COMPARISON OF IMPES, SEQUENTIAL, AND FULLY IMPLICIT FORMULATIONS FOR TWO-PHASE FLOWIN POROUS MEDIA WITH THE ELEMENT-BASED FINITE VOLUME METHOD

Resumo

This paper presents comparative results of IMPES (IMplicit Pressure, Explicit Saturation), sequential, and fully implicit solution schemes for isothermal, immiscible, incompressible two-phase flow reservoir simulation with the Element-based Finite Volume Method (EbFVM). The IMPES method solves pressure implicitly and saturation explicitly, as the acronym suggests. As a result of this explicit calculation its stability is subjected to a restriction of the time step. Nevertheless, this scheme reduces the computational effort and facilitates implementation. The sequential method is a modified IMPES with the aim of improving stability of explicit formulations. The Fully Implicit Method (FIM) solves the system of equations that models the problem simultaneously with the Newton-Raphson method. This formulation implies larger system of equations with many nonlinearities and thus higher computational cost. Regardless the difficulties related to the numerical scheme and its implementation it is a more stable method. Furthermore, in this work it is also presented a variable time step strategy in order to accelerate the performance o the methods. This strategy consists basically in modifying the time step according to the current solution. In this paper, IMPES, sequential and fully implicit methods are compared in terms of stability, computational time and accuracy of their results.