Pore-scale modelling of electrical phenomena in porous media with implications for induced polarization and self-potential methods

In this dissertation theoretical and numerical models are proposed for the induced polarization (IP) phenomenon. The theoretical model takes into account the contribution of Stern layer and membrane polarization in variably saturated sandy soils, while the numerical model can be used to get insight into the origins of the membrane polarization mechanism. In this dissertation the frequency-dependent bulk electrical conductivity of the porous medium is calculated using the Hashin-Shtrickman Average model, which describes the dielectric response of variably saturated porous media. Both stern and membrane polarization can be calculated independently, which allows us to study the effect of different physical parameters to each one. The results show that membrane polarization can be obscured by the Maxwell-Wagner polarization. The model was tested against data from laboratory measurements of sands with variable saturation and a good fit was obtained even though more work has to be done for low saturation levels. Then a numerical model is presented which uses the linearized Poisson-Boltzmann Equation to compute the electrostatic potential of an object in the presence of free ions. The solution is then used to calculate a the dielectric to be used on a numerical solver of Poisson's equation to calculate the impedance of the system. This result corroborates the assumptions behind the Short Narrow Pore model, a simplified and yet effective model describing membrane polarization. The methodology used requires a much lower computational effort than solving the Poisson-Nerst-Planck equation since there are no coupled systems.