  We implement a procedure to simulate the drainage and imbibition in random,
two-dimensional, square networks. We compute the resistivity index, the
relative permeability, and the characteristic lengths of a correlated network
at various saturation states, under the assumption that the surface
conductivity can be neglected. These parameters exhibit a hysteretic behaviour.
Then, we calculate the Spectral Induced Polarization (SIP) response of the
medium, under the assumption that the electrical impedance of each tube follows
a local Warburg conductivity model, with identical DC conductivity and
chargeability for all the tubes. We evidence that the shape of the SIP spectra
depends on the saturation state. The analysis of the evolution of the
macroscopic Cole-Cole parameters of the spectra in function of the saturation
also behaves hysteretically, except for the Cole-Cole exponent. We also observe
a power-law relationship between the macroscopic DC conductivity and time
constant and the relative permeability. We also show that the frequency peak of
the phase spectra is directly related to the characteristic length and to the
relative permeability, underlining the potential interest of SIP measurements
for the estimation of the permeability of unsaturated media.
