Alexis Maineult (Sorbonne Université, CNRS, EPHE - UMR 7619 METIS) will give a seminar in room E001 and on Teams on:
Computing Spectral Induced Polarization response of porous media using networks of complex impedances
The spectral induced polarization (SIP) is a geophysical method which consists in injecting a sinusoidal, electrical current in a medium using two injection electrodes, and measuring the resulting voltage difference between two measurement electrodes. Doing so for a large range of frequencies, one obtains spectra of complex resistivity, with a magnitude and a phase evolving with the frequency. The analysis of the spectra gives access to intrinsic properties of the medium such as its DC resistivity, its chargeability or its characteristic time constant. These parameters depend on various properties of the medium, such as for instance its concentration in metallic particules and the way they are distributed, or its clay content.
Theories are avalaible to explain what happens at the pore scale, and empirical relationships (such as Pelton's model) are used to fit data acquired on samples or in the field. The question is therefore: how to link the responses observed at different scales (pore vs sample/field)?
Here, we use the method called "impedance network modelling". Briefly, we considered a mesh made of complex impedances, on which we applied the appropriate electrical boundary conditions to simulate an acquisition on a sample. Then, using Kirchhoff's law for the conservation of the electrical current, we were able to compute the electrical potential at each node of the mesh, and therefore the electrical flux through each impedance of the mesh. We then deduced the complex resistivity spectrum of the mesh.
We applied this methodology to some particular cases. First we successfully simulated the behavior of the total chargeability of sand-pyrite mixtures with respect to the ore content. Then, we modelled the complex resistivity spectra of clay mixtures, which are also in agreement with the observations. Finally, we implemented an algorithm to simulate the drainage and the imbibition of a porous network, and computed its complex resistivity spectra: we evidenced some relationships between the characteristics of these spectra and the relative permeability or the bulk saturation of the porous network.
All these examples evidence the interest of our approach for the upscaling of the SIP response of materials.