Skip to main content
SpringerLink
Log in

Probability Density Function of Bead-Pack Test Planes and Resolution Limits of Tomography

  • Published:
Transport in Porous Media Aims and scope Submit manuscript

Abstract

Quantitative stereology translates three-dimensional statistics into areal and lineal size distributions. Conversely, cross-sectional data are used to infer volumetric properties. One may thus infer porosity from cross-sectional areal porosity or through segment intersections with void and solid. Cross sections of uniform and spherical-bead packs result in a size distribution of circles, the statistics of which enables us to evaluate packing randomness with multiple test planes. Here, we provide cross-sectional results obtained from micro-CT scans for unimodal and bimodal packs, both of which having a narrow distribution of bead sizes. For nearly uniformly sized beads, the theoretical distributions of circle diameters agree with high-resolution data above a demonstrable threshold. Therefore, the threshold allows us to ascertain the physical resolution of scans, regardless of the voxel resolution of the scanned image. For multimodal distribution of bead sizes within the pack, theory and experiments do not always agree. For example, when beads are premixed, and later packed within a tube, a discrepancy for the number distribution of circular sizes between theory and data is evident. Smaller beads are underrepresented. Reasons for these observations and methods to overcome the underrepresentation are presented in the paper. Estimates for the respective bead fractions are best obtained by direct image analysis and not weight fractions within the premixer.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18

Similar content being viewed by others

References

  • Adler, P.M., Jacquin, C.G., Quiblier, J.A.: Flow in simulated porous media. Int. J. Multiph. Flow 16(4), 691–712 (1990)

    Article  Google Scholar 

  • Andrä, H., Combaret, N., Dvorkin, J., Glatt, E., Han, J., Kabel, M., Keehm, Y., Krzikalla, F., Lee, M., Madonna, C., et al.: Digital rock physics benchmarks? Part I: imaging and segmentation. Computers Geosci. 50, 25–32 (2013)

    Article  Google Scholar 

  • Auzerais, F.M., Dunsmuir, J., Ferreol, B.B., Martys, N., Olson, J., Ramakrishnan, T.S., Rothman, D.H., Schwartz, L.M.: Transport in sandstone: a study based on three dimensional microtomography. Geophys. Res. Lett. 23(7), 705–708 (1996)

    Article  Google Scholar 

  • D’Amico, K.L., Deckman, H.W., Dunsmuir, J.H., Flannery, B.P., Roberge, W.G.: X-ray microtomography with monochromatic synchrotron radiation (invited). Rev. Sci. Instrum. 60(7), 1524–1526 (1989)

    Article  Google Scholar 

  • Elkhoury, J.E., Shankar, R., Ramakrishnan, T.S.: Resolution and limitations of X-ray micro-CT with applications to sandstones and limestones. Trans. Porous Media 129, 413–425 (2019)

    Article  Google Scholar 

  • Farr, R.S., Vukmanovic, Z., Holness, M.B., Griffiths, E.: Reconstructing grain-shape statistics from electron back-scatter diffraction microscopy. Phys. Rev. Mater. 2(7), 073804 (2018)

    Article  Google Scholar 

  • Flannery, B.P., Deckman, H.W., Roberge, W.G., D’Amico, K.L.: Three-dimensional X-ray microtomography. Science 237(4821), 1439–1444 (1987)

    Article  Google Scholar 

  • Mostaghimi, P., Blunt, M.J., Bijeljic, B.: Computations of absolute permeability on micro-CT images. Math. Geosci. 45(1), 103–125 (2013)

    Article  Google Scholar 

  • Saxena, N., Hofmann, R., Alpak, F.O., Dietderich, J., Hunter, S., Day-Stirrat, R.J.: Effect of image segmentation & voxel size on micro-CT computed effective transport & elastic properties. Mar. Petroleum Geol. 86, 972–990 (2017)

    Article  Google Scholar 

  • Shah, S.M., Gray, F., Crawshaw, J.P., Boek, E.S.: Micro-computed tomography pore-scale study of flow in porous media: effect of voxel resolution. Adv. Water Res. 95, 276–287 (2016)

    Article  Google Scholar 

  • Starnoni, M., Pokrajac, D., Neilson, J.: Computation of fluid flow and pore-space properties estimation on micro-CT images of rock samples. Computers Geosci. 106, 118–129 (2017)

    Article  Google Scholar 

  • Thovert, J.F., Adler, P.M.: Grain reconstruction of porous media: Application to a Bentheim sandstone. Phys. Rev. E 83(5), 056116 (2011)

    Article  Google Scholar 

  • Thovert, J.F., Yousefian, F., Spanne, P., Jacquin, C.G., Adler, P.M.: Grain reconstruction of porous media: application to a low-porosity Fontainebleau sandstone. Phys. Rev. E 63(6), 061307 (2001)

    Article  Google Scholar 

  • Underwood, E.E.: Quantitative stereology. Addison-Wesley series in metallurgy and materials, Addison-Wesley Pub. Co. (1970). https://books.google.com/books?id=Epg1AAAAIAAJ

  • Vásárhelyi, L., Kónya, Z., Kukovecz, Á., Vajtai, R.: Microcomputed tomography-based characterization of advanced materials: a review. Mater. Today Adv. 8, 100084 (2020)

    Article  Google Scholar 

Download references

Author information

Author notes

  1. H. Zhang

    Present address: Buckman Laboratories, Memphis, TN, USA

Authors and Affiliations

  1. Schlumberger-Doll Research, 1 Hampshire St., Cambridge, MA, 02139, USA

    T. S. Ramakrishnan & H. Zhang

Authors
  1. T. S. Ramakrishnan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to T. S. Ramakrishnan.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ramakrishnan, T.S., Zhang, H. Probability Density Function of Bead-Pack Test Planes and Resolution Limits of Tomography. Transp Porous Med 136, 677–697 (2021). https://doi.org/10.1007/s11242-020-01537-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11242-020-01537-3

Keywords

Search

Navigation