Finite volume simulations of particle‑laden viscoelastic fuid fows: application to hydraulic fracture processes
Autor(a) principal: | |
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Data de Publicação: | 2022 |
Outros Autores: | , , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | https://hdl.handle.net/1822/76504 |
Resumo: | Accurately resolving the coupled momentum transfer between the liquid and solid phases of complex fluids is a fundamental problem in multiphase transport processes, such as hydraulic fracture operations. Specifically we need to characterize the dependence of the normalized average fluid–particle force ⟨F⟩ on the volume fraction of the dispersed solid phase and on the rheology of the complex fluid matrix, parameterized through the Weissenberg number Wi measuring the relative magnitude of elastic to viscous stresses in the fluid. Here we use direct numerical simulations (DNS) to study the creeping flow (Re≪1) of viscoelastic fluids through static random arrays of monodisperse spherical particles using a finite volume Navier–Stokes/Cauchy momentum solver. The numerical study consists of N=150 different systems, in which the normalized average fluid–particle force ⟨F⟩ is obtained as a function of the volume fraction ϕ (0<ϕ≤0.2) of the dispersed solid phase and the Weissenberg number Wi (0≤Wi≤4). From these predictions a closure law ⟨F(ϕ,Wi)⟩ for the drag force is derived for the quasi-linear Oldroyd-B viscoelastic fluid model (with fixed retardation ratio β=0.5) which is, on average, within 5.7% of the DNS results. In addition, a flow solver able to couple Eulerian and Lagrangian phases (in which the particulate phase is modeled by the discrete particle method (DPM)) is developed, which incorporates the viscoelastic nature of the continuum phase and the closed-form drag law. Two case studies were simulated using this solver, to assess the accuracy and robustness of the newly developed approach for handling particle-laden viscoelastic flow configurations with O(105−106) rigid spheres that are representative of hydraulic fracture operations. Three-dimensional settling processes in a Newtonian fluid and in a quasi-linear Oldroyd-B viscoelastic fluid are both investigated using a rectangular channel and an annular pipe domain. Good agreement is obtained for the particle distribution measured in a Newtonian fluid, when comparing numerical results with experimental data. For the cases in which the continuous fluid phase is viscoelastic we compute the evolution in the velocity fields and predicted particle distributions are presented at different elasticity numbers 0≤El≤30 (where El=Wi/Re) and for different suspension particle volume fractions. |
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Finite volume simulations of particle‑laden viscoelastic fuid fows: application to hydraulic fracture processesRandom arrays of spheresDrag coefcientViscoelastic fuidsOldroyd-B modelEulerian–Lagrangian formulationDiscrete particle methodDrag coefficientViscoelastic fluidsEngenharia e Tecnologia::Engenharia MecânicaScience & TechnologyEnergias renováveis e acessíveisAccurately resolving the coupled momentum transfer between the liquid and solid phases of complex fluids is a fundamental problem in multiphase transport processes, such as hydraulic fracture operations. Specifically we need to characterize the dependence of the normalized average fluid–particle force ⟨F⟩ on the volume fraction of the dispersed solid phase and on the rheology of the complex fluid matrix, parameterized through the Weissenberg number Wi measuring the relative magnitude of elastic to viscous stresses in the fluid. Here we use direct numerical simulations (DNS) to study the creeping flow (Re≪1) of viscoelastic fluids through static random arrays of monodisperse spherical particles using a finite volume Navier–Stokes/Cauchy momentum solver. The numerical study consists of N=150 different systems, in which the normalized average fluid–particle force ⟨F⟩ is obtained as a function of the volume fraction ϕ (0<ϕ≤0.2) of the dispersed solid phase and the Weissenberg number Wi (0≤Wi≤4). From these predictions a closure law ⟨F(ϕ,Wi)⟩ for the drag force is derived for the quasi-linear Oldroyd-B viscoelastic fluid model (with fixed retardation ratio β=0.5) which is, on average, within 5.7% of the DNS results. In addition, a flow solver able to couple Eulerian and Lagrangian phases (in which the particulate phase is modeled by the discrete particle method (DPM)) is developed, which incorporates the viscoelastic nature of the continuum phase and the closed-form drag law. Two case studies were simulated using this solver, to assess the accuracy and robustness of the newly developed approach for handling particle-laden viscoelastic flow configurations with O(105−106) rigid spheres that are representative of hydraulic fracture operations. Three-dimensional settling processes in a Newtonian fluid and in a quasi-linear Oldroyd-B viscoelastic fluid are both investigated using a rectangular channel and an annular pipe domain. Good agreement is obtained for the particle distribution measured in a Newtonian fluid, when comparing numerical results with experimental data. For the cases in which the continuous fluid phase is viscoelastic we compute the evolution in the velocity fields and predicted particle distributions are presented at different elasticity numbers 0≤El≤30 (where El=Wi/Re) and for different suspension particle volume fractions.This work is funded by FEDER funds through the COMPETE 2020 Programme and National Funds through FCT (Portuguese Foundation for Science and Technology) under the projects UID-B/05256/2020, UID-P/05256/2020 and MIT-EXPL/TDI/0038/2019 - APROVA - Deep learning for particle-laden viscoelastic flow modelling (POCI-01-0145-FEDER-016665) under MIT Portugal program. The authors would like to acknowledge the University of Minho cluster under the project NORTE-07-0162-FEDER-000086 (URL: http://search6.di.uminho.pt), the Minho Advanced Computing Center (MACC) (URL: https:// macc.fccn.pt) under the project CPCA_A2_6052_2020, the Texas Advanced Computing Center (TACC) at The University of Texas at Austin (URL: http://www.tacc.utexas.edu), the Gompute HPC Cloud Platform (URL: https://www.gompute.com), and PRACE - Partnership for Advanced Computing in Europe under the project icei-prace-2020-0009, for providing HPC resources that have contributed to the research results reported within this paper.SpringerUniversidade do MinhoFernandes, C.Faroughi, S. A.Ribeiro, R.Isabel, A.McKinley, G. H.20222022-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/1822/76504engFernandes, C., Faroughi, S.A., Ribeiro, R. et al. Finite volume simulations of particle-laden viscoelastic fluid flows: application to hydraulic fracture processes. Engineering with Computers (2022). https://doi.org/10.1007/s00366-022-01626-50177-06671435-566310.1007/s00366-022-01626-5https://link.springer.com/article/10.1007/s00366-022-01626-5info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-07-21T12:17:53Zoai:repositorium.sdum.uminho.pt:1822/76504Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:10:35.183352Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Finite volume simulations of particle‑laden viscoelastic fuid fows: application to hydraulic fracture processes |
title |
Finite volume simulations of particle‑laden viscoelastic fuid fows: application to hydraulic fracture processes |
spellingShingle |
Finite volume simulations of particle‑laden viscoelastic fuid fows: application to hydraulic fracture processes Fernandes, C. Random arrays of spheres Drag coefcient Viscoelastic fuids Oldroyd-B model Eulerian–Lagrangian formulation Discrete particle method Drag coefficient Viscoelastic fluids Engenharia e Tecnologia::Engenharia Mecânica Science & Technology Energias renováveis e acessíveis |
title_short |
Finite volume simulations of particle‑laden viscoelastic fuid fows: application to hydraulic fracture processes |
title_full |
Finite volume simulations of particle‑laden viscoelastic fuid fows: application to hydraulic fracture processes |
title_fullStr |
Finite volume simulations of particle‑laden viscoelastic fuid fows: application to hydraulic fracture processes |
title_full_unstemmed |
Finite volume simulations of particle‑laden viscoelastic fuid fows: application to hydraulic fracture processes |
title_sort |
Finite volume simulations of particle‑laden viscoelastic fuid fows: application to hydraulic fracture processes |
author |
Fernandes, C. |
author_facet |
Fernandes, C. Faroughi, S. A. Ribeiro, R. Isabel, A. McKinley, G. H. |
author_role |
author |
author2 |
Faroughi, S. A. Ribeiro, R. Isabel, A. McKinley, G. H. |
author2_role |
author author author author |
dc.contributor.none.fl_str_mv |
Universidade do Minho |
dc.contributor.author.fl_str_mv |
Fernandes, C. Faroughi, S. A. Ribeiro, R. Isabel, A. McKinley, G. H. |
dc.subject.por.fl_str_mv |
Random arrays of spheres Drag coefcient Viscoelastic fuids Oldroyd-B model Eulerian–Lagrangian formulation Discrete particle method Drag coefficient Viscoelastic fluids Engenharia e Tecnologia::Engenharia Mecânica Science & Technology Energias renováveis e acessíveis |
topic |
Random arrays of spheres Drag coefcient Viscoelastic fuids Oldroyd-B model Eulerian–Lagrangian formulation Discrete particle method Drag coefficient Viscoelastic fluids Engenharia e Tecnologia::Engenharia Mecânica Science & Technology Energias renováveis e acessíveis |
description |
Accurately resolving the coupled momentum transfer between the liquid and solid phases of complex fluids is a fundamental problem in multiphase transport processes, such as hydraulic fracture operations. Specifically we need to characterize the dependence of the normalized average fluid–particle force ⟨F⟩ on the volume fraction of the dispersed solid phase and on the rheology of the complex fluid matrix, parameterized through the Weissenberg number Wi measuring the relative magnitude of elastic to viscous stresses in the fluid. Here we use direct numerical simulations (DNS) to study the creeping flow (Re≪1) of viscoelastic fluids through static random arrays of monodisperse spherical particles using a finite volume Navier–Stokes/Cauchy momentum solver. The numerical study consists of N=150 different systems, in which the normalized average fluid–particle force ⟨F⟩ is obtained as a function of the volume fraction ϕ (0<ϕ≤0.2) of the dispersed solid phase and the Weissenberg number Wi (0≤Wi≤4). From these predictions a closure law ⟨F(ϕ,Wi)⟩ for the drag force is derived for the quasi-linear Oldroyd-B viscoelastic fluid model (with fixed retardation ratio β=0.5) which is, on average, within 5.7% of the DNS results. In addition, a flow solver able to couple Eulerian and Lagrangian phases (in which the particulate phase is modeled by the discrete particle method (DPM)) is developed, which incorporates the viscoelastic nature of the continuum phase and the closed-form drag law. Two case studies were simulated using this solver, to assess the accuracy and robustness of the newly developed approach for handling particle-laden viscoelastic flow configurations with O(105−106) rigid spheres that are representative of hydraulic fracture operations. Three-dimensional settling processes in a Newtonian fluid and in a quasi-linear Oldroyd-B viscoelastic fluid are both investigated using a rectangular channel and an annular pipe domain. Good agreement is obtained for the particle distribution measured in a Newtonian fluid, when comparing numerical results with experimental data. For the cases in which the continuous fluid phase is viscoelastic we compute the evolution in the velocity fields and predicted particle distributions are presented at different elasticity numbers 0≤El≤30 (where El=Wi/Re) and for different suspension particle volume fractions. |
publishDate |
2022 |
dc.date.none.fl_str_mv |
2022 2022-01-01T00:00:00Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
https://hdl.handle.net/1822/76504 |
url |
https://hdl.handle.net/1822/76504 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Fernandes, C., Faroughi, S.A., Ribeiro, R. et al. Finite volume simulations of particle-laden viscoelastic fluid flows: application to hydraulic fracture processes. Engineering with Computers (2022). https://doi.org/10.1007/s00366-022-01626-5 0177-0667 1435-5663 10.1007/s00366-022-01626-5 https://link.springer.com/article/10.1007/s00366-022-01626-5 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Springer |
publisher.none.fl_str_mv |
Springer |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
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RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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1799132535913971712 |