Air entry–based characteristic length for estimation of permeability of variably compacted earth materials

Abstract

[1] The permeability k of a porous medium is a geometrical pore space attribute required for quantifying fluid flows and transport processes for hydrological, civil, agriculture, and petroleum engineering applications. Permeability is often expressed as proportional to a characteristic length squared and inversely proportional to factors accounting for porosity, pore shape, and tortuosity effects. Compaction and diagenesis reduce porosity, mean pore size, and connectivity, resulting in decrease in k. Permeability prediction relies on suitable selection of a characteristic length that may vary from simple hydraulic radius approximation of Kozeny-Carman to more complex critical path analysis to identify flow-limiting pore size. For porous media undergoing significant changes in pore space (e.g., compaction due to anthropogenic activities), the proper choice of a robust characteristic length is particularly challenging. We propose using the air entry pressure, a natural characteristic length that gauges the largest drainable pore size. This choice of a characteristic length is compatible with the Aissen formula that provides robust estimates of k for complex pore shapes. Additionally, the model considers geometrical (tortuosity) factors and links relative changes in porosity to concurrent changes in k. The model was tested against experimental data for sands, sandstones with different cementing agents, and unconsolidated soils. For unconsolidated sands and soils the model provides reasonable predictions of permeability for the entire range of porosities determined in laboratory or field experiments. However, for sandstones, and especially those containing cementing agents such as clay, the model is valid up to a critical porosity where hydraulic connectivity is lost, resulting in drastic reduction in k. The geometrical factor for soils was influenced by silt-to-clay ratio, while for sands, it was correlated with mean grain diameter. The model offers improvement in predicting k and provides a means for incorporating critical pore size and connectivity information in addition to porosity.

Conceptual and Parametric Representation of Soil Hydraulic Properties: A Review

“…Assouline and Or (2008) proposed to consider the air entry matric potential, ψ c , as a natural characteristic length for the porous medium, which integrates aspects of pore size and connectivity in a simple fashion (Katz and Thompson, 1986; Arns et al, 2005). They followed the analysis of Sisavath et al (2000) by capitalizing on the Aissen formula (Aissen, 1951) that represents complex pore shapes in a relatively simple way (see Fig.…”

“…A vertical cross section through a pack of modeling clay spheres (5 mm in diameter) arranged in octahedral packing with an inscribed and circumscribed circles used in the Aissen formulation (Eq. [2.12]) are depicted for a typical pore in the cross section (see Assouline and Or, 2008). …”

“…A large body of studies has investigated the relationships between K s and ρ b (Carman, 1937; Laliberte et al, 1966; Reicovsky et al, 1980; Young and Voorhees, 1982; Mualem and Assouline, 1989; Or et al, 2000a,b; Or and Ghezzehei, 2002; Green et al, 2003; Assouline, 2006b; Berli et al, 2008). A concise review of the different approaches developed to relate the permeability of porous media to porosity can be found in Assouline and Or (2008). An interesting result of that study was that the characteristic length inherent to the relationship between soil structure and permeability could be well represented by the air entry matric potential, ψ c .…”

“…where a and b are empirical coeicients and n e is the efective porosity, calculated as the saturated water content q s minus the water content at a matric tension of 33 kPa, a value usually used to characterize ield capacity. Rawls et al (1998) found that the power value, b, can vary between 1.59 and 3.98, and that it could be related to the pore size distribution index, l, of the Brooks and Corey (1964) Assouline and Or (2008) proposed to consider the air entry matric potential, y c , as a natural characteristic length for the porous medium, which integrates aspects of pore size and connectivity in a simple fashion (Katz and h ompson, 1986;Arns et al, 2005). h ey followed the analysis of Sisavath et al (2000) by capitalizing on the Aissen formula (Aissen, 1951) that represents complex pore shapes in a relatively simple way (see Fig.…”

The effect of compaction and shear deformation of saturated soil on hydraulic conductivity

“…4a in Ahuja et al, 1989). Assouline and Or (2008) outline how, in addition to porosity, the air entry potential can be used in an improved approach to take account of the effects of compaction on hydraulic conductivity. Matthews et al (2010) have proposed a simple model for saturated hydraulic conductivity using the water retention characteristic.…”