Integrating Core Porosity and Well Logging Interpretations for Multivariate Permeability Modeling through Ordinary Kriging and Co-Kriging Algorithms

Estimation of core permeability as a function of well logging records is a pivotal task in reservoir characterization as it is affected by data sparseness, distinct scales, various sources, and lithology structures. In this paper, three specific dataset formats of a well logging and core measurements were considered for the core permeability modeling and prediction using the ordinary kriging and co-kriging interpolation algorithms. The dataset were used as complete dataset of multi-facies and two split datasets of shale- and sand-based measurements. More specifically, the ordinary kriging was first used to model the core permeability as a function of the well logging records only through constructing the variogram given the three mentioned dataset types. The same procedure was repeated by adopting the cross-variogram approach to model the core permeability as a primary factor along with core porosity as a secondary factor, both as a function of the well logging records. The well logging attributes, which were obtained from an oil well, include neutron porosity and water saturation given the well depth. The cross-variogram was adopted to quantify the dissimilarity between known and unknown data for the co-kriging interpolation to provide linear coregionalization modeling of core permeability and porosity. The modeling and prediction accuracy of core permeability through the ordinary kriging and co-kriging algorithms were assessed by applying the leave-one-out cross validation in addition to the visual mismatch between predicted and observed core permeability. Results illustrated that co-kriging interpolation led to a more accurate permeability prediction than the ordinary kriging by achieving the highest adjusted R-square and the lowest root mean square error. The integrated workflow of ordinary kriging and co-kriging was applied on a dataset from an oil well in sandstone reservoir in the South Rumaila oil field, Southern Iraq.