Dynamic effective mass of granular media

We develop the concept of frequency dependent effective mass, M(omega), of jammed granular materials which occupy a rigid cavity to a filling fraction of 48%, the remaining volume being air of normal room condition or controlled humidity. The dominant features of M(omega) provide signatures of the dissipation of acoustic modes, elasticity and aging effects in the granular medium. We perform humidity controlled experiments and interpret the data in terms of a continuum model and a "trap" model of thermally activated capillary bridges at the contact points. The results suggest that attenuation in the granular materials is influenced significantly by the kinetics of capillary condensation between the asperities at the contacts.Comment: 4 pages, 3 figure

Why Effective Medium Theory Fails in Granular Materials

Experimentally it is known that the bulk modulus, K, and shear modulus, \mu, of a granular assembly of elastic spheres increase with pressure, p, faster than the p^1/3 law predicted by effective medium theory (EMT) based on Hertz-Mindlin contact forces. To understand the origin of these discrepancies, we perform numerical simulations of granular aggregates under compression. We show that EMT can describe the moduli pressure dependence if one includes the increasing number of grain-grain contacts with p. Most important, the affine assumption (which underlies EMT), is found to be valid for K(p) but breakdown seriously for \mu(p). This explains why the experimental and numerical values of \mu(p) are much smaller than the EMT predictions.Comment: 4 pages, 5 figures, http://polymer.bu.edu/~hmaks

Etude numérique des propriétés mécaniques et des processus de déformation et d'endommagement des matériaux granulaires

Financement 'BDI' CNRS Schlumberger Doll Research (Ridgefield,CT,USA)The understanding of structural and mechanical properties of granular assemblies remains an open issue. The numerical modeling of granular media, using the Molecular Dynamic approach, brings some answers to critical problems. At first, we are studying the effects of mixture parameters on the degree of order and on the stress distribution in these arrangements of grains. Next, we are interested in the acoustic properties of these media, which are very nonlinear in comparison to continuous elastic solids; ours simulations serve to clarify the deficiencies of Effective Medium Theory, which only partially account for the dependency of elastic moduli with pressure. We show that relaxation of grains, following an infinitesimal deformation is an essential component of the shear modulus. There is clearly a need for an alternative formulation and the traditional elasto-plastic approach is faced with new theories. If the numerical simulations led in this study, which measure the response function of granular media (stress field generated by a point force), show an elastic scaling, it also accounts for important relaxation process. The deformation mechanisms of granular materials were also study by simulating bixial compression tests, which reproduce qualitatively well the classical mechanicals data (stress peak, compaction/dilatancy transition), and also localization of the deformation; while at low pressure, grains rotations accommodate the deformation, at high pressure, the mobilization of friction is more pronounced. Finally, we propose a probabilistic model of damage of granular rocks, which predicts a dependency of damage both with the cementation heterogeneity and with the sample size. These predictions are confirmed by simulations, which also highlight two successive damage behaviors, diffuse at first and then concentrated in clusters.La compréhension des propriétés structurales et mécaniques des assemblages granulaires reste un problème ouvert. La modélisation numérique de ces milieux par Dynamique Moléculaire permet de répondre à certaines interrogations. Tout d'abord, nous étudions les effets des paramètres de mélange sur le degré d'ordre et la distribution des contraintes dans ces arrangements de grains. Ensuite, nous nous intéressons aux propriétés acoustiques de ces milieux, très nonlinéaires comparées aux solides élastiques continus; nos simulations servent à clarifier les déficiences de la Théorie de Milieu Effectif, qui rend partiellement compte de la dépendance en pression des modules élastiques, et elles montrent que la relaxation des grains après une déformation infinitésimale est une composante essentielle du module de cisaillement. Il y a donc un besoin pour une formulation alternative et l'approche traditionnelle élasto-plastique a été remise en cause par des nouveaux modèles. Si l'expérience numérique menée de mesure de la fonction réponse (champ de contrainte généré par une force ponctuelle) montre une remise à l'échelle élastique, elle rend également compte de phénomènes importants de relaxation. Les mécanismes de déformation des matériaux granulaires ont aussi été étudiés en simulant des essais biaxiaux; ils reproduisent qualitativement les données mécaniques classiques (pic de contrainte, transition compaction/dilatance) et aussi la localisation de la déformation; à faible pression, les rotations de grains accommodent la déformation tandis qu'à forte pression, la mobilisation du frottement est plus marquée. Enfin, nous proposons un modèle probabilistique d'endommagement de roches granulaires qui prédit une dépendance de l'endommagement avec à la fois l'hétérogénéité de cimentation et la taille d'échantillon. Ces prédictions sont confirmées par des simulations qui permettent également de mettre en évidence deux régimes d'endommagement successifs, diffus puis concentré en amas

Etude numérique des propriétés mécaniques et des processus de déformation et d'endommagement des matériaux granulaires

La compréhension des propriétés structurales et mécaniques des assemblages granulaires reste un problème ouvert. La modélisation numérique de ces milieux par Dynamique Moléculaire permet de répondre à certaines interrogations. Tout d'abord, nous étudions les effets des paramètres de mélange sur le degré d'ordre et la distribution des contraintes dans ces arrangements de grains. Ensuite, nous nous intéressons aux propriétés acoustiques de ces milieux, très non linéaires comparés aux solides élastiques continus; nos simulations servent à clarifier les déficiences de la Théorie de Milieu Effectif, qui rend partiellement compte de la dépendance en pression des modules élastiques, et elles montrent que la relaxation des grains après une déformation infinitésimale est une composante essentielle du module de cisaillement. Il y a donc un besoin pour une formulation alternative et l'approche traditionnelle élasto-plastique a été remise en cause par des nouveaux modèles. Si l'expérience numérique menée de mesure de la fonction réponse (champ de contrainte généré par une force ponctuelle) montre une remise à l'échelle élastique, elle rend également compte de phénomènes importants de relaxation. Les mécanismes de déformation des matériaux granulaires ont aussi été étudiés en simulant des essais bi axiaux; ils reproduisent qualitativement les données mécaniques classiques (pic de contrainte, transition compaction/dilatance) et aussi la localisation de la déformation; à faible pression, les rotations de grains accommode la déformation tandis qu'à forte pression, la mobilisation du frottement est plus marquée. Enfin, nous proposons un modèle probabilistique d'endommagement de roches granulaires qui prédit une dépendance de l'endommagement avec à la fois l'hétérogénéité de cimentation et la taille d'échantillon. Ces prédictions sont confirmées par des simulations qui permettent également de mettre en évidence deux régimes d'endommagement successifs, diffus puis concentré en amas.The understanding of structural and mechanical properties of granular assemblies remains an open issue. The numerical modelling of granular media, using the Molecular Dynamic approach, brings some answers to critical problems. At first, we are studying the effects of mixture parameters on the degree of order and on the stress distribution in theses arrangements of grains. Next, we are interested in the acoustic properties of these media, which are very nonlinear in comparison to continuous elastic solids; ours simulations serve to clarify the deficiencies of Effective Medium Theory, which only partially account for the dependency of elastic moduli with pressure. We show that relaxation of grains, following an infinitesimal deformation is an essential component of the shear modulus. There is clearly a need for an alternative formulation and the traditional elasto-plastic approach is faced with new theories. If, the numerical simulation led in this study, which measure the response function of granular media (stress field generated by a point force), shows an elastic scaling, it also accounts for important relaxation process. The deformation mechanisms of granular materials were also study by simulating bixial compression tests, which reproduce qualitatively well the classical mechanicals data (stress peak, compaction/dilatancy transition), and also localization of the deformation; while at low pressure, grains rotations accommodate the deformation, at high pressure, the mobilization of friction is more pronounced. Finally, we propose a probabilistic model of damage of granular rocks, which predicts a dependency of damage both with the cementation heterogeneity and with the sample size. These predictions are confirmed by simulations, which also highlight two successive damage behaviours, diffuse at first and then concentrated in clusters.ORSAY-PARIS 11-BU Sciences (914712101) / SudocSudocFranceF

Comportement mécanique du carbonate d’Estaillades en condition drainée: influence du chemin de chargement

On réalise sur des échantillons cylindriques des essais drainés en appliquant divers chemins de chargement, caractérisés par le rapport des contraintes radiale et axiale (K). Le mode d’endommagement et son influence sur la perméabilité dépendent surtout de K, mais dans des régimes intermédiaires, les hétérogénéités jouent un rôle majeur. Nous proposons une normalisation des données expérimentales qui permet de définir sans autre ajustement l’enveloppe de rupture dans le plan des contraintes

Characterization of Foam Flowing in a Granular Medium in Presence of Oil by Small Angle Neutron Scattering

International audienceWe present an experimental study of foam flow characterization inside a 3D granular medium packed in a cell. The foam is formed by coinjecting a surfactant solution and gas inside a cell filled with silica grains. The porous medium is initially saturated with dodecane and water before the gas-surfactant coinjection. To simplify the interpretation of the measurements, a contrast matching methodology has been applied in order to obtain a two phases system regarding the scattering length density values. The combination of transmission and incoherent scattering allow us to estimate the volume fractions of each phase whereas the coherent scattering is used to estimate the surface to volume ratio S/V related to water-oil and water-gas interfaces. Considering the evolution of S/V ratio, volume fractions and pressure difference, we infer some mechanisms of foam generation and transportation as well as oil removal

Localized deformation induced by heterogeneities in porous carbonate analysed by multi−scale digital image correlation

International audienceThe understanding and the prevention of damage mechanisms, which have an impact on the hydrocarbon production and recovery rates, are of paramount interest for reservoir engineers. The modelling of such coupled processes relies essentially on experimentally obtained data, which characterize the macroscopic mechanical and transport properties. This approach however cannot account for the multi-scale structural heterogeneities of the considered rocks, in spite of their fundamental importance. The microstructural characterization of damage is usually based on ‘post-mortem’ observations of the samples, which provide both qualitative and quantitative information about the effects of the mechanisms activated at the grain scale and at intermediate scales, at a pervasive stage of damage after sample unloading. New techniques provide more quantitative and direct methods to follow the deformation history and the eventual development of localization and damage. In this study, the 2D Digital Image Correlation (DIC) technique has been applied to sequences of images taken from carbonate samples during uniaxial compression tests. Several scales have been considered, ranging from the centimetric scale of the samples to the local scale of their microstructure. For this purpose both optical observations and Scanning Electron Microscopy (SEM) were used. Although the macroscopic strain at failure was very small (< 0.2%), the DIC technique has proven to be reliable, provided one selects carefully image acquisition conditions and DIC parameters, as highlighted in our discussion on the uncertainties and the evaluation of errors. This technique has allowed us to quantify both the global and local strain fields during the deformation process. We have thus been able to precisely identify the localizations of damage and the local compaction mechanisms, and to relate them to the characteristic structural heterogeneities of the tested carbonate

Axial and Radial Permeability Evolutions of Compressed Sandstones: End Effects and Shear-band Induced Permeability Anisotropy

International audienceThe influence of hydrostatic and uniaxial stress states on the porosity and permeability of sandstones has been investigated. The experimental procedure uses a special triaxial cell which allows permeability measurements in the axial and radial directions. The core sleeve is equipped with two pressure samplers placed distant from the ends. They provide mid-length axial permeability measure as opposed to the overall permeability measure, which is based on the flow imposed through the pistons of the triaxial cell. The core sleeve is also equipped to perform flows in two directions transverse to the axis of the sample. Two independent measures of axial and complementary radial permeability are thus obtained. Both Fontainebleau sandstone specimens with a porosity of about 5.8% to 8% and low permeability ranging from 2.5 mD to 30 mD and Bentheimer sandstone with a porosity of 24% and a high permeability of 3D have been tested. The initial axial permeability values obtained by each method are in good agreement for the Fontainebleau sandstone. The Bentheimer sandstone samples present an axial mid-length permeability 1.6 times higher than the overall permeability. A similar discrepancy is also observed in the radial direction, also it relates essentially to the shape of flow lines induced by the radial flow. All the tested samples have shown a higher stress dependency of overall and radial permeability than mid-length permeability. The effect of compaction damage at the pistons/sample and radial ports/sample interfaces is discussed. The relevance of directional permeability measurements during continuous uniaxial compression loadings has been shown on the Bentheimer sandstone until the failure of the sample. We can efficiently measure the influence of brittle failure associated to dilatant regime on the permeability: It tends to increase in the failure propagation direction and to decrease strongly in the transverse direction

Apport des mesures de champs par corrélation d’images pour l’étude de la déformation de géomatériaux poreux

La méthode de détermination des champs de déformation à partir de corrélation d’images a été appliquée à toutes les échelles pour des échantillons centimétriques de grès et de carbonates observés sous chargement en microscopie optique et électronique à balayage. On peut ainsi observer les diverses étapes du développement de localisations et des mécanismes parfois antagonistes affectant la perméabilité de l’échantillon, comme la diminution de porosité et l’ouverture de microsfissures

Investigating cyclopentane hydrate nucleation and growth using microfluidics

International audienceThe success of geological storage of carbon dioxide (CO 2 ) in depleted oil and gas reservoirs relies among other aspects on the efficiency of CO 2 injection, especially in the near-wellbore area where flow rates are high. CO 2 hydrates pressure/temperature equilibrium conditions may be reached in this zone due to cooling associated with the Joule–Thomson effect; such CO 2 hydrate formation may lead to strong injectivity loss and impair drastically the onsite well operations. In this study, cyclopentane hydrates (CPH) were employed as CO 2 hydrate proxy ( i.e. formation at atmospheric pressure) to mimic CO 2 hydrate formation at higher pressure. In this study, the nucleation and growth processes were determined using a droplet-based in-house-microfluidic device. The generation of water droplets in cyclopentane liquid using the co-flow method was achieved. Trains of identical water droplets were stored in a serpentine channel. Each isolated droplet in this channel serves as a separate reactor. The temperature was controlled using a Peltier module to initiate hydrate nucleation at low temperatures. The isolated droplets provided the opportunity to statistically analyze the kinetic behaviors by varying key parameters, such as thermal history and water salinity. Detection of the onset of crystallization in water droplets over time and temperature allowed us to plot conversion curves based on imposed parameters. The effect of thermal history and dissociation temperature was first compared using pure water. This study marks the initial investigation into how NaCl influences CPH formation in microfluidic devices, focusing on isolated water droplets within serpentine tubes. The progression of ice nucleation, ice melting, the onset of CPH crystallization, CPH growth, and CPH dissociation are illustrated in water droplets exposed to changing temperatures. The addition of NaCl in the water during the procedure exhibited a noteworthy impact on CPH formations. With the same temperature profile, salt concentration delays nucleation (thermodynamic effect) and slows down growth. Our findings suggest that higher subcooling accelerates nucleation and growth rates. Initial lateral growth rates ranged from 4.22 μm/s to 2.14 μm/s, with a subcooling of 4.2 °C observed between 2 and 7 min for a pure water droplet