Whenever a seismic wave propagates through a fluid-saturated porous rock that contains heterogeneities in the mesoscopic scale range, that is, heterogeneities that are much larger than the typical pore size but much smaller than the predominant wavelengths, local

SUMMARY While the frequency-dependence of permeability under fully saturated conditions has been studied for decades, the corresponding characteristics of partially saturated porous media remain unexplored. Notably, it is not clear whether the use of effective pore fluid approaches under such conditions is valid. To address this issue, we propose a method that allows us to obtain dynamic permeability functions for partially saturated porous media. To this end, we conceptualize the considered pore space as a bundle of capillary tubes of different radii saturated by two immiscible fluid phases. We then solve the Navier–Stokes equations within the pore space and define a capillary pressure–saturation relationship, which permits to obtain saturation- and frequency-dependent effective permeability estimates. The application of this method to a realistic model of an unconsolidated granular sediment demonstrates that dynamic effective permeability functions for wetting and non-wetting fluid phases exhibit distinct characteristics, thus rendering effective pore fluid approaches inadequate. Finally, we explore the capability of the seminal dynamic permeability model developed by Johnson et al.[J. Fluid Mech. 176, 379 (1987)] to account for the effects of partial saturation. We find that the frequency scaling proposed by Johnson et al. prevails in partially saturated scenarios. However, the parameters associated with this model need to be redefined to account for saturation-dependent effects.

The seismoelectric method is based on the capacity of seismic waves to generate measurable modifications of the electrical field in porous media. Even though it combines the advantage of both seismic and geoelectrical methods, it remains largely under-used in hydrogeophysics. Its signal results from an electrokinetic coupling that can be modeled using either the coupling coefficient or the effective excess charge density. The traditional approach is based on the frequency dependent coupling coefficient, which relates the pressure drop with the change in the electrical potential. A more recent approach consists of describing the excess charge that is effectively dragged by water flowing within the pores. In this work, we present a new model for the frequency dependent effective excess charge density. For this, we make use of a mechanistic up-scaling of the electrokinetic coupling in a capillary. This novel flux-averaging approach takes into account inertial effects arising within the pore space to explain the frequency dependence of the effective excess charge density. The presented model is successfully compared to previous models and published data. This new upscaling approach has the potential of fundamentally improving our current understanding of the seismoelectrical signal in more complex environments, such as partially saturated and fractured media.

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.

Quantifying seismic attenuation during laboratory imbibition experiments can provide useful information toward the use of seismic waves for monitoring injection and extraction of fluids in the Earth's crust. However, a deeper understanding of the physical causes producing the observed attenuation is needed for this purpose. In this work, we analyze seismic attenuation due to mesoscopic wave‐induced fluid flow (WIFF) produced by realistic fluid distributions representative of imbibition experiments. To do so, we first perform two‐phase flow simulations in a heterogeneous rock sample to emulate a forced imbibition experiment. We then select a subsample of the considered rock containing the resulting time‐dependent saturation fields and apply a numerical upscaling procedure to compute the associated seismic attenuation. By exploring both saturation distributions and seismic attenuation, we observe that two manifestations of WIFF arise during imbibition experiments: the first one is produced by the compressibility contrast associated with the saturation front, whereas the second one is due to the presence of patches containing very high amounts of water that are located behind the saturation front. We demonstrate that while the former process is expected to play a significant role in the case of high injection rates, which are associated with viscous‐dominated imbibition processes, the latter becomes predominant during capillary‐dominated processes, that is, for relatively low injection rates. We conclude that this kind of joint numerical analysis constitutes a useful tool for improving our understanding of the physical mechanisms producing seismic attenuation during laboratory imbibition experiments.