Geostatistics on Unstructured Grids, Theoretical Background, and Applications

Abstract

Traditionally, geostatistical simulations are performed on regular grids, in IJK coordinates system, simulating centroids of the cells. This approach (commonly used) has severe drawbacks: the support size effect is not taken into account and some artifacts due to cells distortion may appear. On the other hand, reservoir engineers and hydrogeologists are increasingly referring to new genera-tion of grids to perform dynamic simulation (Voronoï grids, tetrahedral grids …) which require addressing the volume support effect. In this paper, we present a theoretical framework to simulate variables directly on this new generation of grids, using a depositional coordinates system (UVT) and taking into account the support size effect. A real field case study is subsequently presented (lithology and petrophysical modeling) to illustrate the possibilities of the new generation of simulation tools. A conclusion is provided and the remaining problems are discussed to propose some guidelines for future works.