A Comparative Evaluation of Different Versions Of the Strongly Implicit Procedure (SIP)

Abstract

American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc. Abstract The well-known Strongly Implicit Procedure (SIP), introduced by Weinstein, Stone, and Kwan, was tested for two- and three-dimensional, two-phase reservoir flow problems. Additionally, it was evaluated for the two-dimensional Laplace's equation, where the exact solution was known. The evaluation consisted in the comparison of the convergence behavior of the SIP algorithm where a single set of equations is used for all iterations, with the algorithm employing two sets of equations, one for odd-numbered iterations, and the other for even-numbered iterations. Also, the effect of the number and ordering of the iteration parameters on convergence was investigated. The algorithm for odd numbered iterations has already been reported by Weinstein et al. The algorithm for even numbered iterations was derived, and is given in this paper. It was found that less than 10% additional computational effort was expended when using the odd-even iterations algorithm as compared to the original odd-numbered iterations algorithm. However, the odd-even iterations algorithm permitted a significant improvement in the permitted a significant improvement in the results: the material balance errors decreased, and the residuals were lower. The residuals decreased by several orders of magnitude when the convergence tolerance was tightened. For both versions of SIP, the number and ordering of the iteration parameters was found to have a profound effect on the convergence behavior. Any significant trend was not apparent, however. It is recommended that the odd-even iterations version of SIP should be used for reservoir problems, and that trial runs should be carried out to determine the optimum number of parameters and the best (e.g. increasing, parameters and the best (e.g. increasing, decreasing, etc.) ordering of the same. The paper discusses these factors for the reservoir paper discusses these factors for the reservoir problems tested. problems tested Introduction The Strongly Implicit Procedure (herein-after referred to as SIP) is a highly successful algorithm for the iterative solution of systems of linear equations arising from the application of implicit differences to reservoir flow problems. The advantages of SIP over Alternating problems. The advantages of SIP over Alternating Direction Implicit (hereinafter referred to as ADI) and Successive Overrelaxation (hereinafter referred to as SOR) procedures have been discussed in the literature.