Formulações de elementos finitos bi e tridimensionais para simulação em paralelo de escoamentos em reservatórios de petróleo

Abstract

Finite element formulations oriented to distributed memory parallel machines are proposed and analized to simulate incompressible miscible flow in porous media with applicationto petroleum reservoir engineering. The mathematical model consists in a system of a partial differential equations given by an elliptic subsystem which describes the pressure and the velocity of mixture, and a convection-diffusion equation which describes the concentration of the injected fluid. Global and local post-processing techniques are employed to accurately compute the velocity field. A stabilized consistent Petrov-Galerkin method is applied to the concentration equation combined with a implicit finite difference scheme in time. To solve the large systems of linear equations iterative Krylov projection type methods combined with an element-by-element strategy are implemented in a parallel machine. Numerical results for two and three dimensional simulations of tracer injection and tertiary recover processes are carried out showing the good performance of the proposed numerical formulations and efficiency of parallel implementation.