Representative Elementary Volume Determination for Permeability and Porosity Using Numerical Three-Dimensional Experiments in Microtomography Data
Publication: International Journal of Geomechanics
Volume 18, Issue 2
Abstract
Combining tomographical reconstructed volumes and direct pore-scale flow simulations has proven to be an efficient tool in modern soil sciences. The main objective of the present paper is to present an extensive study about the usage of micro–computed tomography to obtain transport properties of porous media. The transport properties are obtained by means of pore-scale simulations whose domains are the pore space of the tomographical images of three different materials: glass spheres, sand, and clay. The main discussion in the present paper regards the definition of the representative elementary volume (REV). To address this issue, statistical analyses were carried out, showing that the REV concept is scale-dependent. Also, some guidelines considering the specification of the numerical domain size are discussed. It is shown that, for the glass spheres and sand, the coefficient of variation (CV) of the permeability decreases as the simulation domain increases, reaching values as low as 20%. In contrast, for clay samples, the CV does not show a clear decreasing tendency, and its values are approximately 75% for the largest domain size considered. Hypothesis tests were used to show that more than one domain size can be considered a REV (i.e., there are different minimum domain sizes for which permeability and porosity can be evaluated), and these values can be used to predict the transport properties of a larger part of the domain at a given scale.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The authors thank the National Council for Scientific and Technological Development (CNPq), the Coordination for the Improvement of Higher Education Personnel (CAPES), and the University of Brasília for the partial financial support. In particular, L. C. de S. M. Ozelim thanks the Brazilian Research Council (CNPq) for funding his postdoctoral fellowship at the University of Brasilia (Grant 153657/2016-2). The authors also thank Dr. Dan Gostovic for kindly providing a license of Avizo Fire and its XLab extension. The data used in the present paper is available to the readership and can be requested by sending an email to the corresponding author.
References
ASTM. (1986). “D2487 standard: Classification of soils for engineering purposes (Unified Soil Classification System).” Annual book of ASTM standards, Vol. 04.08, West Conshohocken, PA.
Avizo Fire [Computer software]. FEI Visualization Science Group, Hillsboro, OR.
Bear, J. (1988). Dynamics of fluids in porous media, Dover Publications, New York, p. 764.
Carrier, W. D. (2003). “Goodbye, Hazen; Hello, Kozeny-Carman.” J. Geotech. Geoenviron. Eng., 1054–1056.
Chen, S., et al. (1991). “Lattice gas automata for flow through porous media.” Physica D: Nonlinear Phenomena, 47(1–2), 72–84.
Clausnitzer, V., and Hopmans, J. W. (1999). “Determination of phase-volume fractions from tomographic measurements in two-phase systems.” Adv. Water Resour., 22(6), 577–584.
Corbett, P. W. M., Anggraeni, S., and Bowden, D. (1999). “The use of the probe permeameter in carbonates-addressing the problems of permeability support and stationarity.” Log. Anal., 40(5), 316–326.
Costanza-Robinson, M. S., Estabrook, B. D., and Fouhey, D. F. (2011). “Representative elementary volume estimation for porosity, moisture saturation, and air-water interfacial areas in unsaturated porous media: Data quality implications.” Water Resour. Res., 47(7), W07513.
Crestana, S., Mascarenhas, S., and Pozzi-Mucelli, R. S. (1985). “Static and dynamic three dimensional studies of water in soil using computed tomographic scanning.” Soil Sci., 140(5), 326–332.
Darcy, H. (1856). Les fontaines publiques de la ville de dijon, Dalmont, Paris, p. 647.
Efron, B. (1979). “Bootstrap method: Another look at the Jackknife.” Anal. Stat., 7(1), 1–26.
Efron, B. (1982). The jackknife, the bootstrap and other resampling plans, Society for Industrial and Applied Mathematics CBMS-NSF Monographs 38, Society for Industrial and Applied Mathematics, Philadelphia, p. 135.
Efron, B., and Tibshirani, R. (1993). An introduction to the bootstrap, Champman and Hall, London, p. 436.
Elliott, J. C., and Dover, S. D. (1982). “X-ray microtomography.” J. Microsc., 126(2), 211–213.
Fonseca, J., O'Sullivan, C., Coop, M. R., and Lee, P. D. (2012). “Non-invasive characterization of particle morphology of natural sands.” Soils Found., 52(4), 712–722.
Glusker, J. P. (1995). “To W.C. Röntgen 100 years later.” Rigaku J., 12(2), 4–9.
Hainsworth, J. M., and Aylmore, L. A. G. (1983). “The use of computer assisted tomography to determine spatial distribution of soil water content.” Aust. J. Soil Res., 21(4), 435–440.
Harlow, F. H., and Welch, J. E. (1965). “Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface.” Phys. Fluids, 8(12), 2182–2189.
Haussener, S., Coray, P., Lipiński, W., Wyss, P., and Steinfeld, A. (2010). “Tomography-based heat and mass transfer characterization of reticulate porous ceramics for high-temperature processing.” J. Heat Transf., 132(2), 023305.
He, G., He, Y., and Chen, Z. (2008). “A penalty finite volume method for the transient Navier–Stokes equations.” Appl. Numer. Math., 58(11), 1583–1613.
Herman, G. T. (2009). Fundamentals of computerized tomography: Image reconstruction from projection, Springer, London, p. 300.
Jassogne, L., McNeill, A., and Chittleborough, D. (2007). “3D-visualization and analysis of macro-and meso-porosity of the upper horizons of a sodic, texture-contrast soil.” Eur. J. Soil Sci., 58(3), 589–598.
Ketcham, R. A., and Iturrino, G. J. (2005). “Nondestructive high-resolution visualization and measurement of anisotropic effective porosity in complex lithologies using high-resolution X-ray computed tomography.” J. Hydrol., 302(1–4), 92–106.
Kim, S., and Karrila, S. J. (2005). Microhydrodynamics: Principles and selected applications, Butterworth-Heinemann, Stoneham, MA, p. 544.
Knoll, G. F. (2010). Radiation detection and measurement, John Wiley, New York, p. 860.
Lake, L. W., and Srinivasan, S. (2004). “Statistical scale-up of reservoir properties: Concepts and applications.” J. Pet. Sci. Eng., 44(1–2), 27–39.
Lontoc-Roy, M., Dutilleul, P., Prasher, S. O., Han, L., Brouillet, T., and Smith, D. L. (2006). “Advances in the acquisition and analysis of CT scan data to isolate a crop root system from the soil medium and quantify root system complexity in 3-D space.” Geoderma, 137(1–2), 231–241.
Mathematica 0.9 [Computer software]. Wolfram Research, Champaign, IL.
Menon, M., et al. (2011). “Assessment of physical and hydrological properties of biological soil crusts using X-ray microtomography and modeling.” J. Hydrol., 397(1–2), 47–54.
Miller, K. J., Zhu, W., Montési, L. G. J., and Gaetani, G. A. (2014). “Experimental quantification of permeability of partially molten mantle rock.” Earth Planet. Sci. Lett., 388, 273–282.
Nogami, J. S., and Villibor, D. F. (1985). “Additional considerations about a new geotechnical classification for tropical soils.” Proc., First Int. Conf. on Geomechanics in Tropical Lateritic and Saprolitic Soils, Brazilian Society for Soils Mechanics and Geotechnical Engineering, Brasília, DF, Brazil, Vol. 1, pp. 165–174.
Papafotiou, A., et al. (2008). “From the pore scale to the lab scale: 3-D lab experiment and numerical simulation of drainage in heterogeneous porous media.” Adv. Water Resour., 31(9), 1253–1268.
Peng, S., Marone, F., and Dultz, S. (2014). “Resolution effect in X-ray microcomputed tomography imaging and small pores’s contribution to permeability for Berea sandstone.” J. Hydrol., 510, 403–411.
Petrovic, A. M., Siebert, J. E., and Rieke, P. E. (1982). “Soil bulk density analysis in three dimensions by computed tomographic scanning.” Soil Sci. Soc. Am. J., 46(3), 445–450.
Radon, J. (1917). “Uber die Bestimmung von Funktionen durch ihre Integralwerte Langs Gewisser Mannigfaltigkeiten.” Ber. Saechsische Akad. Wiss, 29, 262–277.
Radon, J. (1986). “On the determination of functions from their integral values along certain manifolds.” IEEE Trans. Med. Imaging, 5(4), 170–176.
Razavi, M. R., Muhunthan, B., and Hattamleh, O. A. (2007). “Representative elementary volume analysis of sands using X-ray computed tomography.” Geotech. Test. J., 30(3), 212–219.
Röntgen, W. C. (1896). “On a new kind of rays.” Nature, 53(1369), 274–277.
Röntgen, W. C. (1898). “Ueber eine neue Art von Strahlen.” Ann. Phys., 300(1), 12–17.
Rozenbaum, O., and Roscoat, S. R. (2014). “Representative elementary volume assessment of three-dimensional X-ray microtomography images of heterogeneous materials: Application to limestones.” Phys. Rev. E: Stat. Nonlinear Soft Matter Phys., 89(5), 053304.
Sander, T., Gerke, H. H., and Rogasik, H. (2008). “Assessment of Chinese paddlysoil structure using X-ray computed tomography.” Geoderma, 145, 303–314.
Shang, Y. (2013). “Parallel defect-correction algorithms based on finite element discretization for the Navier–Stokes equations.” Comput. Fluids, 79, 200–212.
Stock, S. R. (2008). “Recent advances in X-ray microtomography applied to materials.” Int. Mater. Rev., 53(3), 129–181.
Sun, Y., Indraratna, B., and Nimbalkar, S. (2014). “Three-dimensional characterisation of particle size and shape for ballast.” Géotechnique Lett., 4(3), 197–202.
Svärd, M., Carpenter, M. H., and Nordström, J. (2007). “A stable high-order finite difference scheme for the compressible Navier–Stokes equations, far-field boundary conditions.” J. Comput. Phys., 225(1), 1020–1038.
Taylor, H. F., O’Sullivan, C., and Sim, W. W. (2015). “A new method to identify void constrictions in micro-CT images of sand.” Comput. Geotech., 69, 279–290.
Taylor, H. F., O’Sullivan, C., and Sim, W. W. (2016). “Geometric and hydraulic void constrictions in granular media.” J. Geotech. Geoenviron. Eng.,
Torquato, S. (2002). Random heterogeneous materials: Microstructure and macroscopic properties, Vol. 16, Springer, New York.
Udawatta, R. P., and Anderson, S. H. (2008). “CT-measured pore characteristics of surface and subsurface soils influenced by agroforestry and grass buffers.” Geoderma, 145(3–4), 381–389.
Vaz, C. M. P., de Maria, I. C., Lasso, P. O., and Tuller, M. (2011). “Evaluation of an advanced benchtop micro-computed tomography system for quantifying porosities and pore-size distributions of two Brazilian oxisols.” Soil Sci. Soc. Am. J., 75(3), 832–841.
Wang, C. H., Willis, D. L., and Loveland, W. D. (1975). Radiotracer methodology in the biological environmental, and physical sciences, Prentice Hall, Upper Saddle River, NJ, p. 496.
Wildenschild, D., Vaz, C. M. P., Rivers, M. L., Rikard, D., and Christensen, B. S. B. (2002). “Using X-ray computed tomography in hydrology: Systems, resolutions, and limitations.” J. Hydrol., 267(3-4), 285–297.
Zermatten, E., Haussener, S., Schneebeli, M., and Steinfeld, A. (2011). “Tomography-based determination of permeability and Dupuit–Forchheimer coefficient of characteristic snow samples.” J. Glaciol., 57(205), 811–816.
Zermatten, E., Schneebeli, M., Arakawa, H., and Steinfeld, A. (2014). “Tomography-based determination of porosity, specific area and permeability of snow and comparison with measurements.” Cold Regions Sci. Technol., 97, 33–40.
Zhu, J., and Ma, J. (2013). “An improved gray lattice Boltzmann model for simulating fluid flow in multi-scale porous media.” Adv. Water Resour., 56, 61–76.
Zubeldia, E. H. (2013). “Uso dos autômatos celulares bidimensionais e imagens tomográficas na geração de meios porosos artificiais.” Masters thesis, G.DM-231/2013, Dept. of Civil and Environmental Engineering, Univ. of Brasilia, Brasília, DF, Brazil, p. 93.
Zubeldia, E. H., Ozelim, L. C. S. M., Cavalcante, A. L. B., and Crestana, S. (2016). “Cellular automata and X-ray microcomputed tomography images for generating artificial porous media.” Int. J. Geomech., 04015057.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 18 • Issue 2 • February 2018
Copyright
© 2017 American Society of Civil Engineers.
History
Received: May 5, 2017
Accepted: Aug 14, 2017
Published online: Dec 14, 2017
Published in print: Feb 1, 2018
Discussion open until: May 14, 2018
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.