A comparative study of implicit and explicit methods using unstructured voronoi meshes in petroleum reservoir simulation

Abstract

This work presents a comparative study among three linearization schemes widely used in petroleum reservoir simulation, namely the Implicit Pressure Explicit Saturation (IMPES), Fully Implicit (FI) and Adaptive Implicit Method (AIM). Attention is given to the criterion used for switching from IMPES to FI and vice-versa. The black-oil model considering the oil-water flow is employed. The equations are discretized using an unstructured Voronoi mesh in a finite-volume framework. The numerical results are analyzed based on the number of iterations in the Newton and solver procedures, number of implicit volumes, and mass balance error of components. The effect of the stopping criterion on Newton's iterations is also investigated. The outcome of the study reveals that adaptive implicit methodologies can be a good choice when unstructured grids are present, allowing the use of time steps with the same order of magnitude as the ones used in FI procedures, but with reduction in the computational effort.