Relating relative hydraulic and electrical conductivity in the unsaturated zone

Abstract

Numerical modeling was used to generate pore-scale structures with different structural properties. They were partially saturated according to wetting and drainage regimes using morphological operations for a range of saturations. The hydraulic and electrical conductivities of the resulting partially saturated grain packs were numerically computed to produce relative hydraulic conductivity versus saturation and relative electrical conductivity versus saturation curves. The relative hydraulic conductivities were then compared to the relative electrical conductivities for the same saturations and it was found that relative hydraulic conductivity could be expressed as relative electrical conductivity to a power law exponent, β. This exponent β was not correlated to porosity, specific surface area, or tortuosity. It did change according to whether the soil was wetting or draining. However, a β value of 2.1 reproduced relative hydraulic conductivity from relative electrical conductivity with little added error. The effects of surface conduction on the observed power law relationship due to either low fluid electrical conductivity or increased clay content were analyzed. The relationship was found to hold for fluid conductivities typical of groundwater and for clay content of less than 5% if the clays were layered perpendicular to electrical flow. The relationship breaks down for electrical flow parallel to clay layers, which makes the choice of electrode arrangement important in cases where clay may be present. This relationship can be used with secondary pressure or saturation data to characterize a soil's hydraulic conductivity curve.