Fabien Ors

Unsupervised classification of multivariate geostatistical data

With the increasing development of remote sensing platforms and the evolution of sampling facilities in mining and oil industry, spatial datasets are becoming increasingly large, inform a growing number of variables and cover wider and wider areas. Therefore, it is often necessary to split the domain of study to account for radically different behaviors of the natural phenomenon over the domain and to simplify the subsequent modeling step. The definition of these areas can be seen as a problem of unsupervised classification, or clustering, where we try to divide the domain into homogeneous domains with respect to the values taken by the variables in hand. The application of classical clustering methods, designed for independent observations, does not ensure the spatial coherence of the resulting classes. Image segmentation methods, based on e.g. Markov random fields, are not adapted to irregularly sampled data. Other existing approaches, based on mixtures of Gaussian random functions estimated via the expectation-maximization algorithm, are limited to reasonable sample sizes and a small number of variables. In this work, we propose two algorithms based on adaptations of classical algorithms to multivariate geostatistical data. Both algorithms are model free and can handle large volumes of multivariate, irregularly spaced data. The first one proceeds by agglomerative hierarchical clustering. The spatial coherence is ensured by a proximity condition imposed for two clusters to merge. This proximity condition relies on a graph organizing the data in the coordinates space. The hierarchical algorithm can then be seen as a graph-partitioning algorithm. Following this interpretation, a spatial version of the spectral clustering algorithm is also proposed. The performances of both algorithms are assessed on toy examples and a mining dataset.

Automatic Determination of Sedimentary Units from Well Data

In order to create realistic models of a reservoir with a vertical heterogeneity, it is often better to firstly divide it into several horizontal homogeneous geological units. The Vertical Proportion Curve (VPC) of wells extracted from the reservoir can illustrate the heterogeneity, but the choice of the geological units is usually based on a visual criterion. In the present paper, a new numerical method of wells VPC analysis is proposed. It consists in a geostatistical hierarchical clustering of VPC elementary intervals which results in the division of the reservoir into more homogeneous units that can be further used for modeling. The method is illustrated on two synthetic cases generated by the meandering channelized reservoir model Flumy and a real data case-study.

Potential of FLUMY, a Meandering Fluvial Process-based Model, to Simulate Submarine Channels

Sinuous submarine channels are a very common feature of deep-water environments. The hydrocarbon reservoir potential of the associated deposits has been proved and many of them are exploited in several areas in the world. Several approaches exist to model submarine channels but all with limitations. The process-based and stochastic FLUMY model simulates meandering channelized reservoirs. It represents realistic geometries of an evolving meandering river migrating on a floodplain and the resulting sedimentary bodies such as point-bars, crevasse splays, overbank alluvium... The planform geometry and geomorphologic features (e.g. point bars, abandoned loop, levees, overbank, crevasse splays, or avulsion) of sinuous submarine channels and meandering rivers are analogous and it was confirmed by our data: the comparison of meandering river and sinuous submarine channel geometrical characteristics reveals that the wavelength and the amplitude for submarine channels are 2 to 3 times greater than the ones of sinuous rivers for a given bankfull width. Consequently, we propose to adapt the FLUMY model to the submarine environment. The submarine channel simulation carried out with FLUMY, taking into account the correction factor, shows that the simulated submarine channel planform morphology is consistent with natural systems, even if the number of meander cutoffs is very high.

Dynamic Modelling of Meandering Fluvial Systems at the Reservoir Scale, FLUMY Software

Meandering fossil systems are very common in terrestrial systems. Meander loops development induced by the migration processes, although still debated, are attributed to the deformation of the velocity field in relation to the channel path irregularities. In the following, we propose a comparison of the channel and channel belt patterns obtained from the initial global slope model proposed by Ikeda (1981), modified by Johannesson (1889b) and a local slope model that we developed and implemented in the process-based modelling tool FLUMY. The results point to more realistic meander developments in the local slope simulations than with the global slope one. This improvement can particularly be observed in individual meanders, whose rate of extension decreases with the age. It is also noticeable in the overall river behaviour, which self-confines in a meander belt, resulting in a lower tortuosity and a reduced sandbody extension to wavelength ratio. Moreover, the implementation of the local slope algorithm provides a description of the flow variations along the stream path that is to serve as a basis of a transport module to describe the grain-size variations within the point bar deposits in relation to the geometry of the individual meander loops.