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The gradual deformation method (GDM) is a geostatistical parameterization technique that generates a sequence of realizations evolving smoothly while preserving the statistical characteristics of the model. Combined with an optimization algorithm, it enables to constrain 3-D reservoir models to both static data (log data, prior geological information…) and dynamic data (production data such as pressure or water cut at wells…). The gradual deformation is based on the weighted combination of several realizations using deformation parameters. It can thus be applied both globally, with the same deformation parameters for the entire domain, or locally. In this case, the domain is partitioned into non-overlapping subregions and each of these areas is attributed one or several deformation parameters independent from the other region parameters. This method, called local GDM, is more flexible than the global one. It can have several applications such as the integration of new data to improve the reservoir model, or the simultaneous deformation of regions with different geological properties or dynamic behaviors. An application of this method for history matching on a real data set is proposed in this paper. One major issue when using local deformations is the definition of the reservoir partitions. Several approaches are considered in this paper, mainly based on the characterization of drainage areas and on geometrical criteria using Voronoi diagrams. |
