Reservoir Characterization Improvement by Accounting for Well Test Extracted Effective Permeabilities

Geostatistical simulation of permeabilities on a geologically detailed resolution will account for permeabilities in the cells containing wells through kriging. These permeabilities are typically based on porosity logs and core plug measurements of both porosity and permeability. No direct measurement of permeability on the geomodelling grid scale exists. However, well tests give information on the effective permeability in an area close to the well region, covering several grid cells, and are therefore data on an aggregate scale. Given an assumption of radial flow into a vertical well, the effective permeability becomes a convolution of the permeabilities in the well test region. Downscaling of the well test data is possible by co-kriging the aggregate scaled permeability field with that of the geomodelling grid scale. Thereby, the geomodelling grid permeabilities will honour data on both scales. The effective permeability is downscaled through inverse block kriging, which implies a deconvolution procedure. Keeping the computation costs low when introducing a new conditioning parameter is ensured by transforming into the Fourier domain, since the Fast Fourier Transform algorithm is an efficient method for solving the inverse block co-kriging. Initial testing of the implemented algorithm has been made on real data from a StatoilHydro operated field on the Norwegian continental shelf in a proof of concept test. Three wells with well test data were chosen, and their derived effective permeabilities were included in the permeability simulations. Cases both with and without well test conditioning were run, and compared in a well test simulation software. All three near well regions showed a significant improvement. These tests indicate that the conditioning method can be a useful contribution in bringing dynamic data into the reservoir characterization.