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

Un modelo fractal para estimar la permeabilidad a partir de la porosidad

En este trabajo se presenta un modelo fractal para estimar la permeabilidad de una roca en función de su porosidad. El modelo asume que el medio poroso se puede representar mediante un conjunto de tubos capilares constrictivos con una distribución fractal de tamaño de poro. La relación obtenida es una ley de potencias que depende de tres parámetros independientes con significado físico o geométrico. Cabe resaltar que el exponente de la relación propuesta depende de la dimensión fractal y resulta siempre mayor a 3. En el caso límite de un exponente igual a 3, la relación propuesta es similar al modelo semi-empírico de Kozeny-Carman (KC). El modelo fractal se validó con datos experimentales de la literatura obteniéndose un buen ajuste para distintas texturas de suelo. La comparación con datos experimentales muestra que la relación propuesta predice mejor los valores de permeabilidad que la ecuación de KC para todo el rango de magnitudes.Eje: Ciencias Hidrológicas y Criósfera.Facultad de Ciencias Astronómicas y Geofísica

An analytical study of seismoelectric signals produced by 1-D mesoscopic heterogeneities

The presence of mesoscopic heterogeneities in fluid-saturated porous rocks can produce measurable seismoelectric signals due to wave-induced fluid flow between regions of differing compressibility. The dependence of these signals on the petrophysical and structural characteristics of the probed rock mass remains largely unexplored. In this work, we derive an analytical solution to describe the seismoelectric response of a rock sample, containing a horizontal layer at its center, that is subjected to an oscillatory compressibility test. We then adapt this general solution to compute the seismoelectric signature of a particular case related to a sample that is permeated by a horizontal fracture located at its center. Analyses of the general and particular solutions are performed to study the impact of different petrophysical and structural parameters on the seismoelectric response. We find that the amplitude of the seismoelectric signal is directly proportional to the applied stress, to the Skempton coefficient contrast between the host rock and the layer, and to a weighted average of the effective excess charge of the two materials. Our results also demonstrate that the frequency at which the maximum electrical potential amplitude prevails does not depend on the applied stress or the Skempton coefficient contrast. In presence of strong permeability variations, this frequency is rather controlled by the permeability and thickness of the less permeable material. The results of this study thus indicate that seismoelectric measurements can potentially be used to estimate key mechanical and hydraulic rock properties of mesoscopic heterogeneities, such as compressibility, permeability, and fracture compliance.Comment: 14 pages, 8 figure

Self-Potential as a Predictor of Seawater Intrusion in Coastal Groundwater Boreholes

This work was supported by the Natural Environment Research Council in the UK, as part of the Science and Solutions for a Changing Planet Doctor Training Partnership, run by the Grantham Institute for Climate Change at Imperial College London. We thank Southern Water for access to the boreholes at Saltdean and Balsdean. We thank Southern Water and Atkins Global for funding the installation of the equipment. We also thank Dr Amadi Ijioma for providing a prototype of the electrodynamic modelling code in MATLAB, which has since been adapted for use in a coastal chalk aquifer. Three anonymous reviewers are thanked for their comments, which greatly helped to improve the manuscript. The data used in this paper are in the tables, figures and cited information. The authors have no conflicts of interest to declare.Peer reviewedPublisher PDFPublisher PD

Diffusion of ions in unsaturated porous materials

International audienceIn a salinity gradient, the diffusion of ions through the connected porosity of a porous and charged material is influenced by the charged nature of the interface between the pore water and the solid. This influence is exerted through the generation of a macroscopic electrical field termed the diffusion or membrane potential. This electrical field depends on the excess of counterions located in the pore space counterbalancing the charge density of the surface of the solid. In unsaturated porous materials, we have to consider (1) the effect of the charged nature of the air/water interface, (2) the increase of the counterion density as the counterions are packed in a smaller volume when the saturation of the nonwetting phase (air) increases, and (3) the influence of the water saturation upon the tortuosity of the water phase. The volume average of the Nernst–Planck equation is used to determine the constitutive equations for the coupled diffusion flux and current density of a multicomponent electrolyte in unsaturated conditions. We assume that water is the wetting phase for the solid phase. We neglect the electro-osmotic flow in the coupled constitutive equations and the deformation of the medium (the medium is assumed to be both isotropic and rigid). This model explains well the observed tendency of strong decreases of the apparent diffusion coefficient of ions with the decrease of the saturation of the water phase under steady-state conditions. This decrease is mainly due to the influence of the saturation upon the tortuosity of the water phase

Self-potentials in partially saturated media: the importance of explicit modeling of electrode effects

Self-potential (SP) data are of interest to vadose zone hydrology because of their direct sensitivity to water flow and ionic transport. There is unfortunately little consensus in the literature about how to best model SP data under partially saturated conditions, and different approaches (often supported by one laboratory data set alone) have been proposed. We argue that this lack of agreement can largely be traced to electrode effects that have not been properly taken into account. A series of drainage and imbibition experiments were considered in which we found that previously proposed approaches to remove electrode effects were unlikely to provide adequate corrections. Instead, we explicitly modeled the electrode effects together with classical SP contributions using a flow and transport model. The simulated data agreed overall with the observed SP signals and allowed decomposing the different signal contributions to analyze them separately. After reviewing other published experimental data, we suggest that most of them include electrode effects that have not been properly taken into account. Our results suggest that previously presented SP theory works well when considering the modeling uncertainties presently associated with electrode effects. Additional work is warranted to not only develop suitable electrodes for laboratory experiments but also to assure that associated electrode effects that appear inevitable in longer term experiments are predictable, so that they can be incorporated into the modeling framework

Modeling the evolution of complex conductivity during calcite precipitation on glass beads

When pH and alkalinity increase, calcite frequently precipitates and hence modifies the petrophysical properties of porous media. The compl ex conductivity method can be used to directly monitor calcite precipitation in porous me dia because it is sensitive to the evolution of the mineralogy, pore structure and its connectivity . We have developed a mechanistic grain polarization model considering the electrochemical polarization of the Stern and diffuse layer surrounding calcite particles. Our complex conducti vity model depends on the surface charge density of the Stern layer and on the electrical po tential at the onset of the diffuse layer, which ar e computed using a basic Stern model of the calcite/w ater interface. The complex conductivity measurements of Wu et al. (2010) on a column packed with glass beads where ca lcite precipitation occurs are reproduced by our surface complexation and complex conductivity models. The evolution of the size and shape of calc ite particles during the calcite precipitation experiment is estimated by our complex conductivity model. At the early stage of the calcite precipitation experiment, modeled particles sizes i ncrease and calcite particles flatten with time because calcite crystals nucleate at the surface of glass beads and grow into larger calcite grains around glass beads. At the later stage of the calci te precipitation experiment, modeled sizes and cementation exponents of calcite particles decrease with time because large calcite grains aggregate over multiple glass beads, a percolation threshold is achieved, and small and discrete calcite crystals polarize