Selection methods regulate evolution of cooperation in digital evolution.

A key, yet often neglected, component of digital evolution and evolutionary models is the 'selection method' which assigns fitness (number of offspring) to individuals based on their performance scores (efficiency in performing tasks). Here, we study with formal analysis and numerical experiments the evolution of cooperation under the five most common selection methods (proportionate, rank, truncation-proportionate, truncation-uniform and tournament). We consider related individuals engaging in a Prisoner's Dilemma game where individuals can either cooperate or defect. A cooperator pays a cost, whereas its partner receives a benefit, which affect their performance scores. These performance scores are translated into fitness by one of the five selection methods. We show that cooperation is positively associated with the relatedness between individuals under all selection methods. By contrast, the change in the performance benefit of cooperation affects the populations' average level of cooperation only under the proportionate methods. We also demonstrate that the truncation and tournament methods may introduce negative frequency-dependence and lead to the evolution of polymorphic populations. Using the example of the evolution of cooperation, we show that the choice of selection method, though it is often marginalized, can considerably affect the evolutionary dynamics.

On the problematic of reserving and stochastic loss models

Abstract Traditionally, the common reserving methods used by the non-life actuaries are based on the assumption that future claims are going to behave in the same way as they did in the past. There are two main sources of variability in the processus of development of the claims: the variability of the speed with which the claims are settled and the variability between the severity of the claims from different accident years. High changes in these processes will generate distortions in the estimation of the claims reserves. The main objective of this thesis is to provide an indicator which firstly identifies and quantifies these two influences and secondly to determine which model is adequate for a specific situation. Two stochastic models were analysed and the predictive distributions of the future claims were obtained. The main advantage of the stochastic models is that they provide measures of variability of the reserves estimates. The first model (PDM) combines one conjugate family Dirichlet - Multinomial with the Poisson distribution. The second model (NBDM) improves the first one by combining two conjugate families Poisson -Gamma (for distribution of the ultimate amounts) and Dirichlet Multinomial (for distribution of the incremental claims payments). It was found that the second model allows to find the speed variability in the reporting process and development of the claims severity as function of two above mentioned distributions' parameters. These are the shape parameter of the Gamma distribution and the Dirichlet parameter. Depending on the relation between them we can decide on the adequacy of the claims reserve estimation method. The parameters have been estimated by the Methods of Moments and Maximum Likelihood. The results were tested using chosen simulation data and then using real data originating from the three lines of business: Property/Casualty, General Liability, and Accident Insurance. These data include different developments and specificities. The outcome of the thesis shows that when the Dirichlet parameter is greater than the shape parameter of the Gamma, resulting in a model with positive correlation between the past and future claims payments, suggests the Chain-Ladder method as appropriate for the claims reserve estimation. In terms of claims reserves, if the cumulated payments are high the positive correlation will imply high expectations for the future payments resulting in high claims reserves estimates. The negative correlation appears when the Dirichlet parameter is lower than the shape parameter of the Gamma, meaning low expected future payments for the same high observed cumulated payments. This corresponds to the situation when claims are reported rapidly and fewer claims remain expected subsequently. The extreme case appears in the situation when all claims are reported at the same time leading to expectations for the future payments of zero or equal to the aggregated amount of the ultimate paid claims. For this latter case, the Chain-Ladder is not recommended.

Data-driven clustering : new methods and applications

Abstract : This work is concerned with the development and application of novel unsupervised learning methods, having in mind two target applications: the analysis of forensic case data and the classification of remote sensing images. First, a method based on a symbolic optimization of the inter-sample distance measure is proposed to improve the flexibility of spectral clustering algorithms, and applied to the problem of forensic case data. This distance is optimized using a loss function related to the preservation of neighborhood structure between the input space and the space of principal components, and solutions are found using genetic programming. Results are compared to a variety of state-of--the-art clustering algorithms. Subsequently, a new large-scale clustering method based on a joint optimization of feature extraction and classification is proposed and applied to various databases, including two hyperspectral remote sensing images. The algorithm makes uses of a functional model (e.g., a neural network) for clustering which is trained by stochastic gradient descent. Results indicate that such a technique can easily scale to huge databases, can avoid the so-called out-of-sample problem, and can compete with or even outperform existing clustering algorithms on both artificial data and real remote sensing images. This is verified on small databases as well as very large problems. Résumé : Ce travail de recherche porte sur le développement et l'application de méthodes d'apprentissage dites non supervisées. Les applications visées par ces méthodes sont l'analyse de données forensiques et la classification d'images hyperspectrales en télédétection. Dans un premier temps, une méthodologie de classification non supervisée fondée sur l'optimisation symbolique d'une mesure de distance inter-échantillons est proposée. Cette mesure est obtenue en optimisant une fonction de coût reliée à la préservation de la structure de voisinage d'un point entre l'espace des variables initiales et l'espace des composantes principales. Cette méthode est appliquée à l'analyse de données forensiques et comparée à un éventail de méthodes déjà existantes. En second lieu, une méthode fondée sur une optimisation conjointe des tâches de sélection de variables et de classification est implémentée dans un réseau de neurones et appliquée à diverses bases de données, dont deux images hyperspectrales. Le réseau de neurones est entraîné à l'aide d'un algorithme de gradient stochastique, ce qui rend cette technique applicable à des images de très haute résolution. Les résultats de l'application de cette dernière montrent que l'utilisation d'une telle technique permet de classifier de très grandes bases de données sans difficulté et donne des résultats avantageusement comparables aux méthodes existantes.

Prothèses totales de genoux. Analyse clinique et numérique des micromouvements de l'implant tibial [Total knee prosthesis. Clinical and numerical study of micromovements of the tibial implant].

INTRODUCTION: The importance of the micromovements in the mechanism of aseptic loosening is clinically difficult to evaluate. To complete the analysis of a series of total knee arthroplasties (TKA), we used a tridimensional numerical model to study the micromovements of the tibial implant. MATERIAL AND METHODS: Fifty one patients (with 57 cemented Porous Coated Anatomic TKAs) were reviewed (mean follow-up 4.5 year). Radiolucency at the tibial bone-cement interface was sought on the AP radiographs and divided in 7 areas. The distribution of the radiolucency was then correlated with the axis of the lower limb as measured on the orthoradiograms. The tridimensional numerical model is based on the finite element method. It allowed the measurement of the cemented prosthetic tibial implant's displacements and the micromovements generated at bone-ciment interface. A total load (2000 Newton) was applied at first vertically and asymetrically on the tibial plateau, thereby simulating an axial deviation of the lower limbs. The vector's posterior inclination then permitted the addition of a tangential component to the axial load. This type of effort is generated by complex biomechanical phenomena such as knee flexion. RESULTS: 81 per cent of the 57 knees had a radiolucent line of at least 1 mm, at one or more of the tibial cement-epiphysis jonctional areas. The distribution of these lucent lines showed that they came out more frequently at the periphery of the implant. The lucent lines appeared most often under the unloaded margin of the tibial plateau, when axial deviation of lower limbs was present. Numerical simulations showed that asymetrical loading on the tibial plateau induced a subsidence of the loaded margin (0-100 microns) and lifting off at the opposite border (0-70 microns). The postero-anterior tangential component induced an anterior displacement of the tibial implant (160-220 microns), and horizontal micromovements with non homogenous distribution at the bone-ciment interface (28-54 microns). DISCUSSION: Comparison of clinical and numerical results showed a relation between the development of radiolucent lines and the unloading of the tibial implant's margin. The deleterious effect of lower limbs' axial deviation is thereby proven. The irregular distribution of lucent lines under the tibial plateau was similar of the micromovements' repartition at the bone-cement interface when tangential forces were present. A causative relation between the two phenomenaes could not however be established. Numerical simulation is a truly useful method of study; it permits to calculate micromovements which are relative, non homogenous and of very low amplitude. However, comparative clinical studies remain as essential to ensure the credibility of results.

Kernel-based Mapping of Meteorological Fields in Complex Orography

Due to the advances in sensor networks and remote sensing technologies, the acquisition and storage rates of meteorological and climatological data increases every day and ask for novel and efficient processing algorithms. A fundamental problem of data analysis and modeling is the spatial prediction of meteorological variables in complex orography, which serves among others to extended climatological analyses, for the assimilation of data into numerical weather prediction models, for preparing inputs to hydrological models and for real time monitoring and short-term forecasting of weather.In this thesis, a new framework for spatial estimation is proposed by taking advantage of a class of algorithms emerging from the statistical learning theory. Nonparametric kernel-based methods for nonlinear data classification, regression and target detection, known as support vector machines (SVM), are adapted for mapping of meteorological variables in complex orography.With the advent of high resolution digital elevation models, the field of spatial prediction met new horizons. In fact, by exploiting image processing tools along with physical heuristics, an incredible number of terrain features which account for the topographic conditions at multiple spatial scales can be extracted. Such features are highly relevant for the mapping of meteorological variables because they control a considerable part of the spatial variability of meteorological fields in the complex Alpine orography. For instance, patterns of orographic rainfall, wind speed and cold air pools are known to be correlated with particular terrain forms, e.g. convex/concave surfaces and upwind sides of mountain slopes.Kernel-based methods are employed to learn the nonlinear statistical dependence which links the multidimensional space of geographical and topographic explanatory variables to the variable of interest, that is the wind speed as measured at the weather stations or the occurrence of orographic rainfall patterns as extracted from sequences of radar images. Compared to low dimensional models integrating only the geographical coordinates, the proposed framework opens a way to regionalize meteorological variables which are multidimensional in nature and rarely show spatial auto-correlation in the original space making the use of classical geostatistics tangled.The challenges which are explored during the thesis are manifolds. First, the complexity of models is optimized to impose appropriate smoothness properties and reduce the impact of noisy measurements. Secondly, a multiple kernel extension of SVM is considered to select the multiscale features which explain most of the spatial variability of wind speed. Then, SVM target detection methods are implemented to describe the orographic conditions which cause persistent and stationary rainfall patterns. Finally, the optimal splitting of the data is studied to estimate realistic performances and confidence intervals characterizing the uncertainty of predictions.The resulting maps of average wind speeds find applications within renewable resources assessment and opens a route to decrease the temporal scale of analysis to meet hydrological requirements. Furthermore, the maps depicting the susceptibility to orographic rainfall enhancement can be used to improve current radar-based quantitative precipitation estimation and forecasting systems and to generate stochastic ensembles of precipitation fields conditioned upon the orography.

Integrated application of geochemical and geophysical methods for hydrogeological impact assessment for tunneling in fractured rock

The interaction of tunneling with groundwater is a problem both from an environmental and an engineering point of view. In fact, tunnel drilling may cause a drawdown of piezometric levels and water inflows into tunnels that may cause problems during excavation of the tunnel. While the influence of tunneling on the regional groundwater systems may be adequately predicted in porous media using analytical solutions, such an approach is difficult to apply in fractured rocks. Numerical solutions are preferable and various conceptual approaches have been proposed to describe and model groundwater flow through fractured rock masses, ranging from equivalent continuum models to discrete fracture network simulation models. However, their application needs many preliminary investigations on the behavior of the groundwater system based on hydrochemical and structural data. To study large scale flow systems in fractured rocks of mountainous terrains, a comprehensive study was conducted in southern Switzerland, using as case studies two infrastructures actually under construction: (i) the Monte Ceneri base railway tunnel (Ticino), and the (ii) San Fedele highway tunnel (Roveredo, Graubiinden). The chosen approach in this study combines the temporal and spatial variation of geochemical and geophysical measurements. About 60 localities from both surface and underlying tunnels were temporarily and spatially monitored during more than one year. At first, the project was focused on the collection of hydrochemical and structural data. A number of springs, selected in the area surrounding the infrastructures, were monitored for discharge, electric conductivity, pH, and temperature. Water samples (springs, tunnel inflows and rains) were taken for isotopic analysis; in particular the stable isotope composition (δ2Η, δ180 values) can reflect the origin of the water, because of spatial (recharge altitude, topography, etc.) and temporal (seasonal) effects on precipitation which in turn strongly influence the isotopic composition of groundwater. Tunnel inflows in the accessible parts of the tunnels were also sampled and, if possible, monitored with time. Noble-gas concentrations and their isotope ratios were used in selected locations to better understand the origin and the circulation of the groundwater. In addition, electrical resistivity and VLF-type electromagnetic surveys were performed to identify water bearing fractures and/or weathered areas that could be intersected at depth during tunnel construction. The main goal of this work was to demonstrate that these hydrogeological data and geophysical methods, combined with structural and hydrogeological information, can be successfully used in order to develop hydrogeological conceptual models of the groundwater flow in regions to be exploited for tunnels. The main results of the project are: (i) to have successfully tested the application of electrical resistivity and VLF-electromagnetic surveys to asses water-bearing zones during tunnel drilling; (ii) to have verified the usefulness of noble gas, major ion and stable isotope compositions as proxies for the detection of faults and to understand the origin of the groundwater and its flow regimes (direct rain water infiltration or groundwater of long residence time); and (iii) to have convincingly tested the combined application of a geochemical and geophysical approach to assess and predict the vulnerability of springs to tunnel drilling. - L'interférence entre eaux souterraines et des tunnels pose des problèmes environnementaux et de génie civile. En fait, la construction d'un tunnel peut faire abaisser le niveau des nappes piézométriques et faire infiltrer de l'eau dans le tunnel et ainsi créer des problème pendant l'excavation. Alors que l'influence de la construction d'un tunnel sur la circulation régionale de l'eau souterraine dans des milieux poreux peut être prédite relativement facilement par des solution analytiques de modèles, ceci devient difficile dans des milieux fissurés. Dans ce cas-là, des solutions numériques sont préférables et plusieurs approches conceptuelles ont été proposées pour décrire et modéliser la circulation d'eau souterraine à travers les roches fissurées, en allant de modèles d'équivalence continue à des modèles de simulation de réseaux de fissures discrètes. Par contre, leur application demande des investigations importantes concernant le comportement du système d'eau souterraine basées sur des données hydrochimiques et structurales. Dans le but d'étudier des grands systèmes de circulation d'eau souterraine dans une région de montagnes, une étude complète a été fait en Suisse italienne, basée sur deux grandes infrastructures actuellement en construction: (i) Le tunnel ferroviaire de base du Monte Ceneri (Tessin) et (ii) le tunnel routière de San Fedele (Roveredo, Grisons). L'approche choisie dans cette étude est la combinaison de variations temporelles et spatiales des mesures géochimiques et géophysiques. Environs 60 localités situées à la surface ainsi que dans les tunnels soujacents ont été suiviès du point de vue temporel et spatial pendant plus de un an. Dans un premier temps le projet se focalisait sur la collecte de données hydrochimiques et structurales. Un certain nombre de sources, sélectionnées dans les environs des infrastructures étudiées ont été suivies pour le débit, la conductivité électrique, le pH et la température. De l'eau (sources, infiltration d'eau de tunnel et pluie) a été échantillonnés pour des analyses isotopiques; ce sont surtout les isotopes stables (δ2Η, δ180) qui peuvent indiquer l'origine d'une eaux, à cause de la dépendance d'effets spatiaux (altitude de recharge, topographie etc.) ainsi que temporels (saisonaux) sur les précipitations météoriques , qui de suite influencent ainsi la composition isotopique de l'eau souterraine. Les infiltrations d'eau dans les tunnels dans les parties accessibles ont également été échantillonnées et si possible suivies au cours du temps. La concentration de gaz nobles et leurs rapports isotopiques ont également été utilisées pour quelques localités pour mieux comprendre l'origine et la circulation de l'eau souterraine. En plus, des campagnes de mesures de la résistivité électrique et électromagnétique de type VLF ont été menées afin d'identifier des zone de fractures ou d'altération qui pourraient interférer avec les tunnels en profondeur pendant la construction. Le but principal de cette étude était de démontrer que ces données hydrogéologiques et géophysiques peuvent être utilisées avec succès pour développer des modèles hydrogéologiques conceptionels de tunnels. Les résultats principaux de ce travail sont : i) d'avoir testé avec succès l'application de méthodes de la tomographie électrique et des campagnes de mesures électromagnétiques de type VLF afin de trouver des zones riches en eau pendant l'excavation d'un tunnel ; ii) d'avoir prouvé l'utilité des gaz nobles, des analyses ioniques et d'isotopes stables pour déterminer l'origine de l'eau infiltrée (de la pluie par le haut ou ascendant de l'eau remontant des profondeurs) et leur flux et pour déterminer la position de failles ; et iii) d'avoir testé d'une manière convainquant l'application combinée de méthodes géochimiques et géophysiques pour juger et prédire la vulnérabilité de sources lors de la construction de tunnels. - L'interazione dei tunnel con il circuito idrico sotterraneo costituisce un problema sia dal punto di vista ambientale che ingegneristico. Lo scavo di un tunnel puô infatti causare abbassamenti dei livelli piezometrici, inoltre le venute d'acqua in galleria sono un notevole problema sia in fase costruttiva che di esercizio. Nel caso di acquiferi in materiale sciolto, l'influenza dello scavo di un tunnel sul circuito idrico sotterraneo, in genere, puô essere adeguatamente predetta attraverso l'applicazione di soluzioni analitiche; al contrario un approccio di questo tipo appare inadeguato nel caso di scavo in roccia. Per gli ammassi rocciosi fratturati sono piuttosto preferibili soluzioni numeriche e, a tal proposito, sono stati proposti diversi approcci concettuali; nella fattispecie l'ammasso roccioso puô essere modellato come un mezzo discreto ο continuo équivalente. Tuttavia, una corretta applicazione di qualsiasi modello numerico richiede necessariamente indagini preliminari sul comportamento del sistema idrico sotterraneo basate su dati idrogeochimici e geologico strutturali. Per approfondire il tema dell'idrogeologia in ammassi rocciosi fratturati tipici di ambienti montani, è stato condotto uno studio multidisciplinare nel sud della Svizzera sfruttando come casi studio due infrastrutture attualmente in costruzione: (i) il tunnel di base del Monte Ceneri (canton Ticino) e (ii) il tunnel autostradale di San Fedele (Roveredo, canton Grigioni). L'approccio di studio scelto ha cercato di integrare misure idrogeochimiche sulla qualité e quantité delle acque e indagini geofisiche. Nella fattispecie sono state campionate le acque in circa 60 punti spazialmente distribuiti sia in superficie che in sotterraneo; laddove possibile il monitoraggio si è temporalmente prolungato per più di un anno. In una prima fase, il progetto di ricerca si è concentrato sull'acquisizione dati. Diverse sorgenti, selezionate nelle aree di possibile influenza attorno allé infrastrutture esaminate, sono state monitorate per quel che concerne i parametri fisico-chimici: portata, conduttività elettrica, pH e temperatura. Campioni d'acqua sono stati prelevati mensilmente su sorgenti, venute d'acqua e precipitazioni, per analisi isotopiche; nella fattispecie, la composizione in isotopi stabili (δ2Η, δ180) tende a riflettere l'origine delle acque, in quanto, variazioni sia spaziali (altitudine di ricarica, topografia, etc.) che temporali (variazioni stagionali) della composizione isotopica delle precipitazioni influenzano anche le acque sotterranee. Laddove possibile, sono state campionate le venute d'acqua in galleria sia puntualmente che al variare del tempo. Le concentrazioni dei gas nobili disciolti nell'acqua e i loro rapporti isotopici sono stati altresi utilizzati in alcuni casi specifici per meglio spiegare l'origine delle acque e le tipologie di circuiti idrici sotterranei. Inoltre, diverse indagini geofisiche di resistività elettrica ed elettromagnetiche a bassissima frequenza (VLF) sono state condotte al fine di individuare le acque sotterranee circolanti attraverso fratture dell'ammasso roccioso. Principale obiettivo di questo lavoro è stato dimostrare come misure idrogeochimiche ed indagini geofisiche possano essere integrate alio scopo di sviluppare opportuni modelli idrogeologici concettuali utili per lo scavo di opere sotterranee. I principali risultati ottenuti al termine di questa ricerca sono stati: (i) aver testato con successo indagini geofisiche (ERT e VLF-EM) per l'individuazione di acque sotterranee circolanti attraverso fratture dell'ammasso roccioso e che possano essere causa di venute d'acqua in galleria durante lo scavo di tunnel; (ii) aver provato l'utilità di analisi su gas nobili, ioni maggiori e isotopi stabili per l'individuazione di faglie e per comprendere l'origine delle acque sotterranee (acque di recente infiltrazione ο provenienti da circolazioni profonde); (iii) aver testato in maniera convincente l'integrazione delle indagini geofisiche e di misure geochimiche per la valutazione della vulnérabilité delle sorgenti durante lo scavo di nuovi tunnel. - "La NLFA (Nouvelle Ligne Ferroviaire à travers les Alpes) axe du Saint-Gothard est le plus important projet de construction de Suisse. En bâtissant la nouvelle ligne du Saint-Gothard, la Suisse réalise un des plus grands projets de protection de l'environnement d'Europe". Cette phrase, qu'on lit comme présentation du projet Alptransit est particulièrement éloquente pour expliquer l'utilité des nouvelles lignes ferroviaires transeuropéens pour le développement durable. Toutefois, comme toutes grandes infrastructures, la construction de nouveaux tunnels ont des impacts inévitables sur l'environnement. En particulier, le possible drainage des eaux souterraines réalisées par le tunnel peut provoquer un abaissement du niveau des nappes piézométriques. De plus, l'écoulement de l'eau à l'intérieur du tunnel, conduit souvent à des problèmes d'ingénierie. Par exemple, d'importantes infiltrations d'eau dans le tunnel peuvent compliquer les phases d'excavation, provoquant un retard dans l'avancement et dans le pire des cas, peuvent mettre en danger la sécurité des travailleurs. Enfin, l'infiltration d'eau peut être un gros problème pendant le fonctionnement du tunnel. Du point de vue de la science, avoir accès à des infrastructures souterraines représente une occasion unique d'obtenir des informations géologiques en profondeur et pour échantillonner des eaux autrement inaccessibles. Dans ce travail, nous avons utilisé une approche pluridisciplinaire qui intègre des mesures d'étude hydrogéochimiques effectués sur les eaux de surface et des investigations géophysiques indirects, tels que la tomographic de résistivité électrique (TRE) et les mesures électromagnétiques de type VLF. L'étude complète a été fait en Suisse italienne, basée sur deux grandes infrastructures actuellement en construction, qui sont le tunnel ferroviaire de base du Monte Ceneri, une partie du susmentionné projet Alptransit, situé entièrement dans le canton Tessin, et le tunnel routière de San Fedele, situé a Roveredo dans le canton des Grisons. Le principal objectif était de montrer comment il était possible d'intégrer les deux approches, géophysiques et géochimiques, afin de répondre à la question de ce que pourraient être les effets possibles dû au drainage causés par les travaux souterrains. L'accès aux galeries ci-dessus a permis une validation adéquate des enquêtes menées confirmant, dans chaque cas, les hypothèses proposées. A cette fin, nous avons fait environ 50 profils géophysiques (28 imageries électrique bidimensionnels et 23 électromagnétiques) dans les zones de possible influence par le tunnel, dans le but d'identifier les fractures et les discontinuités dans lesquelles l'eau souterraine peut circuler. De plus, des eaux ont été échantillonnés dans 60 localités situées la surface ainsi que dans les tunnels subjacents, le suivi mensuelle a duré plus d'un an. Nous avons mesurés tous les principaux paramètres physiques et chimiques: débit, conductivité électrique, pH et température. De plus, des échantillons d'eaux ont été prélevés pour l'analyse mensuelle des isotopes stables de l'hydrogène et de l'oxygène (δ2Η, δ180). Avec ces analyses, ainsi que par la mesure des concentrations des gaz rares dissous dans les eaux et de leurs rapports isotopiques que nous avons effectués dans certains cas spécifiques, il était possible d'expliquer l'origine des différents eaux souterraines, les divers modes de recharge des nappes souterraines, la présence de possible phénomènes de mélange et, en général, de mieux expliquer les circulations d'eaux dans le sous-sol. Le travail, même en constituant qu'une réponse partielle à une question très complexe, a permis d'atteindre certains importants objectifs. D'abord, nous avons testé avec succès l'applicabilité des méthodes géophysiques indirectes (TRE et électromagnétiques de type VLF) pour prédire la présence d'eaux souterraines dans le sous-sol des massifs rocheux. De plus, nous avons démontré l'utilité de l'analyse des gaz rares, des isotopes stables et de l'analyses des ions majeurs pour la détection de failles et pour comprendre l'origine des eaux souterraines (eau de pluie par le haut ou eau remontant des profondeurs). En conclusion, avec cette recherche, on a montré que l'intégration des ces informations (géophysiques et géochimiques) permet le développement de modèles conceptuels appropriés, qui permettant d'expliquer comment l'eau souterraine circule. Ces modèles permettent de prévoir les infiltrations d'eau dans les tunnels et de prédire la vulnérabilité de sources et des autres ressources en eau lors de construction de tunnels.

Direct numerical simulations of interface dynamics to link capillary pressure and total surface energy

The flow of two immiscible fluids through a porous medium depends on the complex interplay between gravity, capillarity, and viscous forces. The interaction between these forces and the geometry of the medium gives rise to a variety of complex flow regimes that are difficult to describe using continuum models. Although a number of pore-scale models have been employed, a careful investigation of the macroscopic effects of pore-scale processes requires methods based on conservation principles in order to reduce the number of modeling assumptions. In this work we perform direct numerical simulations of drainage by solving Navier-Stokes equations in the pore space and employing the Volume Of Fluid (VOF) method to track the evolution of the fluid-fluid interface. After demonstrating that the method is able to deal with large viscosity contrasts and model the transition from stable flow to viscous fingering, we focus on the macroscopic capillary pressure and we compare different definitions of this quantity under quasi-static and dynamic conditions. We show that the difference between the intrinsic phase-average pressures, which is commonly used as definition of Darcy-scale capillary pressure, is subject to several limitations and it is not accurate in presence of viscous effects or trapping. In contrast, a definition based on the variation of the total surface energy provides an accurate estimate of the macroscopic capillary pressure. This definition, which links the capillary pressure to its physical origin, allows a better separation of viscous effects and does not depend on the presence of trapped fluid clusters.

Stochastic inversion of tracer test and electrical geophysical data to estimate hydraulic conductivities.

Quantifying the spatial configuration of hydraulic conductivity (K) in heterogeneous geological environments is essential for accurate predictions of contaminant transport, but is difficult because of the inherent limitations in resolution and coverage associated with traditional hydrological measurements. To address this issue, we consider crosshole and surface-based electrical resistivity geophysical measurements, collected in time during a saline tracer experiment. We use a Bayesian Markov-chain-Monte-Carlo (McMC) methodology to jointly invert the dynamic resistivity data, together with borehole tracer concentration data, to generate multiple posterior realizations of K that are consistent with all available information. We do this within a coupled inversion framework, whereby the geophysical and hydrological forward models are linked through an uncertain relationship between electrical resistivity and concentration. To minimize computational expense, a facies-based subsurface parameterization is developed. The Bayesian-McMC methodology allows us to explore the potential benefits of including the geophysical data into the inverse problem by examining their effect on our ability to identify fast flowpaths in the subsurface, and their impact on hydrological prediction uncertainty. Using a complex, geostatistically generated, two-dimensional numerical example representative of a fluvial environment, we demonstrate that flow model calibration is improved and prediction error is decreased when the electrical resistivity data are included. The worth of the geophysical data is found to be greatest for long spatial correlation lengths of subsurface heterogeneity with respect to wellbore separation, where flow and transport are largely controlled by highly connected flowpaths.

Statistical methods for river runoff prediction

Methods used to analyze one type of nonstationary stochastic processes?the periodically correlated process?are considered. Two methods of one-step-forward prediction of periodically correlated time series are examined. One-step-forward predictions made in accordance with an autoregression model and a model of an artificial neural network with one latent neuron layer and with an adaptation mechanism of network parameters in a moving time window were compared in terms of efficiency. The comparison showed that, in the case of prediction for one time step for time series of mean monthly water discharge, the simpler autoregression model is more efficient.

Modélisation par automate cellulaire des phénomènes diagénétiques des plateformes carbonatées : calibration et paramétrage à partir de deux cas d'études : l'Urgonien du Vercors (Crétacé inférieur, SE France) et les Calcaires Gris du Mont Compomolon (Lias, NE Italie)

Une fois déposé, un sédiment est affecté au cours de son enfouissement par un ensemble de processus, regroupé sous le terme diagenèse, le transformant parfois légèrement ou bien suffisamment pour le rendre méconnaissable. Ces modifications ont des conséquences sur les propriétés pétrophysiques qui peuvent être positives ou négatives, c'est-à-dire les améliorer ou bien les détériorer. Une voie alternative de représentation numérique des processus, affranchie de l'utilisation des réactions physico-chimiques, a été adoptée et développée en mimant le déplacement du ou des fluides diagénétiques. Cette méthode s'appuie sur le principe d'un automate cellulaire et permet de simplifier les phénomènes sans sacrifier le résultat et permet de représenter les phénomènes diagénétiques à une échelle fine. Les paramètres sont essentiellement numériques ou mathématiques et nécessitent d'être mieux compris et renseignés à partir de données réelles issues d'études d'affleurements et du travail analytique effectué. La représentation des phénomènes de dolomitisation de faible profondeur suivie d'une phase de dédolomitisation a été dans un premier temps effectuée. Le secteur concerne une portion de la série carbonatée de l'Urgonien (Barrémien-Aptien), localisée dans le massif du Vercors en France. Ce travail a été réalisé à l'échelle de la section afin de reproduire les géométries complexes associées aux phénomènes diagénétiques et de respecter les proportions mesurées en dolomite. De plus, la dolomitisation a été simulée selon trois modèles d'écoulement. En effet, la dédolomitisation étant omniprésente, plusieurs hypothèses sur le mécanisme de dolomitisation ont été énoncées et testées. Plusieurs phases de dolomitisation per ascensum ont été également simulées sur des séries du Lias appartenant aux formations du groupe des Calcaire Gris, localisées au nord-est de l'Italie. Ces fluides diagénétiques empruntent le réseau de fracturation comme vecteur et affectent préférentiellement les lithologies les plus micritisées. Cette étude a permis de mettre en évidence la propagation des phénomènes à l'échelle de l'affleurement. - Once deposited, sediment is affected by diagenetic processes during their burial history. These diagenetic processes are able to affect the petrophysical properties of the sedimentary rocks and also improve as such their reservoir capacity. The modelling of diagenetic processes in carbonate reservoirs is still a challenge as far as neither stochastic nor physicochemical simulations can correctly reproduce the complexity of features and the reservoir heterogeneity generated by these processes. An alternative way to reach this objective deals with process-like methods, which simplify the algorithms while preserving all geological concepts in the modelling process. The aim of the methodology is to conceive a consistent and realistic 3D model of diagenetic overprints on initial facies resulting in petrophysical properties at a reservoir scale. The principle of the method used here is related to a lattice gas automata used to mimic diagenetic fluid flows and to reproduce the diagenetic effects through the evolution of mineralogical composition and petrophysical properties. This method developed in a research group is well adapted to handle dolomite reservoirs through the propagation of dolomitising fluids and has been applied on two case studies. The first study concerns a mid-Cretaceous rudist and granular platform of carbonate succession (Urgonian Fm., Les Gorges du Nan, Vercors, SE France), in which several main diagenetic stages have been identified. The modelling in 2D is focused on dolomitisation followed by a dédolomitisation stage. For the second study, data collected from outcrops on the Venetian platform (Lias, Mont Compomolon NE Italy), in which several diagenetic stages have been identified. The main one is related to per ascensum dolomitisation along fractures. In both examples, the evolution of the effects of the mimetic diagenetic fluid on mineralogical composition can be followed through space and numerical time and help to understand the heterogeneity in reservoir properties. Carbonates, dolomitisation, dédolomitisation, process-like modelling, lattice gas automata, random walk, memory effect.