An Automatic Time-Step Selector For Reservoir Models

Abstract

ABSTRACT This paper presents an algorithm for the selection of an optimal time step sequence for use in a thermal simulator. The algorithm is based on the observation that a solution vector always tracks the locus of stationary points on the surface mapped by the residual function. This provides a simple relation for obtaining a sensitivity vector which is then used to determine a time step length that gives a global error of the norm less than the prescribed tolerance. In addition, the sensitivity vector is used to seek a close initial solution for Newtonian iteration. When applied to practical problems the numerical scheme results in substantial computer cost savings.