Reconciling data from different scales is a longstanding problem in reservoir characterization. Data from core plugs, well logs of different types, and seismic data must all be accounted for in the construction of a geostatistical reservoir model. These data are at vastly different scales and it is inappropriate to ignore the scale difference when constructing a geostatistical model. Geostatistical scaling laws were devised in the 1960s and 1970s primarily in the mining industry where the concern was ineral grades in selective mining unit (SMU) blocks of different sizes. These principles can be extended to address problems of core, log and seismic data. The adoption of these classic volume - variance or scaling relationships presents some challenges. Some specific concerns are (1) the ill-defined volume of measurement, (2) uncertainty in the small-scale variogram structure, and (3) non-linear averaging of many responses including acoustic properties and permeability. We demonstrate the application of volume-variance relations for upscaling and downscaling techniques to integrate data of different scales. Practical concerns are addressed with data from a chalk reservoir in the Danish North Sea. A direct sequential simulation algorithm accounting for data at all scales is documented.
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