Skip to main content
Log in

Generation of Realistic Porous Media by Grains Sedimentation

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

Abstract

In a recent paper, Tacher and co‐workers proposed an interesting numerical technique to generate granular porous media. In this contribution, we present a similar procedure based on a sedimentation algorithm, that is able to overcome some of the difficulties present in the former technique. These are: (a) the impossibility to choose a priori a grading curve for the generated medium while retaining a realistic stacking where each grain is connected to at least three of its neighbours, and, (b) he random pattern of the grains in the porous medium, arising from their location inside the remaining void space of a box according to an arbitrary space filling criterion. We propose to generate three‐dimensional granular media by simulating the deposition of spherical grains in a viscous fluid. We argue that the resulting chaotic grain pattern, by reflecting the actual generation process of sedimentary aggregates more closely, provides a better image of the complex topology of natural granular porous media. Although the generated medium is made up of spheres, it can be transformed, by changing the geometry of the grains through suitable domain mappings. The resulting three‐dimensional porous media provide a realistic boundary for the numerical solution of linearized Navier–Stokes equations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Adler, P. M.: 1992, Porous Media, Butterworth, Heinemann, London.

    Google Scholar 

  • Allen, J. R. L.: 1985, Principles of Physical Sedimentology, George Allen & Unwin, London.

    Google Scholar 

  • Bachmat, Y. and Bear, J.: 1986, Macroscopic modelling of transport phenomena in porous media: 1. The continuum approach, Transport in Porous Media 1, 213–240.

    Google Scholar 

  • Bear, J.: 1988, Dynamics of Fluids in Porous Media, Dover, New York.

  • Buchalter, B. J. and Bradley, R. M.: 1994, Orientational order in amorphous packings of ellipsoids, Europhys. Lett. 26, 159.

    Google Scholar 

  • Chen, S., Diemer, K., Doolen, G. D., Eggert, K., Fu, C., Gutman, S. and Travis, B. J.: 1991, Lattice gas automata for flow through porous media, Physica D 47, 72–84.

    Google Scholar 

  • Coelho, D., Thovert, J.-F. and Adler, P. M.: 1997, Geometrical and transport properties of random packings of spheres and aspherical particles, Phys. Rev. E 55(2), 1959–1978.

    Google Scholar 

  • Darcy, H. P. G.: 1856, Les fontaines publiques de la ville de Dijon, Dalmont, Paris.

    Google Scholar 

  • DallaGiovanna, S. and Vitali, M.: 1996, Studio sperimentale sulla valutazione della conduttività idraulica degli ammassi sedimentari incoerenti, Tesi di Laurea, Politecnico di Milano.

  • Dexter, A. R. and Tanner, D.W.: 1972, Packing densities of mixtures of spheres with lognormal size distributions, Nature 238, 31–32.

    Google Scholar 

  • Di Pietro, L. B., Melayah, A. and Zaleski, S.: 1994, Modeling water infiltration in unsaturated porous media by interacting lattice gas cellular automata, Water Resour. Res. 30(10), 2785–2792.

    Google Scholar 

  • Garde, R. J.: 1972, Bed material characteristics of alluvial streams, J. Sedim. Geol. 7, 2.

    Google Scholar 

  • Ghilardi, P., Menduni, G. and Rosso, R.: 1991, On the morphogenesis of scaling porous media, Excerpta 6, 207–227.

    Google Scholar 

  • Ghilardi, P., Kai Kai A. and Menduni, G.: 1993, Self-similar heterogeneity in granular porous media at the representative elementary volume scale, Water Resour. Res. 29(4), 1205–1214.

    Google Scholar 

  • Gray, W. A.: 1968, The Packing of Solid Particles, Chapman & Hall, London.

    Google Scholar 

  • Haff, P. K., Anderson, R. S.: 1993, Grain scale simulations of loose sedimentary beds: the example of grain-bed impacts in aeolian saltation, Sedimentology 40, 175–198.

    Google Scholar 

  • Heywood, H.: 1937, Numerical definitions of particle size and shape, Chemistry and Industry, 149–154.

  • Jiang, Z. and Haff, P. K.: 1993, Multiparticle simulation methods applied to the micromechanics of bed load transport, Water Resour. Res. 29(2), 399–412.

    Google Scholar 

  • Jiang, Z.: 1995, The motion of sediment-water mixtures during intense bedload transport: computer simulations, Sedimentology 42, 935–945.

    Google Scholar 

  • Jodrey, W. S. and Tory, E. M.: 1985, Computer simulation of close random packing of equal spheres, Phys. Rev. A 32, 2347.

    Google Scholar 

  • Jullien, R. and Botet, R.: 1987, Aggregation and Fractal Aggregates, World Scientific, Singapore.

    Google Scholar 

  • Jullien, R. and Meakin: 1987, Simple three-dimensional models for ballistic deposition with restructuring, P. Europhys. Lett. 4, 1385.

    Google Scholar 

  • Katz, A. J. and Thompson, A. H.: 1986, Fractal sandstones pores: implications for conductivity and pore formation, Phys. Rev. Lett. 56(19), 2112.

    Google Scholar 

  • Kothyari, U. C.: 1995, Frequency distribution of river bed materials, Sedimentology 42, 283–291.

    Google Scholar 

  • Maier, R. S., Kroll, D. M., Kutsovsky, Y. E., Davis, H. T. and Bernard, R. S.: 1998, Simulation of flow through bead packs using the lattice Boltzmann method, Phys. Fluids 10(1), 60–74.

    Google Scholar 

  • Martys, N. S., Torquato, S. and Bentz, D. P.: 1994, Universal scaling of fluid permeability for sphere packings, Phys. Rev. E 50(1), 403–408.

    Google Scholar 

  • Meagher, D. J.: 1980, Octree encoding: a new technique for the representation, manipulation, and display of arbitrary three dimensional objects by computer, Technical Report IPL-TR-80-111, Image Processing Lab., Rensselaer Polytechnic Inst., Troy, N.Y.

    Google Scholar 

  • Onoda, G. Y. and Liniger, E. G.: 1990, Random loose packings of uniform spheres and the dilatancy onset, Phys. Rev. Lett. 64, 2727.

    Google Scholar 

  • Pilotti, M. and Menduni, G.: 1997, Application of lattice gas techniques to the study of sediment erosion and transport caused by laminar sheetflow, Earth Surface Processes and Landforms 22, 885–893.

    Google Scholar 

  • Quintanilla J. and Torquato, S.: 1996, Clustering properties of d-dimensional overlapping spheres, Phys. Rev. E 54, 5331.

    Google Scholar 

  • Ridgway, K. and Tarbuck, K. J.: 1966, Radial voidage variation in randomly packed beds of spheres of different sizes, J. Pharm. Pharmacol. 18(supplement).

  • Rothman, D.: 1988, Cellular automaton fluids: a model for flow in porous media, Geophysics 53(4), 509–518.

    Google Scholar 

  • Rubinstein, J. and Torquato, S.: 1989, Flow in random porous media: mathematical formulation, variational principles and rigorous bounds, J. Fluid Mech. 206, 25.

    Google Scholar 

  • Spencer, D. W.: 1963, The interpretation of grain size distribution curves of clastic sediments, J. Sedim. Petrol. 33, 180–190.

    Google Scholar 

  • Tacher, L., Perrochet, P. and Parriaux, A.: 1997, Generation of granular media, Transport in Porous Media 26, 99–107.

    Google Scholar 

  • Torquato, S.: 1987, Characterization of the microstructure of disordered media: a unified approach, Phys. Rev. B 35, 5385.

    Google Scholar 

  • Torquato, S. and Lu, B.: 1990, Rigorous bounds on the fluid permeability: effect of polydispersivity in grain size, Phys. Fluids A 2, 487.

    Google Scholar 

  • Torquato, S.: 1992, Connection between the morphology and effective properties of heterogeneous materials, In: S. Torquato and D. Krajcinovic (eds), Macroscopic Behavior of Heterogenous Materials from the Microstructure, American Society of Mechanical Engineers, AMD-Vol. 147, p. 53.

  • Torquato, S.: 1994, Macroscopic behavior of random media from the microstructure, Appl. Mech. Rev. 47.

  • Turcotte, D. L.: 1986, Fractals and fragmentation, J. Geophys. Res. 91(B2), 1921–1926.

    Google Scholar 

  • Turcotte, D. L.: 1992, Fractals and Chaos in Geology and Geophysics, Cambridge University Press, Cambridge.

    Google Scholar 

  • Vischer, G. S.: 1969, Grain size distribution and depositional processes, J. Sedim. Petrol. 39, 1074–1106.

    Google Scholar 

  • Wakeman, R. J.: 1975, Packing densities of particles with lognormal size distributions, Powder Technol. 11, 297–299.

    Google Scholar 

  • Witten, T. A. and Sander, L. M.: 1981, Diffusion limited aggregation, a kinetic critical phenomenon, Phys. Rev. Lett. 47, 1400–1403.

    Google Scholar 

  • Wong P. Z., Howard, J. and Lin, J. S.: 1986, Surface roughening and the fractal nature of rocks, Schlumberger-Doll (Research Preprint).

  • Yerry, M. A. and Shephard, M. S.: 1984, Automatic three-dimensional mesh generation by the modified octree technique, Int. J. Num. Methods Engng. 20, 1965–1990.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pilotti, M. Generation of Realistic Porous Media by Grains Sedimentation. Transport in Porous Media 33, 257–278 (1998). https://doi.org/10.1023/A:1006598029153

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1006598029153

Navigation