A Local Parameterization Method to Improve History Matching

Reservoir characterization needs the integration of various data, especially dynamic data, which requires history matching the measured production and 4D seismic data. However, reservoir facies and heterogeneities are generated with a geostatistical model, and random realizations cannot generally match dynamic data. To constrain the realizations by using measured dynamic data, it is necessary to parameterize the reservoir model, especially geostatistical realizations, and apply an optimization procedure by minimizing an objective function. However, there are only a few methods available to parameterize geostatistical realizations, and they are not always efficient. In this paper, we propose a local parameterization method which allows to improve history matching for better reservoir characterization. The method of gradual deformation, which allows to change continuously geostatistical realization from one to another, has been increasingly used in history matching. The domain of gradual deformation is generally delimited by gridblocks. In this paper, we present first a technique of spatial combination, which can combine geostatistical realizations on arbitrary domains to form a new one by keeping geostatistical consistency. Then, we present a technique of local parameterization to change continuously geometrical forms or sizes of the domains. This parameterization of domains leads to continuous change of geostatistical realizations with the technique of spatial combination. By analyzing values of objective function on each well or 4D seismic region, we can define local domains to be considered in the optimization. By changing forms and sizes of these domains, the proposed local parameterization method can select automatically best realizations in appropriate domains in order to improve the assistant history matching. Several examples of single or two-phase flows are presented with parameterization for radial or elliptical domains. The efficiencies of the local parameterization approach for history matching are illustrated through these examples.