Advertisement

Transport in Porous Media

, Volume 110, Issue 3, pp 521–531 | Cite as

Three-Dimensional Stochastic Characterization of Shale SEM Images

  • Pejman Tahmasebi
  • Farzam Javadpour
  • Muhammad Sahimi
Article

Abstract

Complexity in shale-gas reservoirs lies in the presence of multiscale networks of pores that vary from nanometer to micrometer scale. Scanning electron microscope (SEM) and atomic force microscope imaging are promising tools for a better understanding of such complex microstructures. Obtaining 3D shale images using focused ion beam-SEM for accurate reservoir forecasting and petrophysical assessment is not, however, currently economically feasible. On the other hand, high-quality 2D shale images are widely available. In this paper, a new method based on higher-order statistics of a porous medium (as opposed to the traditional two-point statistics) is proposed in which a single 2D image of a shale sample is used to reconstruct stochastically equiprobable 3D models of the sample. Because some pores may remain undetected in the SEM images, data from other sources, such as the pore-size distribution obtained from nitrogen adsorption data, are integrated with the overall pore network using an object-based technique. The method benefits from a recent algorithm, the cross- correlation-based simulation, by which high-quality, unconditional/conditional realizations of a given sample porous medium are produced. To improve the ultimate 3D model, a novel iterative algorithm is proposed that refines the quality of the realizations significantly. Furthermore, a new histogram matching, which deals with multimodal continuous properties in shale samples, is also proposed. Finally, quantitative comparison is made by computing various statistical and petrophysical properties for the original samples, as well as the reconstructed model.

Keywords

Shale-gas Flow in nanoscale Reconstruction CCSIM 

Notes

Acknowledgments

Work at USC was supported by RPSEA, and at The University of Texas at Austin by the NanoGeosciences Lab. Dr. R. Reed provided the SEM images. We would like to thank FEI Company for use of Aviso software. We also thank Lana Dieterich for her help. Publication authorized by the Director, Bureau of Economic Geology.

References

  1. Cover, T.M., Thomas, J.A.: Elements of Information Theory. Wiley-Interscience, New York (1991)CrossRefGoogle Scholar
  2. Darabi, H., Ettehad, A., Javadpour, F., Sepehrnoori, K.: Gas flow in ultra-tight shale strata. J. Fluid Mech. 710, 641–658 (2012)CrossRefGoogle Scholar
  3. Endres, D.M., Schindelin, J.E.: A new metric for probability distributions. IEEE Trans. Inf. Theory 49(7), 1858–1860 (2003)CrossRefGoogle Scholar
  4. Hall, P.L., Mildner, D.F., Borst, R.L.: Small-angle scattering studies of the pore spaces of shaly rocks. J. Geophys. Res. Solid Earth (1978–2012) 91(B2), 2183–2192 (1986)CrossRefGoogle Scholar
  5. Hester, R., Harrison, R.: Fracking. Royal Society of Chemistry, London (2014)CrossRefGoogle Scholar
  6. Javadpour, F.: Nanopores and apparent permeability of gas flow in mudrocks (shales and siltstone). J. Can. Petrol. Technol. 48(8), 16–21 (2009)CrossRefGoogle Scholar
  7. Javadpour, F., Moravvej, M., Amrein, M.: Atomic force microscopy (AFM) a new tool for gas shale characterization. J. Can. Petrol. Technol. 51(4), 236–243 (2012)CrossRefGoogle Scholar
  8. Krishnan, S., Journel, A.G.: Spatial connectivity: from variograms to multiple-point measures. Math. Geol. 35(8), 915–925 (2003)CrossRefGoogle Scholar
  9. Lemmens, H.J., Butcher, R., Botha, P.W.S.K.: FIB/SEM and SEM/EDX: a new dawn for the SEM in the core lab? Petrophysics 52(6), 452–456 (2011)Google Scholar
  10. Loucks, R.G., Reed, R.M., Ruppel, S.C., Hammes, U.: Spectrum of pore types and networks in mudrocks and a descriptive classification for matrix-related mudrock pores. AAPG Bull. 96(6), 1071–1098 (2012)CrossRefGoogle Scholar
  11. Naraghi, M.E., Javadpour, F.: A stochastic permeability model for the shale-gas systems. Int. J. Coal Geol. 140, 111–124 (2015)CrossRefGoogle Scholar
  12. Okabe, H., Blunt, M.J.: Prediction of permeability for porous media reconstructed using multiple-point statistics. Phys. Rev. E 70(6), 066135 (2004)CrossRefGoogle Scholar
  13. Sahimi, M.: Flow and Transport in Porous Media and Fractured Rock: From Classical Methods to Modern Approaches. Wiley-VCH, New York (2011)CrossRefGoogle Scholar
  14. Tahmasebi, P., Hezarkhani, A., Sahimi, M.: Multiple-point geostatistical modeling based on the cross-correlation functions. Computat. Geosci. 16(3), 779–797 (2012)CrossRefGoogle Scholar
  15. Tahmasebi, P., Sahimi, M.: Reconstruction of three-dimensional porous media using a single thin section. Phys. Rev. E 85, 066709 (2012)CrossRefGoogle Scholar
  16. Tahmasebi, P., Sahimi, M.: Cross-correlation function for accurate reconstruction of heterogeneous media. Phys. Rev. Lett. 110, 078002 (2013)CrossRefGoogle Scholar
  17. Tahmasebi, P., Sahimi, M.: Geostatistical simulation and reconstruction of porous media by a cross-correlation function and integration of hard and soft data. Transport. Porous. Med. 3, 871–905 (2015a)Google Scholar
  18. Tahmasebi, P., Sahimi, M.: Reconstruction of nonstationary disordered materials and media: watershed transform and crosscorrelation function. Phys. Rev. E. 3, 032401 (2015b)Google Scholar
  19. Tahmasebi, P., Sahimi, M., Caers, J.: MS-CCSIM: accelerating pattern-based geostatistical simulation of categorical variables using a multi-scale search in Fourier space. Comput. Geosci. 67, 75–88 (2014)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Pejman Tahmasebi
    • 1
    • 2
  • Farzam Javadpour
    • 1
  • Muhammad Sahimi
    • 2
  1. 1.Bureau of Economic Geology, Jackson School of GeosciencesThe University of Texas at AustinAustinUSA
  2. 2.Mork Family Department of Chemical Engineering and Materials ScienceUniversity of Southern CaliforniaLos AngelesUSA

Personalised recommendations