Modelagem computacional de escoamentos com duas e três fases em reservatórios petrolíferos heterogêneos

• Ano de defesa: 2008
• Autor(a) principal: Souza, Grazione de
• Orientador(a): Pereira, Luis Felipe Feres
• Banca de defesa: Souto, Helio Pedro Amaral , Pires, Adolfo Puime
• Tipo de documento: Dissertação
• 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: Escoamento bifásico Métodos de simulação; Escoamento bifásico Modelos matemáticos; Engenharia de reservatório de óleo Métodos de simulação; Materiais porosos; Histerese Modelos matemáticos; Lei da conservação (Matemática); Método dos elementos finitos; Método de decomposição; Escoamentos bifásicos e trifásicos; Meios porosos heterogêneos; Esquemas centrais para leis de conservação; Método de elementos finitos mistos; Decomposição de operadores
• Palavras-chave em Inglês: Two-phase flow - simulation methods; Two-phase flow - mathematical models; Oil reservoir engineering - simulation methods; Porous media; Hysteresis - mathematical models; Conservation laws (Mathematics); Finite element method; Decomposition method; Two- and three-phase flow; Heterogeneous porous media; Second order finite difference scheme; Mixed finite element method; Operator splitting
• Área do conhecimento CNPq: CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA::MATEMATICA APLICADA
• Link de acesso: http://www.bdtd.uerj.br/handle/1/13773

We consider in this work a mathematical model for two- and three-phase flow problems in petroleum reservoirs and the computational modeling of the governing equations for its numerical solution. We consider two- (water-oil) and three-phase (water-gas-oil) incompressible, immiscible flow problems and the reservoir rock is considered to be heterogeneous. In our model, we also take into account the hysteresis effects in the oil relative permeability functions. In the case of three-phase flow, the choice of general expressions for the relative permeability functions may lead to the loss of strict hyperbolicity and, therefore, to the existence of an elliptic region or umbilic points for the system of nonlinear hyperbolic conservation laws describing the convective transport of the fluid phases. As a consequence, the loss of hyperbolicity may lead to the existence of nonclassical shocks (also called transitional shocks or undercompressive shocks) in three-phase flow solutions. We present a new, accurate fractional time-step method based on an operator splitting technique for the numerical solution of a system of partial differential equations modeling two-phase, immiscible water-oil flow problems in heterogeneous petroleum reservoirs. An efficient two-phase water-oil numerical simulator developed by our research group was sucessfuly extended to take into account hysteresis effects under the hypotesis previously annouced. The numerical results obtained by the procedure proposed indicate numerical evidence the method at hand can be extended for the case of related three-phase water-gas-oil flow problems. A two-level operator splitting technique allows for the use of distinct time steps for the four problems defined by the splitting procedure: convection, diffusion, pressure-velocity and relaxation for hysteresis. The convective transport (hyperbolic) of the fluid phases is approximated by a high resolution, nonoscillatory, second-order, conservative central difference scheme in the convection step. This scheme is combined with locally conservative mixed finite elements for the numerical solution of the diffusive transport (parabolic) and the pressure-velocity (elliptic) problems. The time discretization of the parabolic problem is performed by means of the implicit Backward Euler method. An ordinary diferential equation is solved (analytically) for the relaxation related to hysteresis. Two-phase water-oil numerical results in one space dimensional, in which are in a very good agreement with semi-analitycal results available in the literature, were computationaly reproduced and new numerical results in two dimensional heterogeneous media are also presented and the extension of this technique to the case of three-phase water-oil-gas flows problems is proposed.