Bayesian kriging for reproducing reservoir heterogeneity in a tidal depositional environment of a sandstone formation

Abstract

Spatial permeability modeling is an important step in reservoir characterization as it controls spatial continuity, heterogeneity, and fluid flow modeling. The conventional kriging algorithms, such as simple, ordinary, and universal kriging, have been used for spatial petrophysical property distribution. However, all are unbiased estimators that disregard the impact of uncertainty in the covariance structure, which is first estimated, and then adopted for interpolation. To prevail over the restrictions of unbiased prediction in conventional approaches, Bayesian Kriging has been recently presented to take into account the uncertainty about variogram parameters on subsequent predictions. Bayesian Kriging incorporates prior knowledge about observations, such as expert grasp and outcome from neighboring data, to be incorporated as a qualified guess in the spatial estimation. The uncertainty about model parameters in Bayesian Kriging is then represented in a form of posterior probability distribution to attain optimal unbiased linear interpolation, which then leads to avoid unrealistic small regions within the reservoir. The efficiency of Bayesian Kriging was justified through simulating the reservoir heterogeneity in terms of spatial permeability continuity in a tidal depositional environment of heterogeneous sandstone reservoir in South Rumaila oil field. The Bayesian kriging simulation was implemented in extensive comparison with other conventional geostatistical algorithms, such as simple, ordinary and universal kriging. It was illustrated that Bayesian Kriging algorithm is an efficient geostatistical simulation approach for reproducing reservoir heterogeneity by attaining less estimation variance. Multiple equiprobable stochastic reservoir images (realizations) were created by Bayesian kriging and ranked to select the three quantiles P10, P50, and P90. The entire work was implemented through R, the powerful open-source statistical computing language, and R codes can be used as fast vehicles to conduct the geostatistical simulation in various formations.