Methods and Applications
Two geostatistical approaches are traditionally used to build numerical models of facies spatial distributions: the variogram-based approach and the object-based approach. Variogram-based techniques aim at generating simulated realizations that honor the sample data and reproduce a given semivariogram that models the two-point spatial correlation of the facies. However, because the semivariogram is only a measure of linear continuity, variogram-based algorithms give poor representations of curvilinear or geometrically complex actual facies geometries. In contrast, object-based techniques allow modeling crisp geometries, but the conditioning on sample data requires iterative trial-and-error corrections that can be time consuming, particularly when the data are dense relative to the average object size. This chapter presents an alternative 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 geological structures believed to be present in the subsurface are characterized by multiple-point statistics, which express joint variability or joint continuity at many more than two locations at a time. Multiple-point statistics cannot be inferred from typically sparse sample data, but they can be read from training images depicting the expected patterns of geological heterogeneity. Training images are simply graphical representations of a prior geological or structural concept; they need not carry any locally accurate information about the field to be modeled. The multiple-point patterns borrowed from the training image(s) are exported to the model, where they are anchored to the actual subsurface data, both hard and soft, using a pixel-based sequential simulation algorithm.
This multiple-point statistics simulation algorithm is tested on the modeling of a fluvial hydrocarbon reservoir where flow is controlled by meandering sand channels. The simulated numerical model reproduces channel patterns and honors exactly all well data values at their locations. The methodology proposed appears to be easy to apply, general, and fast.