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The frequency dependent electrical impedance of porous media is studied by modelling the charge transport in the electrolyte filled pore space using COMSOL Multiphysics.  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. The governing equations and boundary conditions for a system of larger and smaller pores with applied 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.