A finite volume scheme coupled with a hybrid-grid method for the 2-d simulation of two-phase flows in naturally fractured reservoirs

Detalhes bibliográficos
Autor(a) principal: CAVALCANTE, Túlio de Moura
Data de Publicação: 2019
Tipo de documento: Dissertação
Idioma: eng
Título da fonte: Repositório Institucional da UFPE
dARK ID: ark:/64986/0013000013xp9
Texto Completo: https://repositorio.ufpe.br/handle/123456789/32952
Resumo: Two-phase flows of oil and water in naturally fractured petroleum reservoirs can be described by a system of nonlinear partial differential equations that comprises an elliptic pressure equation and a hyperbolic saturation equation coupled through the total velocity field. Modeling this problem is a great challenge, due to the complexity of the depositional environments, which can include fractures (channels or barriers). In such cases, it is particularly complex to construct structured meshes which are capable of properly modeling the reservoir. In this work, a locally conservative approach to model the oil and water displacements in naturally fractured reservoirs using general unstructured meshes was developed. A cell-centered Finite-Volume Method with a Multi-Point Flux Approximation that uses the so called “diamond stencil” (MPFA-D) was used to solve the pressure equation, coupled with a Hybrid-Grid Method (HyG) to deal with the fractures. The classical First Order Upwind Method (FOUM) was used to solve the saturation equation. The FOUM was applied in two different segregated schemes, in its explicit and implicit versions, respectively the IMPES (IMplicit Pressure and Explicit Saturation) and the SEQ (SEQuential implicit pressure and saturation). The MPFA-D is a very robust and flexible formulation that is capable of handling highly heterogeneous and anisotropic domains using general polygonal meshes. In the HyG, the mesh that discretizes the domain must fit the spatial positions of the fractures, so that they are associated to edges - as 1-D cells in a 2-D mesh -, therefore, the calculation of the fluxes in these edges is dependent on the pressures on fractures and on the adjacent volumes, but, in this strategy, the fractures are expanded, in the computational domain, to the same dimension of the mesh. In this way, it is possible to get, for example, 2-D fracture cells in a 2-D mesh, but avoiding excessive refinement in the fractured regions, in the original mesh. The proposed formulation presented quite remarkable results when compared with similar formulations using classical full pressure support and triangle pressure support methods, or even the with MPFA-D itself when using an equidimensional approach.
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spelling CAVALCANTE, Túlio de Mourahttp://lattes.cnpq.br/8867705542362809http://lattes.cnpq.br/6568615406054840LYRA, Paulo Roberto MacielCARVALHO, Darlan Karlo Elisiário de2019-09-16T19:07:29Z2019-09-16T19:07:29Z2019-01-18https://repositorio.ufpe.br/handle/123456789/32952ark:/64986/0013000013xp9Two-phase flows of oil and water in naturally fractured petroleum reservoirs can be described by a system of nonlinear partial differential equations that comprises an elliptic pressure equation and a hyperbolic saturation equation coupled through the total velocity field. Modeling this problem is a great challenge, due to the complexity of the depositional environments, which can include fractures (channels or barriers). In such cases, it is particularly complex to construct structured meshes which are capable of properly modeling the reservoir. In this work, a locally conservative approach to model the oil and water displacements in naturally fractured reservoirs using general unstructured meshes was developed. A cell-centered Finite-Volume Method with a Multi-Point Flux Approximation that uses the so called “diamond stencil” (MPFA-D) was used to solve the pressure equation, coupled with a Hybrid-Grid Method (HyG) to deal with the fractures. The classical First Order Upwind Method (FOUM) was used to solve the saturation equation. The FOUM was applied in two different segregated schemes, in its explicit and implicit versions, respectively the IMPES (IMplicit Pressure and Explicit Saturation) and the SEQ (SEQuential implicit pressure and saturation). The MPFA-D is a very robust and flexible formulation that is capable of handling highly heterogeneous and anisotropic domains using general polygonal meshes. In the HyG, the mesh that discretizes the domain must fit the spatial positions of the fractures, so that they are associated to edges - as 1-D cells in a 2-D mesh -, therefore, the calculation of the fluxes in these edges is dependent on the pressures on fractures and on the adjacent volumes, but, in this strategy, the fractures are expanded, in the computational domain, to the same dimension of the mesh. In this way, it is possible to get, for example, 2-D fracture cells in a 2-D mesh, but avoiding excessive refinement in the fractured regions, in the original mesh. The proposed formulation presented quite remarkable results when compared with similar formulations using classical full pressure support and triangle pressure support methods, or even the with MPFA-D itself when using an equidimensional approach.FACEPEEscoamentos bifásicos de óleo e água em reservatórios de petróleo naturalmente fraturados podem ser descritos por um sistema de equações diferenciais parciais não-lineares que compreende uma equação elíptica de pressão e uma equação hiperbólica de saturação acopladas através do campo de velocidade total. Modelar este tipo de problema é um grande desafio, devido à complexidade dos ambientes deposicionais, que pode incluir fraturas (canais ou barreiras). Em tais casos, é particularmente complexo construir malhas estruturadas capazes de modelar adequadamente o reservatório. Neste trabalho, foi desenvolvida uma formulação localmente conservativa para modelar os escoamentos de óleo e água em reservatórios naturalmente fraturados usando malhas não-estruturadas. Para resolver a equação da pressão, foi adaptado um método de volumes finitos centrado na célula com uma aproximação de fluxo por múltiplos pontos que usa o chamado "estêncil de diamante" (MPFA-D) acoplado a um método de malha híbrida (HyG) para lidar com as fraturas. O clássico método de ponderação à montante de primeira ordem (FOUM) foi usado para resolver a equação de saturação. O FOUM foi aplicado em dois esquemas segregados diferentes, em suas versões explícita e implícita, respectivamente o IMPES (solução Implícita para a Pressão e Explícita para a Saturação) e o SEQ (solução SEQuencialmente implícita para pressão e saturação). O MPFA-D é uma formulação muito robusta e flexível que é capaz de lidar com domínios altamente heterogêneos e anisotrópicos usando malhas poligonais quaisquer. No HyG, a malha que discretiza o domínio deve ajustar-se às posições espaciais das fraturas, de forma que elas estejam associadas a arestas - como células 1-D em uma malha 2-D -, portanto, o cálculo dos fluxos nessas arestas é dependente das pressões nas fraturas e nos volumes adjacentes, mas, nessa estratégia, as fraturas são expandidas, no domínio computacional, para a mesma dimensão da malha. Dessa forma, é possível obter, por exemplo, células de fratura 2-D em uma malha 2-D, mas evitando-se refinamentos excessivos nas regiões das fraturas, na malha original. A formulação proposta apresentou bons resultados quando comparada com formulações similares utilizando métodos clássicos com suporte total e suporte triangular para a pressão, ou mesmo com o próprio MPFA-D, numa abordagem equidimensional.engUniversidade Federal de PernambucoPrograma de Pos Graduacao em Engenharia MecanicaUFPEBrasilAttribution-NonCommercial-NoDerivs 3.0 Brazilhttp://creativecommons.org/licenses/by-nc-nd/3.0/br/info:eu-repo/semantics/openAccessEngenharia MecânicaEscoamento bifásico de óleo e águaReservatórios heterogêneos e anisotrópicosReservatórios naturalmente fraturadosModelo de malha híbridaMPFA-DA finite volume scheme coupled with a hybrid-grid method for the 2-d simulation of two-phase flows in naturally fractured reservoirsinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesismestradoreponame:Repositório Institucional da UFPEinstname:Universidade Federal de Pernambuco (UFPE)instacron:UFPETHUMBNAILDISSERTAÇÃO Túlio de Moura Cavalcante.pdf.jpgDISSERTAÇÃO Túlio de Moura Cavalcante.pdf.jpgGenerated Thumbnailimage/jpeg1290https://repositorio.ufpe.br/bitstream/123456789/32952/5/DISSERTA%c3%87%c3%83O%20T%c3%balio%20de%20Moura%20Cavalcante.pdf.jpg280f4735a20dd082d3bea2547675cab1MD55ORIGINALDISSERTAÇÃO Túlio de Moura Cavalcante.pdfDISSERTAÇÃO Túlio de Moura Cavalcante.pdfapplication/pdf4247241https://repositorio.ufpe.br/bitstream/123456789/32952/1/DISSERTA%c3%87%c3%83O%20T%c3%balio%20de%20Moura%20Cavalcante.pdf1af13b8165ed46f0da45cb29536ab9e7MD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; 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dc.title.pt_BR.fl_str_mv A finite volume scheme coupled with a hybrid-grid method for the 2-d simulation of two-phase flows in naturally fractured reservoirs
title A finite volume scheme coupled with a hybrid-grid method for the 2-d simulation of two-phase flows in naturally fractured reservoirs
spellingShingle A finite volume scheme coupled with a hybrid-grid method for the 2-d simulation of two-phase flows in naturally fractured reservoirs
CAVALCANTE, Túlio de Moura
Engenharia Mecânica
Escoamento bifásico de óleo e água
Reservatórios heterogêneos e anisotrópicos
Reservatórios naturalmente fraturados
Modelo de malha híbrida
MPFA-D
title_short A finite volume scheme coupled with a hybrid-grid method for the 2-d simulation of two-phase flows in naturally fractured reservoirs
title_full A finite volume scheme coupled with a hybrid-grid method for the 2-d simulation of two-phase flows in naturally fractured reservoirs
title_fullStr A finite volume scheme coupled with a hybrid-grid method for the 2-d simulation of two-phase flows in naturally fractured reservoirs
title_full_unstemmed A finite volume scheme coupled with a hybrid-grid method for the 2-d simulation of two-phase flows in naturally fractured reservoirs
title_sort A finite volume scheme coupled with a hybrid-grid method for the 2-d simulation of two-phase flows in naturally fractured reservoirs
author CAVALCANTE, Túlio de Moura
author_facet CAVALCANTE, Túlio de Moura
author_role author
dc.contributor.authorLattes.pt_BR.fl_str_mv http://lattes.cnpq.br/8867705542362809
dc.contributor.advisorLattes.pt_BR.fl_str_mv http://lattes.cnpq.br/6568615406054840
dc.contributor.author.fl_str_mv CAVALCANTE, Túlio de Moura
dc.contributor.advisor1.fl_str_mv LYRA, Paulo Roberto Maciel
dc.contributor.advisor-co1.fl_str_mv CARVALHO, Darlan Karlo Elisiário de
contributor_str_mv LYRA, Paulo Roberto Maciel
CARVALHO, Darlan Karlo Elisiário de
dc.subject.por.fl_str_mv Engenharia Mecânica
Escoamento bifásico de óleo e água
Reservatórios heterogêneos e anisotrópicos
Reservatórios naturalmente fraturados
Modelo de malha híbrida
MPFA-D
topic Engenharia Mecânica
Escoamento bifásico de óleo e água
Reservatórios heterogêneos e anisotrópicos
Reservatórios naturalmente fraturados
Modelo de malha híbrida
MPFA-D
description Two-phase flows of oil and water in naturally fractured petroleum reservoirs can be described by a system of nonlinear partial differential equations that comprises an elliptic pressure equation and a hyperbolic saturation equation coupled through the total velocity field. Modeling this problem is a great challenge, due to the complexity of the depositional environments, which can include fractures (channels or barriers). In such cases, it is particularly complex to construct structured meshes which are capable of properly modeling the reservoir. In this work, a locally conservative approach to model the oil and water displacements in naturally fractured reservoirs using general unstructured meshes was developed. A cell-centered Finite-Volume Method with a Multi-Point Flux Approximation that uses the so called “diamond stencil” (MPFA-D) was used to solve the pressure equation, coupled with a Hybrid-Grid Method (HyG) to deal with the fractures. The classical First Order Upwind Method (FOUM) was used to solve the saturation equation. The FOUM was applied in two different segregated schemes, in its explicit and implicit versions, respectively the IMPES (IMplicit Pressure and Explicit Saturation) and the SEQ (SEQuential implicit pressure and saturation). The MPFA-D is a very robust and flexible formulation that is capable of handling highly heterogeneous and anisotropic domains using general polygonal meshes. In the HyG, the mesh that discretizes the domain must fit the spatial positions of the fractures, so that they are associated to edges - as 1-D cells in a 2-D mesh -, therefore, the calculation of the fluxes in these edges is dependent on the pressures on fractures and on the adjacent volumes, but, in this strategy, the fractures are expanded, in the computational domain, to the same dimension of the mesh. In this way, it is possible to get, for example, 2-D fracture cells in a 2-D mesh, but avoiding excessive refinement in the fractured regions, in the original mesh. The proposed formulation presented quite remarkable results when compared with similar formulations using classical full pressure support and triangle pressure support methods, or even the with MPFA-D itself when using an equidimensional approach.
publishDate 2019
dc.date.accessioned.fl_str_mv 2019-09-16T19:07:29Z
dc.date.available.fl_str_mv 2019-09-16T19:07:29Z
dc.date.issued.fl_str_mv 2019-01-18
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
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dc.identifier.uri.fl_str_mv https://repositorio.ufpe.br/handle/123456789/32952
dc.identifier.dark.fl_str_mv ark:/64986/0013000013xp9
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dc.language.iso.fl_str_mv eng
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dc.rights.driver.fl_str_mv Attribution-NonCommercial-NoDerivs 3.0 Brazil
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rights_invalid_str_mv Attribution-NonCommercial-NoDerivs 3.0 Brazil
http://creativecommons.org/licenses/by-nc-nd/3.0/br/
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dc.publisher.none.fl_str_mv Universidade Federal de Pernambuco
dc.publisher.program.fl_str_mv Programa de Pos Graduacao em Engenharia Mecanica
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dc.publisher.country.fl_str_mv Brasil
publisher.none.fl_str_mv Universidade Federal de Pernambuco
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