Injection of the tracers in petroleum reservoir: multiscale modeling and numerical simulation / Injeção de traçadores em reservatórios de petróleo: modelagem multi-escala e simulação numérica

AUTOR(ES)
DATA DE PUBLICAÇÃO

2006

RESUMO

The spatial variations in porous media (aquifers and petroleum reservoirs) occur at all length scales (from the pore scale to the reservoir scale) and are incorporated in the governing equations for multiphase flow problems on the basis of random fields (geostatistical models). As a consequence, the velocity field is a random function of space. The randomness of the velocity field gives rise to a mixing region between fluids, which can be characterized by a mixing length . Here we focus on the scale-up for the tracer flow problem. In the limit of small heterogeneity strengths it has been derived by perturbation theories that the scaling behavior of the mixing region is related to the scaling properties of the self-similar (or fractal) geological heterogeneity through the relation , where ; the Hurst coefficient that controls the relative importance of short vs. large scales in the geology. The objectives of this work were: i) the derivation of a new, mathematically rigorous, scaling analysis for the tracer flow problem subject to self-similar heterogeneities. This theoretical development relates the large strength to the small strength heterogeneity regime by a simple scaling of solutions. It follows from this analysis that the scaling laws derived by perturbation theory are valid for any strength of the underlying geology, thereby extending the current available results. To the knowledge of the authors this is the only rigorous result available in the literature for the large strength heterogeneity regime; ii) the presentation of a Monte Carlo study of highly resolved simulations, which are in excellent agreement with the predictions of our new theory. In this study, both numerical and statistical convergence have been considered. Large computational regions have been used in order to reduce boundary effects, which have not been included in the theory. The results indicates that our Monte Carlo results are accurate and can be applied to other models for stochastic geology.

ASSUNTO(S)

escoamento bifásico mixing lenght porous media métodos de simulação região de mistura simulação (computadores) tracer flow scale-up escoamento em meios porosos two-phase flow análise de escalas transferência de escalas meios porosos porous media flow simulation methods traçador passivo engenharia de reservatório de óleo scaling analysis matematica aplicada computer simulation oil reservoir engineering

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