Análise matemática de soluções descontínuas de leis de conservação hiperbólicas e resoluções numéricas para a captura de ondas de choque em escoamentos multifásicos em meios porosos

• Autor(a) principal: Barbosa, Nelson Machado
• Data de Publicação: 2014
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações da UERJ
• Texto Completo: http://www.bdtd.uerj.br/handle/1/13673
• topic: Secondary recuperation process of petroleum; Nonlinear hyperbolic equation; Conservation laws; LWLF-k composite scheme; Nonstandard scheme; Recuperação secundária de petróleo; Leis de conservação; Método composto LWLF-k; Esquema nonStandard; Escoamento multifásico - Métodos de simulação; Equações diferenciais hiperbólicas - Métodos de simulação; Lei da conservação (Física) - Métodos de simulação; Petróleo Prospecção - Métodos de simulação; Análise matemática incomum - Métodos de simulação; Escoamento em meios porosos - Métodos de simulação; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA::MATEMATICA APLICADA

The process of secondary oil recovery is commonly accomplished by injecting water or gas into the reservoir to maintain the necessary pressure for their extraction. So that the investment is viable spending extraction must be smaller than the financial return to oil production. Aiming to study possible scenarios for the exploration process, it is customary to use simulations of extraction processes. The equations that model this process of recovery are hyperbolic and nonlinear, which can be interpreted as Conservation Laws , whose solutions are complex by their discontinuous nature . These discontinuities or jumps are known as shock waves. Due to this importance, this work will be discussed a mathematical analysis of the phenomena arising from conservation laws, to then use it in the understanding of this problem. Weak solutions that physically can be interpreted as shock waves or rarefaction, so that they might be distinguished physically admissible were studied, was considered the principle of entropy, in its various forms. The simulations were performed in the fields of two-phase and three-phase flow, in which the fluids are immiscible and gravitational and diffusive effects due to capillary pressure, were discarded. Initially a comparative study of numerical resolutions in the capture of shock waves in water-oil two-phase flow was made. This study highlights LWLF k Composite method and Nonstandard. Was also presented a new renormalization function for nonstandard scheme with satisfactory results, especially in regions where the oil viscosity is much higher than the viscosity of the water. In twodimensional flow, a new method will be presented. The same is a generalization of onedimensional nonstandard schema. Finally, the adaptation of nonstandard and LWLF-4 methods for simulating in three-phase one-dimensional flows. In general, the nonstandard scheme was considered the most efficient method in problems addressed, since its twodimensional version was satisfactory in capturing shock waves in two-phase flow in porous media.