Novos esquemas centrais de diferenças finitas para a simulação de escoamentos multifásicos em reservatórios de petróleo

• Ano de defesa: 2007
• Autor(a) principal: Ribeiro, Simone Sousa
• Orientador(a): Pereira, Luis Felipe Feres
• Banca de defesa: Souto, Helio Pedro Amaral , Furtado, Frederico , Dufour, Steven , Almeida, César Guilherme de
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade do Estado do Rio de Janeiro
• Programa de Pós-Graduação: Programa de Pós-Graduação em Modelagem Computacional
• Departamento: Centro de Tecnologia e Ciências::Instituto Politécnico
• País: BR
• Palavras-chave em Português: Escoamentos bifásicos; Esquemas centrais para leis de conservação; Velocidade local de propagação; Algoritmo REA; Escoamento bifásico - Métodos de simulação; Massa - Transferência - Soluções numéricas; Lei da conservação (Matemática); Engenharia de reservatório de óleo; Equações diferenciais parciais - Soluções numéricas; Diferenças finitas
• Palavras-chave em Inglês: Two-phase flows; Central schemes for conservation laws; Local speed of propagation; REA algorithm; Two-phase flow - Simulation methods; Mass transfer - Numerical solutions; Conservation law (Mathematics); Oil reservoir engineering; Differential equations, Partial - Numerical solutions; Finite differences
• Área do conhecimento CNPq: CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA::MATEMATICA APLICADA
• Link de acesso: http://www.bdtd.uerj.br/handle/1/13653

Incompressible two-phase flows aremodeled by a non-linear system of partial differential equations involving velocity, pressure and saturation. In this work we present a new numerical method in two spatial dimensions to solve the fluid transport equation. Its main features are computational eficiency, accuracy of solutions and absense of spurious oscillations with descontinuous initial conditions. The mathematical model used to develop this numerical method combines and extends ideias from Lax-Friedrichs, Rusanov, Nessyahu, Tadmor and Kurganov s central schemes to two spatial dimensions, i.e., it uses central differences, local speed of propagation and the REA algorithm. This new central scheme has second order accuracy and allows for a semi-discrete formulation, which makes its small numerical diffusion independent of the time step size used to integrate the differential equation. This provides the main feature of this new central scheme: no extra numerical diffusion is added if one needs to reduce the time step. This behavior is very important for applications to multiphase flows in highly heterogeneous pretoleum reservoirs, since this implies a big variability of the velocity field which demands a reduction of the time step. The very simple final formulation of the scheme is a system of ordinary differential equations involving the saturation for each cell in the computational domain. These equations are solved using a explicit second-order Runge-Kutta method. The numerical results obtained are very accurate when compared with the Nessyahu-Tadmor s totally discrete second-order central scheme. These results indicate that one needs tomultiply the number of computational cells in theNessyahu-Tadmor s scheme by 16 in order to obtain a solution comparable to the one provided by the new method.