Reservoir Modeling Using Multiple-Point Statistics

Abstract

Two approaches are traditionally used to build numerical models for facies distributions within a reservoir. Pixel-based techniques aim at generating simulated realizations that honor the well data values, and reproduce a given variogram which models two-point spatial correlation. However, because the variogram cannot look at spatial continuity between more than two locations at a time, pixel-based algorithms give poor representations of the actual facies geometries. In contrast, object-based techniques allow reproducing crisp geometries, but the conditioning on well data requires iterative "trial-and-error" corrections, which can be time-consuming, particularly when the data are dense with regard to the average object size. This paper presents a new approach that combines the easy conditioning of pixel-based algorithms with the ability to reproduce "shapes" of object-based techniques, without being too time and memory demanding. In this new approach, the complex geological structures expected to be present in the reservoir are characterized by multiple-point statistics, which express joint variability at many more than two locations at a time. Such multiple-point statistics cannot be inferred from typically sparse well data but could be read from training images depicting the expected subsurface heterogeneities. A training image need not carry any locally accurate information on the reservoir; it need only reflect a prior stationary geological/structural concept. Thus training images can be generated by object-based algorithms freed of the constraint of data conditioning. The multiple-point statistics inferred from the training image(s) are then exported to the reservoir model, where they are anchored to the well data using a pixel-based sequential simulation algorithm. This algorithm is tested for the simulation of a turbidite system where flow is controlled by meandering channels with cross-bedding. The training image reflecting the channel patterns is an unconditional realization generated by an object-based algorithm. The final simulated numerical models reproduce these channel patterns, and honor exactly all well data values at their locations. The methodology proposed appears to be practical, general, and fast.