Thermal conductivity of unsaturated clay-rocks

The parameters used to describe the electrical conductivity of a porous material can be used to describe also its thermal conductivity. A new relationship is developed to connect the thermal conductivity of an unsaturated porous material to the thermal conductivity of the different phases of the composite, and two electrical parameters called the first and second Archie's exponents. A good agreement is obtained between the new model and thermal conductivity measurements performed using packs of glass beads and core samples of the Callovo-Oxfordian clay-rocks at different saturations of the water phase. We showed that the three model parameters optimised to fit the new model against experimental data (namely the thermal conductivity of the solid phase and the two Archie's exponents) are consistent with independent estimates. We also observed that the anisotropy of the effective thermal conductivity of the Callovo-Oxfordian clay-rock was mainly due to the anisotropy of the thermal conductivity of the solid phase

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

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

Streaming potential modeling in fractured rock: Insights into the identification of hydraulically active fractures

Numerous field experiments suggest that the self-potential (SP) geophysical method may allow for the detection of hydraulically active fractures and provide information about fracture properties. However, a lack of suitable numerical tools for modeling streaming potentials in fractured media prevents quantitative interpretation and limits our understanding of how the SP method can be used in this regard. To address this issue, we present a highly efficient two-dimensional discrete-dual-porosity approach for solving the fluid flow and associated self-potential problems in fractured rock. Our approach is specifically designed for complex fracture networks that cannot be investigated using standard numerical methods. We then simulate SP signals associated with pumping conditions for a number of examples to show that (i) accounting for matrix fluid flow is essential for accurate SP modeling and (ii) the sensitivity of SP to hydraulically active fractures is intimately linked with fracture-matrix fluid interactions. This implies that fractures associated with strong SP amplitudes are likely to be hydraulically conductive, attracting fluid flow from the surrounding matrix.Comment: 8 pages, 2 figure

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