Quantifying uncertainties in multi-scale studies of fractured reservoir analogues: Implemented statistical analysis of scan line data from carbonate rocks
In this study we performed a fracture analysis on a Cretaceous bedded carbonate succession well exposed in the Sorrento Peninsula. The studied succession includes stratigraphic units that are very similar to the productive units of the buried Apulian Platform reservoir rocks in southern Italy. We analyzed eight carbonate beds, including both limestones and dolomites. The basic technique used in this study consisted of measuring fractures along bedding-parallel scan lines. For one limestone bed, a microscale scan line, about 15 cm long, was also analyzed using a digital microcamera. Provided the cumulative distribution of fracture apertures is well described by a power law, our analysis shows how the uncertainty in the estimate of fracture aperture cumulative frequencies grows for large aperture values. This feature results in a large uncertainty in the estimate of the slope of the least-squares line (in a bi-logarithmic diagram) approximating the data distribution, which is the exponent of the power law. As the latter represents a fundamental parameter characterizing a fracture set and fracture distribution over different scales, reducing the uncertainty in the estimate of the slope of the curve represents an important objective of quantitative fracture analysis. This is obtained in this study by the application of multi-scale analysis, and by integrating micro-scan line data with classic outcrop-based scan line analysis. The quantification of uncertainties in the cumulative distribution estimates of fracture apertures is performed by analyzing in detail the spacing distribution - and consequently fracture-density distribution - for each aperture value. Our results suggests that a meaningful statistical analysis of fracture attributes such as aperture (or opening displacement) may be effectively carried out by using properly determined confidence intervals and by the integration of outcrop-based and micro-scan line data sets.