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Master's Dissertation
DOI
https://doi.org/10.11606/D.55.2020.tde-19022021-142635
Document
Author
Full name
Anna Caroline Felix Santos de Jesus
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2020
Supervisor
Committee
Sousa, Fabrício Simeoni de (President)
Castelo Filho, Antonio
Pereira, Luis Felipe Feres
Souto, Helio Pedro Amaral
Title in Portuguese
Solução numérica do modelo de Stokes-Brinkman para escoamentos em meios porosos
Keywords in Portuguese
Escoamento bifásico
Escoamento em meios porosos
Modelo Darcy
Modelo de Stokes
Modelo Stokes-Brinkman
Abstract in Portuguese
Em escoamentos em meios porosos, especialmente os provenientes de problemas de extração de petróleo, o modelo de Darcy é amplamente utilizado quando a escala de referência do escoamento é muito maior que a escala da estrutura de poros do meio poroso. Na presença de canais livres ou em domínio com alta porosidade (como em fraturas no material poroso, por exemplo), o modelo de Stokes-Brinkman é mais adequado, sendo um intermediário entre o modelo de Darcy puro e a solução direta na escala do poro através das equações de Stokes. Este trabalho propõe a simulação numérica do modelo de Stokes-Brinkman para escoamentos em meios porosos, com o objetivo de investigar os limites dessa modelagem, os desafios numéricos na sua discretização e apresentar uma nova abordagem para escoamento bifásico (água e óleo) em meios porosos heterogêneos. O modelo bifásico proposto consiste em equações de pressão-velocidade (assumindo o fluxo de Stokes-Brinkman) acopladas a uma equação hiperbólica não linear que governa o balanço de massa (equação de saturação).
Title in English
Numerical solution of the Stokes-Brinkman model for porous media flows
Keywords in English
Darcy model
Flow in porous media
Stokes model
Stokes- Brinkman model
Two phase flow
Abstract in English
In porous media flows, specially those arising from petroleum exploration, the Darcy model is largely employed, which is suitable when the domain scale is much larger than the pore scale structure of the porous material. When free channels or high-porosity media are considered (such as fractures in the porous material, for instance), the Stokes-Brinkman model is more adequate, as an intermediate model between Darcy and direct solution in the pore scale modelled by the Stokes equations. This work is to concerned about the numerical solution of the Stokes- Brinkman modeling porous media flow. We investigate the limits of this formulation, the numerical challenges in its discretization and a new approach for two-phase flow (water and oil) in heterogeneous porous media. The proposed model consists of pressure-velocity equations (assuming the Stokes-Brinkman flow) coupled to a non-linear hyperbolic equation that governs the mass balance (saturation equation).
 
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Publishing Date
2021-02-19
 
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