Skip to main content
SpringerLink
Log in

Dependency of Tortuosity and Permeability of Porous Media on Directional Distribution of Pore Voids

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

Abstract

Single-phase fluid flow in porous media is usually direction dependent owing to the tortuosity associated with the internal structures of materials that exhibit inherent anisotropy. This article presents an approach to determine the tortuosity and permeability of porous materials using a structural measure quantifying the anisotropic distribution of pore voids. The approach uses a volume averaging method through which the macroscopic tortuosity tensor is related to both the average porosity and the directional distribution of pore spaces. The permeability tensor is derived from the macroscopic momentum balance equation of fluid in a porous medium and expressed as a function of the tortuosity tensor and the internal structure of the material. The analytical results generally agree with experimental data in the literature.

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

Similar content being viewed by others

References

  • Al-Omari A., Masad E.: Three dimensional simulation of fluid flow in X-ray CT images of porous media. Int. J. Numer. Anal. Methods Geomech. 28, 1327–1360 (2004). doi:10.1002/nag.389

    Article  Google Scholar 

  • Bachmat Y., Bear J.: Microscopic modelling of transport phenomena in porous media. I: the continuum approach. Transp. Porous Media 1, 213–240 (1986)

    Article  Google Scholar 

  • Barrande M., Bouchet R., Denoyel R.: Tortuosity of porous particles. Anal. Chem. 79, 9115–9121 (2007)

    Article  Google Scholar 

  • Bear J.: Dynamics of Fluids in Porous Media. Elsevier, New York (1972)

    Google Scholar 

  • Bear J., Bensabat J.: Advective fluxes in multiphase porous media under nonisothermal conditions. Transp. Porous Media 4(5), 423–448 (1989)

    Article  Google Scholar 

  • Bear J., Bachmat Y.: Introduction to Modeling of Transport Phenomena in Porous Media. Kluwer Academic Publishers, Dordrecht (1990)

    Book  Google Scholar 

  • Boudreau B.P., Meysman F.J.R.: Predicted tortuosity of muds. Geology 34, 693–696 (2006)

    Article  Google Scholar 

  • Bourbié T., Coussy O., Zinszner B.: Acoustics of Porous Media. Gulf Publishing Co., Houston (1987)

    Google Scholar 

  • Carman P.C.: Fluid flow through granular beds. Trans. Inst. Chem. Eng. 15, 150–166 (1937)

    Google Scholar 

  • Chapuis R.P., Gill D.E.: Hydraulic anisotropy of homogeneous soils and rocks: influence of the densification process. Bull. Eng. Geol. Environ. 39(1), 75–86 (1989)

    Google Scholar 

  • Chapuis R.P., Gill D.E., Baass K.: Laboratory permeability tests on sand: influence of the compaction method on anisotropy. Can. Geotech. J. 26, 614–622 (1989)

    Article  Google Scholar 

  • Clennell, M.B.: Tortuosity: a guide through the maze. In: Lovell, M.A., Harvey, P.K (eds.) Developments in Petrophysics, vol. 122, pp. 299–344. Geological Society, London. Special Publication (1997)

  • Comiti J., Renaud M.: A new model for determining mean structure parameters of fixed beds from pressure drop measurements: application to beds packed with parallelepipedal particles. Chem. Eng. Sci. 44(7), 1539–1545 (1989)

    Article  Google Scholar 

  • Dagan G.: Flow and Transport in Porous Formations. Springer, Heidelberg (1989)

    Book  Google Scholar 

  • Daigle H., Dugan B.: Permeability anisotropy and fabric development: a mechanistic explanation. Water Resour. Res. 47(W12517), 1–11 (2011)

    Google Scholar 

  • Das B.M.: Advanced Soil Mechanics, 3rd edn, pp. 567. Taylor & Francis, London (2008)

    Google Scholar 

  • Dias R., Teixeira J.A., Mota M., Yelshin A.: Tortuosity variation in a low density binary particulate bed. Sep. Purif. Technol. 51(2), 180–184 (2006)

    Article  Google Scholar 

  • Diedericks G.P.J., Du Plessis J.P.: On tortuosity and areosity tensors for porous media. Transp. Porous Media 20, 265–279 (1995)

    Article  Google Scholar 

  • Duda A., Koza Z., Matyka M.: Hydraulic tortuosity in arbitrary porous media flow. Phys. Rev. E 84, 036319 (2011)

    Article  Google Scholar 

  • Dullien F.A.L.: Prediction of “tortuosity factors” from pore structure data. AIChE J. 21, 820–822 (1975)

    Article  Google Scholar 

  • Dullien F.A.L.: Porous Media: Fluid Transport And Pore Structure. Academic Press, New York (1979)

    Google Scholar 

  • Gao Y., Zhang X., Rama P., Liu Y., Chen R., Ostadi H., Jiang K.: Calculating the anisotropic permeability of porous media using the Lattice Boltzmann method and X-ray computed tomography. Transp. Porous Media 92(2), 457–462 (2012)

    Article  Google Scholar 

  • Gomez C.T., Dvorkin J., Vanorio T.: Laboratory measurements of porosity, permeability, resistivity, and velocity on Fontainebleau sandstones. Geophysics 75(6), E191–E204 (2010)

    Google Scholar 

  • Gommes C.J., Bons A.-J., Blacher S., Dunsmuir J.H., Tsou A.H.: Practical methods for measuring the tortuosity of porous materials from binary or gray-tone tomographic reconstructions. AIChE J. 55(8), 2000–2012 (2009)

    Article  Google Scholar 

  • Greenkorn, R.A., Kessler, D.P.: Dispersion in heterogeneous non-uniform anisotropic porous media. In: Flow through Porous Media (6th state-of-the-art Symposium sponsored by Industrial and Engineering Chemistry), 159–178, R.J. Nunge, Chairman, American Chemical Society Publications, Washington, DC, USA (1970)

  • Ho F.-G., Strieder W.: A variational calculation of the effective surface diffusion coefficient and tortuosity. Chem. Eng. Sci. 36, 253–258 (1981)

    Article  Google Scholar 

  • Iversen N., Jorgensen B.B.: Diffusion coefficients of sulphate and methane in marine sediments: influence of porosity. Geochim. Cosmochim. Acta 57, 571–578 (1993)

    Article  Google Scholar 

  • Jankovich I., Fiori A., Dagan G.: Effective conductivity of an isotropic heterogeneous medium of lognormal conductivity distribution. Multiscale Model. Simul. 1(1), 40–56 (2003)

    Article  Google Scholar 

  • Khan F., Enzmann F., Kersten M., Wiegmann A., Steiner K.: 3D simulation of the permeability tensor in a soil aggregate on basis of nanotomographic imaging and LBE solver. J. Soil Sediment 12(1), 86–96 (2012)

    Article  Google Scholar 

  • Kim J.-H., Ochoa J.A., Whitaker S.: Diffusion in anisotropic porous media. Transp. Porous Media 2, 327–356 (1987)

    Article  Google Scholar 

  • Kovács G.: Seepage Hydraulics (Developments in Water Science), Elsevier, Amsterdam, pp. 730 (1981)

    Google Scholar 

  • Koza Z., Matyka M., Khalili A.: Finite-size anisotropy in statistically uniform porous media. Phys. Rev. E 79, 066306 (2009)

    Article  Google Scholar 

  • Kozeny J.: Uber Kapillore Leintung des Wossers im Boden, Stizungsber. Akad. Wiss. Wien 136, 271–306 (1927)

    Google Scholar 

  • Kreamer D.K., Weeks E.P., Thompson G.M.: A field technique to measure the tortuosity and sorption-affected porosity for gaseous diffusion in the unsaturated zone with experimental results from near Barnborehole. South Carolina. Water Resour. Res. 24, 331–341 (1988)

    Article  Google Scholar 

  • Lanfrey P.-Y., Kuzeljevic Z.V., Dudukovic M.P.: Tortuosity model for fixed beds randomly packed with identical particles. Chem. Eng. Sci. 65(5), 1891–1896 (2010)

    Article  Google Scholar 

  • Masad E., Muhunthan B.: Three-dimensional characterization and simulation of anisotropic soil fabric. J. Geotech. Geoenviron. Eng. 126(3), 199–207 (2000)

    Article  Google Scholar 

  • Mast R.F., Potter P.E.: Sedimentary structures, sand shape fabrics, and permeability. II. J. Geol. 71(5), 548–565 (1963)

    Article  Google Scholar 

  • Matyka M., Khalili A., Koza Z.: Tortuosity–porosity relation in the porous media flow. Phys. Rev. E 78, 026306 (2008)

    Article  Google Scholar 

  • Mauret E., Renaud M.: Transport phenomena in multi-particle systems-I. Limits of applicability of capillary model in high voidage beds–application to fixed beds of fibers and fluidized beds of spheres. Chem. Eng. Sci. 52(11), 1807–1817 (1997)

    Article  Google Scholar 

  • Mota M., Teixeira J.A., Yelshin A.: Binary spherical particle mixed beds porosity and permeability relationship measurement. Trans. Filtr. Soc. 1, 101–106 (2001)

    Google Scholar 

  • Ohkubo T.: Tortuosity based on anisotropic diffusion process in structured plate-like obstacles by Monte Carlo simulation. Transp. Porous Media 72, 339–350 (2008)

    Article  Google Scholar 

  • Pietruszczak S., Krucinski S.: Description of anisotropic response of clays using a tensorial measure of structural disorder. Mech. Mater. 8, 237–249 (1989)

    Article  Google Scholar 

  • Rice P.A., Fontugne D.J., Latini R.G., Barduhn A.J.: Anisotropic permeability in porous media. Ind. Eng. Chem. 62, 23–31 (1970)

    Article  Google Scholar 

  • Salem H., Chilingarian G.V.: Influence of porosity and direction of flow on tortuosity in unconsolidated porous media. Energy Source 22, 207–213 (2000)

    Article  Google Scholar 

  • Samarasinghe A.M., Huang Y.M., Drnecich V.P.: Permeability and consolidation of normally consolidated soils. J. Geotech. Eng. 108(GT6), 835–850 (1982)

    Google Scholar 

  • Scheidegger A.E.: Directional permeability of porous media to homogeneous fluids. Geofis. Pura. Appl. 28, 75–90 (1954)

    Article  Google Scholar 

  • Selomulya C., Tran T.M., Jia X., Williams R.A.: An integrated methodology to evaluate permeability from measured microstructures. AIChE J. 52(10), 3394–3400 (2006)

    Article  Google Scholar 

  • Suribhatla R., Jankovic I., Fiori A., Dagan G.: Effective conductivity of an anisotropic heterogeneous medium of random conductivity distribution. Multiscale Model. Simul. 9(3), 933–954 (2011)

    Article  Google Scholar 

  • Weissberg H.: Effective diffusion coefficients in porous media. J. App. Phys. 34, 2636–2639 (1963)

    Article  Google Scholar 

  • Whitaker S.: Flow in porous media I: a theoretical derivation of Darcy’s law. Transp. Porous Media 1, 3–25 (1986)

    Article  Google Scholar 

  • Whitaker S.: The Method of Volume Averaging. Kluwer Academic Publishers, Dordrecht (1999)

    Google Scholar 

  • Witt K.-J., Brauns J.: Permeability-anisotropy due to particle shape. J. Geotech. Eng. 109(9), 1181–1187 (1983)

    Article  Google Scholar 

  • Yazdchi K., Srivastava S., Luding S.: Microstructural effects on the permeability of periodic fibrous porous media. Int. J. Multiphase Flow 37(8), 956–966 (2011)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Civil Engineering, McMaster University, Hamilton, ON, L8S 4L7, Canada

    Peijun Guo

Authors
  1. Peijun Guo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Peijun Guo.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Guo, P. Dependency of Tortuosity and Permeability of Porous Media on Directional Distribution of Pore Voids. Transp Porous Med 95, 285–303 (2012). https://doi.org/10.1007/s11242-012-0043-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11242-012-0043-8

Keywords

Search

Navigation