Linear Coregionalization Modeling: Cross-Variogram for Multivariate Core Permeability Given Core Porosity and Well Log Interpretations Available to Purchase

Core permeability modeling as a function of well logging data is a crucial issue to obtain accurate prediction for the same well or other wells, which have lack of core measurements. The distinct scale measurement of well logging of few feet and core of few inches is one source of that prediction problem. Additionally, the well logging data might have joint effect on the core porosity measurements, which is usually neglected for its correlation in the core permeability modeling. In this paper, an integrated cross-variogram approach was developed and applied to model the core permeability as a primary factor along with core porosity as a secondary factor given the well logging data. The available well logging interpretations for the available oil well include neutron porosity and water saturation as well as depth. The cross-variogram was developed for the co-kriging interpolation to provide linear Coregionalization modeling of core permeability and porosity. Since an auxiliary variable measured at the same points as the target, its effect, besides the target value of interest is cross-correlated to be used when predicting the target values at unsampled intervals. The co-kriging was adopted in comparison with the ordinary kriging. The accuracy of permeability prediction were quantified with respect to training/testing cross-validation of dataset as well as the mismatch between predicted and measured core permeability through the co-kriging and ordinary kriging algorithms. Results showed that co-kriging has much more accurate permeability modeling and reasonable prediction than the ordinary kriging by attaining the least root mean square error and highest adjusted R-square. That workflow was applied on a well in sandstone reservoir from Zubair formation in South Rumaila oil field, Located in Iraq.