Skip to main content
SpringerLink
Log in

Evaluation of hydraulic conductivity of reconstructed granular media generated using low-order probability functions

  • Geotechnical Engineering
  • Published:
KSCE Journal of Civil Engineering Aims and scope

Abstract

The hydraulic conductivity of three-dimensional artificial two-phase (fluid phase and solid phase) models with varying solid clustering sizes are evaluated to explore the effect of phase clustering, using low-order probability functions. The original random and heterogeneous microstructure models are made by placing randomly dispersed voxels with varying clustering sizes and the same porosity. The two-point correlation and lineal-path functions are applied to extract characteristics of phase clustering. The reconstructed models whose low-order probability functions are analogous to the original models are then made by a stochastic optimization process. This process allows one to generate equivalent reconstructed models to the original microstructure. The hydraulic conductivity values of both original and reconstructed models along three perpendicular directions are evaluated by solving Navier-Stoke’s equation and averaging local velocity values of fluids with the aid of finite element scheme. Results are analyzed to evaluate the applicability of reconstruction approach depending on the phase clustering. The fluid flow through porous media is further examined with the observation of flow resistance and percolation path. The effects of anisotropy of the fluid phase are also discussed to explore the applicability of stochastic optimization process. It is concluded that the low-order probabilistic functions provide an efficient tool to reconstruct three dimensional microstructures up to certain degree of clustering sizes and to simulate the flow behavior in porous media.

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

  • Adler, P. M., Jacquin, C. G., and Quiblier, J. A. (1990). “Flow in simulated porous media.” International Journal of Multiphase Flow, Elsevier, Vol. 16, No. 4, pp. 691–712.

    Article  MATH  Google Scholar 

  • Bakke, S. and Øren, P.-E. (1997). “3-D pore scale modelling of sandstones and flow simulations in the pore networks.” SPE Journal, OnePetro, Vol. 2, No. 2, pp. 136–149.

    Google Scholar 

  • Bosl, W. J., Dvorkin, J., and Nur, A. (1998). “A study of porosity and permeability using a Lattice-Boltzmann simulation.” Geophysical Research Letters, AGU, Vol. 25, No. 9, pp. 1475–1478.

    Article  Google Scholar 

  • Bryant, S. and Blunt, M. (1992). “Prediction of relative permeability in simple porous media.” Physical Review A, APS Physics, Vol. 46, No. 4, pp. 2004–2011.

    Article  Google Scholar 

  • Chung, S.-Y. and Han, T.-S. (2010). “Reconstruction of random two-phase polycrystalline solids using low-order probability functions and evaluation of mechanical behavior.” Computational Materials Science, Elsevier, Vol. 49, No. 4, pp. 705–719.

    Article  Google Scholar 

  • Cinlar, E. and Torquato, S. (1995). “Exact determination of the two-point cluster function for one-dimentional continuum percolation.” Journal of Statistical Physics, Springer, Vol. 78, Nos. 3–4, pp. 827–839.

    Article  MATH  MathSciNet  Google Scholar 

  • Corson, P. B. (1974a). “Correlation functions for predicting properties of heterogeneous materials. I. Experimental measurement of spatial correlation functions in multiphase solids.” Journal of Applied Physics, APS Physics, Vol. 45, No. 1, pp. 3159–3164.

    Article  Google Scholar 

  • Corson, P. B. (1974b). “Correlation functions for predicting properties of heterogeneous materials: III. Effective elastic moduli of twophase solids.” Journal of Applied Physics, APS Physics, Vol. 45,No. 1, pp. 3171–3179.

    Article  Google Scholar 

  • Cule, D. and Torquato, S. (1999). “Generating random media from limited microstructural information via stochastic optimization.” Journal of Applied Physics, APS Physics, Vol. 86, No. 6, pp. 3428–3437.

    Article  Google Scholar 

  • Daian, J.-F., Fernandes, C. P., Philippi, P. C., and Bellini da Cunha Neto, J. A. (2004). “3D reconstitution of porous media from image processing data using a multiscale percolation system.” Journal of Petroleum Science and Engineering, Elsevier, Vol. 42, No. 1, pp. 15–28.

    Article  Google Scholar 

  • Dechter, R. and Pearl, J. (1985). “Generalized best-first search strategies and the optimality of A*.” Journal of The Association for Computing Machinery, ACM, Vol. 32, No. 3, pp. 505–536.

    Article  MATH  MathSciNet  Google Scholar 

  • Garboczi, E. J., Snyder, K. A., Douglas, J. K., and Thorpe, M. F. (1995). “Geometrical percolation threshold of overlapping ellipsoids.” Physical Review E, APS Physics, Vol. 52, No. 1, pp. 819–828.

    Google Scholar 

  • Gokhale, A., Tewari, A., and Garmestani, H. (2005). “Constraints on microstructural two-point correlation functions.” Scripta Materialia, Elsevier, Vol. 53, No. 8, pp. 989–993.

    Article  Google Scholar 

  • Hart, P. E. and Nilson, N. J. (1968). “A formal basis for the heuristic determination of minimum cost paths.” IEEE Transcactions of Systems Science and Cybernetics, IEEE, Vol. 4, No. 2, pp. 100–107.

    Article  Google Scholar 

  • Kumar, H., Briant, C. L., and Curtin, W. A. (2006). “Using microstructure reconstruction to model mechanical behavior in complex microstructures.” Mechanics of Materials, Elsevier, Vol. 38, No. 8–10, pp. 818–832.

    Article  Google Scholar 

  • Lu, B. and Torquato, S. (1992). “Lineal-path function for random heterogeneous materials.” Physical Review A, APS Physics, Vol. 45, No. 2, pp. 922–929.

    Article  Google Scholar 

  • Manwart, C. and Hilfer, R. (1999). “Reconstruction of random media using monte carlo methods.” Physical Review E, APS Physics, Vol. 59, No. 5, pp. 5596–5599.

    Google Scholar 

  • Montes, J. M., Cuevas, E. G., and Cintas, J. (2007). “Electrical and thermal tortuosity in powder compacts.” Granular Matter, Springer, Vol. 9, No. 6, pp. 401–406.

    Article  Google Scholar 

  • Narsilio, G., Buzzi, O., Fityus, S., Yun, T. S., and Smith, D. W. (2009). “Upscaling of Navier-Stokes equations in porous media: Theoretical, numerical and experimental approach.” Computers and Geotechnics, Elsevier, Vol. 36, No. 7, pp. 1200–1206.

    Article  Google Scholar 

  • Narsilio, G., Kress, J., and Yun, T. S. (2010). “Characterisation of conduction phenomena in soils at the particle-scale: Finite element analyses in conjunction with synthetic 3D imaging.” Computers and Geotechnics, Elsevier, Vol. 37, Nos. 7–8, pp. 828–836.

    Article  Google Scholar 

  • Okabe, H. and Blunt, M. J. (2004). “Prediction of permeability for porous media reconstructed using multiple-point statistics.” Physical Review E, APS physics, Vol. 70, No. 066135, pp. 1–11.

    Google Scholar 

  • Raab, A. L., Manas-Zloczower, I., and Feke, D. L. (1997). “Influence of structure and interfacial chemistry on the permeability of particle clusters.” Journal of Colloid and Interface Science, Elsevier, Vol. 189, No. 1, pp. 131–136.

    Article  Google Scholar 

  • Tewari, A., Gokhale, A. M., Spowart, J. E., and Miracle, D. B. (2004). “Quantitative characterization of spatial clustering in three-dimensional microstructures using two-point correlation functions.” Acta Materialia, Elsevier, Vol. 52, No. 2, pp. 307–319.

    Article  Google Scholar 

  • Torquato, S. (1998). “Morphology and effective properties of disordered heterogeneous media.” International Journal of Solids and Structures, Elsevier, Vol. 35, No. 19, pp. 2385–2406.

    Article  MATH  Google Scholar 

  • Torquato, S. (2002). Random heterogeneous materials, Springer, New York.

    Book  MATH  Google Scholar 

  • Vervoort, R. W. and Cattle, S. R. (2003). “Linking hydraulic conductivity and tortuosity parameters to pore space geometry and pore-size distribution.” Journal of Hydrology, Elsevier, Vol. 272, Nos. 1–4, pp. 36–49.

    Article  Google Scholar 

  • Werner, E., Siegmund, T., Weinhandl, H., and Fischer, F. D. (1994). “Properties of random polycrystalline two-phase materials.” Applied Mechanics Reviews, ASME, Vol. 47, No. 1, pp. 125–134.

    Google Scholar 

  • Wu, K., Van Dijke, M. I. J., Couples, G. D., Jiang, Z., Ma, J., Sorbie, K. S., Crawford, J., Young, I., and Zhang, X. (2006). “3D stochastic modelling of heterogeneous porous media — Applications to reservoir rocks.” Transport in Porous Media, Springer, Vol. 65, No. 3, pp. 443–467.

    Article  Google Scholar 

  • Yeong, C. L. Y. and Torquato, S. (1998). “Reconstructing random media. II. Three-dimensional media from two-dimensional cuts.” Physical Review E, APS Physics, Vol. 58, No. 1, pp. 224–233.

    MathSciNet  Google Scholar 

  • Zaman, E. and Jalali, P. (2010). “On hydraulic permeability of random packs of monodisperse spheres: Direct flow simulations versus correlations.” Physica A, Elsevier, Vol. 389, No. 2, pp. 205–214.

    Article  Google Scholar 

  • Zaretskiy, Y., Geiger, S., Sorbie, K., and Forster, M. (2010). “Efficient flow and transport simulation in reconstructed 3D pore geometries.” Advances in Water Resources, Elsevier, Vol. 33, No. 12, pp. 1508–1516.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Civil and Environmental Engineering, Yonsei University, Seoul, 120-749, Korea

    Tae Sup Yun, Tong-Seok Han & Sang-Yeop Chung

  2. Melbourne Engineering Research Institute (MERIT), Dept. of Infrastructure Engineering, The University of Melbourne, Parkville, VIC, 3010, Australia

    Guillermo A. Narsilio

  3. CSIRO Earth Science and Resource Engineering, Clayton, VIC, 3168, Australia

    Guillermo A. Narsilio

Authors
  1. Tae Sup Yun
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tong-Seok Han
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sang-Yeop Chung
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Guillermo A. Narsilio
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tong-Seok Han.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yun, T.S., Han, TS., Chung, SY. et al. Evaluation of hydraulic conductivity of reconstructed granular media generated using low-order probability functions. KSCE J Civ Eng 18, 132–141 (2014). https://doi.org/10.1007/s12205-013-0381-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12205-013-0381-2

Keywords

Search

Navigation