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 can reproduce thin irregularly-shaped surfaces such as clay drapes but is often computationally very intensive. This paper describes and applies a methodology to simulate thin irregularly-shaped surfaces with a smaller CPU and RAM demand than the conventional multiple-point statistical methods. The proposed method uses edge properties for indicating the presence of thin irregularly-shaped surfaces. This method allows directly simulating edge properties instead of pixel properties to make it possible to perform multiple-point geostatistical simulations with a larger cell size and thus a smaller computation time and memory demand.