A Simple Hysteretic Constitutive Model for Unsaturated Flow

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.Facultad de Ciencias Astronómicas y Geofísica

Influence of Pore Size Distribution on the Electrokinetic Coupling Coefficient in Two-Phase Flow Conditions

Author Contributions: J.V.: Conceptualisation, Formal analysis, Methodology, Software, Supervision, Writing—original draft and Writing—review and editing. R.H.: Data curation, Formal analysis, Software, Validation, Visualization, Writing—review and editing. D.J.: Conceptualisation, Formal analysis, Methodology, Supervision and Writing—review and editing. All authors have read and agreed to the published version of the manuscript.Peer reviewedPublisher PD

A physically-based analytical model to describe effective excess charge for streaming potential generation in saturated porous media

Different approaches have been proposed to predict streaming potentials in porous media. One approach is based on the excess charge which is effectively dragged in the medium by the water flow. Following the recent theoretical framework of Jougnot et al. (2012), we developed a physically-based analytical model to predict the effective excess charge in saturated porous media. The proposed model allows the determination of the effective excess charge as a function of pore water salinity, fractal dimension and hydraulic parameters like porosity and permeability. This new model has been successfully tested against data from the literature for different porous media. One of the main finding of this study is that it provides a mechanistic explanation to the empirical dependence between the effective excess charge and the permeability that has been found by various researchers. This model is also able to reproduce the evolution of this parameter with respect to the electrolyte concentration.Facultad de Ciencias Astronómicas y Geofísica

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

International audienceIn the context of seismoelectric and self-potential surveying, the effective excess charge density and the electrokinetic coupling coefficient are key parameters relating the measured electrical potential and the hydraulic characteristics of the explored porous media. In this work, we present a novel flux averaging approach that permits to estimate the frequency-dependent effective excess charge density in partially saturated porous media. For this, we conceptualize the porous medium as a partially saturated bundle of capillary tubes under oscillatory flux conditions. We account for the pore size distribution (PSD) to determine the capillary-pressure saturation relationship of the corresponding medium, which, in turn, permits to determine the pore scale saturation. We then solve the Navier-Stokes equations within the saturated capillaries and, by means of a flux-averaging procedure, obtain upscaled expressions for: (i) the effective excess charge density, (ii) the effective permeability, and (iii) the electrokinetic coupling coefficient, which are functions of the saturation and the probing frequency. We analyze and explain the characteristics of these functions for three different PSDs: fractal, lognormal, and double lognormal. It is shown that the PSD characteristics have a strong effect on the corresponding electrokinetic response. The proposed flux-averaging approach has an excellent capability for reproducing experimental measurements and models in the literature, which are otherwise based on well-known empirical relationships. The results of this work constitute a useful framework for the interpretation of electrokinetic signals in partially saturated media

An effective excess charge model to describe hysteresis effects on streaming potential

Streaming potentials are produced by the coupling between the water flow and the electrical current generated by the drag of electrical charges within the pore water of the media. This electrokinetic coupling is strongly influenced by the hydraulic properties that control groundwater flow (permeability, saturation and pressure head). Under unsaturated conditions, hydrogeologic studies have widely established that the relationships of permeability and saturation with pressure head are different for drainage and imbibition experiments. The hysteresis phenomenon present on these properties produces a hysteretic behaviour on the streaming potential which has been recently observed in experimental data. Hysteresis can be explained by the presence of irregularities in the pore geometry of the media which affects the water flow and, therefore, the excess charge density that is effectively dragged by the flow. In this study, we present a physically-based analytical model to describe the hysteresis phenomenon in the estimates of the effective excess charge density. Under the assumptions of a porous medium represented by a bundle of tortuous capillary tubes with throats and a fractal pore size distribution, hysteretic curves are obtained for the effective excess charge density as a function of pressure head using a flux averaging technique. These analytical expressions are closed-form and depend on the medium petrophysical and chemical properties. The predictions of the proposed model are consistent with laboratory data from drainage-imbibition experiments. These results open up exciting possibilities for studies involving water movement and processes in the vadose zone.Facultad de Ciencias Astronómicas y Geofísica

Surface‐Wave Dispersion in Partially Saturated Soils: The Role of Capillary Forces

International audienceThe critical zone is a region of the shallow subsurface that ranges from the top of the vegetation canopy to the base of superficial aquifers. It comprises rocks, soils, water, air, and living organisms; contains the vast majority of life-sustaining resources; and regulates the interaction between the atmosphere and aquifers (e.g., Binley et al., 2015; Parsekian et al., 2015). The combined use of geophysical multiscale probing and imaging techniques along with the integration of hydrological, hydrogeological, and geochemical data is widely practiced for the observation of the partially saturated region of the critical zone, that is, the vadose zone (e.g., Parsekian et al., 2015). This approach to geophysical subsurface characterization, referred to as hydrogeophysics (e.g., Hubbard & Linde, 2011; Rubin & Hubbard, 2006), is dominated by electrical and electromagnetic methods due to their strong sensitivity with regard to water content and salinity (e.g., Friedman, 2005). However, given that seismic waves are inherently sensitive to key hydraulic properties of porous media, such as, porosity, permeability

Modeling the evolution of spectral induced polarization during calcite precipitation on glass beads

International audienceWhen pH and alkalinity increase, calcite frequently precipitates and hence modifies the petrophysical properties of porous media. The complex conductivity method can be used to directly monitor calcite precipitation in porous media because it is very sensitive to the evolution of the pore structure and its connectivity. We have developed a mechanistic grain polarization model considering the electrochemical polarization of the Stern layer surrounding calcite particles. This model depends on the surface charge density and mobility of the counter-ions in the Stern layer. Our induced polarization model predicts the evolution of the size of calcite particles, of the pore structure and connectivity during spectral induced polarization experiments of calcite precipitation on glass beads pack. Model predictions are in very good agreement with the complex conductivity measurements. During the first phase of calcite precipitation experiment, calcite crystals growth, and the inverted particle size distribution moves towards larger calcite particles. When calcite continues to precipitate and during pore clogging, inverted particle size distribution moves towards smaller particles because large particles do not polarize sufficiently. The pore clogging is also responsible for the decrease of the connectivity of the pores, which is observed through the increasing electrical formation factor of the porous medium

Un modelo analítico para estimar el exceso de densidad de carga efectiva a partir del flujo de agua en la zona no saturada

El método de potencial espontáneo (PE) es un método geofísico pasivo que se basa en la medición de las diferencias de potencial eléctrico natural. Una de las contribuciones a la señal de PE es la debida al potencial electrocinético que resulta de particular interés para la hidrogeofísica ya que se origina principalmente por el movimiento de agua en el subsuelo, en particular en la zona no saturada del terreno. El potencial electrocinético se genera por el arrastre del exceso de cargas ubicado en la capa difusa de la lámina de agua que rodea la superficie del mineral. En este estudio, desarrollamos un modelo analítico para estimar el exceso de densidad de carga efectiva que es arrastrado por el flujo de agua en condiciones de saturación parcial. El modelo propuesto asume que los medios porosos pueden representarse mediante un conjunto de tubos capilares tortuosos con una distribución fractal de tamaño de poro. El exceso de densidad de carga que es efectivamente arrastrado por el flujo de agua se estima utilizando el método de promediación del flujo. Bajo estas hipótesis, se obtiene una expresión analítica cerrada para este nuevo modelo que describe el exceso de densidad de carga efectiva en función de la saturación y de la permeabilidad relativa del medio. Asimismo, el modelo depende de las propiedades químicas del agua y de los parámetros petrofísicos del medio. El modelo propuesto se validó con modelos previos, y con diferentes conjuntos de datos experimentales de la literatura. Las predicciones del modelo propuesto proporcionan un muy buen ajuste a los datos experimentales tanto de laboratorio como de campo, y muestran mejores estimaciones de la magnitud del exceso de densidad de carga efectiva sobre los modelos previos. Una relación entre el exceso de densidad de carga efectiva y la permeabilidad también puede derivarse del modelo propuesto, que representa una generalización a condiciones de saturación parcial de una relación empírica ampliamente utilizada. Este nuevo modelo propone una manera simple y eficiente de modelar la generación del potencial electrocinético para medios porosos parcialmente saturados. Además, constituye la base de una novedosa técnica para medir el flujo de agua in situ y estudiar procesos físicos que tienen lugar en la zona no saturada del subsuelo tales como el flujo de contaminantes, las inyecciones de CO2 o la absorción de agua de las raíces.Universidad Nacional de La Plat