Pore-scale modelling of complex conductivity of saturated granular materials

摘要

The complex conductivity method has been frequently used in solving hydrogeological, engineering, and environmental problems in practice. Macroscopic geophysical responses are governed by pore-scale rock properties; therefore, a clear petrophysical understanding of how the pore-scale structure controls electric conduction and polarization in geomaterials is necessary to fully interpret laboratory-/field-scale geophysical observations. In this study, we have developed a pore-scale numerical approach to calculate the complex conductivity of water-saturated granular materials. This physics-based model has advantage over phenomenological or empirical models such that the intrinsic relations between pore structure and geoelectrical signals could be revealed. In the modelling, the influence of electrical double layer, which is quantified by complex surface conductance, can be converted to an apparent volumetric complex conductivity of either solid particles or pore fluid. The effective complex conductivity of the sample is determined by directly solving the finite-difference representation of the Laplace equation in the domain of a representative elementary volume. The numerical approach is tested on one synthetic sample and one glass beads sample. For the synthetic sample, the consistency between the numerical and the analytical solution confirms the accuracy of the approach. Comparison with experimental measurements of the glass beads sample reported previously indicates that the developed numerical approach can well reproduce the key characteristics of the complex conductivity of water-saturated granular materials in the frequency range between 10(-1) and 10(4) Hz. Furthermore, the numerical examples also show that the proposed approach can capture the salinity-dependent electric conduction and polarization in saturated granular materials.