An Adaptive-Implicit Switching Criterion Based on Numerical Stability Analysis

Abstract

Summary: A new switching criterion for adaptive-implicit reservoir simulation, based on the numerical stability of the local amplification matrix, is discussed. Adaptive-implicit methods can be used to achieve substantial savings in computing time and storage. The success of their application, however, depends critically on an appropriate switching criterion. The standard criterion discussed in the literature is the application of threshold changes in the primary variables, which are usually determined by some preliminary testing and chosen conservatively because of their empirical nature. Further, backward switching (implicit to explicit) is not normally feasible. With the switching criterion discussed in this paper, these disadvantages are eliminated. The method has been applied to a variety of black-oil reservoir simulation problems, including the first and second SPE Comparative Solution Projects and a water-injection problem. In all cases tested, the new criterion is shown to perform satisfactorily. For the waterflood problem in particular, the new criterion with backward switching was found to decrease computing time and storage significantly compared with the standard switching criterion. This criterion can easily be extended to other types of reservoir simulators.