A Statistical Method for Judging the Adequacy of a Numerical Reservoir Simulation

Abstract

Abstract The confidence that one places in predictions made by a numerical reservoir predictions made by a numerical reservoir simulation study can only be qualitatively expressed at present. The criterion generally used for judging the adequacy of these predictions is the "goodness" or the "badness" of a performance history match over a period of time. If a "good match" is obtained, then rules of thumb say that the predictions may be valid for a like period of time. Many rules of thumb exist, but most are quite similar. This paper outlines a method and gives criteria for quantitatively judging the adequacy not only of the predictions, but also of the performance match period. Generally, simulation models are based on the finite difference solution of a partial differential equation describing flow through porous media. The authors show that this equation can be expressed in the form of a linear algebraic equation whose coefficients correspond to the transmissibility and storage terms of the finite difference equation. The variates correspond to combinations of pressures in adjoining grid blocks and to injection and production rates. Thereby, reservoir history matching is analogous to an estimation of these coefficients. Statistics measuring the adequacy of the estimation by regression, methods might then be extended to numerical simulation models. In particular, the multiple correlation coefficient and particular, the multiple correlation coefficient and the observed F-ratio (regression mean square/ residual mean square) are the criteria for judging the goodness of the ensuing prediction in regression analysis. The adaptation of the multiple correlation coefficient to reservoir simulation models is discussed. There is no straightforward adaptation of the F-ratio, but a relationship similar to the F-ratio may provide a useful indication of the goodness of the prediction, likewise, the concept of the standard error and confidence intervals may prove valuable in estimating the quality of a numerical simulation.