Solução numérica usando métodos adaptativos-implícitos e malha de Voronoi de problemas de reservatórios de petróleo

Abstract

The main goal of the present work is the development of a numerical model using Voronoi grids for the solution of fluid flow in petroleum reservoirs. The scheme uses the twophase (oil-water) black-oil model with the equations discretized using finite-volume method. Three metodologies were implemented, namely, the IMPES - Implicit Pressure Explicit Saturation, TI - Totaly Implicit e AIM - Adaptive Implicit Method. Despite the use of these metodologies for several authors, the criteria employed for switching from IMPES to TI and vice-versa, and for stopping the Newton iterations are not cleary presented and discussed in the available literature. Therefore, one of the contributions of this work is to address these topics using grids with variable connectivity. Voronoi grids are strongly used in this work due their flexibility in representing the flow around wells. An extensive study is realized where the methods for solving the linear systems of equations are analyzed considering ordering schemes and convergence accelerators. With respect to the ordering schemes both, natural ordering, like the ones used in cartesian, as well as schemes basead on the structure of the Jacobian are considered. The latter one uses the numerical value of the Jacobian, and it is know in the literature as MDF - Minimum Discarded Fill. With respect to the convergence accelerator three well know methods, ORTHOMIN, GMRES e Bi-CGSTAB were used. They are fully compared among them. The numerical model developed is evaluated using available numerical results and also applied to practical situations where hybrid Voronoi grids are suitable.