Skip to main content
SpringerLink
Log in

Particle Shape Effects on Hydraulic and Electric Tortuosities: A Novel Empirical Tortuosity Model Based on van Genuchten-Type Function

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

Abstract

The tortuosity is one of the key parameters to characterize the transport properties of porous media. Since the tortuosity is strongly related with the shape of particles constituting the porous media, we need to investigate the shape effect of particles on the tortuosities. We have, respectively, performed a series of finite element simulations for the hydraulic and the electric tortuosity to reveal the relationship between the tortuosity and the particle shape. The results reveal that: (1) A concise computational expression for tortuosities proposed by Duda et al. is numerically validated through our simulations. (2) On average, the hydraulic tortuosity is 15 % greater than the electric tortuosity within the porosity range from 0.5 to 0.9. (3) The high particle aspect ratio (5.0) results in the amplifications of both the hydraulic and the electric tortuosities up to 15 % greater than the values with the low particle aspect ratio (1.0). Using the simulation results, we propose a novel tortuosity model based on the van Genuchten-type function, which can precisely describe the relationship between the tortuosities and the porosity for elliptic particle having the aspect ratio ranging from 1.0 to 5.0.

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

Similar content being viewed by others

References

  • Ahmadi, M.M., Mohammadi, S., Hayati, A.N.: Analytical derivation of tortuosity and permeability of monosized spheres: a volume averaging approach. Phys. Rev. E (2011). doi:10.1103/PhysRevE.83.026312

  • Ahuja, L.R., Swartzendruber, D.: An improved form of soil–water diffusivity function. Soil Sci. Soc. Am. J. 36, 9–14 (1972)

    Article  Google Scholar 

  • Archie, G.E.: The electrical resistivity log as an aid in determining some reservoir characteristics. Pet. Trans. AIME 146, 54–62 (1942)

    Article  Google Scholar 

  • Barrande, M., Bouchet, R., Denoyel, R.: Tortuosity of porous particles. Anal. Chem. 79(23), 9115–9121 (2007)

    Article  Google Scholar 

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

    Google Scholar 

  • Beeckman, J.W.: Mathematical description of heterogeneous materials. Chem. Eng. Sci. 45, 2603–2610 (1990)

    Article  Google Scholar 

  • Brutsaert, W.: Probability laws for pore size distributions. Soil Sci. 101, 85–92 (1966)

    Article  Google Scholar 

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

    Google Scholar 

  • Clennell, M.B.: Tortuosity: a guide through the maze. Geol. Soc. Lond. Spec. Publ. 122, 299–344 (1997)

    Article  Google Scholar 

  • Coleman, S.W., Vassilicos, J.C.: Transport properties of saturated and unsaturated porous fractal materials. Phys. Rev. Lett. (2008). doi:10.1103/PhysRevLett.100.035504

  • 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 

  • Duda, A., Koza, Z., Matyka, M.: Hydraulic tortuosity in arbitrary porous media flow. Phys. Rev. E (2011). doi:10.1103/PhysRevE.84.036319

  • Du Plessis, J.P., Masliyah, J.H.: Flow through isotropic granular porous media. Transp. Porous Media 6(3), 207–221 (1991)

    Article  Google Scholar 

  • Ewing, R.P., Hunt, A.G.: Dependence of the electrical conductivity on saturation in real porous media. Vadose Zone J. 5(2), 731–741 (2006)

    Article  Google Scholar 

  • Friedman, S.P., Seaton, N.A.: Critical path analysis of the relationship between permeability and electrical conductivity of three-dimensional pore networks. Water Resour. Res. 34(7), 1703–1710 (1998)

    Article  Google Scholar 

  • Ghanbarian, B., Hunt, A.G., Ewing, R.P., Sahimi, M.: Tortuosity in porous media: a critical review. Soil Sci. Soc. Am. J. 77(5), 1461–1477 (2013)

    Article  Google Scholar 

  • Haverkamp, R., Vauclin, M., Touma, J., Wierenga, P.J., Vachaud, G.: A comparison of numerical simulation models for one-dimensional infiltration. Soil Sci. Soc. Am. J. 41, 285–294 (1977)

    Article  Google Scholar 

  • Havlin, S., Ben-Avraham, D.: Diffusion in disordered media. Adv. Phys. 36, 695–798 (1987)

    Article  Google Scholar 

  • Hunt, A.G.: Applications of percolation theory to porous media with distributed local conductances. Adv. Water Resour. 24, 279–307 (2001)

    Article  Google Scholar 

  • Koponen, A., Kataja, M., Timonen, J.: Tortuous flow in porous media. Phys. Rev. E (1996). doi:10.1103/PhysRevE.54.406

  • Koponen, A., Kataja, M., Timonen, J.: Permeability and effective porosity of porous media. Phys. Rev. E (1997). doi:10.1103/PhysRevE.56.3319

  • Kostek, S., Schwartz, L.M., Johnson, D.L.: Fluid permeability in porous media: comparison of electrical estimates with hydrodynamical calculations. Phys. Rev. B (1992). doi:10.1103/PhysRevB.45.186

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

    Article  Google Scholar 

  • Martys, N., Garboczi, E.J.: Length scales relating the fluid permeability and electrical conductivity in random two-dimensional model porous media. Phys. Rev. B (1992). doi:10.1103/PhysRevB.46.6080

  • Matyka, M., Khalili, A., Koza, Z.: Tortuosity-porosity relation in porous media flow. Phys. Rev. E (2008). doi:10.1103/PhysRevE.78.026306

  • 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 

  • Maxwell, J.C.: A Treatise on Electricity and Magnetism, vol. 1. Clarendon Press, London (1873)

    Google Scholar 

  • Morse, D.R., Lawton, J.H., Dodson, M.M., Williamson, M.H.: Fractal dimension of vegetation and the distribution of arthropod body lengths. Nature (1985). doi:10.1038/314731a0

  • Mota, M., Teixeira, J.A., Bowen, W.R., Yelshin, A.: Binary spherical particle mixed beds: porosity and permeability relationship measurement. Trans. Filtr. Soc. 44, 101–106 (2001)

    Google Scholar 

  • Pech, D.: Etude de la perméabilité des lits compressibles constitués de copeaux de bois partiellement destructurés. Thése de 3éme cycle, INP Grenoble, France (1984)

  • Saeger, R.B., Scriven, L.E., Davis, H.T.: Flow, conduction, and a characteristic length in periodic bicontinuous porous media. Phys. Rev. A (1991). doi:10.1103/PhysRevA.44.5087

  • Schopper, J.R.: A theoretical investigation on the formation factor/permeability/porosity relationship using a network model. Geophys. Prospect. 14, 301–341 (1966)

    Article  Google Scholar 

  • Tsai, D.S., Strieder, W.: Effective conductivities of random fiber beds. Chem. Eng. Commun. 40, 207–218 (1986)

    Article  Google Scholar 

  • van Genuchten, M.T.: Calculating the Unsaturated Hydraulic Conductivity with a New Closed-form Analytical Model. Res. Rep., 78-WR-08. Princeton University, Princeton (1978)

  • van Genuchten, M.T.: A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J. 44, 892–898 (1980)

    Article  Google Scholar 

  • van Genuchten, M.T., Nielsen, D.R.: On describing and predicting the hydraulic properties of unsaturated soils. Ann. Geophys. 3, 615–628 (1985)

    Google Scholar 

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

    Article  Google Scholar 

  • Wong, P.: Conductivity, permeability and electrokinetics. In: Wong, P. (ed.) Methods in the Physics of Porous Media, pp. 119–159. Academic Press, New York (1999)

    Chapter  Google Scholar 

  • Wyllie, M.R.J., Gregory, A.R.: Fluid flow through unconsolidated porous aggregates. Ind. Eng. Chem. Process. Des. Dev. 47, 1379–1388 (1955)

    Google Scholar 

  • Wyllie, M.R.J.: The Fundamentals of Electric Log Interpretation. Academic Press, New York (1957)

    Google Scholar 

  • Yazdchi, K., Srivastava, S., Luding, S.: On the validity of the Carman-Kozeny equation in random fibrous media. In: International Conference on Particle-based Methods II, PARTICLES 2011, October 26–28, Barcelona, Spain (2011)

  • Yu, B.-M., Li, J.-H.: A geometry model for tortuosity of flow path in porous media. Chin. Phys. Lett. 21(8), 1569–1571 (2004)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Earthquake and Volcano Geology, National Institute of Advanced Industrial Science and Technology, Central 7, Higashi 1-1-1, Tsukuba, Ibaraki, 305-8567, Japan

    Hidetaka Saomoto

  2. Methane Hydrate Research Center, National Institute of Advanced Industrial Science and Technology, Onogawa 16-1, Tsukuba, Ibaraki, 305-8569, Japan

    Jun Katagiri

Authors
  1. Hidetaka Saomoto
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jun Katagiri
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hidetaka Saomoto.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Saomoto, H., Katagiri, J. Particle Shape Effects on Hydraulic and Electric Tortuosities: A Novel Empirical Tortuosity Model Based on van Genuchten-Type Function. Transp Porous Med 107, 781–798 (2015). https://doi.org/10.1007/s11242-015-0467-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11242-015-0467-z

Keywords

Search

Navigation