Geostatistics on Unstructured Grid - Coordinate Systems, Connections and Volumes

The current trend in reservoir simulators is to solve transport of energy and flow equations on unstructured grids. This work addresses three challenges for geomodelers wanting to perform geostatistics directly on unstructured grids: (1) the large range of cell volumes and their arbitrary shapes, (2) the complex cell topology and its need for explicit connection specifications and (3) the use of alternate coordinate systems to better conform to geological features. This work uses triangular, hexagonal, and tetrahedral 3D grids to demonstrate the adaptation of geostatistical algorithms on unstructured grids. Hard data conditioning and locally-varying trends are also addressed. Finally we present three approaches to simulate on unstructured grid (1) the simulation on cell centroids, (2) the simulation on a finely discretized grid followed by upscaling and (3) a direct cell geostatistical algorithms.