EFFICIENCY OF PRECONDITIONING METHODS APPLIED TO THE TRANSMISSIBILITY MATRIX OF MULTI-SCALE FORMULATIONS IN HETEROGENEOUS AND ANISOTROPIC PETROLEUM RESERVOIRS BASED ON A SPECTRAL ANALYSIS

At times, the application of numerical methods to solve engineering problems can be challenging. An example of such challenge is the numerical simulation of oil flow in reservoirs, which exhibit high heterogeneity and anisotropy due to the formation processes. Since these peculiar characteristics affect algebraic operators directly, becoming highly ill-conditioned, classical linear systems problem solvers find it difficult to achieve convergence. The search to improve the results offered using these methods are very promising. This paper investigates the use of different solvers and preconditioners for linear systems of equations and their effectiveness based on the spectral properties of the transmissibility matrix. Furthermore, this study applies the algebraic multiscale solver for the modified multiscale control volume method (I-MMVCM) as a first stage of the two-stage preconditioning method, contributing to data optimization in the modeling and simulation of fluid flow in petroleum reservoirs. The examples analyzed consider different permeability fields in the evaluation of the efficiency of the preconditioning, considering computational costs and accuracy of solution.