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.
Figures & Tables
Since publication of the first volume of Stochastic Modeling and Geostatistics in 1994, there has been an explosion of interest and activity in geostatistical methods and spatial stochastic modeling techniques. Many of the computational algorithms and methodological approaches that were available then have greatly matured, and new, even better ones have come to the forefront. Advances in computing and increased focus on software commercialization have resulted in improved access to, and usability of, the available tools and techniques. Against this backdrop, Stochastic Modeling and Geostatistics Volume II provides a much-needed update on this important technology. As in the case of the first volume, it largely focuses on applications and case studies from the petroleum and related fields, but it also contains an appropriate mix of the theory and methods developed throughout the past decade. Geologists, petroleum engineers, and other individuals working in the earth and environmental sciences will find Stochastic Modeling and Geostatistics Volume II to be an important addition to their technical information resources.