Microscale modelling of the frequency dependent resistivity of porous media

The frequency dependent electrical impedance of porous media is studied by modelling the charge transport in the electrolyte filled pore space. The corresponding experimental method, called Spectral Induced Polarization (or Impedance Spectroscopy), shows a frequency dependent phase shift between a measured electric current and an applied alternating voltage. It is caused by microscopic polarization effects depending on inner rock structure and electrolyte properties. To study these effects we use a membrane polarization model similar to a model proposed by Marshall and Madden (1959) with different ion-mobilities for cations and anions in smaller pores. The governing equations and boundary conditions for a system of larger and smaller pores with apllied voltage are expressed in frequency domain using a time harmonic approach, the electric current is determined to obtain information about amplitude and phase of the complex resistivity. The resulting resistivity-spectra show a frequency dependence as expected from experiments. Scaling up the pore sizes produces a shift of the characteristic curves.