Simulation of membrane polarization of porous media with impedance networks
The spectral induced polarization method is supposed to have some potential to provide useful information on hydraulic properties of the subsurface. One difficulty for the practical implementation is the simulation of underlying physical processes at the pore scale and their upscaling to hydraulically relevant scales. We extend an existing semi-analytical membrane polarization model to two- and three-dimensional impedance networks, which are numerically solved to obtain a spectral induced polarization response that can be compared to measured data. The original model consists of two cylinders with different sizes. The model has been shown to be able to reproduce some basic features of spectral induced polarization spectra measured in the laboratory, but it is unable to meet the complexity of macroscopic porous media structures, which can be found within unconsolidated sediments or rocks. To approach realistic pore space geometry, we connect different combinations of cylinders to networks. We treat the smaller of the two cylinders as a pore throat. The pore throat distribution in the network is chosen by matching measured pore throat radii distributions obtained from the mercury injection method. The large cylinder is treated as the (large) pore body, and its radii are associated to the pore throats using existing relationships. We compare the behaviour of the networks with real porous media by using sandstone samples for which both the electrical and petrophysical properties have been measured. We adjust the geometrical parameters of the network, i.e., pore lengths, pore radii, and their relative occurrences, such that they match the measured parameters (specific internal surface area, pore throat distribution, and porosity) of the sandstone samples. The measured spectral induced polarization parameters, like the maximum phase shift and the characteristic relaxation time, are qualitatively consistent with our simulation results.