It is well-accepted that Archie's law is only applicable to “clean” rocks and soils but fails in “dirty” ones where clay minerals possess an additional component of surface conductivity. Although several models, for example, Waxman-Smits model, were presented to account for this phenomenon, surface conductivity is always inappropriately treated as constant, which actually only holds at high salinities. The essential non-linear characteristic differing over fluid salinities has not been physically or mathematically explained well in those models. We scrutinize the conduction mechanism of clayey rocks and soils and ascribe this non-linear feature to (a) variation of the electrical double layer and (b) the intrinsic clay-and-water conduction pattern. With effective medium theory, we develop an easy-to-use non-linear model that both reflects electrochemical theories and explains the measurement data well. Our model can be used to produce more accurate results for laboratory- and field-scale petrophysical parameter evaluations than the previous models.

The past decades have witnessed the increased applications of induced polarization (IP) method in the critical zone studies with ubiquitous clay minerals. Although IP outperforms traditional electrical and electromagnetic methods through its unique ability to measure quadrature conductivity, the nonlinearity that quadrature conductivity behaves with salinities and frequencies greatly tortures IP practitioners, as (a) salinity-dependency makes the quadrature conductivity a varyingly unstable parameter to quantitatively estimate hydraulic properties and clay content; (b) frequency-dependent Cole-Cole and Debye/Warburg decomposition models, although mathematically sound, physically mingle the properties of pore water and clay minerals and are empirical in nature. From basic principles, we demonstrate that quadrature conductivity remains a hybrid property involving both clay and water, and develop relevant models to distinguish them. Our models are validated by theories, experiments, simulations, and comparisons, all of which proclaim considerable advantages over previous models and offer the prospect of quantitative applications.

Among the subsurface geophysical methods used in the critical zone investigations, induced polarization (IP) shows great vitality thanks to its unique ability to assess porosity via bulk conduction and estimate permeability through surface conduction and/or polarization. However, such an advantageous separation between bulk and surface is mostly implemented by multi-salinity experiments in the laboratory, which is incredibly difficult to realize in the field. One promising approach to address such an obstinate issue is to gauge the surface conductivity (σs) from the quadrature conductivity (σ″) or normalized chargeability (Mn) with the ratios between (l = σ″/σs, lmn = Mn/σs). While these ratios are known not to be universal, the underlying principles are not fully understood and relevant theoretical studies are rare, which makes quantitative IP applications difficult. Here we scrutinize the conduction and polarization mechanisms of geomaterials and pinpoint that the two ratios are inherently functions of salinities and frequencies rather than only determined by the properties of the electrical double layer (EDL), hence representative samples from the investigated field must be calibrated in the laboratory and a characteristic frequency should be chosen for their usage. Besides the macro-scale ratios l and lmn, we define two micro-scale ratios χ and χmn directly from the EDL, such that the new ratios exclude the effect of salinity and frequency and offer the opportunity to characterize and monitor changes of the EDL. Our study demonstrates that the existing macro-scale ratios converge toward the values of novel micro-scale ratios at high water salinity.