Transport in Porous Media

, Volume 124, Issue 3, pp 883–901 | Cite as

A Simple Relation for Estimating Shale Permeability

  • Huy Tran
  • A. Sakhaee-Pour
  • Steven L. Bryant


Estimating matrix permeability from mercury injection capillary pressure measurements is one of the routine tasks in the petrophysical characterization of a formation. Performing this task is not yet possible for shale formations due to the absence of a realistic, convenient model, similar to those of Purcell (J Pet Technol 1(2):39–48, 1949) and Swanson (J Pet Technol 33(12):2498–2504, 1981). With this in mind, we present a simple relation, based on the acyclic pore model, for estimating shale permeability. We test the simple relation for seven samples extracted from three different formations. We discuss why other models, which are based on the random spatial distribution of the pore-throat sizes, are not applicable. The simple relation has major applications in the petroleum industry on a daily basis.


Acyclic pore model Shale Permeability Mercury injection capillary pressure (MICP) 


  1. Abgrall, P., Nguyen, N.T.: Nanofluidic devices and their applications. Anal. Chem. 80(7), 2326–2341 (2008)CrossRefGoogle Scholar
  2. Bailey, S.: Closure and compressibility corrections to capillary pressure data in shales. Oral Presentation given at DWLS 2009 Fall Workshop, Beyond the Basic Capillary Pressure: Advanced Topics and Emerging Applications. Colorado School of Mines, USA, 19 October (2009)Google Scholar
  3. Bethe, H.A.: Statistical theory of superlattices. Proc. R. Soc. Lond. Ser. A Math. Phys. Sci. 150(871), 552–575 (1935)CrossRefGoogle Scholar
  4. Bhandari, A.R., Flemings, P.B., Polito, P.J., Cronin, M.B., Bryant, S.L.: Anisotropy and stress dependence of permeability in the Barnett shale. Transp. Porous Media 108(2), 393–411 (2015)CrossRefGoogle Scholar
  5. Broadbent, S.R., Hammersley, J.M.: Percolation processes: I Crystals and mazes. Math. Proc. Camb. Philos. Soc. 53(3), 629–641 (1957)CrossRefGoogle Scholar
  6. Bryant, S.L., Mellor, D.W., Cade, C.A.: Physically representative network models of transport in porous media. AIChE J. 39(3), 387–396 (1993)CrossRefGoogle Scholar
  7. Comisky, J.T., Santiago, M., McCollom, B., Buddhala, A., Newsham, K.E.: Sample size effects on the application of mercury injection capillary pressure for determining the storage capacity of tight gas and oil shales. In: Canadian Unconventional Resources Conference. Society of Petroleum Engineers (2011)Google Scholar
  8. Fatt, I.: The network model of porous media. I. Capillary pressure characteristics. AIME Pet. Trans. 207, 144–159 (1956)Google Scholar
  9. Holditch, S.A.: Tight gas sands. J. Pet. Technol. 58(06), 86–93 (2006)CrossRefGoogle Scholar
  10. Ikonnikova, S., Vankov, E., Gülen, G., Browning, J.: Understanding shale resource production: what are the key variables?. In: Paper SPE–179984–MS Presented at the SPE/IAEE Hydrocarbon Economics and Evaluation Symposium held in Houston, Texas, USA, 17ֺ–18 May (2016)Google Scholar
  11. Jacobsen, J.L.: High-precision percolation thresholds and Potts-model critical manifolds from graph polynomials. J Phys A Math Theor 47(13), 135001 (2014)CrossRefGoogle Scholar
  12. Jiang, C.: Pore structure characterization of shale at the micro- and macro-scale. Ph.D. dissertation. University of Texas at Austin (2016)Google Scholar
  13. Jiang, C., Bryant, S., Daigle, H.: A bundle of short conduits model of the pore structure of gas shale. Unconventional Resources Technology Conference (URTEC) (2015)Google Scholar
  14. Kamath, J.: Evaluation of accuracy of estimating air permeability from mercury-injection data. SPE Form. Eval. 7(04), 304–310 (1992)CrossRefGoogle Scholar
  15. Katz, A.J., Thompson, A.H.: Quantitative prediction of permeability in porous rock. Phys. Rev. B 34(11), 8179 (1986)CrossRefGoogle Scholar
  16. Letham, E.A., Bustin, R.M.: Klinkenberg gas slippage measurements as a means for shale pore structure characterization. Geofluids 16, 264–278 (2016)CrossRefGoogle Scholar
  17. Luffel, D.L., Hopkins, C.W., Schettler Jr, P.D.: Matrix permeability measurement of gas productive shales. In: SPE Annual Technical Conference and Exhibition. Society of Petroleum Engineers (1993)Google Scholar
  18. Mason, G.: Desaturation of porous media. I. Unconsolidated materials. J. Colloid Interface Sci. 41(2), 208–227 (1972)CrossRefGoogle Scholar
  19. Mellor, D.W.: Random close packing (RCP) of equal spheres: structure and implications for use as a model porous medium. Ph.D. dissertation, Open University (1989)Google Scholar
  20. Peters, E.J.: Advanced Petrophysics: Geology, Porosity, Absolute Permeability, Heterogeneity, and Geostatistics. Greenleaf Book Group, Austin (2012)Google Scholar
  21. Pride, S.: Governing equations for the coupled electromagnetics and acoustics of porous media. Phys. Rev. B 50(21), 15678 (1994)CrossRefGoogle Scholar
  22. Prodanovic, M., Mehmani, A., Sheppard, A.P.: Imaged-based multiscale network modelling of microporosity in carbonates. Geol. Soc. Lond. Spec. Publ. 406(1), 95–113 (2015)CrossRefGoogle Scholar
  23. Purcell, W.R.: Capillary pressures-their measurement using mercury and the calculation of permeability therefrom. J. Pet. Technol. 1(2), 39–48 (1949)CrossRefGoogle Scholar
  24. Revil, A., Woodruff, W.F., Torres-Verdin, C., Prasad, M.: Complex conductivity tensor of anisotropic hydrocarbon-bearing shales and mudrocks. Geophysics 78(6), 403–418 (2013)CrossRefGoogle Scholar
  25. Sakhaee-Pour, A.: Pore-scale modeling of The Geysers. Geothermics 60, 58–65 (2016)CrossRefGoogle Scholar
  26. Sakhaee-Pour, A., Bryant, S.L.: Gas permeability of shale. SPE Reserv. Eval. Eng. 15(4), 401–409 (2012)CrossRefGoogle Scholar
  27. Sakhaee-Pour, A., Bryant, S.L.: Effect of pore structure on the producibility of tight-gas sandstones. AAPG Bull. 98(4), 663–694 (2014)CrossRefGoogle Scholar
  28. Sakhaee-Pour, A., Bryant, S.L.: Pore structure of shale. Fuel 143, 467–475 (2015)CrossRefGoogle Scholar
  29. Sakhaee-Pour, A., Li, W.: Fractal dimensions of shale. J. Nat. Gas Sci. Eng. 30, 578–582 (2016)CrossRefGoogle Scholar
  30. Sanaei, A, Jamili, A., Callard, J.: Production modeling in the eagle ford gas condensate window: integrating new relationships between core permeability, pore size, and confined PVT properties. In: Paper SPE-169493 Presented at the SPE Western North American and Rock Mountain Joint Regional Meeting held at Denver, Colorado, USA, 16–18 April (2014)Google Scholar
  31. Suding, P.N., Ziff, R.M.: Site percolation thresholds for Archimedean lattices. Phys. Rev. E 60(1), 275 (1999)CrossRefGoogle Scholar
  32. Swanson, B.F.: A simple correlation between permeabilities and mercury capillary pressures. J. Pet. Technol. 33(12), 2498–2504 (1981)CrossRefGoogle Scholar
  33. Tran, H., Sakhaee-Pour, A.: Viscosity of shale gas. Fuel 191, 87–96 (2017)CrossRefGoogle Scholar
  34. van der Marck, S.C.: Percolation thresholds and universal formulas. Phys. Rev. E 55(2), 1514 (1997)CrossRefGoogle Scholar
  35. Walls, J.D., Amaefule, J.O.: Capillary pressure and permeability relationships in tight gas sands. In: Paper SPE-13879 Presented at the SPE/DOE Low Permeability Gas Reservoirs Symposium held at Denver, Colorado, USA, 19–22 March (1985)Google Scholar
  36. Walsh, M.P., Lake, L.W.: A Generalized Approach to Primary Hydrocarbon Recovery. Elsevier, Boston (2003)Google Scholar
  37. Washburn, E.W.: The dynamics of capillary flow. Phys. Rev. 17(3), 273 (1921)CrossRefGoogle Scholar
  38. Whitby, M., Cagnon, L., Thanou, M., Quirke, N.: Enhanced fluid flow through nanoscale carbon pipes. Nano Lett. 8(9), 2632–2637 (2008)CrossRefGoogle Scholar
  39. Winland, H.D.: Oil accumulation in response to pore size changes, Weyburn field, Saskatchewan. Amoco Production Company Report F72-G-25, p 20 (1972)Google Scholar
  40. Winland, H.D.: Evaluation of gas slippage and pore aperture size in carbonate and sandstone reservoirs. Amoco Production Company Report F76-G-5, p 25 (1976)Google Scholar
  41. Woodruff, W.F., Revil, A., Prasad, M., Torres-Verdin, C.: Measurements of elastic and electrical properties of an unconventional organic shale under differential loading. Geophysics 80(4), 363–383 (2015)CrossRefGoogle Scholar
  42. Zapata, Y., Sakhaee-Pour, A.: Modeling adsorption–desorption hysteresis in shales: acyclic pore model. Fuel 181, 557–565 (2016)CrossRefGoogle Scholar
  43. Zapata, Y., Sakhaee-Pour, A.: Pore-body and -throat size distributions of The Geysers. Geothermics 65, 313–321 (2017)CrossRefGoogle Scholar
  44. Zhang, J., Scherer, G.W.: Permeability of shale by the beam-bending method. Int. J. Rock Mech. Min. Sci. 53, 179–191 (2012)CrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.Department of Petroleum EngineeringUniversity of HoustonHoustonUSA
  2. 2.Department of Petroleum EngineeringUniversity of HoustonHoustonUSA
  3. 3.Department of Chemical and Petroleum Engineering, Schulich School of EngineeringUniversity of CalgaryCalgaryCanada

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