Building reservoir geological models that are consistent with all available information is necessary to reduce uncertainties in production forecasts. The geostatistical approach is the only feasible way for integrating all kinds of data ranging from geological knowledge to production history. This paper presents an integrated methodology based on inversion techniques for constraining 3-D stochastic reservoir models to well test data and production history. Several complementary methods are proposed for the integration of production data in a consistent geostatistical reservoir model:
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A first approach, based on the combination of numerical simulation with inversion algorithms, allows to constrain reservoir models to multiple well tests. The facies petrophysical properties (permeability and porosity) of an initial model realization are characterized with a fixed facies distribution. This approach allows to simulate well tests with a complex reservoir description, and is particularly well suited for constraining geostatistical models to transient pressure data. Several well tests corresponding to different investigation areas or to different measurement periods can be associated in the same inversion to obtain a better global model characterization.
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A second approach consists in modifying globally or locally the initial model realization itself to improve the match. Starting from an initial realization, a gradual deformation process is performed to better constrain the heterogeneity distribution and the geostatistical parameters. The inversion process is controlled by a limited number of deformation parameters to improve the history matching efficiency. Structural parameters such as correlation lengths and anisotropy orientation can also be constrained if sufficient dynamic information is available.
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The pilot point method is an alternative to the local gradual deformation. It allows local changes in the mean distribution of geostatistical models. This method increases the flexibility of the model perturbation and can be advantageously used after a global inversion process in order to improve history matching in a particular area of the model.
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Finally, the gradual deformation process can be generalized to perform history matching with the full field reservoir model. An integrated approach is presented, based on the updating of the entire simulation workflow in the same inversion procedure. In this approach, an inversion toolbox allows to easily combine several simulation, parameterization and optimization algorithms to allow history matching within a geostatistical framework. A successful history matching example is presented, in which the gradual deformation and the pilot point methods are combined to constrain a 3D stochastic model.
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