Flujo Bidimensional de Petróleo en Medios Porosos: Simulación Numérica y Análisis de Estabilidad

Abstract

The radial flow of oil towards a well in two dimensions is modeled by a family of finite difference schemes. This family depends on one parameter θ, 0≤θ≤1. The stability of the proposed schemes is analyzed applying the matrix method which takes into account boundary conditions. An "almost pentadiagonal" matrix is obtained choosing an appropriate order of equations and unknowns. We prove that this matrix may be symmetrized by a similarity
transformation. Therefore, studying bounds for the corresponding eigenvalues, unconditional stability is found for θ≥1/2 and stability restrictions are established for θ<1/2. Numerical simulations are presented using the BSOR (Block Successive Over Relaxation) Method to
solve the resulting system of linear equations. The finite difference solution has perfectly reproduced the analytical solution of a simplified 1-D model.