Advertisement

Transport in Porous Media

, Volume 125, Issue 1, pp 23–39 | Cite as

An Object-Based Shale Permeability Model: Non-Darcy Gas Flow, Sorption, and Surface Diffusion Effects

  • Morteza E. Naraghi
  • Farzam JavadpourEmail author
  • Lucy T. Ko
Article

Abstract

Shale samples consist of two major components: organic matter (OM) and inorganic mineral component (iOM). Each component has its distinct pore network topology and morphology, which necessitates generating a model capable of distinguishing the two media. We constructed an object-based model using the OM and iOM composition of shale samples. In the model, we integrated information such as OM population and size distribution, as well as its associated pore-size distribution. For the iOM part, we used mineralogy and pore-size information derived from X-ray diffraction, scanning electron microscopy, and nitrogen sorption measurements. Our proposed model results in millimeter-scale 2D realizations of shale samples by honoring OM and mineral types, their compositions, shapes, and size distributions. The model can capture heterogeneities smaller than 1 mm. We studied the effects of different gas flow processes and found that Knudsen diffusion and gas slippage dominate the flow, but surface diffusion has little impact on total gas flow.

Keywords

Gas flow in shale Nanopore Stochastic Reconstruction of porous media 

Notes

Acknowledgements

This work was supported partly by the NanoGeosciences laboratory and by the Mudrock Systems Research Laboratory (MSRL) consortium at the Bureau of Economic Geology, The University of Texas at Austin. MSRL member companies are Anadarko, BP, Cenovus, Centrica, Chesapeake, Cima, Cimarex, Chevron, Concho, ConocoPhillips, Cypress, Devon, Encana, Eni, EOG, EXCO, ExxonMobil, Hess, Husky, Kerogen, Marathon, Murphy, Newfield, Penn Virginia, Penn West, Pioneer, Samson, Shell, Statoil, Talisman, Texas American Resources, The Unconventionals, U.S. Enercorp, Valence, and YPF. We appreciate Drs S. Ruppel and R. Reed’s instructive comments. Susie Doenges edited the manuscript. Publication was authorized by the Director, Bureau of Economic Geology.

References

  1. Akkutlu, I.Y., Fathi, E.: Multiscale gas transport in shales with local kerogen heterogeneities. SPE J. 17(4), 1002–1011 (2012)CrossRefGoogle Scholar
  2. Alfi, M., Nasrabadi. H., Banerjee, D.: Confinement effects on phase behavior of hydrocarbon in nanochannels. In: ASME 2015 International Mechanical Engineering Congress and Exposition (American Society of Mechanical Engineers) (2015)Google Scholar
  3. Alfi, M., Nasrabadi, H., Banerjee, D.: Experimental investigation of confinement effect on phase behavior of hexane, heptane and octane using lab-on-a-chip technology. Fluid Phase Equilib. 423, 25–33 (2016)CrossRefGoogle Scholar
  4. Biswal, B., Manwart, C., Hilfer, R., Bakke, S., Øren, P.E.: Quantitative analysis of experimental and synthetic microstructures for sedimentary rock. Physica A 273(3), 452–475 (1999)CrossRefGoogle Scholar
  5. Biswal, B., Øren, P.E., Held, R.J., Bakke, S., Hilfer, R.: Stochastic multiscale model for carbonate rocks. Phys. Rev. E 75(6), 061303 (2007)CrossRefGoogle Scholar
  6. Chen, L., Zhang, L., Kang, Q., Viswanathan, H.S., Yao, J., Tao, W.: Nanoscale simulation of shale transport properties using the lattice Boltzmann method: permeability and diffusivity. Sci. Rep. 5, 8089 (2015)CrossRefGoogle Scholar
  7. Civan, F.: Effective correlation of apparent gas permeability in tight porous media. Transp. Porous Media 82(2), 375–384 (2010)CrossRefGoogle Scholar
  8. Cundall, P.A., Strack, O.D.L.: A discrete numerical model for granular assemblies. Geotechnique 29(1), 47–65 (1979)CrossRefGoogle Scholar
  9. Darabi, H., Ettehad, A., Javadpour, F., Sepehrnoori, K.: Gas flow in ultra-tight shale strata. J. Fluid Mech. 710, 641–658 (2012)CrossRefGoogle Scholar
  10. Drach, A., Khalighi, A.H., ter Huurne, F.M., Lee, C.-H., Bloodworth, C., Pierce, E.L., Jensen, M.O., Yoganathan, A.P., Sacks, M.S.: Population-averaged geometric model of mitral valve from patient-specific imaging data. J. Med. Dev. 9(3), 030952 (2015)CrossRefGoogle Scholar
  11. Drach, A., Khalighi, A.H., Sacks, M.S.: A comprehensive pipeline for multi-resolution modeling of the mitral valve: validation, computational efficiency, and predictive capability. Int. J. Numer. Methods Biomed. Eng. https://doi.org/10.1002/cnm.2921 (2017)
  12. Javadpour, F.: Nanopores and apparent permeability of gas flow in mudrocks (shales and siltstone). J. Can. Pet. Technol. 48, 16–21 (2009)CrossRefGoogle Scholar
  13. Javadpour, F., Ettehadtavakkol, A.: Gas transport processes in shale. In: Fundamentals of Gas Shale Reservoirs, pp. 245–266 (2015)Google Scholar
  14. Javadpour, F., McClure, M., Naraghi, M.E.: Slip-corrected liquid permeability and its effect on hydraulic fracturing and fluid loss in shale. Fuel 160, 549–559 (2015)CrossRefGoogle Scholar
  15. Katagiri, J., Matsushima, T., Yamada, Y.: Simple shear simulation of 3D irregularly-shaped particles by image-based DEM. Granul. Matter. 12(5), 491–497 (2010)CrossRefGoogle Scholar
  16. Kelly, S., El-Sobky, H., Torres-Verdín, C., Balhoff, M.T.: Assessing the utility of FIB-SEM images for shale digital rock physics. Adv. Water Resour. 95, 302–316 (2016)CrossRefGoogle Scholar
  17. Khalighi, A.H., Drach, A., ter Huurne, F.M., Lee, C.-H., Bloodworth, C., Pierce, E.L., Jensen, M.O., Yoganathan, A.P., Sacks, M.S.: A comprehensive framework for the characterization of the complete mitral valve geometry for the development of a population-averaged model. In: International Conference on Functional Imaging and Modeling of the Heart, pp. 164–171. Springer (2015)Google Scholar
  18. Khalighi, A.H., Drach, A., Bloodworth IV, C.H., Pierce, E.L., Yganathan, A.P., Gorman, R.C., Gorman III, J.H., Sacks, M.S.: Mitral valve chordae tendineae: topological and geometrical characterization. Ann. Biomed. Eng. 45(2), 378–393 (2017)CrossRefGoogle Scholar
  19. Khalighi, A. H., Drach, A., Gorman, R. C., Gorman, J. H., Sacks, M. S.: Multi-resolution geometric modeling of the mitral heart valve leaflets. In: Biomechanics and Modeling in Mechanobiology, pp. 1–16 (2017)Google Scholar
  20. Klaver, J., Desbois, G., Urai, J.L., Littke, R.: BIB-SEM study of the pore space morphology in early mature Posidonia Shale from the Hils area, Germany. Int. J. Coal Geol. 103, 12–25 (2012)CrossRefGoogle Scholar
  21. Ko, L.T., Loucks, R.G., Ruppel, S.C., Zhang, T., Peng, S.: Origin and characterization of Eagle Ford pore networks in the south Texas Upper Cretaceous shelf. AAPG Bull. 101, 387–418 (2017)CrossRefGoogle Scholar
  22. 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
  23. Mehmani, A., Prodanović, M., Javadpour, F.: Multiscale, multiphysics network modeling of shale matrix gas flows. Transp. Porous Media 99(2), 377–390 (2013)CrossRefGoogle Scholar
  24. Milliken, K.L., Ergene, S.M., Ozkan, A.: Quartz types, authigenic and detrital, in the Upper Cretaceous Eagle Ford Formation, south Texas. USA. Sediment. Geol. 339, 273–288 (2016)CrossRefGoogle Scholar
  25. Naraghi, M.E.: 3-D reconstruction of porous media and rock characterization. In: SPE Annual Technical Conference and Exhibition. Soc. Pet. Eng. (2016)Google Scholar
  26. Naraghi, M.E., Javadpour, F.: A stochastic permeability model for the shale-gas systems. Int. J. Coal Geol. 140, 111–124 (2015)CrossRefGoogle Scholar
  27. Naraghi, M.E., Javadpour, F.: Langmuir slip-Langmuir sorption stochastic permeability model of shale. In: Unconventional Resources Technology Conference, San Antonio, Texas, 1–3 August 2016. Society of Exploration Geophysicists, American Association of Petroleum Geologists, Soc. Pet. Eng. 323–341 (2016)Google Scholar
  28. Naraghi, M.E., Spikes, K., Srinivasan, S.: 3-D reconstruction of porous media from a 2-D section and comparisons of transport and elastic properties. In: SPE Western Regional Meeting. Soc. Pet. Eng. (2016)Google Scholar
  29. Naraghi, M.E., Spikes, K., Srinivasan, S.: 3D Reconstruction of porous media from a 2D section and comparisons of transport and elastic properties. SPE Reserv. Eval. Eng. 20(02), 342–352 (2017)CrossRefGoogle Scholar
  30. Rezaveisi, M., Javadpour, F., Sepehrnoori, K.: Modeling chromatographic separation of produced gas in shale wells. Int. J. Coal Geol. 121, 110–122 (2014)CrossRefGoogle Scholar
  31. Roberts, J.N., Schwartz, L.M.: Grain consolidation and electrical conductivity in porous media. Phys. Rev. B 31(9), 5990 (1985)CrossRefGoogle Scholar
  32. Sakhaee-pour, A., Bryant, S.: Gas permeability of shale. SPE Reserv. Eval. Eng. 15(4), 401–409 (2012)CrossRefGoogle Scholar
  33. Salot, C., Gotteland, P., Villard, P.: Influence of relative density on granular materials behavior: DEM simulations of triaxial tests. Granul. Matter. 11(4), 221–236 (2009)CrossRefGoogle Scholar
  34. Shabro, V., Torres-Verdín, C., Javadpour, F., Sepehrnoori, K.: Finite-difference approximation for fluid-flow simulation and calculation of permeability in porous media. Transp. Porous Media 94(3), 775–793 (2012)CrossRefGoogle Scholar
  35. Singh, H., Javadpour, F.: Langmuir slip-Langmuir sorption permeability model of shale. Fuel 164, 28–37 (2016)CrossRefGoogle Scholar
  36. Singh, H., Javadpour, F., Ettehadtavakkol, A., Darabi, H.: Nonempirical apparent permeability of shale. SPE Reserv. Eval. Eng. 17(3), 414–424 (2014)CrossRefGoogle Scholar
  37. Spikes, K.T., Naraghi, M.E.: Deformation of digital images and trends of porosity versus numerical elastic properties. In: International Geophysical Conference, Qingdao, China, 17–20 April 2017, pp. 1119–1123. Society of Exploration Geophysicists and Chinese Petroleum Society (2017)Google Scholar
  38. Stahl, M., Konietzky, H.: Discrete element simulation of ballast and gravel under special consideration of grain-shape, grain-size and relative density. Granul. Matter. 13(4), 417–428 (2011)CrossRefGoogle Scholar
  39. Tahmasebi, P., Javadpour, F., Sahimi, M.: Multiscale and multiresolution modeling of shales and their flow and morphological properties. Sci. Rep. (Nat) 5, 16373 (2015).  https://doi.org/10.1038/srep16373. Nov. 12CrossRefGoogle Scholar
  40. Tahmasebi, P., Javadpour, F., Sahimi, M.: Three dimensional stochastic characterization of shale SEM images. Transp. Porous Media 110, 521–531 (2015b).  https://doi.org/10.1007/s11242-015-0570-1 CrossRefGoogle Scholar
  41. Tahmasebi, P., Javadpour, F., Sahimi, M.: Multiscale study for stochastic characterization of shale samples. Adv. Water Resour. 89, 91–103 (2016).  https://doi.org/10.1016/j.advwaters.2016.01.008 CrossRefGoogle Scholar
  42. Tahmasebi, P., Sahimi, M., Andrade, J.E.: Image-based modeling of granular porous media. Geophys. Res. Lett. 44, 4738–4746 (2017)CrossRefGoogle Scholar
  43. Yang, B., Kang, Y., You, L., Li, X., Chen, Q.: Measurement of the surface diffusion coefficient for adsorbed gas in the fine mesopores and micropores of shale organic matter. Fuel 181, 793–804 (2016)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Bureau of Economic Geology, Jackson School of GeosciencesThe University of Texas at AustinAustinUSA

Personalised recommendations