Kriging, cokriging or stochastical simulations, and the choice between deterministic or sequential approaches

Abstract

This new research presented here for the first time in the Croatian geomathematical community, aims to establish several criteria which will aid in the selection of deterministic or stochastic geostatistical methods of estimation. This review associates the theoretical background of kriging, cokriging or stochastic simulations with some results obtained by mapping Badenian clastic reservoirs in the Drava Depression. The selected reservoirs are located in the Stari Gradac-Barcs Nyugat field, in the Western part of the Drava Depression, and at the Beničanci field in the Eastern part of this depression. Both datasets (each with 14 points) include mean porosity values taken from well log analysis in the reservoir interval at the well sites. This resulted in significant uncertainties in the variogram models, especially with the determination of range (at the secondary variogram axis). The critical advantage was the availability of a seismic attribute that could be used as a secondary and co-regionalized variable (porosity is the primary variable). In the first example (the Beni?anci field) the seismic attribute was correlated with the average logged porosities. This made it possible to apply the cokriging method as the best interpolation option. The cross-validation result was 2.19 for 14 wells. In contrast, the existence of only a primary variable at the Stari Gradac-Barcs Nyugat field, forced the application of stochastic simulations as the better estimation tool, which can better describe the porosity changes in inter-well areas.