Reservoir Modeling Using Multiple-Point Statistics

摘要

Two approaches are traditionally used to build numericalrnmodels for facies distributions within a reservoir. Pixel-basedrntechniques aim at generating simulated realizations that honorrnthe well data values, and reproduce a given variogram whichrnmodels two-point spatial correlation. However, because thernvariogram cannot look at spatial continuity between more thanrntwo locations at a time, pixel-based algorithms give poorrnrepresentations of the actual facies geometries. In contrast,rnobject-based techniques allow reproducing crisp geometries,rnbut the conditioning on well data requires iterative ``trial-and-error''rncorrections, which can be time-consuming, particularlyrnwhen the data are dense with regard to the average object size.rnThis paper presents a new approach that combines the easyrnconditioning of pixel-based algorithms with the ability tornreproduce ``shapes'' of object-based techniques, without beingrntoo time and memory demanding.rnIn this new approach, the complex geological structuresrnexpected to be present in the reservoir are characterized byrnmultiple-point statistics, which express joint variability atrnmany more than two locations at a time. Such multiple-pointrnstatistics cannot be inferred from typically sparse well data butrncould be read from training images depicting the expectedrnsubsurface heterogeneities. A training image need not carryrnany locally accurate information on the reservoir; it need onlyrnreflect a prior stationary geological/structural concept. Thusrntraining images can be generated by object-based algorithmsrnfreed of the constraint of data conditioning. The multiple-pointrnstatistics inferred from the training image(s) are then exportedrnto the reservoir model, where they are anchored to the wellrndata using a pixel-based sequential simulation algorithm.rnThis algorithm is tested for the simulation of a turbiditernsystem where flow is controlled by meandering channels withrncross-bedding. The training image reflecting the channelrnpatterns is an unconditional realization generated by an object-basedrnalgorithm. The final simulated numerical modelsrnreproduce these channel patterns, and honor exactly all wellrndata values at their locations. The methodology proposedrnappears to be practical, general, and fast.