Geostatistical Simulations on Irregular Reservoir Models Using Methods of Nonlinear Geostatistics

SUMMARY Classical approaches to geostatistical simulations are not applicable directly on irregular reservoir models (such as Voronoi polygon and tetrahedron meshed models). One of the main difficulties is that the block marginal distributions are unique for every block due to volume support effect. We propose a methodology for geostatistical simulations which overcomes this difficulty in an analytical manner and provides a robust utilization of the small support petrophysical property distribution and the covariance model for irregular reservoir models. The proposed solution is based on the discrete Gaussian (DGM) model and operates directly on blocks of the target grid. This solution is also capable to improve the quality of the classical reservoir models, such as tartan meshes, by including the volume support effect into consideration and thus-providing geologically more realistic results. Applications to Voronoi polygon grid with local grid refinements and to a tartan-meshed offshore gas reservoir model are demonstrated.