Quantifying uncertainties in multi-scale studies of fractured reservoir analogues: Implemented statistical analysis of scan line data in carbonate rocks

New methods are proposed for the statistical analysis of tensile fracture attributes (spacing, density, aperture). The statistical methods are applied to a fractured Lower Cretaceous carbonate succession cropping out in the Sorrento Peninsula (Naples area, Italy), representing a geological analogue of buried reservoirs of southern Apennines major oil fields. As fracture networks (observable from outcrop to the crystal scale) can significantly affect the hydraulic behaviour of a fractured reservoir, the definition of appropriate models of fracture spacing and aperture probability distribution at several scales represents an important goal of structural analysis. In order to achieve such an objective, sampling is carried out at different scales, by means of traditional scan lines at outcrop, as well as micro-scan lines carried out both by a digital micro-camera (at a magnification of 50x, on polished slabs/outcrop) and by the optical microscope (at a magnification of 200x, in thin section). Fracture spacing and density analysis is mainly aimed at establishing the characteristics of joint spatial distribution over a range of scales. Aperture analysis is aimed at verifying that the aperture cumulative frequency is described by a power law and, in the latter instance, to provide an effective method for a more precise determination of the exponent of the power law. Furthermore, new expressions are provided to calculate the confidence interval of the power-law exponent