Pore-Scale Modelling of Complex Conductivity of Saturated Granular Materials

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  10⁴  Hz.  Furthermore,  the  numerical  examples  also  show  that  the  proposed approach can capture the salinity-dependent electric conduction and polarization in saturated granular materials.