Renard, Philippe

2016, Bonneau, F, Caumon, G, Renard, Philippe

Stochastic discrete fracture networks (DFNs) are classically simulated using stochastic point processes which neglect mechanical interactions between fractures and yield a low spatial correlation in a network. We propose a sequential parent-daughter Poisson point process that organizes fracture objects according to mechanical interactions while honoring statistical characterization data. The hierarchical organization of the resulting DFNs has been investigated in 3-D by computing their correlation dimension. Sensitivity analysis on the input simulation parameters shows that various degrees of spatial correlation emerge from this process. A large number of realizations have been performed in order to statistically validate the method. The connectivity of these correlated fracture networks has been investigated at several scales and compared to those described in the literature. Our study quantitatively confirms that spatial correlations can affect the percolation threshold and the connectivity at a particular scale.

2008, Kerrou, Jaouhar, Renard, Philippe, Hendricks Franssen, Harrie-Jan, Lunatic, Ivan

The performances of kriging, stochastic simulations and sequential self-calibration inversion are assessed when characterizing a non-multiGaussian synthetic 2D braided channel aquifer. The comparison is based on a series of criteria such as the reproduction of the original reference transmissivity or head fields, but also in terms of accuracy of flow and transport (capture zone) forecasts when the flow conditions are modified. We observe that the errors remain large even for a dense data network. In addition some unexpected behaviours are observed when large transmissivity datasets are used. In particular, we observe an increase of the bias with the number of transmissivity data and an increasing uncertainty with the number of head data. This is interpreted as a consequence of the use of an inadequate multiGaussian stochastic model that is not able to reproduce the connectivity of the original field.The performances of kriging, stochastic simulations and sequential self-calibration inversion are assessed when characterizing a non-multiGaussian synthetic 2D braided channel aquifer. The comparison is based on a series of criteria such as the reproduction of the original reference transmissivity or head fields, but also in terms of accuracy of flow and transport (capture zone) forecasts when the flow conditions are modified. We observe that the errors remain large even for a dense data network. In addition some unexpected behaviours are observed when large transmissivity datasets are used. In particular, we observe an increase of the bias with the number of transmissivity data and an increasing uncertainty with the number of head data. This is interpreted as a consequence of the use of an inadequate multiGaussian stochastic model that is not able to reproduce the connectivity of the original field.

, Rongier, Guillaume, Renard, Philippe, Sausse, Judith, Collon, Pauline

Les chenaux sont des structures sédimentaires clefs dans le transport et le dépôt de sédiments depuis les continents jusqu'aux planchers océaniques. Leurs dépôts perméables permettent la circulation et le stockage de fluides. Comme illustré avec les systèmes turbiditiques, le remplissage de ces chenaux est très hétérogène. Son impact sur la connectivité des dépôts perméables est amplifié par les variations d'organisation spatiale des chenaux. Mais du fait de l'aspect lacunaire des données, l'architecture de ces structures souterraines n'est que partiellement connue. Dans ce cas, les simulations stochastiques permettent d'estimer les ressources et les incertitudes associées. De nombreuses méthodes ont été développées pour reproduire ces environnements. Elles soulèvent deux questions capitales : comment analyser et comparer la connectivité de simulations stochastiques ? Comment améliorer la représentation de la connectivité dans les simulations stochastiques de chenaux et réduire les incertitudes ?
La première question nous a conduits à développer une méthode pour comparer objectivement des réalisations en se concentrant sur la connectivité. L'approche proposée s'appuie sur les composantes connexes des simulations, sur lesquelles sont calculés plusieurs indicateurs. Une représentation par positionnement multidimensionnel (MDS) facilite la comparaison des réalisations. Les observations faites grâce au MDS sont ensuite validées par une carte de chaleur et les indicateurs. L'application à un cas synthétique de complexes chenaux/levées montre les différences de connectivité entre des méthodes et des valeurs de paramètres différentes. En particulier, certaines méthodes sont loin de reproduire des objets avec une forme de chenaux.
La seconde question amène deux principaux problèmes. Premièrement, il apparaît difficile de conditionner des objets très allongés, comme des chenaux, à des données de puits ou dérivées de données sismiques. Nous nous appuyons sur une grammaire formelle, le système de Lindenmayer, pour simuler stochastiquement des objets chenaux conditionnés. Des règles de croissance prédéfinies contrôlent la morphologie du chenal, de rectiligne à sinueuse. Cette morphologie conditionne les données au fur et à mesure de son développement grâce à des contraintes attractives ou répulsives. Ces contraintes assurent le conditionnement tout en préservant au mieux la morphologie. Deuxièmement, l'organisation spatiale des chenaux apparaît peu contrôlable. Nous proposons de traiter ce problème en intégrant les processus qui déterminent l'organisation des chenaux. Un premier chenal est simulé avec un système de Lindenmayer. Puis ce chenal migre à l'aide d'une simulation gaussienne séquentielle ou d'une simulation multipoints. Cette approche reproduit les relations complexes entre des chenaux successifs sans s'appuyer sur des modèles physiques partiellement validés et au paramétrage souvent contraignant.
L'application de ces travaux à des cas synthétiques démontre le potentiel de ces approches. Elles ouvrent des perspectives intéressantes pour mieux prendre en compte la connectivité dans les simulations stochastiques de chenaux., Channels are the main sedimentary structures for sediment transportation and deposition from the continents to the ocean floor. The significant permeability of their deposits enables fluid circulation and storage. As illustrated with turbiditic systems, those channel fill is highly heterogeneous. Combined with the spatial organization of the channels, this impacts significantly the connectivity between the permeable deposits. The scarcity of the field data involves an incomplete knowledge of these subsurface reservoir architectures. In such environments, stochastic simulations are used to estimate the resources and give an insight on the associated uncertainties. Several methods have been developed to reproduce these complex environments. They raise two main concerns: how to analyze and compare the connectivity of a set of stochastic simulations? How to improve the representation of the connectivity within stochastic simulations of channels and reduce the uncertainties?
The first concern leads to the development of a method to objectively compare realizations in terms of connectivity. The proposed approach relies on the connected components of the simulations, on which several indicators are computed. A muldimensional scaling (MDS) representation facilitates the realization comparison. The observations on the MDS are then validated by the analysis of the heatmap and the indicators. The application to a synthetic case study highlights the difference of connectivity between several methods and parameter values to model channel/levee complexes. In particular, some methods are far from representing channel-shaped bodies.
Two main issues derive from the second concern. The first issue is the difficulty to simulate a highly elongated object, here a channel, conditioned to well or seismic-derived data. We rely on a formal grammar, the Lindenmayer system, to stochastically simulate conditional channel objects. Predefined growth rules control the channel morphology to simulate straight to sinuous channels. That morphology conditions the data during its development thanks to attractive and repulsive constraints. Such constraints ensure the conditioning while preserving at best the channel morphology. The second issue arises from the limited control on the channel organization. This aspect is addressed by taking into account the evolution processes underlying channel organization. An initial channel is simulated with a Lindenmayer system. Then that channel migrates using sequential Gaussian simulation or multiple-point simulation. This process reproduces the complex relationships between successive channels without relying on partially validated physical models with an often constraining parameterization.
The applications of those various works to synthetic cases highlight the potentiality of the approaches. They open up interesting prospects to better take into account the connectivity when stochastically simulating channels.