Esquemas de alta resolução para controle da dispersão numerica em simulação de reservatorios

AUTOR(ES)
DATA DE PUBLICAÇÃO

1991

RESUMO

Standard finite-diference reservoir simulation normally uses single-point upstream welghting to approximate the components of the convective flow term at the interfaces between blocks. This procedure stabilizes the numerical solution, but introduces high levels of numerical dispersion, difficulting the correct interpretation of the simulated results. Exponential schemes are reasonable when diffusion dominates, but, as we show in this work, reduce to single-point uspstream when the flow is toa convective. Higher-order finite-difference methods, like Leonard s scheme, are, in general, able to reduce the numerical dispersion, but may produce non-physical solutions when the conservation equation assumes a hyperbolic formo We demonstrate, through the numerical solution of some classical non-linear equations, that this occurs because the entropy condition is violated. The entropy condition is a mathematical cri teria to select the correct solution among weak solutions of the problem. Total Variation Diminishing (TVD) methods have the remarkable property of producing high resolution solutions which obey the entropy condition, and, consequently, are physically consistent. A comparison of the performance of the various methods is presented for some reservoir engineering problems: lD convection-diffusion equation, Buckley-Leverett equation and 2D single-phase tracer flow. TVD schemes were also implemented on a two-phase black-oil model, and resuIts are discussed for various formuIations, such as IMPES, semi-implicit and fully-implicit. We also included options of tracer injection in the water phase, considering fuIl dispersion tensor and adsorption with the rock. Comparisons are made with refined grid single-point upstream solutions and, whenever possible, with analytical solutions. Grid orientation effect is investigated. Practical examples are also included

ASSUNTO(S)

petroleo - reservas campos petroliferos

ACESSO AO ARTIGO

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