Electrical Conductivity and Resistivity
Electrical conductivity (σ) is a measure of the ability of the material to conduct an electrical current. The units of conductivity are Siemens per meter (S/m), or more commonly milliSiemens per meter (mS/m). The Siemen, which is the unit of conductance, is the reciprocal of the Ohm, the unit of resistance. The units of conductivity are sometimes given as mhos/meter or millimhos/meter. Resistivity (ρ) is the inverse of conductivity (ρ = 1 / σ). The units of resistivity are Ohm meters (Ωm).
The electrical conductivity of earth materials is influenced by metal content (e.g., sulfides), porosity, clay content, permeability, and the saturation.
All metal objects of interest at environmental sites typically have a very large conductivity contrast with surrounding materials. This contrast can usually be detected with electrical and electromagnetic methods. If metals are present, their electrical conductivity is governed by ohmic conduction via electron propagation like in electrical wiring.
In the absence of metals, formation conductivity is related to the volume and conductivity of the water in earth materials and is effectively electrolytic conduction. Groundwater conducts electrical current via ions; therefore, the conductivity of groundwater depends strongly on the total dissolved solids and the chemistry of the groundwater. Archie’s Law (Archie, 1942) describes this relationship within a porous, clay-free medium with a non-conducting matrix.
ρe = a φ-m S-n ρw
where, ρe = resistivity of the formation as geophysically measured electrical resistivity; ρw = resistivity of the water; a, m and n = empirical constants value dependent on the matrix type; φ = fractional pore volume (i.e. porosity); and S= the fraction of pores containing water (i.e., the electrolyte).
The inverse of this can be used for conductivity. Archie’s Law allows the calculation of various geophysical and hydrogeologic parameters depending on known measurements. For example, porosity be estimated if other parameters are known via geophysical and hydrogeological data.
If clays and/or shales are present, these hydrated minerals with high porosities and low permeabilities may not be very electrically conductive, but their surface properties cause an excess of cations in the pore fluid immediately adjacent to the clay surfaces. This results in high conductivity near the clay surfaces, which can dominate the overall conductance if the pore water conductivity is low. Waxman and Smits, (1968) can be investigate for more on this topic.
To conduct electricity a rock, or volume of sediment, with a non-conducting matrix must be permeable as well as porous. Mazac, et. al, (1985) presents of summary of the relationship between Darcy’s Law for fluid flow and Ohm’s Law for electrical current flow. Archie's Law predicts an inverse relationship between resistivity (rho) and (effective) porosity (phi), which determines hydraulic conductivity (k). However, for some materials hydraulic conductivity increases and porosity decreases with grain size, leading to a direct relationship between ρ and k. Mazac, et al., (1985) can be referenced for an in-depth analysis of this relationship.
Archie, G.E. (1942). "The electrical resistivity log as an aid in determining some reservoir characteristics". Petroleum Transactions of AIME. 146: 54–62. doi:10.2118/942054-g.
Mazac, O., Kelly,W.E., Landa,I., A hydrogeophysical model for relations between electrical and hydraulic properties of aquifers, Journal of Hydrology, vol. 79, Issues1-10, 10 July 1985, https://doi.org/10.1016/0022-1694(85)90178-7
Waxman, M.H. and Smits, L.J.M. (1968) Electrical Conductivities in Oil-Bearing Shaly Sands. Society of Petroleum Engineers Journal, 8, 107-122.
http://dx.doi.org/10.2118/1863-A