Variations of petrophysical properties and spectral induced polarization in response to drainage and imbibition: a study on a correlated random tube network

Abstract

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.