Utilização da biblioteca numérica PETSc na solução de sistemas algébricos na simulação de reservatórios

Abstract

In this dissertation, we used the numerical library Portable Extensible Toolkit for Scientific Computation (PETSc) to obtain the solution of the system of algebraic equations arising from the discretization of the governing equation of a two-dimensional oil flow in a porous medium, where both are slightly compressible. Typically, this step is responsible for the highest computational cost compared to the others. Thus, in addition to the search for an accurate solution, we also aimed to achieve better computational performance. We determined the numerical solution in terms of the pressures in the reservoir and the producing well (via a well-reservoir coupling technique), using a Picard method of linearization and a time-implicit formulation. We obtained the pressure variations as a function of time by using different computational meshes, modifying the physical properties, and using the methods for solving algebraic systems available at PETSc. The solutions presented the expected physical behavior, and we conclude that the use of this numerical library has been successful.