Abstract
A porous medium with a broad pore-size distribution is described on the basis of the Multiscale Percolation System concept. The representative structure is the superposition of several constitutive elementary networks, of which mesh sizes are proportional to the diameter of the class of pores considered. To account for the contribution of each class to the connection of the medium, a recurrent building process, involving rescaling and superposition, is defined. This process leads to an equivalent monoscale network, involving elements representative of the various classes. Mercury intrusion at increasing pressure into a finite-size sample of this equivalent network is modelled. The inverse problem is solved, leading to the identification of the representative multiscale structure of a given material from the experimental intrusion curve.
Similar content being viewed by others
References
Adler, P. M.: 1992, Porous Media. Geometry and Transports, Butterworth-Heineman, London.
Bentz, D. P. and Martys, N.: 1995, Hydraulic radius and transport in reconstructed three-dimensional porous media, Transport in Porous Media 17(3), 201–220.
Berkowitz, B. and Balberg, I.: 1993, Percolation theory and its application to groundwater hydrology, Water Resour. Res. 29(4), 775–794.
Bernasconi, J.: 1978, Real space renormalization of bond-disordered conductances lattices, Phys. Rev. B. 18(3), 2185–2191.
Charlaix, E., Guyon, E. and Roux, S.: 1987, Permeability of a random array of fractures of widely varying apertures, Transport in Porous Media 2, 31–43.
Daian, J.-F., Xu, K. and Quenard, D.: 1994, Invasion and transport processes in multiscale model structure for porous media, in: J. Rouquerol, F. Rodriguez-Reinoso, K. S. W. Sing and K. K. Unger, (eds), Characterization of Porous Solids III, Elsevier, Amsterdam.
Diaz, C. E., Chatzis, I. and Dullien, F. A. L.: 1987, Simulation of capillary pressure curves using bond correlated site percolation on a simple cubic network, Transport in Porous Media 2(3), 215–240.
Dullien, F. A. L.: 1979, Porous Media: Fluid Transport and Pore Structure, Academic Press, New York.
Fernandes, C. P., Magnani, F. S., Philippi, P. C. and Daïan, J.-F.: 1996, Multiscale geometrical reconstruction of porous sructures, Phys. Rev. E 54(1), in press.
Fuentes, C., Vauclin, M., Parlange, J.-Y. and Haverkamp, R.: 1996, A note on the soil-water conductivity of a fractal soil, Transport in Porous Media 23(1), 31–36.
Garboczi, E. J. and Bentz, D. P.: 1992, Computer simulation of the diffusivity of cement-based materials, J. Materials Sci. 27, 2083–2092.
Haverkamp, R. and Parlange, J.-Y.: 1986, Predicting the water-retention curve from particle-size distribution: 1. Sandy soil without organic matter, Soil Sci. 142, 325–339.
Hinrichsen, E. L., Aharony, A., Feder, J., Hansen, A., Tortstein, J. and Hardy, H. H.: 1993, A fast algorithm for estimating large-scale permeabilities of correlated anisotropic media, Transport in Porous Media 12(1), 55–72.
Hollewand M. P. and Gladden L. F.: 1992, Bond percolation and conduction in random and regular networks: topological effects at lowcoordination number, J. Phys:Condens.Matter 4, 5757–5762.
Ioannidis, M. A. and Chatzis, I.: 1993, A mixed-percolation model of capillary hysteresis and entrapment in mercury porosimetry, J. Colloïd Interface Sci. 161, 278–291.
King, P. R.: 1989, The use of renormalization for calculating effective permeability, Transport in Porous Media 4(1), 37–58.
King, P. R., Muggerride, A. H. and Price, W. G.: 1993, Renormalization calculation of immiscible flow, Transport in Porous Media 12(3), 237–260.
Kirkpatrick, S.: 1973, Percolation and conduction, Rev. Mod. Phys. 45, 574–588.
Neimark, A. V.: 1989, Multiscale percolation systems, Sov. Phys. JETP 69(4), 786–791.
Perrier, E., Mullon, C., Rieu, M., de Marsilly, G.: 1995, Computer construction of fractal soil structures: simulation of their hydraulic and shrinkage properties, Water Resour. Res. 31(12), 2927–2944.
Quenard, D. and Sallée, H.: 1992, Water vapour adsorption and transfer in cement-based materials, Materials and Structures 25, 515–522.
Renault, P.: 1991, The effect of spatially correlated blocking-up of some bonds or nodes of a network on the percolation threshold, Transport in Porous Media 6(4), 451–468.
Parlar, M. and Yortsos, C.: 1988, Percolation Theory of vapor adsorption-desorption processes in porous materials, J. Colloïd Interface Sci. 124(1), 162–176.
Rieu, M. and Sposito, G.: 1991, Fractal fragmentation, soil porosity, and soil water properties: 1. Theory, Soil Sci. Soc. Am. J. 55, 1231–1238.
Rieu, M. and Sposito, G.: 1991, Fractal fragmentation, soil porosity, and soil water properties: 2. Applications, Soil Sci. Soc. Am. J. 55, 1239–1243.
Sahimi, M.: 1994, Applicatons of Percolation Theory, Taylor and Francis, London.
Saliba, J. and Daian, J.-F.: 1991, Détermination d'un réseau aléatoire de pores pour modéliser la sorption et la migration d'humidité dans un mortier de ciment, Int. J. Heat Mass Transfer 34(8), 2081–2096
Sallès, J., Thovert, J. F., and Adler, P.M.: 1993, Reconstructed porous media and their application to fluid flow and solute transport, J. Contaminant Hydrol. 13, 3–22.
Schwartz, L. M., Auzerais, F., Dunsmuir, J., Martys, N., Bentz, D. P., and Torquato, S.: 1993, Transport and diffusion in three-dimensional composite media, Physica A: Proceedings of the 3rd international meeting on electrical transport and optical properties of inhomogeneous media.
Stauffer, D.: 1985, Introduction to Percolation Theory, Taylor and Francis, London.
Stauffer, D. and Aharony, A.: 1994, Introduction to Percolation Theory (rev. 2nd edn), Taylor and Francis, London.
Stauffer, D., Adler, J. and Aharony, A.: 1994, Universality at the three-dimensional percolation threshold, J. Phys. A 27, L475–L480.
Thompson, A. H., Katz, A. J. and Krohn, C. E.: 1987, The microgeometry and transport properties of sedimentary rocks, Adv. Phys. 36(5), 625–694.
Tsakiroglou, C. and Payatakes, A.: 1990, A new simulator of mercury porosimetry for the characterization of porous materials, J. Colloïd Interface Sci. 137(2), 315–339.
Tsakiroglou, C. and Payatakes, A.: 1991, Effects of pore size correlations on mercury porosimetry curves, J. Colloïd Interface Sci. 146(2), 479–496.
Wilkinson, D. and Willemsen, J. F.: 1983, Invasion percolation: a new form of percolation theory, J. Phys. A: Math. Gen. 16, 3365–3376.
Wilkinson, D. and Barsony, M.: 1984, Monte Carlo study of invasion percolation clusters in two and three dimensions, J. Phys. A: Math. Gen. 17, L129–L135.
Wilson, K. G.: 1971, Renormalization and critical phenomena, Phys. Rev. B. 4(9), 174–184.
Xu, K.: 1995, Structures multiéchelles modèles pour la description des matériaux poreux et l'estimation de leurs propriétés de transport, Thèse de Doctorat, Université Joseph Fourier, Grenoble, France.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Xu, K., Daian, Jf. & Quenard, D. Multiscale Structures to Describe Porous Media Part I: Theoretical Background and Invasion by Fluids. Transport in Porous Media 26, 51–73 (1997). https://doi.org/10.1023/A:1006557915438
Issue Date:
DOI: https://doi.org/10.1023/A:1006557915438