• Revil, André
• Leroy, Philippe

Abstract

Water-saturated clay-rich media exhibit low-frequency (1 Hz to 1 MHz) effective conductivity and effective permittivity dispersions that are the consequence of both the polarization of the mineral/water interface coating the surface of the grains and the Maxwell-Wagner polarization. These low-frequency properties are modeled by combining (1) a complexation model of the surface properties of clay minerals (kaolinite, illite, and smectite), (2) a polarization model of the Stern layer (the inner portion of the electrical double layer coating the surface of the minerals), and (3) a macroscopic model comprising the electrochemical polarization of the grains and the contribution of the Maxwell-Wagner effect. The macroscopic model is based on the differential effective medium theory. It includes a convolution product with the grain size distribution. For kaolinite, the diffuse layer occupies a small fraction of the pore space and is considered as part of the surface of the grains. This is due to the low specific surface area of kaolinite. In the case of illite and smectite, the situation is different. Because of the high specific surface areas of these minerals, the diffuse layer occupies a large fraction of the pore space and is considered as part of the pore space and is described using a Donnan equilibrium model. We obtain excellent comparisons between various experimental data reported in the literature and our model. Then, we considered low-porosity (compacted or cemented) clay rocks and shales. Here too, we obtained a good agreement between the data and the predictions of a model based on a volume-averaging approach. We also note that at very low frequencies (<1 Hz), another polarization mechanism exists that is not reproduced by our model. We believe that this polarization corresponds to a nonlinear membrane polarization contribution.

Topics

• impedance spectroscopy
• pore
• mineral
• dispersion
• surface
• grain
• grain size
• theory
• porosity