Abstract
Gas dispersion in a set of three different porous materials with similar particle size, as a function of material tortuosity and anisotropy ratio, was investigated. The materials were packed with different spatial orientations of the individual particles so as to create media with different tortuosity and anisotropy ratios. Three different media (slate chips, wood chips, and pebbles) and four particle orientations have been used to generate a total of nine different porous media mimicking single porosity, dual porosity isotropic, anisotropic, aggregated, or granular materials. Resulting values of tortuosity and anisotropy ratio for each medium were determined via measurements of gas permeability and molecular gas diffusion coefficient. These values were then compared to measured values of gas dispersivity for each medium. The results showed that dispersivity is inversely proportional to tortuosity but directly proportional to anisotropy ratio and that the relations were approximately linear within the range of tortuosities and anisotropy ratios investigated. Wood chips (dual porosity material) yielded higher values of gas dispersivity compared to slate chips (single porosity material). A likely reason is in part the difference in pore structure between the materials and in part a difference in particle surface roughness (which was highest for wood chips) both of which affects dispersion.
Similar content being viewed by others
References
Bagarello, V., Sferlazza, S., & Sgroi, A. (2009). Testing laboratory methods to determine the anisotropy of saturated conductivity in a sandy-loam soil. Geoderma, 154, 52–58.
Barrande, M., Bouchet, R., & Denoyel, R. (2007). Tortuosity of porous particles. Analytical Chemistry, 79, 9115–9121.
Basak, P., & Anandakr, M. (1970). Depth dependent hydraulic conductivity. Journal of Soil Science, 109, 351–355.
Bear, J. (1961). On the tensor form of dispersion. Journal of Geophysical Research, 66, 1185–1197.
Berner, R. A. (1980). Early diagenesis: a theoretical approach. Princeton: Princeton University Press.
Blackwell, P. S., Ringrose-Voase, A. J., Jayawardane, N. S., Olsson, K. A., McKenzie, D. C., & Mason, W. K. (1990). The use of air-filled porosity and intrinsic permeability to characterize macropore structure and saturated hydraulic conductivity of clay soils. Journal of Soil Science, 41, 215–228.
Boudreau, B. P. (1996). The diffusive tortuosity of fine-grained unlithified sediments. Geochimica et Cosmochimica Acta, 60, 3139–3142.
Boving, T. B., & Grathwohl, P. (2001). Tracer diffusion coefficients in sedimentary rocks: correlation to porosity and hydraulic conductivity. Journal of Contaminant Hydrology, 53, 85–100.
Breyer, D., Fridley, K., Pollock, D., & Cobeen, K. (2006). Design of wood structure—ASD/LRFD. New York: McGraw-Hill.
Carman, P. C. (1939). Permeability of saturated sands, soils and clays. Journal of Agricultural Science, 29, 262–273.
Chapuis, R. P., & Gill, D. E. (1989). Hydraulic anisotropy of homogeneous soils and rock: influence of the densification process. Engineering Geology, 39, 75–86.
Comiti, J., & Renaud, M. (1989). A new model for determining mean structure parameters of fixed-beds from pressure-drop measurements—application to beds packed with parallelepipedal particles. Chemical Engineering Science, 44, 1539–1545.
CRC Handbook of Chemistry and Physics (92nd edition), 2011, Boca Raton: CRC.
Dorner, J., & Horn, R. (2009). Direction-dependent behavior of hydraulic and mechanical properties in structured soil under conventional and conservation tillage. Soil and Tillage Research, 102, 225–232.
Delgado, J. M. P. Q. (2006). A critical review of dispersion in packed beds. Heat and Mass Transfer, 42, 270–310.
Evans, H. E. (1962). A note on the average coefficient of permeability for a stratified soil mass. Geotechnique, 12, 145–146.
Forchheimer, P. H. (1901). Wasserbewegung durch boden. Zeitschrift ver deutscher ingenieure, 50, 1782–1788 (in German).
Garcia-Gutierrez, M., Cormenzana, J. L., Missana, T., Mingarro, M., & Martin, P. L. (2006). Large-scale laboratory diffusion experiments in clay rocks. Physics and Chemistry of the Earth, 31, 523–530.
Gelhar, L. V., Welty, C., & Rehfeldt, K. R. (1992). A critical review of data on field-scale dispersion in aquifers. Water Resources Research, 28, 1955–1974.
Ghassemi, A., & Pak, A. (2011). Pore scale study of permeability and tortuosity for flow through particulate media using Lattice Boltzmann method. International Journal for Numerical and Analytical Methods in Geomechanics, 35, 886–901.
Greenkorn, R. A., & Kessler, D. P. (1969). Flow through porous media symposium—dispersion in heterogeneous nonuniform anisotropic porous media. Industrial and Engineering Chemistry, 61, 14–32.
Guin, J. A., Kessler, D. P., & Greenkorn, R. A. (1972). Dispersion tensor in anisotropic porous media. Industrial & Engineering Chemistry Fundamentals, 11, 477–482.
Hamamoto, S., Moldrup, P., Kawamoto, K., Komatsu, T., & Rolston, D. E. (2009). Unified measurement system for the gas dispersion coefficient, air permeability and gas diffusion coefficient in variably saturated soil. Soil Science Society of America Journal, 73, 1921–1930.
Hamamoto, S., Moldrup, P., Kawamoto, K., Wickramarachchi, P. N., Nagamori, M., & Komatsu, T. (2011). Extreme compaction effects on gas transport parameters and estimated climate gas exchange for a landfill final cover soil. Journal of Geotechnical and Geoenvironmental Engineering, 137, 653–662.
Hiby, J.W. (1962). Longitudinal dispersion in single-phase liquid flow through ordered and random packings. Interaction Between Fluid & Particles (London Institution of Chemical Engineers), 312–325
Hunt, A. G., Blank, L. A., & Skinner, T. E. (2006). Distribution of hydraulic conductivity in single scale anisotropy. Philosophical Magazine, 86, 2407–2428.
Hunt, A. G., & Skinner, T. E. (2010). Predicting dispersion in porous media. Complexity, 16, 43–55.
Kallel, A., Tanaka, N., & Matsuto, T. (2004). Gas permeability and tortuosity for packed layers of processed municipal solid wastes and incinerator residue. Waste Management and Research, 22, 186–194.
Kenney, T. C. (1963). Permeability ratio of repeatedly layered soils. Geotechnique, 13, 325–333.
Kirkham, D., De Boodt, M., De Leenheer, L. (1958). Air permeability at the field capacity as related to soil structure and yields. Proceedings of the International Symposium on Soil Structure, 377-391.
Koponen, A., Kataja, M., & Timonen, J. (1997). Permeability and effective porosity of porous media. Physical Review, E56, 3319–3325.
Kozeny, J. (1927). Uber kapillare leitung des wassers im boden. Sitzungsberichte der akadämie der wissenschaften in wien abteilung IIa, 136, 271–301 (in German).
Maerki, M., Wehrli, B., Dinkel, C., & Muller, B. (2004). The influence of tortuosity on molecular diffusion in freshwater sediments of high porosity. Geochimica et Cosmochimica Acta, 68, 1519–1528.
Marcus, H., Evenson, D.E. (1961). Directional permeability in anisotropic porous media. Water Resources Center Contribution 31.
Masland, M. (1957). Soil anisotropy and land drainage. In J. N. Luthin (Ed.), Drainage of agricultural lands (pp. 216–285). Madison: American Society of Agronomy.
Matyka, M., Khalili, A., & Koza, Z. (2008). Tortuosity–porosity relation in porous media flow. Physical Review E, 78, 026306.
Mauret, E., & Renaud, M. (1997). Transport phenomena in multi-particle system. Limits of applicability of capillary model in high voidage beds—application to fixed beds of fibers and fluidized beds of spheres. Chemical Engineering Science, 52, 1807–1817.
Millington, R. J., & Quirk, J. M. (1964). Formation factor and permeability equations. Nature, 202, 143–145.
Moldrup, P., Olesen, T., Komatsu, T., Schjonning, P., & Rolston, D. E. (2001). Tortuosity, diffusivity, and permeability in the soil liquid and gaseous phases. Soil Science Society of America Journal, 65, 613–623.
Moldrup, P., Olesen, T., Blendstrup, H., Komatsu, T., de Jonge, L. W., & Rolston, D. E. (2007). Predictive–descriptive models for gas and solute diffusion coefficients in variably saturated porous media coupled to pore-size distribution: IV. Solute diffusivity and the liquid phase impedance factor. Soil Science, 172, 741–750.
Nabovati, A., & Sousa, A. C. M. (2007). Fluid flow simulation in random porous media at pore level using the Lattice Boltzmann Method. Journal of Engineering Science and Technology, 2, 226–237.
Nakashima, Y., Kamiya, S., & Nakano, T. (2008). Diffusion ellipsoids of anisotropic porous rocks calculated by X-ray computed tomography-based random walk simulations. Water Resource Research, 44, W12435.
Neumann, S. P. (1990). Universal scaling of hydraulic conductivities and dispersivities in geological media. Water Resources Research, 26, 1749–1758.
Nikolaevskii, V. N. (1959). Convective diffusion in porous media. Journal of Applied Mathematics and Mechanics, 23, 1042–1050.
Nunge, R. J., & Gill, W. N. (1969). Flow through porous media symposium—mechanisms affecting dispersion and miscible displacement. Industrial and Engineering Chemistry, 61, 33–49.
Pisani, L. (2011). Simple expression for the tortuosity of porous media. Transport in Porous Media, 88, 193–203.
Poulsen, T. G., Iversen, B. V., Yamaguchi, T., Moldrup, P., & Schjønning, P. (2001). Spatial and temporal dynamics of air permeability in a constructed, agricultural field. Soil Science, 166, 153–162.
Poulsen, T., Moldrup, P., Yoshikawa, S., & Komatsu, T. (2006). Bimodal probability law model for unified description of water retention, air and water permeability, and gas diffusivity in variably saturated soil. Vadose Zone Journal, 5, 1119–1128.
Poulsen, T., Moldrup, G., Thorbjorn, A., & Schjonning, P. (2007). Predicting air permeability in undisturbed, subsurface sandy soils from air-filled porosity. Journal of Environmental Engineering—ASCE, 133, 995–1001.
Poulsen, T. G., Suwarnarat, W., Hostrup, M. K., & Kalluri, P. N. V. (2008). Simple and rapid method for measuring gas dispersion in porous media: methodology and applications. Soil Science, 173, 169–174.
Prager, S. (1960). Diffusion in inhomogeneous media. Journal of Chemical Physics, 33, 122–127.
Rowshanzamir, M. A., & Askari, A. M. (2010). An investigation on the strength anisotropy of compacted clays. Applied Clay Science, 50, 520–524.
Scheidegger, A. E. (1960). The physics of flow through porous media (pp. 26–30). University of Toronto Press: Toronto.
Schjønning, P. (1989). Long-term reduced cultivation. Soil pore characteristics as shown by gas diffusivities and permeabilities and air-filled porosities. Soil and Tillage Research., 15, 91–103.
Schulze-Makuch, D., & Cherkauer, D. S. (1995). Facies dependent scale behaviour of hydraulic conductivity and longitudinal dispersivity. Groundwater Quality: Remediation and Protection, 225, 157–164.
Schulze-Makuch, D. (2005). Longitudinal dispersivity data and implications for scaling behavior. Ground Water, 43, 443–456.
Sharma, P., & Poulsen, T. G. (2009). Gas phase dispersion in compost as a function of different water contents and air flow rates. Journal of Contaminant Hydrology, 107, 101–107.
Sharma, P., & Poulsen, T. G. (2010a). Gas dispersion and immobile gas volume in solid and porous particle biofilter materials at low air flow velocities. Journal of the Air and Waste Management Association, 60, 830–837.
Sharma, P., & Poulsen, T. G. (2010b). Gas dispersion and immobile gas content in granular porous media: effect of particle size nonuniformity. Soil Science, 175, 426–431.
Shen, L., & Chen, Z. X. (2007). Critical review of the impact of tortuosity on diffusion. Chemical Engineering Science, 62, 3748–3755.
Soler, J. M., Samper, J., Yllera, A., Hernandez, A., Quejido, A., Fernandez, M., Yang, C., Naves, A., Hernand, P., & Wersine, P. (2008). The DI-B in situ diffusion experiment at Mont Terri: results and modeling. Physics and Chemistry of the Earth, 33, S196–S207.
Switzer, C., & Kosson, D. S. (2007). Evaluation of air permeability in layered unsaturated materials. Journal of Contaminant Hydrology, 90, 125–145.
Takeda, M., Hiratsuka, T., Ito, K., & Finsterle, S. (2011). An axisymmetric diffusion experiment for the determination of diffusion and sorption coefficients of rock samples. Journal of Contaminant Hydrology, 123, 114–129.
Terzaghi, K. (1943). Theoretical soil mechanics. New York: Wiley.
Usta, Ü. (2003). Comparative study of wood density by specific amount of void volume. Turkish Journal of Agriculture and Forestry, 27, 1–6.
Van Brakel, J., & Heertjes, P. M. (1974). Analysis of diffusion in macroporous media in terms of a porosity, a tortuosity and a constrictivity factor. International Journal of Heat and Mass Transfer, 17, 1093–1103.
Van Loon, L. R., Wersin, J. M., Soler, J. M., Eikenberg, J., Gimmi, T., Hernan, P., Dewonck, S., & Savoye, S. (2004). In-situ diffusion of HTO, 22Na+, Cs+ and I− in Opalinus clay at the Mont Terri underground rock laboratory. Radiochimica Acta, 92, 757–763.
Weerts, A. H., Kandhai, D., Bouten, W., & Sloot, P. M. A. (2001). Tortuosity of an unsaturated sandy soil estimated using gas diffusion and bulk soil electrical conductivity. Soil Science Society of America Journal, 65, 1577–1584.
Weissberg, H. L. (1963). Effective diffusion coefficients in porous media. Journal of Applied Physics, 34, 2636–2639.
Wilcox, R. R. (1997). Introduction to robust estimation and hypothesis testing. San Diego: Academic.
Wyllie, M. R. J., & Rose, W. D. (1950). Application of the Kozeny equation to consolidated porous media. Nature, 165, 972.
Zhaowen, L., & Mingzhe, D. (2010). Experimental study of diffusive tortuosity of liquid-saturated consolidated porous media. Industrial Engineering Chemistry Research, 49, 6231–6237.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Pugliese, L., Poulsen, T.G. & Andreasen, R.R. Relating Gas Dispersion in Porous Media to Medium Tortuosity and Anisotropy Ratio. Water Air Soil Pollut 223, 4101–4118 (2012). https://doi.org/10.1007/s11270-012-1176-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11270-012-1176-7