equation and generalized Gassmann modulus for multimineral porous media
dc.creator.none.fl_str_mv Carcione, Jose M.
Helle, Hans B.
Santos, Juan Enrique
Ravazzoli, Claudia Leonor
author Carcione, Jose M.
author_facet Carcione, Jose M.
Helle, Hans B.
Santos, Juan Enrique
Ravazzoli, Claudia Leonor
author_role author
author2 Helle, Hans B.
Santos, Juan Enrique
Ravazzoli, Claudia Leonor
author2_role author
author
author
dc.subject.none.fl_str_mv Gassmann
Porous media
topic Gassmann
Porous media
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.5
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We derive the time-domain stress-strain relation for a porous medium composed of n - 1 solid frames and a saturating fluid. The relation holds for nonuniform porosity and can be used for numerical simulation of wave propagation. The strain-energy density can be expressed in such a way that the two phases (solid and fluid) can be mathematically equivalent. From this simplified expression of strain energy, we analogize two-, three-, and n-phase porous media and obtain the corresponding coefficients (stiffnesses). Moreover, we obtain an approx imation for the generalized Gassmann modulus. The Gassmann modulus is the bulk modulus of a saturated porous medium whose matrix (frame) is homogeneous. That is, the medium consists of two homogeneous constituents: a mineral composing the frame and a fluid. Gassmann's modulus is obtained at the low-frequency limit of Biot's theory of poroelasticity. Here, we assume that all constituents move in phase, a condition similar to the dynamic compatibility condition used by Biot, by which the P-wave velocity is equal to Gassmann's velocity at all frequencies. Our results are compared with those of the Berryman-Milton (BM) model, which provides an exact generalization of Gassmann's modulus to the three-phase case. The model is then compared to the wet-rock moduli obtained by static finite-element simulations on digitized images of microstructure and is used to fit experimental data for shaly sandstones. Finally, an example of a multimineral rock (n > 3) saturated with different fluids is given.
Fil: Carcione, Jose M.. Istituto Nazionale di Oceanografia e di Geofisica Sperimentale; Italia
Fil: Helle, Hans B.. Norsk Hydro; Noruega
Fil: Santos, Juan Enrique. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentina. Universidad de Buenos Aires. Facultad de Ingeniería. Instituto del Gas y del Petróleo; Argentina
Fil: Ravazzoli, Claudia Leonor. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentina
description We derive the time-domain stress-strain relation for a porous medium composed of n - 1 solid frames and a saturating fluid. The relation holds for nonuniform porosity and can be used for numerical simulation of wave propagation. The strain-energy density can be expressed in such a way that the two phases (solid and fluid) can be mathematically equivalent. From this simplified expression of strain energy, we analogize two-, three-, and n-phase porous media and obtain the corresponding coefficients (stiffnesses). Moreover, we obtain an approx imation for the generalized Gassmann modulus. The Gassmann modulus is the bulk modulus of a saturated porous medium whose matrix (frame) is homogeneous. That is, the medium consists of two homogeneous constituents: a mineral composing the frame and a fluid. Gassmann's modulus is obtained at the low-frequency limit of Biot's theory of poroelasticity. Here, we assume that all constituents move in phase, a condition similar to the dynamic compatibility condition used by Biot, by which the P-wave velocity is equal to Gassmann's velocity at all frequencies. Our results are compared with those of the Berryman-Milton (BM) model, which provides an exact generalization of Gassmann's modulus to the three-phase case. The model is then compared to the wet-rock moduli obtained by static finite-element simulations on digitized images of microstructure and is used to fit experimental data for shaly sandstones. Finally, an example of a multimineral rock (n > 3) saturated with different fluids is given.
publishDate 2005
dc.date.none.fl_str_mv 2005-03-22
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/11336/148916
Carcione, Jose M.; Helle, Hans B.; Santos, Juan Enrique; Ravazzoli, Claudia Leonor; A constitutive equation and generalized Gassmann modulus for multimineral porous media; Society of Exploration Geophysicists; Geophysics; 70; 2; 22-3-2005; 17-26
0016-8033
1942-2156
CONICET Digital
CONICET
url http://hdl.handle.net/11336/148916
identifier_str_mv Carcione, Jose M.; Helle, Hans B.; Santos, Juan Enrique; Ravazzoli, Claudia Leonor; A constitutive equation and generalized Gassmann modulus for multimineral porous media; Society of Exploration Geophysicists; Geophysics; 70; 2; 22-3-2005; 17-26
0016-8033
1942-2156
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://library.seg.org/doi/10.1190/1.1897035
info:eu-repo/semantics/altIdentifier/doi/10.1190/1.1897035
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
dc.publisher.none.fl_str_mv Society of Exploration Geophysicists
publisher.none.fl_str_mv Society of Exploration Geophysicists
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
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score 12.603104

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