Abstract
The basic aim of this work is to present a combination of techniques for the reconstruction of the porous structure and the study of transport properties in porous media. The disordered structure of porous systems like random sphere packing, Vycor glass and North Sea chalk, is represented by three-dimensional binary images. The random sphere pack is generated by a standard ballistic deposition procedure, while the chalk and the Vycor matrices by a stochastic reconstruction technique. The transport properties (Knudsen diffusivity, molecular diffusivity and permeability) of the resulting 3-dimensional binary domains are investigated through computer simulations. Furthermore, physically sound spatial distributions of two phases filling the pore space are determined by the use of a simulated annealing algorithm. The wetting and the non-wetting phases are initially randomly distributed in the pore space and trial-and-error swaps are performed in order to attain the global minimum of the total interfacial energy. The effective diffusivities of the resulting domains are then computed and a parametric study with respect to the pore volume fraction occupied by each phase is performed. Reasonable agreement with available data is obtained in the single- and multi-phase transport cases.
Key words
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Adler, P. M.: 1992, Porous Media: Geometry and Transports. Butterworth, London.
Adler, P. M., Jacquin C. J. and Quiblier J. A.: 1990, Flow in simulated porous media. Int. J. Multiphase Flow 16, 691.
Archie, G. E.: 1942, The electrical resistivity log as an aid in determining some reservoir characteristics. Trans. AIME 54, 146.
Bekri, S., Vizika, O., Thovert, J.-F. and Adler P. M.: 2002, Binary two-phase flow with phase change in porous media, Int. J. Multiphase Flow 27, 477.
Bekri, S., Xu, K., Yousefian, F., Adler, P. M., Thovert, J.-F., Muller, J., Iden, K., Psyllos, A., Stubos, A. K. and Ioannidis M. A.: 2000, Pore geometry and transport properties in North Sea chalk. J. Petroleum Sci. Eng. 25, 107.
Berkowitz, B. and Hansen D. P.: 2001, A numerical study of the distribution of water in partially saturated porous rock. Transport Porous Media 45, 301.
Bernal, J. D.: 1959, A geometrical approach to the structure of liquids. Nature 183, 141.
Bird, G. A.: 1976, Molecular Gas Dynamics. Clarendon, Oxford.
Bird, R. B., Stewart, W. E. and Lightfoot E. N.: 1960, Transport Phenomena. John Wiley and Sons.
Boving, T. B. and Grathwohl, P.: 2001, Tracer diffusion coefficients in sedimentary rocks: correlation to porosity and hydraulic conductivity. J. Contam. Hydrol. 53, 85.
Bryant, S, Mason, G and Mellor, D.: 1996, Quantification of spatial correlation in porous media and its effect on mercury porosimetry. J. Colloid Interface Sci. 177, 88.
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, 1959.
Coker, D. A. and Torquato, S.: 1995, Simulation of diffusion and trapping in digitized porous media. J. Appl. Phys. 77, 6087.
Debye, P., Anderson, H. R. and Brumberger, H.: 1957, J. Appl. Phys. 28, 679.
Gelb, L. D., Gubbins, K. E.: 1998, Characterization of porous glasses: simulation models, adsorption isotherms, and the Brunauer-Emmett-Teller analysis method. Langmuir 14, 2097.
Glover, P. W. J., Hole, M. J., Pous, J.: 2000, A modified Archie's law for two conducting phases. Earth Planet Sci. Lett. 180, 369.
Joshi, M. Y.: 1974, A Class of stochastic models for porous media, PhD Thesis, University of Kansas.
Kainourgiakis, M. E., Kikkinides, E. S., Steriotis, Th.A., Stubos, A. K., Tzevelekos K. P. and Kanellopoulos, N. K.: 2000, Structural and transport properties of alumina porous membranes from process-based and statistical reconstruction techniques. J. Colloid Interface Sci. 231, 158.
Kainourgiakis, M. E., Kikkinides, E. S., Stubos, A. K. and Kanellopoulos N. K.: 1999, Simulation of self-diffusion of point-like and finite-size tracers in stochastically reconstructed Vycor porous glasses. J. Chem. Phys. 111, 2735.
Kim, I. C. and Torquato, S.: 1992, Diffusion of finite-sized Brownian particles in porous media. J. Chem. Phys. 96, 1498.
Kirkpatrick, S., Gelatt C. D. and Vecchi, M. P.: 1983, Optimization by simulated annealing. Science 200, 671.
Knight, R., Chapman, A. and Knoll, M.: 1990, Numerical modeling of microscopic fluid distribution in porous media. J. Appl. Phys. 68, 994.
Leverett, M. C.: 1939, Flow of oil-water mixtures through unconsolidated sands. Trans. AIME 132, 149.
Levitz, P., Ehret, G., Sinha, S. K. and Drake, J. M.: 1991, Porous Vucor glass — The microstructure as probed by electron-microscopy, direct energy-transfer, small-angle scattering, and molecular adsorption. J. Chem. Phys. 95, 6151.
Levitz, P., and Tchoubar, D.: 1992, Disordered porous solids — from chord distributions to small angle scattering. J. Phys. I 2, 771.
Lin, M. Y., Abeles, B., Huang, J. S., Stasiewski, H. E. and Zhang, Q.: 1992, Viscous flow and diffusion of liquids in microporous glasses. Phys. Rev. B 46, 10701.
Makri, P. K., Romanos, G., Steriotis Th., Kanellopoulos, N. K. and Mitropoulos A. Ch.: 1998, Diffusion in a fractal system. J. Colloid Interface Sci. 206, 605.
Manwart, C., Torquato, S and Hilfer, R.: 2000, Stochastic reconstruction of sandstones. Phys. Rev. E 62, 893.
Martys N. S.: 1999, Diffusion in partially-saturated porous materials. Materi. Struct. 32, 555.
Martys, N. and Garboczi, E. J.: 1992, Length scales relating the fluid permeability and electrical conductivity in random two-dimensional model porous media. Phys. Rev. B 46, 6080.
Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H. and Teller, F.: 1953, Equations of state calculations by fast computing machines. J. Chem. Phys. 21, 1087.
Mohanty, S.: 1997, Effect of multiphase fluid saturation on the thermal conductivity of geologic media. J. Phys. D: Appl. Phys. 30, L80.
Papadopoulos, G.: 1993, Study of adsorption, diffusion and gas relative permeability in mesoporous alumina membranes, in relation to their porous and macroscopic structure, Ph.D. thesis (in Greek), University of Athens.
Pavlovitch, A., Jullien, R. and Meakin, P.: 1991, Geometrical properties of a random packing of hard spheres. Physica A 176, 206.
Press W. H., Teukolsky S. A., Vetterling W. T., Flannery B. P.: 1992, Numerical Recipes in Fortran. Cambridge University Press.
Quiblier J. A.: 1986, New 3-dimensional modeling technique for studying porous media. J. Colloid Interface Sci. 98, 84.
Reiss, H.: 1992, Statistical geometry in the study of fluids and porous media. J. Phys. Chem. 96, 4736.
Roberts, J. N. and Schwartz, L. M.: 1985, Grain consolidation and electrical conductivity in porous media. Phys. Rev. B 31 5990.
Rosanne, M., Mammar, N., Koudina, N., Prunet-Foch, B, Thovert, J.-F., Tevissen, E. and Adler P. M.: 2003, Transport properties of compact clays — II. Diffusion. J. Colloid Interface Sci. 260, 195.
Schwartz, L. M., Garboczi, E. J. and Bentz, D. P.: 1995, Interfacial transport in porous media — Application to DC electrical conductivity of mortars. J. Appl. Phys. 78, 5898.
Silverstein, D. L. and Fort, T.: 2000, Prediction of air-water interfacial area in wet unsaturated porous media. Langmuir 16, 829.
Silverstein, D. L. and Fort, T.: 2000a, Incorporating low hydraulic conductivity in a numerical model for predicting air-water interfacial area in wet unsaturated particulate porous media. Langmuir 16, 835.
Silverstein, D. L. and Fort, T.: 2000b, Prediction of water configuration in wet unsaturated porous media. Langmuir 16, 839.
Stefanopoulos, K. L., Beltsios, K., Makri, P. K., Steriotis, T. A., Mitropoulos, A. Ch. and Kanellopoulos, N. K.: 2000, Characterization of the flow properties in Vycor by combining dynamic and scattering techniques. Physica B 276, 477.
Tomadakis, M. M. and Sotirchos, S. V.: 1993, Ordinary and transition regime diffusion in random fiber structures. AIChE J. 39, 397.
Visscher, W. M. and Bolsterli, M: 1972, Random packing of equal and unequal spheres in 2 and 3 dimensions. Nature 239, 504.
Vold M. J.: 1960, The sediment volume in dilute dispersions of spherical particles. J. Phys. Chem. 64, 1616.
Yao, J., Frykman, P., Kalaydjian, F., Thovert, J. F. and Adler, P M.: 1993, High order moments of the phase function for real and reconstructed model porous media. A comparison. J. Colloid Interface Sci. 156, 478.
Yeong, C. L. Y. and Torquato, S.: 1998a, Reconstructing random media. Phys. Rev. E 57, 495.
Yeong, C. L. Y. and Torquato S.: 1998b, Reconstructing random media. II. Three-dimensional media from two-dimensional cuts. Phys. Rev. E 58, 224.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer
About this chapter
Cite this chapter
Kainourgiakis, M.E., Kikkinides, E.S., Galani, A., Charalambopoulou, G.C., Stubos, A.K. (2005). Digitally Reconstructed Porous Media: Transport and Sorption Properties. In: Das, D., Hassanizadeh, S. (eds) Upscaling Multiphase Flow in Porous Media. Springer, Dordrecht. https://doi.org/10.1007/1-4020-3604-3_4
Download citation
DOI: https://doi.org/10.1007/1-4020-3604-3_4
Received:
Revised:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-3513-5
Online ISBN: 978-1-4020-3604-0
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)