Among the different contributions generating self‐potential, the streaming potential is of particular interest in hydrogeology for its sensitivity to water flow. Estimating water flux in porous media using streaming potential data relies on our capacity to understand, model, and upscale the electrokinetic coupling at the mineral‐solution interface. Different approaches have been proposed to predict streaming potential generation in porous media. One of these approaches is the flux averaging which is based on determining the excess charge which is effectively dragged in the medium by water flow. In this study, we develop a physically based analytical model to predict the effective excess charge in saturated porous media using a flux‐averaging approach in a bundle of capillary tubes with a fractal pore size distribution. The proposed model allows the determination of the effective excess charge as a function of pore water ionic concentration and hydrogeological parameters like porosity, permeability, and tortuosity. The new model has been successfully tested against different set of experimental data from the literature. One of the main findings of this study is the mechanistic explanation to the empirical dependence between the effective excess charge and the permeability that has been found by several researchers. The proposed model also highlights the link to other lithological properties, and it is able to reproduce the evolution of effective excess charge with electrolyte concentrations.

Wave-induced fluid flow (WIFF) between fractures and the embedding matrix as well as within connected fractures tends to produce significant seismic attenuation and velocity dispersion. While WIFF between fractures and matrix is well understood, the corresponding effects related to fracture connectivity and the characteristics of the energy dissipation due to flow within fractures are largely unexplored. In this work, we use oscillatory relaxation simulations based on the quasi-static poroelastic equations to study these phenomena. We first consider synthetic rock samples containing connected and unconnected fractures and compute the corresponding attenuation and phase velocity. We also determine the relative fluid displacement and pressure fields in order to gain insight into the physical processes involved in the two manifestations of WIFF in fractured media. To quantify the contributions of the two WIFF mechanisms to the total seismic attenuation, we compute the spatial distribution of the local energy dissipation. Finally, we perform an exhaustive sensitivity analysis to study the role played by different characteristics of fracture networks on the seismic signatures. We show that in the presence of connected fractures both P wave attenuation and phase velocity are sensitive to some key characteristics of the probed medium, notably to the lengths, permeabilities, and intersection angles of the fractures as well as to the overall degree of connectivity of the fracture network. This, in turn, indicates that a deeper understanding of these two manifestations of WIFF in fractured media may eventually allow for the extraction of some of these properties from seismic data.

In this paper we present a constitutive model to describe unsaturated flow that considers the hysteresis phenomena. This constitutive model provides simple mathematical expressions for both saturation and hydraulic conductivity curves, and a relationship between permeability and porosity. The model is based on the assumption that the porous media can be represented by a bundle of capillary tubes with throats or "ink-bottles" and a fractal pore size distribution. Under these hypotheses, hysteretic curves are obtained for saturation and relative hydraulic conductivity in terms of pressure head. However, a non-hysteretic relationship is obtained when relative hydraulic conductivity is expressed as a function of saturation. The proposed relationship between permeability and porosity is similar to the well-known Kozeny-Carman equation but depends on the fractal dimension. The performance of the constitutive model is tested against different sets of experimental data and previous models. In all of the cases the proposed expressions fit fairly well the experimental data and predicts values of permeability and hydraulic conductivity better than others models.

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Self-potential signals can be generated by different sources and can be decomposed in various contributions. Streaming potential is the contribution due to the water flux in the subsurface and is of particular interest in hydrogeophysics and reservoir characterization. Being able to estimate water fluxes in porous and fractured media using streaming potential data relies on our understanding of the electrokinetic coupling at the mineral-solution interface and our capacity to understand, model, and upscale it. Two main approaches have been proposed to predict streaming potential generation in geological media. One of these approaches is based on determining the excess charge which is effectively dragged in the medium by water flow. In this chapter, we describe how to model the streaming potential by considering this effective excess charge density, how it can be defined, calculated and upscaled. We provide a short overview of the theoretical basis of this approach and we describe different applications to both water saturated and partially saturated soils and fractured media.

.[1] A defining characteristic of fractured rocks is their very high level of seismic attenuation, which so far has been assumed to be mainly due to wave-induced fluid flow (WIFF) between the fractures and the pore space of the embedding matrix. Using oscillatory compressibility simulations based on the quasi-static poroelastic equations, we show that another important, and as of yet undocumented, manifestation of WIFF is at play in the presence of fracture connectivity. This additional energy loss is predominantly due to fluid flow within the connected fractures and is sensitive to their lengths, permeabilities, and intersection angles. Correspondingly, it contains key information on the governing hydraulic properties of fractured rock masses and hence should be accounted for whenever realistic seismic models of such media are needed. Citation: Rubino, J. G., L. Guarracino, T. M. Müller, and K. Holliger (2013), Do seismic waves sense fracture connectivity?, Geophys. Res. Lett., 40,[692][693][694][695][696]

The self-potential (SP) method is a passive geophysical method that relies on the measurement of naturally occurring electrical field. One of the contributions to the SP signal is the streaming potential, which is of particular interest in hydrogeophysics as it is directly related to both the water flow and porous medium properties. The streaming current is generated by the relative displacement of an excess of electrical charges located in the electrical double layer surrounding the minerals of the porous media. In this study, we develop a physically based analytical model to estimate the effective excess charge density dragged by the water flow under partially saturated conditions. The proposed model is based on the assumption that the porous media can be represented by a bundle of tortuous capillary tubes with a fractal pore size distribution. The excess charge that is effectively dragged by the water flow is estimated using a flux averaging approach. Under these hypotheses, this new model describes the effective excess charge density as a function of saturation and relative permeability while also depending on the chemical and interface properties, and on petrophysical parameters of the media. The expression of the model has an analytical single closed-form which is consistent with a previous model developed from a different approach. The performance of the proposed model is then tested against previous models and different sets of laboratory and field data from the literature. The predictions of the proposed model fits fairly well the experimental data and shows improvements to estimate the magnitude of the effective excess charge density over the previous models. A relationship between the effective excess charge density and permeability can also be derived from the proposed model, representing a generalization to unsaturated conditions of a widely used empirical relationship. This new model proposes a simple and efficient way to model the streaming current generation for partially saturated porous media.