Practical application of geostatistical scaling laws for data integration

Reconciling data from different scales is a long-standing 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. 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 mineral grades in selective mining unit 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. Three specific concerns are the ill-defined volume of measurement, uncertainty in the small-scale variogram structure, and 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 carbonate reservoir and a clastic reservoir in the Danish North Sea.