The spatial heterogeneity of rock properties within a hydrocarbon reservoir has a large effect on fluid flow. Reservoir heterogeneity can be described over a wide range of spatial scales. Each data source that is integrated into the geological model represents a specific scale of information. For example, well data generally provide finer-scale information than do seismic data. The proper integration of different data types into the geological model should account for their difference of scale. Recently, several geostatistical methods have been developed to account for variation in different scales of heterogeneity. Deficiencies in those methods include an inability to identify spatial components that have physical interpretations (factorial kriging), a difficulty in controlling model perturbations (sequential gaussian simulation with non stationary kriging or block cokriging). These deficiencies are particularly true when integrating seismic information into the geological model. In this context, we propose a methodology which allows integration of reservoir properties (known at wells, with high vertical resolution) and seismic attributes (laterally dense but with low vertical resolution) overcoming these deficiencies. Our methodology is based on a spectral decomposition of high resolution well information using spectral characteristics of seismic attributes. Different components are then simulated with seismic information as a constraint for the component which bandpass is consistent between well and seismic data. All components are then recombined and transformed to generate the desired reservoir property. This methodology is evaluated against others in terms of easiness of implementation, computing time, impact of the seismic data and similarity to a synthetic model. An application of this methodology to a real data set is presented. The geological environment of the reservoir is a mixed carbonate platform. Porosities are simulated at a fine scale constrained by a 3D impedance cube. Introduction Modeling the spatial distribution of reservoir properties, such as porosity or permeability, is essential for reserves assessment, flow simulation or reservoir monitoring. To reduce the uncertainty on reservoir property between wells and to ensure data consistency, all relevant information should be taken into account in reservoir modeling. For this reason, stochastic simulations of a reservoir property (known at wells, laterally sparse, with high vertical resolution) commonly integrate seismic data (provided on 2D or 3D grids, laterally dense, but with low vertical resolution) as "soft" secondary information. Still, the problem of scale (or resolution) difference between well log data and seismic data (of a much larger volume support) should be addressed (Fig. 1). Authors consider often only one specific 2D seismic map extracted from the seismic dataset (generally a seismic attribute map at the top or bottom of the reservoir under study), which they relate to the vertically averaged reservoir property. For example, Behrens et al.1, Yao and Journel2, and Doyen et al.3 proposed a two-step methodology; in the first step, a 2D seismic-derived reservoir property average map is estimated; in the second step, this estimated map is used as a constraint in the simulation of the 3D reservoir property cube (at quasi-point scale). Deutsch et al.4 proposed a more straightforward approach for modelling a 3D reservoir property cube, based on the simulated annealing technique: a 3D reference image of the reservoir property is iteratively re-arranged according to a user-defined objective function. However, all these approaches, based on the integration of one 2D seismic map, underlie that the seismic volume support is 1D vertical. This raises two concerns; in case of an actual seismic resolution greater than the reservoir thickness, part of the seismic information is not used; in the opposite case, correlating one specific seismic map to the vertically averaged reservoir property is not very accurate.
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