Geostatistical Assignment of Reservoir Properties on Unstructured Grids Available to Purchase

Reservoir simulation is often performed on irregular nonCartesian grids. A common methodology for building the input reservoir models is to perform geostatistical reservoir models on a fine grid and then to average them to the coarser unstructured grid. This method is computationally expensive; a more efficient approach is to modify the geostatistical algorithms to directly populate the unstructured grid.

The required modifications are described in this paper. First, direct simulation must be used in place of the more common Gaussian simulation. This is required because reservoir properties do not average linearly after Gaussian transformation; averaging is required because each grid block potentially has a different volume. Second, volume averaged variogram or covariance values are required between two arbitrary blocks v₁(u) and v₂(u’). These must be calculated quickly and efficiently. Third, to maintain a reasonable speed of geostatistical simulation on unstructured grids a customized search and a non-stationary covariance lookup table of the average covariance between blocks is required. Finally, directional permeability requires a special transformation to account for the nature of averaging.

We present the implementation details and some results using tartan and radial grids.