Direct Geostatistical Simulation on Unstructured Grids

Unstructured grids are commonly used in reservoir modeling and are being increasingly considered in complex mining engineering applications. Block kriging of the attributes can be easily implemented; however, this implicitly assumes linear averaging, which is not the case after Gaussian transformation or with variables such as permeability. Direct simulation has been proposed as a solution; however, there are a number of important implementation considerations. This paper addresses the following considerations: (1) search for nearby relevant block and point data, (2) stabilization of the kriging equations and weights in presence of complex screening, (3) correction of the homoscedastic kriging variance to account for realistic proportional effect, (4) determination of valid conditional distribution shapes, (5) accounting for geological controls including stratigraphic surfaces and mixture of multiple facies within an unstructured grid block, and (6) accounting for directional permeability that does not average linearly. Direct simulation on unstructured grids is made practical by addressing these six considerations.