Geostatistical Simulations on Irregular Reservoir Models

The new generation of reservoir computer models based on unstructured meshes requires appropriate methods for filling the cells with petrophysical data. Classical methods are not applicable to unstructured reservoir models since they can neither treat complicated geometry nor reproduce correctly the statistical properties of the model (as marginal distributions and covariance between the blocks). In order to overcome these difficulties, we develop new statistical methods for model filling which work directly on unstructured grids. The most important problem in the model filling is the transfer of the small scale data available from well cores and laboratory analysis to multiple different scales which are defined by various grid blocks. This problem is known in as the volume support effect and can be addressed by the methods of non-linear geostatistics. In the proposed solution, we use non-linear geostatistics to address the problem of simulating heterogeneities on unstructured grids (Zaytsev et al., 2015). We present a workflow for approximating the block distributions by the means of the discrete Gaussian model and for performing geostatistical simulations directly on block support. Theoretical model and case studies are presented.