M. Darot

Complex conductivity measurements and fractal nature of porosity

Complex resistivity measurements were performed on 22 saturated samples (sandstones, slate, shale, and granites) at room temperature and pressure over a frequency range from 1 Hz to 5 MHz, using a two‐terminal sample holder. Although low‐frequency measurements (from 1 Hz to 1–10 kHz) are perturbed by electrode polarization phenomena, we observed classical behavior for 20 samples, i.e., behavior that can be fitted to a Cole and Cole response function, and different behavior for the other two (two slates). These two last samples exhibit an almost constant imaginary part of the complex resistivity. Since the frequency dependence is caused by interfacial effects, it is possible to characterize the internal surface area from electrical measurements. We use models developed by Le Mehaute and Crepy (1983) and Po Zen Wong (1987) to calculate the fractal dimension d of the internal surface area from experimental data. An independent measurement confirms that the specific surface area correlates with d. The two mod...

Permeability of thermally cracked granite

Permeability of granite specimens heated up to 650°C were measured in the laboratory with respect to both confining and pore pressure. An unexpected behavior (permeability decrease) was found in the low temperature range (20–125°C). Permeability variations are interpreted with the help of a theoretical model of porosity. Complementary measurements of porosity and absolute surface area have also been obtained. A discussion in terms of microstructural controlling parameters concludes to a decrease of crack aperture at low temperatures (20–125°C), followed by an increase at higher temperatures (T >125°C).

Q−1 of forsterite single crystals

Abstract Internal friction ( Q −1 ) experiments have been performed on synthetic forsterite single crystals in order to investigate the role of temperature, frequency and dislocation density on the Q −1 factor. Data have been obtained for both deformed and undeformed specimens over a frequency range from 10 to 10 −4 Hz at 15, 1000, 1200 and 1400°C. Measurements were done using a torsional pendulum operating in forced oscillations on specimens with dimensions of 20 mm × 5 mm × 1 mm. Samples were maintained in vacuum. Stress amplitudes were 0.1 MPa and strains 10 −6 -10 −5 . Pre-deformation experiments were creep tests performed at 1600°C and 20 MPa. The amount of strain was 10 −2 . Dislocation microstructures were investigated by transmission electron microscopy. At room temperature, undeformed samples show low attenuation with no frequency dependence. At high temperature (1400°C), Q −1 increases up to 5 × 10 −2 for very low frequencies (10 −4 Hz). Deformed specimens show the same trend but there is a more pronounced increase in Q −1 with both frequency and temperature ( Q −1 = 2 × 10 −1 , 10 −4 Hz at 1400°C). This high-temperature attenuation is the result of dislocation processes which are probably non-linear in the strain range explored by the present experiments ( ϵ > 10 −6 ). Non-linearity appears to be the best explanation for the disagreement between high Q −1 data reported in laboratory and low Q 1 data reported for the upper mantle.

Transport properties and microstructural characteristics of a thermally cracked mylonite

An experimental study was carried out on a granitic mylonite (La Bresse, France) to analyze the influence of pore microstructure on transport properties. Different crack networks were obtained by a controlled thermal treatment. Microstructures were analyzed by means of gas adsorption and mercury porosimetry. Transport properties have been investigated by measuring gas permeability and electrical conductivity. The dependence of permeability on confining pressure shows an exponential decrease, characteristic of a porosity made of cracks. Correlations between measured parameters have been analyzed by comparing them with relations deduced from theoretical models. Linking the formation factor to the porosity leads to a rather low tortuosity value (about 2.4), characterizing a medium with a well connected porosity. Correlation between permeabilityk and formation factorF leads to a power-law relationk ∝ F−n wheren≈2.9, which is consistent with a crack model describing the behavior of the thermally treated rock.

Pore Structures and Transport Properties of Sandstone

We report laboratory measurements of pore structure, capillarity, water permeability, and electrical conductivity on Fontainebleau sandstone specimens. Experimental equipment and techniques are described. Water permeability measurements were performed on saturated cores with a 100 MPa permeameter. Various combinations of pore and confining pressures were used and an effective pressure law was determined. In addition, electrical conductivity of samples saturated with KCl brines was measured over a wide range of electrolyte conductivities (10−3 to 1 Sm−1). The well-known relationshipF=Φ−1 fits well our data, and empirical parameters such as the cementation exponent and tortuosity factor are derived. Differences between transport properties of the three types of sandstone are related to the microstructural characteristics of the pore network of each rock.

Slow crack growth in minerals and rocks: Theory and experiments

Strength and mechanical behavior of rocks and minerals are modified by aqueous environments. This results in two effects: mechanical and chemical. The chemical effect is investigated from both a theoretical and an experimental point of view. It is shown that a thermodynamic approach leads to a satisfactory understanding of the chemical effect through an ‘extended griffith concept’. Predictions of the model have been tested using slow crack growth experiments. The experiments have been performed with a special Double Torsion apparatus which was built for this purpose. The good agreement observed between theory and experiments suggests that subcritical crack growth in rocks is controlled by adsorption onto the crack tip. This result was previously suggested by other authors (Dunninget al., 1984). However, the important consequences of the model are that (1) there should exist a threshold stress below which subcritical crack growth stops, and this threshold depends on the environment; (2) subcritical crack growth and time-dependent phenomena could take place in the crust in a stress interval which could be as high as 50% of the rupture stress.

From surface electrical properties to spontaneous potentials in porous media

This paper deals with the electrical double layer and the related properties of porous media. In particular, the electrical conductivity, the streaming potential, and the membrane potential are described in a self-consistent set of equations. All these properties are shown to be governed by fluid-matrix interface properties, as well as four geometrical parameters.

Influence of the electrical diffuse layer and microgeometry on the effective ionic diffusion coefficient in porous media

This study models the effect of the electrical diffuse layer at the pore matrix interface on ionic diffusion processes in a porous medium in presence of a concentration gradient. We find that the equation D = Df/Fo usually used to compute in steady state conditions the effective diffusion coefficient, D, of a porous medium as a function of the salt diffusion coefficient, Df, the electrical formation factor, F, and the porosity, o, should be replaced by: D = ( Df/Fo)ξ, in the presence of an electrical diffuse layer at the pore-matrix interface. The correction factor, ξ arises from the cross-coupling of ionic fluxes due to electroneutrality requirement.

Single-crack behaviour and crack statistics

Physical and mechanical properties of rocks are controlled by their crack content and crack behaviour. In general, rocks contain a random population of cracks, not necessarily isotropic and homogeneous, more or less interacting, so that the physical properties are those of a complex structure. In such a situation, understanding of the behaviour of a single crack may appear to be irrelevant. It should be looked at rather as a necessary, although not sufficient, preliminary step. With some approximations, fracture mechanics appears to be a useful tool with which to understand the behaviour of a single crack (Rudnicki 1980; Atkinson 1984, 1987; Swanson 1984). Fracture mechanics gives a basic rationale for the various regimes of crack propagation; crack healing, subcritical crack growth, and dynamic (overcritical) crack growth. It points to the importance of extensional cracks at the microscopic level (Lawn & Wilshaw 1975, Section 3.3). Macroscopic behaviour is to be interpreted in terms of microscopic processes. As far as cracks are concerned, important microscopic processes are nucleation and propagation of extensional cracks. However, in order to take into account the fact that a real rock contains a population of cracks, statistical methods are required. Statistical crack mechanics was developed by Dienes (1978, 1982) to calculate the permeability of a cracked rock. Percolation theory also appears to be useful to discuss permeability in terms of crack concentration (Dienes 1982, Gueguen etal. 1986).

Mechanical and transport properties of crustal rocks: from single cracks to crack statistics

Abstract Cracks control the physical and mechanical properties of rocks. Using fracture mechanics, it is possible to analyse the behaviour of a single crack. From standard tests (double torsion, double cantilever beam), experimental data, obtained on various minerals and rocks in the sub-critical crack growth regime, lead to the conclusion that fracture strength is weakly rate dependent. Real rocks contain a population of cracks. Physical and mechanical properties of rocks must therefore be interpreted by combining the behaviour of a single crack with statistical methods. Two properties are considered here: permeability and fracture strength. Statistics and percolation theory show that there are two important thresholds for crack concentration: the first corresponds to the onset of permeability and the second to the development of macroscopic fracture.