Influence of Heterogeneity on Carbonate Permeability Upscaling: A Renormalization Approach Coupled with the Pore Network Model

Permeability upscaling in carbonate rocks is challenging due to the heterogeneity at multiple scales. Although there are several computational methods for permeability upscaling, the applicability, computational time, and the associated accuracy of these methods may vary significantly. This article modified an established Karim and Krabbenhoft renormalization method (KRM) and proposed a regression-based renormalization for permeability upscaling in carbonate rocks, and the results are compared with the classical KRM. To this end, permeability at the small-scale samples (size = 500³and 600³voxels, from 405 to 7944 μm³) and the whole core plug scale are computed from three carbonate samples of varying heterogeneity and composition using pore network models extracted from 3D micro-CT images. Subsequently, the modified regression-based renormalization method is applied to calculate the regression (upscaled) permeability. Our results indicate that the regression permeability is in good agreement with experimental permeability for full-size core plug estimations (maximum error = 11.07%) using the proposed RKRM approach-suggesting the accuracy of this method. Furthermore, the relative error of the permeability estimation from small-scale samples using KRM was much higher than those of the RKRM-suggesting the superiority of the proposed approach over the classical one. The observed errors in permeability using the RKRM approach, despite being lower than the classical KRM approach, are attributed to the heterogeneity of carbonate samples at the sub-core and core scales. The results of this study thus add to the general understanding of permeability upscaling in carbonates and the associated impact of heterogeneity.