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Scale-Independent Rock Heterogeneity Classification Algorithm Applied to Microtomography Images

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Abstract

Typical geological systems are composed of a broad spectrum of porous media with regionalized rock properties such as porosity or permeability varying by orders of magnitude within a volume of study. Upscaling the petrophysical rock properties is controlled by the rock pore size and type heterogeneity, which is a scale-dependent variable. At the same time, recent advances in high-resolution imaging techniques have provided a wealth of 2D and 3D datasets that reveal the microstructure of rocks and soil on scales ranging from nanometres to centimetres. However, the images can vary greatly based on the imaging technique and research objective. Automating the rock heterogeneity estimation, regardless of the type of imaged input, would greatly interest geology and engineering communities. It can save the time spent in investigating the rock fabric and evaluating the rock heterogeneity, based on expertise. Hence, it would provide a fast priori-information tool for further investigation and uncertainty analysis of geological and engineering models built on that rock. We provide an automatic scale-independent method for classifying rock heterogeneity. Our method modifies local order metrics by Torquato et al. (J Phys Math Theor 55:274003, 2022. https://doi.org/10.1088/1751-8121/ac72d7). They used synthetic, two-phase porous materials and compared the relative disorder ranking for materials with the same length scale and porosity. Our modification introduces length scale independence and was verified against three categories of benchmarks consisting of 87 geologic and synthetic 3D computed tomography (CT) datasets found on the Digital Rocks Portal (https://www.digitalrocksportal.org/). Further, the method performs better than other geostatistical heterogeneity coefficients, including Dykstra–Parsons, Lorenz, and pore heterogeneity coefficients. A sensitivity analysis has revealed significantly faster performance and greater reliability when evaluating true heterogeneity in 3D compared to the apparent heterogeneity seen when splitting 3D volume in its 2D cross section. Thus, whenever possible, 3D datasets should be used to analyze porous media. While we apply this to the images in Digital Rocks Portal in the hopes that it will ease automated curation of images in the future, the method should extend easily to any porous media images.

Article Highlights

  • Heterogeneity of digital rock images can be detected regardless of the length scale in a wide variety of benchmark images from Digital Rocks Portal

  • The scale-independent variance algorithm is developed, including defining heterogeneity/homogeneity threshold

  • The scale-independent variance algorithm can be modified to evaluate the heterogeneity of the spatial distribution of rock properties (e.g., porosity, permeability, etc.) in both 2D and 3D images. We find strong evidence to use 3D images for characterization if at all possible.

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Data Availability

The datasets generated or analyzed in the current study are available in the cited references or can be obtained from the corresponding author on reasonable request. The algorithm's Python code can also be accessed through the GitHub link https://github.com/PG-Ali-E-Mohamed/Heterogeneity_classifier.

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Acknowledgements

Ali Mohamed thanks United States Agency for International Development for the research visit to The University of Texas at Austin that made this collaboration possible. Maša Prodanović thanks Digital Porous Media Industry Affiliate Program at The University of Texas at Austin for their support. Ali Mohamed is grateful for the insightful discussions of this paper with Lei Liu and Bernard Chang, the PhD candidates at the University of Texas at Austin.

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The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.

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Authors and Affiliations

  1. Geology Department, Faculty of Science, Aswan University, Aswan, 81528, Egypt

    Ali Mohamed

  2. Hildebrand Department of Petroleum and Geosystems Engineering, The University of Texas at Austin, Austin, TX, 78712-1585, USA

    Ali Mohamed & Maša Prodanović

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  1. Ali Mohamed
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  2. Maša Prodanović
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All authors contributed to the study conception and design. The first draft of the manuscript was written by AM and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Ali Mohamed.

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Mohamed, A., Prodanović, M. Scale-Independent Rock Heterogeneity Classification Algorithm Applied to Microtomography Images. Transp Porous Med 150, 257–284 (2023). https://doi.org/10.1007/s11242-023-02008-1

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