Alexis Maineult, André Revil, Christian Camerlynck, Nicolas Florsch, Konstantin Titov; Upscaling of spectral induced polarization response using random tube networks. Geophys J Int 2017 ggx066. doi: 10.1093/gji/ggx066
In order to upscale the induced polarization (IP) response of porous media, from the pore scale to the sample scale, we implement a procedure to compute the macroscopic complex resistivity response of random tube networks. A network is made of a 2D square-meshed grid of connected tubes, which obey to a given tube radius distribution. In a simplified approach, the electrical impedance of each tube follows a local Pelton resistivity model, with identical resistivity, chargeability and Cole-Cole exponent values for all the tubes – only the time constant varies, as it depends on the radius of each tube and on a diffusion coefficient also identical for all the tubes. By solving the conservation law for the electrical charge, the macroscopic IP response of the network is obtained. We fit successfully the macroscopic complex resistivity also by a Pelton resistivity model. Simulations on uncorrelated and correlated networks, for which the tube radius distribution is so that the decimal logarithm of the radius is normally distributed, evidence that the local and macroscopic model parameters are the same, except the Cole-Cole exponent: its macroscopic value diminishes with increasing heterogeneity (i.e., with increasing standard deviation of the radius distribution), compared to its local value. The methodology is also applied to six siliciclastic rock samples, for which the pore radius distributions from mercury porosimetry are available. These samples exhibit the same behaviour as synthetic media, i.e., the macroscopic Cole-Cole exponent is always lower than the local one. As a conclusion, the pore network method seems to be a promising tool for studying the upscaling of the IP response of porous media.