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Porous Media Characterization Using Minkowski Functionals: Theories, Applications and Future Directions

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Abstract

An elementary question in porous media research is in regard to the relationship between structure and function. In most fields, the porosity and permeability of porous media are properties of key interest. There is, however, no universal relationship between porosity and permeability since not only does the fraction of void space matter for permeability but also the connectivity of the void fraction. With the evolution of modern day X-ray microcomputed tomography (micro-CT) and advanced computing, it is now possible to visualize porous media at an unprecedented level of detail. Approaches in analyzing micro-CT data of porous structures vary in the literature from phenomenological characterization to network analysis to geometrical and/or topological measurements. This leads to a question about how to consistently characterize porous media in a way that facilitates theoretical developments. In this effort, the Minkowski functionals (MF) emerge from the field of statistical physics where it is evident that many physical processes depend on the geometry and topology of bodies or multiple bodies in 3D space. Herein we review the theoretical basis of the MF, mathematical theorems and methods necessary for porous media characterization, common measurement errors when using micro-CT data and recent findings relating the MF to macroscale porous media properties. This paper is written to provide the basics necessary for porous media characterization and theoretical developments. With the wealth of information generated from 3D imaging of porous media, it is necessary to develop an understanding of the limitations and opportunities in this exciting area of research.

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Acknowledgements

We thank the Tyree X-Ray Laboratory in the School of Minerals and Energy Resources Engineering, UNSW for assistance with image collection and data processing. Professors Stephen Foster (fiber-reinforced concrete) and Melissa Knothe-Tate and Dr. Tzong-Tyng Hung (mouse leg) are acknowledged for graciously sharing their microtomography data. We thank Ji-Youn Arns and Zhenghuai Guo for their persistence in contrast optimization for the mouse leg and visualization of the fiber-reinforced concrete samples. Funding was provided from the Australian Research Council Discovery Grant DP160104995. VR is supported by ARC Future Fellowship FT140100604. An award of computer time was provided by the Department of Energy INCITE program. This research also used resources of the Oak Ridge Leadership Computing Facility, which is a DOE Office of Science User Facility supported under Contract DE-AC05-00OR22725.

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Authors and Affiliations

  1. School of Minerals and Energy Resoureces Engineering, University of New South Wales, Sydney, 2033, Australia

    Ryan T. Armstrong, Zhishang Liu & Christoph H. Arns

  2. Advanced Research Computing, Virginia Tech, Blacksburg, VA, 24061, USA

    James E. McClure

  3. Research School of Physics and Engineering, Australian National University, Canberra, ACT, 2601, Australia

    Vanessa Robins

  4. Helmholtz-Centre for Environmental Research, Theodor-Lieser-Str. 4, 06120, Halle, Germany

    Steffen Schlüter

  5. Shell Global Solutions International B.V., Kesslerpark 1, 2288 GS, Rijswijk, The Netherlands

    Steffen Berg

  6. Department of Earth Science and Engineering, Department of Chemical Engineering, Imperial College London, London, UK

    Steffen Berg

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  1. Ryan T. Armstrong
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Correspondence to Ryan T. Armstrong.

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Armstrong, R.T., McClure, J.E., Robins, V. et al. Porous Media Characterization Using Minkowski Functionals: Theories, Applications and Future Directions. Transp Porous Med 130, 305–335 (2019). https://doi.org/10.1007/s11242-018-1201-4

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