Bayesian Kriging for Improved Spatial Heterogeneity Modeling in Clastic Reservoirs

Many conventional kriging algorithms have been adopted for spatial petrophysical property modeling, such as simple, ordinary, and universal kriging. These approaches are linear unbiased estimators as covariance structure is estimated first, and then used for interpolation, leading to disregard the effect of uncertainty in the covariance structure on subsequent predictions. To overcome the restrictions of unbiased prediction in conventional approaches, Bayesian Kriging has been recently suggested to take into account the uncertainty about variogram parameters on subsequent predictions. Bayesian Kriging incorporates a prior distribution in terms of the variogram parameters, such as coefficients, data variance, range, and nugget to be adopted as a qualified guess in the spatial estimation. The qualified guess allows uncertainty estimation reduction to achieve more realistic spatial modeling and improved reservoir characterization. In this paper, The Bayesian Kriging was adopted in comparison to Universal Kriging to for reproducing the spatial permeability in a clastic reservoir. The permeability data has been collected from 60 wells distributed around the reservoir with distinct locations. The comparison was attained with respect to the variance estimation through the cross-validation procedure. It was concluded that Bayesian Kriging is more accurate prediction of formation permeability than the universal Kriging.