Abstract
Abstract. 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.
Highlights
Filtration of impure water by soils has been studied from many points of view and at many different scales
Bradford et al (2006, 2009) report recent experimental evidence that indicates that straining may explain many of the reported limitations of former filtration theories that did not include the potential influence of physical factors such as soil pore size distribution and surface roughness and that the latter can play an important role in colloid deposition and microbe retention
From the theoretical point of view, we have shown that the multiscale percolation approach developed by Bird and Perrier (2009) extends to the 3-D case in a straightforward way, and that a 3-D mass fractal model can allow for both percolation of the pore network to enable fluid flow and percolation of the solid phase to ensure stability
Summary
Filtration of impure water by soils has been studied from many points of view and at many different scales. In the present theoretical paper, we will neglect all dynamical properties of filtration processes to focus on the link between the size of filtered entities and the size of pores, using a simple percolation model in a new, multiscale approach. It is well-known that the range of pore sizes occurring in most soils is very large, and fractal geometry has been widely used to quantify a pore size distribution by means of a power-law function with few parameters: e.g. the largest pore size and a fractal dimension in a mass fractal model (e.g. Rieu and Sposito, 1991; Perrier et al, 1996; Bird and Dexter, 1997). The final section will discuss how far these first 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
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