Permeability Upscaling in Carbonates. An Integrated Case Study From the Albion R&D Project

In carbonates, predicting permeability values for gridded reservoir models is very challenging as it involves both the difficult characterization of a very heterogeneous medium, the uncertain extrapolation far from well data, and the up-scaling concern. The quantification of effective permeability for model gridblocks using small scale data from plug measurements or log interpretation is a recurrent concern since the change of support for permeability has proved to be definitively non linear. When a well test interpretation is available, it gives the evolution of the permeability in the vicinity of the wells for a volume much larger than the volumes characterized by cores and logs. In that case, the consistency has to be found between the transient pressure analysis-derived large scale equivalent permeability and the small scale permeability issued from conventional core analysis or log interpretation. It is known that the upscaling can be expressed as some power average of the permeability distribution, and that an analytical formula relates the horizontal permeability in the volume investigated by the well test and the original small-scale permeability distribution in this volume. However, the relation between the upscaling law and the permeability structures is usually documented for a few number of structures, leading to recurrent problems when large scale permeability has to be extrapolated outside the volume explored by the well test. A new formulation of the power averaging coefficient has been proposed, which relates the power averaging coefficient to the geostatistical description of the permeability structures, the direction of the flow, and the volume for which the equivalent permeability is computed. The new methodology has been applied to the Buissonniere field laboratory, a site from the ALBION R&D Project. Thanks to a characterization at an unusual scale, the integration of geological, petrophysical, geophysical and pressure transient data has successfully validated the use of this new formulation.