Joint Inversion of Fracture Model Properties for CO2 Storage Monitoring or Oil Recovery History Matching

International audienceFor oil recovery or CO2 storage, "reservoirs" are commonly used to designate geological structures where oil can be found or CO2 can be stored. All reservoirs present a heterogeneity in terms of rock type and properties (such as porosity and permeability). In addition, some of these reservoirs present fractures and faults. Fractured reservoirs are an important part of the oil reserves in the world (Middle East, Gulf of Mexico, etc.) and some of them are important reservoirs in terms of oil volume and productivity in spite of the fractures. In addition, studies of reservoirs for geologic storage of CO2 have shown the existence of diffuse fractures and faults and their strong impacts on flow. A key point in fractured reservoirs is to understand the geometry and hydraulic conductivity of the network formed by the fractures. This requires the construction of a reservoir model that integrates all available conceptual knowledge and quantitative data. The topic of the present paper deals with a new methodology able to perform the history matching of a fractured reservoir model by adapting the sub-seismic fault properties and positions. The main difficulty of this work is to generate a sub-seismic fault network whose fault positions can be easily modified while respecting the statistical fault model. The sub-seismic fault model we have chosen allows us to obtain a sub-seismic fault network that is consistent with the seismic fault network and that succeeds in capturing the specific spatial organization of the faults. In a first step, the geometry of the seismic fault network is characterized using fractal methods. Sub-seismic faults are then generated according to a stochastic algorithm. Finally, the geometry of this discrete fracture network is optimized in order to match the hydrodynamic data about the reservoir. The optimization algorithm modifies the sub-seismic fault positions, leading to the history matching of the reservoir model. Fractal properties are preserved during the deformation process. These different steps are demonstrated on a realistic synthetic case

GEOSTATISTICAL ANALYSIS OF VALIDATION DATA OF AN AIR POLLUTION SIMULATOR

International audienceChemistry-transport models for air quality forecasting are affected by the uncertainty on the input data (emissions of pollutants and meteorological conditions), the approximations in the modelling of the physicochemical reactions, and numerical approximations (space and time discretization). The validation of the accuracy of these simulators can be done by comparing predictions with actual measurements. This exercise has been carried out for a model for daily forecasting at the scale of Europe, with reference to daily measurements at about one hundred stations over one year. A thorough variographic analysis shows that the error field cannot be characterized independently of the predicted and observed fields. Indeed the forecasts usually display space and time variations similar to those of the measurement data, up to a multiplicative factor, but are often poorly correlated with the reality. These results can be used to define priorities in the improvement of the chemistrytransport model. The presentation is focused on sulphates and nitrogen dioxide

La modélisation géostatistique de la variabilité spatiale et ses applications

The first part of this synthesis deals with statistical models used to describe the variability of natural variables distributed in space, to predict their value at unsampled locations, to build numerical models that account for spatial variability, and to characterize the uncertainty of data and models. It covers the full range of geostatistics as it was developed over the second half of the 20th century under the impetus of Georges Matheron: structural analysis (variogram computation and fitting), linear prediction (kriging), nonstationary models, multivariate methods, change of support and nonlinear methods (disjunctive kriging), conditional simulations, scale effect and inverse problems. The presentation offers an accurate perspective of the different geostatistical methods. Practical and theoretical aspects of geostatistics balance each other. Real-world applications are presented, such as a modelling of the geological formations for the Channel tunnel and a comparison between prediction and reality. The second part presents the developments carried out for the stochastic modelling of fractured media, and especially of fracture networks, from borehole and outcrop measurements. Two very flexible models have been developed from the observation of actual sites, one for granite (random discs, possibly in clusters or with a regionalized density), the other for stratified sedimentary media (hierarchical model). Parameter identification methods are available, as well as conditional simulation methods. Scale effects and the link with flow modelling are also presented. The last section is devoted to works which are currently carried out or in project: identification of nonstationary marginal distributions, multipoint statistics and model choice, space-time models, 3D geological modelling, stochastic process-based models, territorial data and data on graphs, data assimilation, interpretation of flow tests and simulation of fracture networks.La synthèse comporte trois parties. La première présente les modèles probabilistes développés en géostatistique pour décrire la variabilité de variables naturelles réparties dans l'espace, estimer leur valeur en dehors des points de mesure, construire des modèles numériques rendant compte de la variabilité spatiale, et caractériser l'incertitude des données et des modèles numériques. Elle couvre l'ensemble de la géostatistique qui s'est développée au long de la deuxième moitié du 20e siècle sous l'impulsion de Georges Matheron : analyse structurale (calcul et modélisation du variogramme), estimation linéaire (krigeage), modèles non stationnaires, méthodes multivariables, changement de support et méthodes non linéaires (krigeage disjonctif), simulations conditionnelles, effet d'échelle et problèmes inverses. Les différentes méthodes géostatistiques sont mises en perspective en présentant à la fois les aspects théoriques et pratiques. Des applications réelles sont présentées, comme une modélisation des formations géologiques pour le tunnel sous la Manche et la comparaison entre prédiction et réalité. La seconde partie présente les développements réalisés pour la modélisation stochastique des milieux fracturés, et principalement pour la modélisation de réseaux de fractures à partir d'observations en forage ou sur affleurement. Deux modèles très flexibles ont été développés à partir d'observations de sites réels, l'un pour les granites (disques aléatoires éventuellement en salves ou à densité régionalisée), l'autre pour des milieux sédimentaires stratifiés (modèle hiérarchique). Des méthodes d'identification des paramètres sont proposées, ainsi que des méthodes de simulation conditionnelle. Les effets d'échelle et le lien avec la modélisation des écoulements sont également abordés. La dernière partie est consacrée aux travaux en cours ou en projet : identification de lois marginales non stationnaires, statistiques multipoints et choix de modèles, modèles spatiotemporels, modélisation géologique 3D, données territoriales ou sur graphes, modèles génétiques stochastiques, assimilation de données, prise en compte d'essais hydrauliques dans la simulation de réseaux de fractures

Validity range of the discrete Gaussian change-of-support model and its variant

International audienc

Is there still room for new developments in geostatistics?

Georges Matheron lecture of the IAMGInternational audienc

Reserve classification challenges and modelling of the kaolin deposits of Charentes Basin, France

International audienc

Geostatistical study of Al-Khabra phosphate ore body with calcination cut-off grades

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Geostatistics: Modeling Spatial Uncertainty, Second edition

International audienc

Variances for mineral resources classification

International audienc