Numerical modeling of the role of water and clay content in soils' and rocks' bulk electrical conductivity

Abstract

[1] The influence of clay and water content in the electrical conductivity of rocks and soils has been experimentally established and is expressed by simple empirical laws: the Archie's law and the addition law between volume water conductivity and surface shale conductivity. Two independent numerical modeling techniques, the moment method and the finite difference method, are presented here and are used, first, to verify the agreement between Maxwell's equation based theoretical approaches and the empirical laws and, second, to begin to investigate for a possible effect of the microscopic geometry over macroscopic conductivity. A good agreement between simulation results and Archie's law is obtained when both randomly distributed isotropic and elongated microvolumes of conducting water are considered and a slight difference appears between these two microstructures. For low clay contents in clay-dispersed media, the clay-associated conductivity is shown to be proportional to a specific clay area, which is in good agreement with the addition empirical law.INDEX TERMS: 3914 Mineral Physics: Electrical properties; 0619 Electromagnetics: Electromagnetic theory; 0644 Electromagnetics: Numerical methods; 0999 Exploration Geophysics: General or miscellaneous; KEYWORDS: numerical modeling, electrical conductivity, water content Citation: Tabbagh, A., C. Panissod, R. Guérin, and P. Cosenza, Numerical modeling of the role of water and clay content in soils' and rocks' bulk electrical conductivity,

Integrated geophysical and geological investigation of a heterogeneous fluvial aquifer in Columbus Mississippi

“…As discussed above, this conclusion is supported by comparison of predictions of clay + silt fractions based on resistivity to lithologies observed in outcrop in the channels and within the sandier parts of the facies away from the core location. The linear resistivity vs. clay + silt content observed is consistent with theoretical and numerical models of the electrical properties of clay-bearing sediments (e.g., Waxman and Smits, 1968;Tabbagh et al, 2002). The lack of significant clay fraction in the braided fluvial system complicates efforts to asses the viability of the use of resistivity as a predictor of lithology in this facies.…”

“…Their work and the work of others (e.g., Waxman and Smits, 1968) has demonstrated that the bulk electrical conductivity of rocks and sediments is given by the sum of two terms, one of which describes conduction within the pore space and one of which depends on clay mineral surface conductivity. This leads to a linear relationship between electrical conductivity and clay content (e.g., Tabbagh et al, 2002), and a linear log-log relationship between hydraulic conductivity and electrical conductivity (e.g., Bernabe and Revil, 1995;Purvance and Andrivicec, 2000). These relations provide a basis for using electrical resistivity data to estimate clay content and in-situ hydraulic conductivity in freshwater aquifers.…”

Groundwater salinity mapping using airborne electromagnetics and borehole data within the lower Balonne catchment, Queensland, Australia

“…Later workers extended this relationship to account for the non-linearity of the salinity: bulk conductivity relationship through detailed theoretical and empirical analysis of the surface conduction mechanisms and the geometric effects of the arrangement of the pores (e.g. Rock Physics, 1988aPhysics, ,b, 1989Tabbagh et al, 2002). The critical factors which influence the relationship between bulk conductivity and water conductivity/ salinity are:…”

Modelling of Maxwell–Wagner induced polarisation amplitude for clayey materials

“…The electric field or electric potential generated outside the volume can be used to compute its effective permittivity, by defining it to be the relative permittivity of an identical volume of homogeneous material, generating the same external field or potential (Tabbagh et al, 2002). The effective relative permittivity can also be written as the ratio of the internal resultant electrical induction vector to the internal resultant electric field: e eff = Y D e 0 Y E .…”