References

Biogeosciences

1726-4189

Copernicus Publications

Göttingen, Germany

10.5194/bg-7-3177-2010

Percolation properties of 3-D multiscale pore networks: how connectivity controls soil filtration processes

Perrier

E. M. A.

¹ Bird

N. R. A.

² Rieutord

T. B.

UMI UMMISCO, Centre IRD Ile de France, and RNSC (French National Network for Complex Systems), Bondy Cedex, 93143, France

Department of Soil Science, Rothamsted Research, Harpenden, Herts, AL5 2JQ, UK

Ecole Normale Supérieure Cachan Bretagne, Computer Department, Campus de Ker Lann, Bruz, 35170, France

18 10 2010

7 10 3177 3186

2010

This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/3.0/

This article is available from https://bg.copernicus.org/articles/7/3177/2010/bg-7-3177-2010.html

The full text article is available as a PDF file from https://bg.copernicus.org/articles/7/3177/2010/bg-7-3177-2010.pdf

Quantifying the connectivity of pore networks is a key issue not only for modelling fluid flow and solute transport in porous media but also for assessing the ability of soil ecosystems to filter bacteria, viruses and any type of living microorganisms as well inert particles which pose a contamination risk. Straining is the main mechanical component of filtration processes: it is due to size effects, when a given soil retains a conveyed entity larger than the pores through which it is attempting to pass. We postulate that the range of sizes of entities which can be trapped inside soils has to be associated with the large range of scales involved in natural soil structures and that information on the pore size distribution has to be complemented by information on a critical filtration size (CFS) delimiting the transition between percolating and non percolating regimes in multiscale pore networks. We show that the mass fractal dimensions which are classically used in soil science to quantify scaling laws in observed pore size distributions can also be used to build 3-D multiscale models of pore networks exhibiting such a critical transition. We extend to the 3-D case a new theoretical approach recently developed to address the connectivity of 2-D fractal networks (Bird and Perrier, 2009). Theoretical arguments based on renormalisation functions provide insight into multi-scale connectivity and a first estimation of CFS. Numerical experiments on 3-D prefractal media confirm the qualitative theory. These results open the way towards a new methodology to estimate soil filtration efficiency from the construction of soil structural models to be calibrated on available multiscale data.

References 1

American Filtration Society: <a href="http://www.afssociety.org/education/1108oneminute.htm">http://www.afssociety.org/education/1108oneminute.htm</a>, last access: 7 October, 2010.

Bartoli, F., Bird, N. R. A., Gomendy, V., Vivier, H., and Niquet, S.: The relation between silty soil structures and their mercury porosimetry curve counterparts: fractals and percolation, Eur. J. Soil Sci., 50(1), 9–22, 1999.

Bird, N. R. A. and Dexter, A. R.: Simulation of soil water retention using random fractal networks, Eur. J. Soil Sci., 48, 633–641, 1997.

Bird, N. R. A., Perrier, E., and Rieu, M.: The water retention curve for a model of soil structure with Pore and Solid Fractal distributions, Eur. J. Soil Sci., 55(1), 55–65, 2000.

Bird, N. R. A. and Perrier, E.: Percolation properties of multiscale pore networks In Press Special Issue Complexity and Nonlinearity in soils, Geoderma, available at:<a href="http://dx.doi.org/10.1016/j.geoderma.2009.10.009">http://dx.doi.org/10.1016/j.geoderma.2009.10.009</a>, last access: 7 October 2010, 2009.

Blanchart, E., Marilleau, N., Cambier, C., Drogoul, A., Perrier, E., and Chotte, J. L.: SWORM, an agent-based model to simulate the effect of earthworms on soil structure, Eur. J. Soil Sci., 60(1), 13–21, 2009.

Bradford, S. A., Simunek, J., Bettahar, M., Van Genuchten, M. T., and Yates, S. R.: Modelling colloid attachment, straining and exclusion in saturated porous media, J. Environ. Qual., 34, 469–478, 2003.

Bradford, S. A. and Bettahar, M.: Straining, attachment, and detachment of Cryptosporidium oocysts in saturated porous media, J. Environ. Qual., 34, 469–478, 2005.

Bradford, S. A., Simunek, J., Bettahar, M., Van Genuchten, M. T., and Yates, S. R.: Significance of straining in colloid deposition: evidence and implications, Water Resour. Res., 42, W12S15, https://doi.org/10.1029/2005WR004791, 2006.

Bradford, S. A., Torkzaban, S., Leij, F., Simunek, J., and Van Genuchten, M. T.: Modeling the Coupled Effects of Pore Space Geometry and Velocity on Colloid Transport and Retention, Water Resour. Res., 45, 1–15, 2009.

de Gryse, S., Jassogne, L., Six, J., Bossuyt, H., Wevers, M., and Mercks, R.: Pore structure changes during decomposition of fresh residue: X-ray tomography analyses, Geoderma, 134, 82–96, 2005.

Diaz, J., Rendueles, M., and Diaz, M.: Straining phenomena in bacteria transport through natural porous media, Environ. Sci. Pollut. R., 17(2), 400–409, 2010.

Johnson, A., Roy, I. M., Matthews, G. P., and Patel, D.: An improved simulation of void structure, water retention and hydraulic conductivity in soil with the Pore-Cor three-dimensional network, Eur. J. Soil Sci., 54, 477–489, 2003.

Kaiser, C.: A directed percolation model for clogging in a porous medium with small inhomogeneities, Transport in porous media, 26(2), 33–146, 1997.

Keller, A. and Auset, M.: A review of visualization techniques of biocolloid transport processes at the pore scale under saturated and unsaturated conditions, Adv. Water Resour., 30, 1392–1407, 2007.

Lesne, A.: Renormalization methods: critical phenomena, chaos, fractal structures, Wiley Ed., Chichester, ISBN 0-471-96689-4, 1998.

Marilleau, N., Cambier, C., Drogoul, A., Chotte, J. L., Perrier, E., and Blanchart, E.: Multiscale MAS modelling to simulate the soil environment: application to soil ecology, Simul. Model. Pract. Th., 16(7), 736–745, 2008.

McGechan, M. B.: Transport of particulate and colloid-sorbed contaminants through soil, part 2: Trapping processes and soil pore geometry, Biosyst. Eng., 83(4), 387–395, 2002.

Perrier, E., Bird, N. R. A., and Rieu, M.: Generalizing the fractal model of soil structure: the PSF approach, Geoderma, 88, 137–164, 1999.

Perrier, E., Mullon, C., Rieu, M., and de Marsily, G.: Computer construction of fractal soil structures, Simulation of their hydraulic and shrinkage properties, Water Resour. Res., 31(12), 2927–2943, 1995.

Perrier, E., Rieu, M., Sposito, G., and de Marsily, G.: Models of the Water Retention Curve for soils with a fractal pore-size distribution, Water Resour. Res., 32(10), 3025–3031, 1996.

Perrier, E., Tarquis, A., and Dathe, A.: A program for fractal and multifractal analysis of two-dimensional binary images: Computer algorithms versus mathematical theory, Geoderma, 134(3–4), 284–294, 2006.

Price, J. C., Matthews, G. P., Quinlan, K., Sexton, J., and Matthews, A. G.: A Depth Filtration Model of Straining Within the Void Networks of Stainless Steel Filters, Aiche J., 55(12), 3134–3144, 2009.

Rappoldt, C. and Crawford, J. W.: The distribution of anoxic volume in a fractal model of soil, Geoderma, 88, 329–347, 1999.

Stauffer, D. and Aharony, A.: Introduction to Percolation Theory, 2nd edition, 1994, Taylor and Francis, London, 1992.

Sukop, M.,C., Van Dijk, G.-J., Perfect, E., and Van Loon, W. K. P.: Percolation thresholds in 2-dimensional prefractal models of porous media, Transport in Porous Media, 48, 187–208, 2002.

Tiggermann, D.: Simulation of percolation on massively-parallel computers, Int. J. Mod. Phys. C, 12, 871, 2001.

Turcotte, D. L.: Fractals and Chaos in geology and geophysics, Cambridge, 1992.

Xu, S. P. and Saiers, J. E.: Colloid straining within water-saturated porous media: Effects of colloid size nonuniformity, Water Resour. Res., 45, W05501, https://doi.org/10.1029/2008WR007258, 2009.