Permeability Samples for Uncertainty Assessment by a Predictor-corrector Technique, with Application to RML

Permeability samples for performance forecasting should be consistent with all available information. Markov chain Monte Carlo (McMC) samples correctly from the posterior distribution, but is computationally extremely intensive. RML is a good approximation to McMC. RML involves history matching of each permeability sample, and although RML is computationally less intensive than McMC, the computational effort to generate a sufficiently large number of samples is huge for all but very small reservoir models. In this work, we have investigated if the sampling procedure can be made more efficient by using a predictor-corrector approach in the history matching step of RML. The predictor applies sequential parameter estimation to obtain an estimate with few degrees of freedom, utilizing only part of the available information. The corrector downscales the predictor estimate in a two-step procedure involving all available information, including the estimate obtained with the predictor. The first corrector step is a variant of Kriging. The second corrector step is parameter estimation, again involving few degrees of freedom, with basis functions derived from the results of the predictor.