Éditeur(s) : HAL CCSD American Geophysical Union
Résumé : International audience
We present a set of single-well injection withdrawal tracer tests in a paleoreef porous reservoir displaying important small-scale heterogeneity. An improved dual-packer probe was designed to perform dirac-like tracer injection and accurate downhole automatic measurements of the tracer concentration during the recovery phase. By flushing the tracer, at constant flow rate, for increasing time duration, we can probe distinctly different reservoir volumes and test the multiscale predictability of the (non-Fickian) dispersion models. First we describe the characteristics, from microscale to meter scale, of the reservoir rock. Second, the specificity of the tracer test setup and the results obtained using two different tracers and measurement methods (salinity-conductivity and fluorescent dye­optical measurement, respectively) are presented. All the tracer tests display strongly tailed breakthrough curves (BTC) consistent with diffusion in immobile regions. Conductivity results, measured over 3 orders of magnitude only, could have been easily interpreted by the conventional mobile-immobile (MIM) diffusive mass transfer model of asymptotic log-log slope of 2. However, the fluorescent dye sensor, which allows exploring much lower concentration values, shows that a change in the log-log slope occurs at larger time with an asymptotic value of 1.5, corresponding to the double-porosity model. These results suggest that the conventional, one-slope MIM transfer rate model is too simplistic to account for the real multiscale heterogeneity of the diffusion-dominant fraction of the reservoir.
ISSN: 0043-1397

insu-00373695
https://hal-insu.archives-ouvertes.fr/insu-00373695
https://hal-insu.archives-ouvertes.fr/insu-00373695/document
https://hal-insu.archives-ouvertes.fr/insu-00373695/file/Gouze_et_al-2008-Water_Resources_Research.pdf
DOI : 10.1029/2007WR006278

Éditeur(s) : HAL CCSD Elsevier Masson
Résumé : Contaminant migration in aquifers is one of the most debated issues in hydrogeology, as most experimental results display large deviations from the standard (asymptotic) Fickian dispersion theories. Multi-scale investigation and high-resolution sensors are required to determine the origin of non-asymptotic dispersion and validate models. For this, a set of multi-scale Single-Well Injection-Withdrawal (SWIW) tracer tests using a new dual-packer probe CoFIS, including a high resolution optical sensor TELog, are presented. When compared to standard techniques such as salinity measurements, it is shown that high-resolution optical measurements allow an improved characterization of the long-lasting non-asymptotic dispersion mechanisms.
ISSN: 1631-0713

hal-00445250
https://hal.archives-ouvertes.fr/hal-00445250
DOI : 10.1016/j.crte.2009.07.012

Éditeur(s) : Inter-Research
Résumé : The widespread use of Agent Orange (a mixture of phenoxyl herbicides) over Southern Vietnam by US Forces led to the decimation of mangrove forests in the Mekong Delta. Mangrove trees Avicennia alba were sampled across the Mekong Delta; their age was assessed using models based on internode growth and samples were genotyped for 6 microsatellite loci. The evolution of genetic diversity over time elapsed since local extinction was reconstructed and compared with the genetic diversity of an unaffected population from Thailand, The results show that genetic diversity of the A. alba population is still increasing in the Mekong Delta 3 decades after the end of the Vietnam War, but is reaching an asymptotic level that is comparable to the adjacent non-affected population of Thailand. This might be a sign of genetic recovery, but may also reveal a limitation, either of genetic enrichment due to current predominance of auto-recruitment or of demographic increase due to intraspecific competition in this pioneer species. In any case, these results, although encouraging, demonstrate that genetic recovery after complete or almost complete population depletion continues over a longer time-scale than apparent demographic recovery.
Marine Ecology Progress Series (0171-8630) (Inter-Research), 2009-09 , Vol. 390 , P. 129-135

Droits : Inter-Research 2009
http://archimer.ifremer.fr/doc/2009/publication-6898.pdf
DOI:10.3354/meps08183
http://archimer.ifremer.fr/doc/00000/6898/

Éditeur(s) : HAL CCSD Springer Verlag
Résumé : International audience
Starting from a locally convex metrisable topological space and from any asymptotic scale, we construct a generalized extension of this space. To those extensions, we associate Hausdorff topologies. We introduce the notion of a temperate map, with respect to a given asymptotic scale, between two locally convex metrisable semi-normed spaces. We show that such mappings extend in a canonical way to mappings between the respective generalized extensions. We give an application to nonlinear Dirichlet boundary value problems with singular data in the framework of generalized extensions
ISSN: 0026-9255

hal-01529549
https://hal.univ-antilles.fr/hal-01529549

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
Résumé : International audience
Rencontres européennes d'Analyse Non Standard,
Luminy - Marseille, France

hal-01535423
https://hal.univ-antilles.fr/hal-01535423

Éditeur(s) : HAL CCSD EDP Sciences
Résumé : International audience
Aggregation patterns are often visually detected in sets of location data. These clusters may be the result of interesting dynamics or the effect of pure randomness. We build an asymptotically Gaussian test for the hypothesis of randomness corresponding to a homogeneous Poisson point process. We first compute the exact first and second moment of the Ripley K-statistic under the homogeneous Poisson point process model. Then we prove the asymptotic normality of a vector of such statistics for different scales and compute its covariance matrix. From these results, we derive a test statistic that is chi-square distributed. By a Monte-Carlo study, we check that the test is numerically tractable even for large data sets and also correct when only a hundred of points are observed
ISSN: 1292-8100

hal-01502640
https://hal-agroparistech.archives-ouvertes.fr/hal-01502640
DOI : 10.1051/ps/2012027

Éditeur(s) : HAL CCSD
Résumé : International audience
generalized functions 1996,
Novi Sad, Serbia

hal-01535417
https://hal.univ-antilles.fr/hal-01535417

Éditeur(s) : HAL CCSD
Résumé : The geological storage of CO 2 is considered as one of the solutions to the problem of global warming. The most possible scenarios of geological behavior of soil in the long term conditions has to be precisely defined to avoid catastrophic damages in the future. Chemical properties of saline water in the aquifer after the CO 2 injection becomes more acidic with time. Therefore, chemical degradation of rock occurs, which leads to modifications of its mechanical properties (chemo-mechanical coupling) [1]. In this paper an incremental model of chemo-mechanical coupling using homogenization approach (asymptotic expansion method [2,3]) is proposed. The paper is focused on the numerical computations for the X-ray tomography image of carbonate rock microstructure [4]. The chemical degradation of the microstructure is obtained as a homogeneous dissolution in each direction (Fig.1. – Fig.2.) For every porosity state numerical computations to obtain full, orthotropic elasticity tensor are performed. Therefore, the degradations functions for all components of the rigidity tensor were defined (Fig.3.). Moreover, results of numerical calculations of diffusion, tortuosity and permeability tensors are presented [5,6]. The link between geometrical properties and mechanical and transport parameters are discussed. The numerical analysis of the carbonate rock sample in long term conditions shows the increase of porosity and associated mechanical weakening of the rock. Moreover, the increase of diffusion, tortuosity and permeability tensors elements with time were observed. Finally, the solution of the one-dimensional macroscopic problem of soil settlement due to chemical dissolution of rock at constant load is presented. The method is universal, in the sense that the non-dimensional time scale is used.
ALERT Workshop 2013
Aussois, France

hal-01103175
https://hal.archives-ouvertes.fr/hal-01103175

Éditeur(s) : HAL CCSD American Geophysical Union
Résumé : International audience
We aim at testing and validating a mobile-immobile mass transfer model from a set of single-well injection withdrawal tracer tests in a heterogeneous porous aquifer. By varying the duration of the injection phase, different volumes of aquifer are investigated by the tracer. Hence, we focus the transport model validation not only on reproducing a single breakthrough curve (BTC) but also on the model's capacity to predict the amount of mixing as a function of the volume visited by the tracer. All the BTCs are strongly asymmetric, as expected when dispersion is controlled by diffusive mass transfers between the mobile water and the immobile water part of the porosity. However, the BTC cannot be modeled by a conventional mobile-immobile mass transfer model with a simple power law memory function. To account for that, we implement a continuous time random walk model in which the transition time distribution y (t), which is related to the excursion time probability of the tracer in the immobile domain, is a dual-slope power law distribution. The model best fits the BTC data set with a transitional regime controlled by y(t) t2 and an asymptotic regime characteristic of the conventional double-porosity model with y(t) t1.5 . This work emphasizes that high-resolution concentration measurement and multiple-scale tracer tests are required for assessing solute dispersion models in heterogeneous reservoirs and for subsequently obtaining reliable predictions.
ISSN: 0043-1397

insu-00373698
https://hal-insu.archives-ouvertes.fr/insu-00373698
https://hal-insu.archives-ouvertes.fr/insu-00373698/document
https://hal-insu.archives-ouvertes.fr/insu-00373698/file/Borgne_et_al-2008-Water_Resources_Research.pdf
DOI : 10.1029/2007WR006279

Éditeur(s) : HAL CCSD
Résumé : International audience
Given a topological R-module or algebra E and an asymptotic scale MR Λ, we define a natural M-extended topology on the sequence space E Λ, and the M-extension of E as the Hausdorff space associated with the subspace of sequences for which multiplication is continuous with respect to this topology. Colombeau's generalized functions and similar constructions are obtained as special cases, but this new approach also allows the iteration of the construction, which was not possible with previously existing theories. We use only the topology, i.e. neigbourhoods of zero, but not its explicit definition in terms of seminorms, inductive or projective limits etc., which is particularly useful in non-metrizable spaces. Many ideas commonly used in generalized function spaces (functoriality, association, sheaf structure, algebraic analysis, ...) can be applied to a large extent; but reasoning on a category-theoretic level allows the establishment of several results so far only known for particular cases, to the whole class of such spaces.
Integral Transforms and Special Functions
Bedlewo, Poland

hal-00761666
https://hal.univ-antilles.fr/hal-00761666
DOI : 10.1080/10652460802565040

Éditeur(s) : HAL CCSD
Résumé : International audience
Rencontres européennes d'Analyse Non Standard
Luminy - Marseille, France

hal-01535424
https://hal.univ-antilles.fr/hal-01535424

Éditeur(s) : HAL CCSD Taylor & Francis
Résumé : International audience
ISSN: 1065-2469

hal-01529516
https://hal.univ-antilles.fr/hal-01529516