Dynamic streaming potential coupling coefficient in porous media with different pore size distributions

Abstract

Summary Seismoelectric signals are generated by electrokinetic coupling from seismic wave propagation in fluid-filled porous media. This process is directly related to the existence of an electrical double layer at the interface between the pore fluid and minerals composing the pore walls. The seismoelectric method attracts the interest of researchers in different areas, from oil and gas reservoir characterization to hydrogeophysics, due to the sensitivity of the seismoelectric signals to medium and fluid properties. In this work, we propose a physically-based model for the dynamic streaming potential coupling coefficient (SPCC) by conceptualizing a porous medium as a bundle of tortuous capillaries characterized by presenting different pore size distributions (PSD). The results show that the dynamic streaming potential coupling coefficient is a complex function depending on the properties of pore fluid, mineral-pore fluid interfaces, microstructural parameters of porous media and frequency. Parameters influencing the dynamic SPCC are investigated and explained. In particular, we show that the PSD affects the transition frequency as well as the shape of the SPCC response as a function of frequency. The proposed model is then compared with published data and previous models. It is found that the approach using the lognormal distribution is in very good agreement with experimental data as well as with previous models. Conversely, the approach that uses the fractal distribution provides a good match with published data for sandstone samples but not for sand samples. This result implies that the fractal PSD may not be pertinent for the considered sand samples, which exhibit a relatively narrow distribution of pore sizes. Our proposed approach can work for any PSD, for example, including complex ones such as double porosity or inferred from direct measurements. This makes the proposed models more versatile than models available in literature.

Modeling the Frequency‐Dependent Effective Excess Charge Density in Partially Saturated Porous Media

“…Nevertheless, these parameters are similar to those reported by Thanh et al. (2021) for the same sample to model the frequency dependence of the electrokinetic coupling coefficient, that is directly expressed via the Zeta potential rather than the effective excess charge density. Once again, we illustrate the predicted variations of $$\vert {C}_{EK}^{\mathit{rel}}\vert $$ for different saturations (colored lines).…”

“…We remark that, because of computational restrictions involved with the numerical integrations performed in this work, we do not carry out a full inversion of the parameters but empirically find those which provide a relatively good fit with experimental data. Nevertheless, these parameters are similar to those reported by Thanh et al (2021) for the same sample to model frequency dependence of the electrokinetic coupling coefficient, that is directly expressed via the Zeta potential rather than the charge density. Once again, we illustrate the predicted variations of 𝐸𝐸𝐸𝐸 are reported to be 0.3 × 10 −6 , 0.15 × 10 −6 , 0.065 × 10 −6 , 0.035 × 10 −6 and 0.024 × 10 −6 V/Pa for 0.012, 0.048, 0.095, 0.18 and 0.32 S/m, respectively (Zhu & Toksoz, 2013).…”

“…This model has been widely applied to porous media with a certain success (e.g., Reppert, 2001). Recently, Thanh et al (2021) extended the work of Packard (1953) to take into account different pore size distributions (PSD), thus showing the effects of the porous structure on C EK (ω).…”

“…Recently, Thanh et al. (2021) extended the work of Packard (1953) to take into account different pore size distributions (PSD), thus showing the effects of the porous structure on C EK ( ω ). An alternative approach for studying the seismoelectric conversion is to compute the excess charges that are effectively dragged in the diffuse layer, that is, the effective excess charge density $${\hat{Q}}_{\nu }$$, which can be subsequently used to estimate C EK (e.g., Jackson, 2010; Jougnot et al., 2012; Revil & Mahardika, 2013).…”

A Capillary Bundle Model for the Electrical Conductivity of Saturated Frozen Porous Media

“…They both produce significant differences in the predicted electrical conductivity, which increases with decreasing r max or r m . Indeed, when the maximum pore radius decreases, the geometric mean pore radius r m also decreases, and the number of smaller radius capillaries increases as shown in Thanh et al (2021) (their Figures 2b and 2e). Therefore, one can see an increase of the surface conductivity of the REV, hence an increase in electrical conductivity of the frozen porous medium.…”