Direct multiple-point geostatistical simulation of edge properties for modeling thin irregularly-shaped surfaces

Thin irregularly-shaped surfaces such as clay drapes often have a major control on flow and transport in heterogeneous porous media. Clay drapes are often complex curvilinear 3-dimensional surfaces and display a very complex spatial distribution. Variogram-based stochastic approaches are often also not able to describe the spatial distribution of clay drapes since complex, curvilinear, continuous and interconnected structures cannot be characterized using only two-point statistics. Multiple-point geostatistics aims to overcome the limitations of the variogram. The premise of multiple-point geostatistics is to move beyond two-point correlations between variables and to obtain (cross) correlation moments at three or more locations at a time using "training images" to characterize the patterns of geological heterogeneity. Multiple-point geostatistics is able to reproduce thin irregularly-shaped surfaces such as clay drapes but is often computationally intensive. To capture the thin surfaces, a small grid cell size should be adopted for the training image. This results in large training images and a large search template size and thus a large CPU and RAM demand (Huysmans and Dassargues, 2009).