Permeability dependence of streaming potential coefficient in porous media

In theory, the streaming potential coefficient depends not only on the zeta potential but also on the permeability of the rocks that partially determines the surface conductivity of the rocks. However, in practice, it is hard to show the permeability dependence of streaming potential coefficients because of the variation of zeta potential from sample to sample. To study permeability dependence of streaming potential, including the effects of the variation of the zeta potential and surface conductance due to the difference in mineral compositions between samples, we perform measurements on 12 consolidated samples, including natural and artificial samples saturated with 7 different NaCl solutions to determine the streaming potential coefficients. The results have shown that the streaming potential coefficients strongly depend on the permeability of the samples for low fluid conductivity. When the fluid conductivity is larger than than 0.50 S/m for the natural samples or 0.25 S/m for the artificial ceramic samples, the streaming potential coefficient is independent of permeability. This behavior is quantitatively explained by a theoretical model.     

A fractal model for streaming potential coefficient in porous media

Streaming potential is the result of coupling between a fluid flow and an electric current in porous rocks. The modified Helmholtz–Smoluchowski equation derived for capillary tubes is mostly used to determine the streaming potential coefficient of porous media. However, to the best of our knowledge, the fractal geometry theory is not yet applied to analyse the streaming potential in porous media. In this article, a fractal model for the streaming potential coefficient in porous media is developed based on the fractal theory of porous media and on the streaming potential in a capillary. The proposed model is expressed in terms of the zeta potential at the solid?liquid interface, the minimum and maximum pore/capillary radii, the fractal dimension, and the porosity of porous media. The model is also examined by using another capillary size distribution available in published articles. The results obtained from the model using two different capillary size distributions are in good agreement with each other. The model predictions are then compared with experimental data in the literature and those based on the modified Helmholtz–Smoluchowski equation. It is shown that the predictions from the proposed fractal model are in good agreement with experimental data. In addition, the proposed model is able to reproduce the same result as the Helmholtz–Smoluchowski equation, particularly for high fluid conductivity or large grain diameters. Other factors influencing the streaming potential coefficient in porous media are also analysed.     

Zeta potential of porous rocks in contact with mixtures of monovalent and divalent electrolytes

The zeta potential is one of the most important parameters influencing the electrokinetic coupling. Most reservoir rocks are saturated or partially saturated by natural water containing various types of ions (mostly monovalent and divalent ions). Therefore, understanding how the zeta potential behaves for mixtures of electrolytes is very important. In this work, measurements of the zeta potential for four different silica-based samples saturated by seven different mixtures of monovalent and divalent electrolytes are then carried out at a fixed ionic strength. It is seen that the magnitude of the measured zeta potential decreases with increasing divalent cation fraction. The experimental results are then explained by a model developed for mixtures of monovalent and divalent electrolytes. The result shows that the theoretical model is able to reproduce the main trend of the variation of the zeta potential with divalent cation fractions. Additionally, the model can fit the experimental data reported in literature well for reasonable values of the input parameters.