Post-processing of Multiple-point Geostatistical Models to Improve Reproduction of Training Patterns

In most petroleum and groundwater studies, flow performance is highly dependent on the spatial distributions of porosity and permeability. Because both porosity and permeability distributions primarily derive from facies deposition, facies should be the first property to be modeled when characterizing a reservoir. Yet, traditional geostatistical techniques, based on variogram reproduction, typically fail to model geologically-realistic depositional facies. Indeed, variograms only measure facies continuity between any two points in space; they cannot account for curvilinear and/or large-scale continuous structures, such as sinuous channels, that would require inferring facies joint-correlation at many more than two locations at a time. Multiple-point geostatistics is a new emerging approach wherein multiple-point facies joint-correlation is inferred from three-dimensional training images. The simulation is pixel-based, and proceeds sequentially: each node of the simulation grid is visited only once along a random path, and simulated values become conditioning data for nodes visited later in the sequence. At each unsampled node, the probability of occurrence of each facies is estimated using the multiple-point statistics extracted from the training image. This process allows reproducing patterns of the training image, while honoring all conditioning sample data.

However, because of the limited size of the training image, only a very limited amount of multiple-point statistics can be actually inferred from the training image. Therefore, in practice, only a very few conditioning data close to the node to be simulated are used whereas farther away data carrying important large-scale information are generally ignored. Such approximation leads to inaccurate facies probability estimates, which may create “anomalies”, for example channel disconnections, in the simulated realizations. In this paper, a method is proposed to use more data for conditioning, especially data located farther away from the node to be simulated. A measure of consistency between simulated realizations and training image is then defined, based on the number of times each simulated value, although initially identified as a conditioning datum to simulate a nearby node, had to be ignored eventually to be able to infer from the training image the conditional probability distribution at that node. Re-simulating the most inconsistent node values according to that measure enables improvement in the reproduction of training patterns without any significant increase of computation time. As an application, that post-processing process is used to remove channel disconnections from a fluvial reservoir simulated model.