Éditeur(s) : HAL CCSD Springer Verlag (Germany) Springer Verlag
Résumé : Production rates in horizontal shale gas wells display declines that are controlled by the low permeability and the intrinsic heterogeneity of the shale matrix. We present an original multi-continuum approach that yields a physical model able to reproduce the complexity of the decreasing gas rates. The model describes the dynamics of gas rate as function of the physical reservoir parameters and geometry, while the shale matrix heterogeneity is accounted for by a stochastic description of transmissivity field. From the 3D (Dimensional) problem setting, including the heterogeneous shale matrix, the fractures generated by the hydrofracking operations, as well as the production well characteristics, we establish an effective upscaled 1D model for the gas pressures in fracture and matrix as well as the volumetric flux. We analyse the decline curves behaviour, and we identify the time scales that characterize the dynamics of the gas rate decline using explicit analytical Laplace space solutions of the upscaled process model. Asymptotically, the flux curves decrease exponentially, while in an intermediate regime we find a power-law behaviour, in which the flux scales with a power law in time as (t^{-beta }), where (beta ) reflects the medium heterogeneity. We use this solution to fit a set of real data displaying distinctly different decline trends and study the sensitivity of the model to the reservoir parameters in order to identify their respective controls at the different stages of the decline curve dynamics. Results indicate that the initial value of the gas rate is determined by the transmissivity of the fractures and the initial pressure of the gas in the shale matrix. The latter causes mainly a shift in the entire decline curve. The early time of decline curve shape is primarily controlled by the fracture properties (compressibility and transmissivity). During the main part of the economically valuable production times, i.e. before the production rate drops exponentially, the decline curve is strongly controlled by the properties of the shale rocks including their heterogeneity, which is modelled by two parameters describing the non-Fickian pressure diffusion effects in a stochastic framework.
ISSN: 0169-3913

hal-01217247
https://hal.archives-ouvertes.fr/hal-01217247
DOI : 10.1007/s11242-015-0504-y

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
Although first-order rate constants are basic ingredients of physical chemistry, biochemistry and systems modeling, their innermost nature is derived from complex physical chemistry mechanisms. The present study suggests that equivalent conclusions can be more straightly obtained from simple statistics. The different facets of kinetic constants are first classified and clarified with respect to time and energy and the equivalences between traditional flux rate and modern probabilistic modeling are summarized. Then, a naive but rigorous approach is proposed to concretely perceive how the Arrhenius law naturally emerges from the geometric distribution. It appears that (1) the distribution in time of chemical events as well as (2) their mean frequency, are both dictated by randomness only and as such, are accurately described by time-based and spatial exponential processes respectively.
Physica A: Statistical Mechanics and its Applications

hal-00845518
https://hal-univ-rennes1.archives-ouvertes.fr/hal-00845518
https://hal-univ-rennes1.archives-ouvertes.fr/hal-00845518v2/document
ARXIV : 1307.4583
DOI : 10.1016/j.physa.2013.05.036

Éditeur(s) : HAL CCSD
Résumé : International audience
We consider a second-order differential system with Hessian-driven damping . An interesting property of this system is that, after introduction of an auxiliary variable y , it can be equivalently written as a first-order system in time and space. This allows us to extend the analysis to the case of a convex lower semicontinuous potential and so to introduce constraints in the model. When considering the indicator function of a closed convex set, the subdifferential operator takes account of the contact forces. In this setting, by playing with the geometrical damping parameter, we can describe nonelastic shock laws with restitution coefficient. Taking advantage of the infinite dimensional framework, we introduce a nonlinear hyperbolic PDE describing a damped oscillating system with obstacle. The system is dissipative; in the convex case each trajectory weakly converges to a minimizer of the global potential energy function. Exponential stabilization is obtained under strong convexity assumptions.
Differential Equations & Applications

hal-00803214
https://hal.archives-ouvertes.fr/hal-00803214
https://hal.archives-ouvertes.fr/hal-00803214/document
https://hal.archives-ouvertes.fr/hal-00803214/file/Attouch-Mainge-Redont-30August2011.pdf

Éditeur(s) : HAL CCSD American Geophysical Union (AGU)
Résumé : Extensional fault systems in the Earth's crust can exhibit two end-member geometries that we identify as distributed and localized faulting regimes. A satellite image analysis of fault populations from the Main Ethiopian Rift-Afar area reveals that the rift architecture contains these two faulting regimes. The occurrence of these regimes reveals a jump in the scale of fault segmentation and linkage. Strain localization at rift border zones exhibits particularly large-scale fault linkage and a power law size distribution. This regime replaces prior distributed fault systems, showing small-scale fault linkage and an exponential size distribution. The distributed faulting is interpreted as confined to the thick trap basalt carapace. We show that continental fault systems can develop by a combination of these two geometries, and we demonstrate how to quantitatively decipher the jump between them.
ISSN: 0278-7407

hal-00411147
https://hal.archives-ouvertes.fr/hal-00411147
DOI : 10.1029/2007TC002148

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
We developed a new granular material (MatIV) to study experimentally landscape evolution in active mountain belt piedmonts. Its composition and related physical properties have been determined using empirical criteria derived from the scaling of deformation, erosion-transport and sedimentation natural processes. MatIV is a water-saturated composite material made up with 4 granular components (silica powder, glass microbeads, plastic powder and graphite) whose physical, mechanical and erosion-related properties were measured with different laboratory tests. Mechanical measurements were made on a modified Hubbert-type direct shear apparatus. Erosion-related properties were determined using an experimental set-up that allows quantifying the erosion/sedimentation budget from tilted relaxation topographies. For MatIV, we also investigated the evolution of mean erosion rates and stream power erosion law exponents in 1D as a function of slope.;Our results indicate that MatIV satisfies most of the defined criteria. It deforms brittlely according to the linear Mohr-Coulomb failure criterion and localizes deformation along discrete faults. Its erosion pattern is characterized by realistic hillslope and channelized processes (slope diffusion, mass wasting, channel incision). During transport, eroded particles are sorted depending on their density and shape, which results in stratified alluvial deposits displaying lateral fades variations. To evaluate the degree of similitude between model and nature, we used a new experimental device that combines accretionary wedge deformation mechanisms and surface runoff erosion processes. Results indicate that MatIV succeeded in producing detailed morphological and sedi-mentological features (drainage basin, channel network, terrace, syntectonic alluvial fan). Geometric, kinematic and dynamic similarity criteria have been investigated to compare precisely model to nature. Although scaling is incomplete, it yields particularly informative orders of magnitude. With all these characteristics, MatIV appears as a very promising material to investigate experimentally a wide range of scientific questions dealing with relief dynamics and interactions between tectonics, erosion and sedimentation processes.
ISSN: 0040-1951

hal-00669904
https://hal.archives-ouvertes.fr/hal-00669904
DOI : 10.1016/j.tecto.2011.09.029

Éditeur(s) : HAL CCSD Coastal Education and Research Foundation
Résumé : The present work concerns cuspate spits: slightly symmetrical geomorphic features growing along the shoreline in shallow waters. We develop a new formulation for the dynamics of cuspate spits. Our approach relies on classical paradigms such as a conservation law to the shoreface scale and an explicit formula for alongshore sediment transport. We derive a non-linear diffusion equation and a fully explicit solution for the growth of cuspate spits. From this general expression, we found interesting applications to quantify shoreline dynamics in the presence of cuspate spits. In particular, we point out a simple method for the datation of a cuspate spit given a limited number of input parameters. Furthermore, we develop a method to quantify the mean alongshore diffusivity along a shoreline perturbed by well-defined cuspate spits of known sizes. Finally, we introduce a formal relationship between the geometric characteristics (amplitude, length) of cuspate spits, which reproduce the self-similarity of these geomorphic features.
ISSN: 0749-0208

hal-01234952
https://hal.archives-ouvertes.fr/hal-01234952
DOI : 10.2112/SI70-009.1

Éditeur(s) : HAL CCSD AGU and the Geochemical Society
Résumé : International audience
Based on global earthquake catalogs, the hypocenters, nodal planes, and seismic moments of worldwide subduction plate interface earthquakes were extracted for the period between 1900 and 2007. Assuming that the seismogenic zone coincides with the distribution of 5.5 <= M < 7 earthquakes, the subduction interface seismogenic zones were mapped for 80% of the trench systems and characterized with geometrical and mechanical parameters. Using this database, correlations were isolated between significant parameters to identify cause-effect relationships. Empirical laws obtained in previous studies were revisited in light of this more complete, accurate, and uniform description of the subduction interface seismogenic zone. The seismogenic zone was usually found to end in a fore-arc mantle, rather than at a Moho depth. The subduction velocity was the first-order controlling parameter for variations in the physical characteristics of plate interfaces, determining both the geometry and mechanical behavior. As such, the fast subduction zones and cold slabs were associated with large and steep plate interfaces, which, in turn, had large seismic rates. The subduction velocity could not account for the potential earthquake magnitude diversity that was observed along the trenches. Events with M-w >= 8.5 preferentially occurred in the vicinity of slab edges, where the upper plate was continental and the back-arc strain was neutral. This observation was interpreted in terms of compressive normal stresses along the plate interface. Large lateral ruptures should be promoted in neutral subduction zones due to moderate compressive stresses along the plate interface that allow the rupture to propagate laterally.
ISSN: 1525-2027

hal-00617681
https://hal.archives-ouvertes.fr/hal-00617681
https://hal.archives-ouvertes.fr/hal-00617681/document
https://hal.archives-ouvertes.fr/hal-00617681/file/heuretG32011.pdf
DOI : 10.1029/2010GC003230

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
Prediction of ice mass flow and associated dynamics is pivotal at a time of climate change. Ice flow is dominantly accommodated by the motion of crystal defects – the dislocations. In the specific case of ice, their observation is not always accessible by means of the classical tools such as X-ray diffraction or transmission electron microscopy (TEM). Part of the dislocation population, the geometrically necessary dislocations (GNDs) can nevertheless be constrained using crystal orientation measurements via electron backscattering diffraction (EBSD) associated with appropriate analyses based on the Nye (1950) approach. The present study uses the Weighted Burgers Vectors, a reduced formulation of the Nye theory that enables the characterization of GNDs. Applied to ice, this method documents, for the first time, the presence of dislocations with non-basal or Burgers vectors. These or dislocations represent up to of the GNDs observed in laboratory-deformed ice samples. Our findings offer a more complex and comprehensive picture of the key plasticity processes responsible for polycrystalline ice creep and provide better constraints on the constitutive mechanical laws implemented in ice sheet flow models used to predict the response of Earth ice masses to climate change.
ISSN: 0012-821X

hal-01685565
https://hal.archives-ouvertes.fr/hal-01685565
DOI : 10.1016/j.epsl.2017.06.020

Éditeur(s) : HAL CCSD
Résumé : The Lesser Antilles is an area of high volcanic and earthquake activity, characterized by a 1000 km convergence zone resulting from the Atlantic plate subduction under the Caribbean plate with a slow convergent motion (2 cm/year). With five years of available data, the CDSA data base presents a more homogeneous vision of Lesser Antilles arc seismicity and allows detecting low seismic activity zones, in the north near the Virgin Islands, and in the south between St-Lucia and Grenada. The accuracy improvements of location is used to better study the relationship between tectonic structures and seismicity, to better define the subduction slab geometry, and to analyse the spatial variations of the Gutenberg-Richter law b-value. Concerning the 21 november 2004 Les Saintes earthquake, EMS98 intensities in Les Saintes islands were evaluated from an individual request and hypocenter relocalisations of the Les Saintes earthquake and the biggest aftershock of 14 february 2005 were made using a method of master/slave in order to contrain the seismic source of the mainchock. As seismic hazard assessment depends from strong ground motion generated by earthquakes, the last part of this work concerns modeling accelerometric records of the Les Saintes earthquakes, combining a composite source model with an empirical Green Function technique. In our study, we used Les Saintes aftershocks as Empirical Green Function.
L'arc des Petites Antilles situé sur la bordure nord-est de la plaque Caraïbe, résulte d'un phénomène de subduction, les plaques américaines plongeant sous celle de la Caraïbe avec une vitesse de 2 cm/an. Les Antilles Françaises représentent la région française où le risque sismique est le plus important. Ce travail dont l'objectif est d'améliorer la connaissance de l'aléa sismique dans les Antilles Françaises, repose sur les données du Réseau Accélérométrique Permanent (RAP) et sur celles du « Centre de Données des Antilles Françaises ». L'analyse de ces données permet de mieux contraindre la sismicité de l'arc. Deux zones de très faible sismicité sont mises en évidence : au nord près des Iles Vierges et au sud entre Sainte-Lucie et Grenade. D'autres points sont aussi résolus : imagerie de la subduction le long de l'arc, relations entre la sismicité superficielle et la tectonique active, variations de la pente (b-value) de la loi de Gutenberg-Richter. Le séisme majeur du 21 novembre 2004 Mw=6.3 est au cœur des deux derniers chapitres. Plusieurs aspects y sont présentés : macrosismicité avec l'évaluation d'intensités EMS98 obtenues du dépouillement de formulaires individuels recueillis pour les Iles des Saintes, et relocalisation par la méthode de maître/esclave du choc principal et de sa plus forte réplique du 14 février 2005, de façon à mieux contraindre l'imagerie de la source du choc principal, étape primordiale pour la dernière partie portant sur la modélisation des signaux du choc principal des Saintes. Nous tentons dans cette dernière partie de modéliser les enregistrements de mouvements forts avec une approche semi-empirique en se basant sur un modèle stochastique large-bande et proposons l'utilisation de plusieurs Fonctions de Green Empiriques (FGE) sélectionnées parmi les répliques du séisme des Saintes.
https://tel.archives-ouvertes.fr/tel-00409021

tel-00409021
https://tel.archives-ouvertes.fr/tel-00409021
https://tel.archives-ouvertes.fr/tel-00409021/document
https://tel.archives-ouvertes.fr/tel-00409021/file/these_BengoubouMendy_2008.pdf

Éditeur(s) : HAL CCSD
Résumé : International audience
The present work concerns cuspate spits: slightly symmetrical geomorphic features growing along the shoreline in shallow waters. We develop a new formulation for the dynamics of cuspate spits. Our approach relies on classical paradigms such as a conservation law to the shoreface scale and an explicit formula for alongshore sediment transport. We derive a non-linear diffusion equation and a fully explicit solution for the growth of cuspate spits. From this general expression, we found interesting applications to quantify shoreline dynamics in the presence of cuspate spits. In particular, we point out a simple method for the datation of a cuspate spit given a limited number of input parameters. Furthermore, we develop a method to quantify the mean alongshore diffusivity along a shoreline perturbed by well-defined cuspate spits of known sizes. Finally, we introduce a formal relationship between the geometric characteristics (amplitude, length) of cuspate spits, which reproduce the self-similarity of these geomorphic features.
13th International Coastal Symposium
Durban, South Africa

hal-01006569
https://hal.archives-ouvertes.fr/hal-01006569
https://hal.archives-ouvertes.fr/hal-01006569/document
https://hal.archives-ouvertes.fr/hal-01006569/file/JCR_SI_70_009_Bouchette_et_al.pdf

Éditeur(s) : HAL CCSD Springer Verlag (Germany)
Résumé : International audience
We present an N=2 multiplet including a three-index antisymmetric tensor gauge potential, and describe it as a solution to the Bianchi identities for the associated fieldstrength superform, subject to some covariant constraints, in extended central charge superspace. We find that this solution is given in terms of an 8+8 tensor multiplet subject to an additional constraint. We give the transformation laws for the multiplet as well as invariant superfield and component field lagrangians, and mention possible couplings to other multiplets. We also allude to the relevance of the 3-form geometry for generic invariant supergravity actions.
ISSN: 1434-6044

hal-00769902
https://hal.univ-antilles.fr/hal-00769902
DOI : 10.1007/s100520050118

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
Numerical programs for simulating flow and reactive transport in porous media are essential tools for predicting reservoir properties changes triggered by CO2 underground injection. At reservoir scale, meshed models in which equations are solved assuming that constant macroscopic properties can be defined in each cells, are widely used. However, the parameterization of the dissolution-precipitation problem and of the feedback effects of these processes on the flow field is still challenging. The problem arises from the mismatch between the scales at which averaged parameters are defined in the meshed model and the scale at which chemical reactions occur and modify the pore network geometry. In this paper we investigate the links between the dissolution mechanisms that control the porosity changes and the related changes of the reactive surface area and of the permeability. First, the reactive surface area is computed from X-ray microtomography data obtained before and after a set of dissolution experiments of pure calcite rock samples using distinctly different brine-CO2 mixtures characterizing homogeneous to heterogeneous dissolution regimes. The results are used to validate the power law empirical model relating the reactive surface area to porosity proposed by Luquot and Gauze (2009). Second, we investigate the spatial distribution of the effective hydraulic radius and of the tortuosity, two structural parameters that control permeability, in order to explain the different porosity-permeability relationships observed for heterogeneous and homogeneous dissolution regimes. It is shown that the increase of permeability is due to the decrease of the tortuosity for homogeneous dissolution, whereas it is due to the combination of tortuosity decrease and hydraulic radius increase for heterogeneous dissolution. For the intermediate dissolution regime, identified to be the optimal regime for increasing permeability with small changes in porosity, the increase of permeability results from a large increase in the mean effective hydraulic radius of the sample.
ISSN: 0169-7722

hal-00617671
https://hal.archives-ouvertes.fr/hal-00617671
DOI : 10.1016/j.jconhyd.2010.07.004