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Analysis of Variance of Porosity and Heterogeneity of Permeability at the Pore Scale

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We present a new statistical variance approach for characterizing heterogeneities related to pore spaces in reservoir rocks. Laboratory-based computer microtomography data for reservoir sandstone samples were acquired and processed using advanced image segmentation techniques. The samples were processed using a method based on the digital rock physics concept using the high-performance Navier–Stokes flow solver in the GeoDict commercial software package. The digitized structures were subjected to computational fluid dynamic simulations. The effects of structural matrix modifications caused by the precipitation of minerals on the porosity–permeability relationship and the characterization of the representative elementary volume were assessed. The variances of the digital flow fields were compared at the pore scale (6 µm). The algorithm for analysing variance was benchmarked using a synthetic dataset that provided artificial repetitive structural patterns at both low and high resolutions. This gave an estimate of the sensitivity of the proposed algorithm to minor inhomogeneities. Representative elementary volume variance analysis was performed by comparing the correlation coefficients for various pore–grain composition patterns with the variances of simulated mean flow velocities. Probability density functions indicate that the flow velocities and pore space geometries differed greatly for different samples. The normalized probability density functions of the mean flows shifted to higher velocities as the resolution decreased. We found that a representative elementary volume analysis was more reliably achieved by analysing the mean flow velocity variance than by analysing the pore microstructure alone.

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This work was supported by the German Federal Ministry of Education and Research (BMBF) ‘Geological Research for Sustainability (GEO:N)’ program, which is part of the BMBF ‘Research for Sustainable Development (FONA3)’ framework program. It is part of the project ResKin (Reaction kinetics in reservoir rocks, 03G0871E). We would like to thank our team at the JGU Mainz for considerable support during the difficult process of writing and debugging the automatized C++ code and while writing this manuscript.

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Correspondence to Arne Jacob.

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Jacob, A., Enzmann, F., Hinz, C. et al. Analysis of Variance of Porosity and Heterogeneity of Permeability at the Pore Scale. Transp Porous Med 130, 867–887 (2019). https://doi.org/10.1007/s11242-019-01342-7

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  • Pore-scale variance analysis
  • REV estimation
  • Porous media
  • Digital rock physics