Block Iterative Methods for Fully Implicit Reservoir Simulation

Abstract

Abstract This paper describes the development of iterative methods suitable for the block-structured Jacobian matrices that occur in multiphase reservoir simulation. Most iterative methods consist of an approximate factorization followed by an acceleration procedure. The acceleration procedure used here is ORTHOMIN1. Four factorization methods have been investigated that, when coupled with ORTHOMIN, provide four possible iterative algorithms. The first three factorization methods differ only in the number of bands included in the approximate decomposition. The fourth factorization is the most involved and the most powerful of the four methods. It is intended to be used on the equations that occur in thermal simulation, which previously have been considered difficult to solve iteratively. Several examples illustrating the use of the iterative algorithms are described. The algorithms described here are compared with several others on the basis of theoretical work and storage. Introduction The objective of this work was to provide an iterative method that was powerful enough to solve the highly nonsymmetric matrices that occur in thermal reservoir simulation. Four methods have been programmed and tested. They are described in order of increasing complexity in the following sections. Even the least powerful of these methods, Dupont-Kendall-Rachford (DKR), is capable of solving the matrices arising from steamdrive simulation.