A Technique for Analyzing the Spatial Distribution of Fracture Attributes

Current techniques for analyzing fracture data on attributes such as dip and aperture acquired from well-logs and scan lines treat them separately from the spacing values at which they are recorded. As a consequence, a power-law cumulative frequency for fracture apertures for example, tells nothing about their spatial distribution. Likewise, analysis of spacing data, may delineate trends like presence of fracture clusters and their organization, but throws no light on the distribution of magnitudes of fracture attributes. Lacunarity is technique for analyzing multi-scale binary and non-binary data and is ideally suited for analysis that relates an attribute (e.g., aperture) to its spatial distribution. We introduce the novel concept of lacunarity ratio, R, which is the lacunarity of a given non-binary dataset normalized to the lacunarity of its random counterpart. This type of analysis can determine scaledependent changes in persistence and anti-persistence thereby delineating if large fractures alter with smaller ones within a fracture cluster or, if such fracture attribute values are randomly distributed at a given scale of observation. The technique is then applied to three different data sets with spacing values together with aperture, length and dip values respectively. Such analyses can help improve DFN modeling and upscaling by incorporating data driven spatial distribution of fracture attributes.