Statistical Assessment of Fracture Areal Intensity (P21) Representative Elementary Area in Digital Outcrop Models

Among the geometrical parameters that can be calculated from an outcrop analogue, fracture areal intensity (P21), defined as the ratio between the total sum of fracture trace length and the sampling area, represents the stopping criterion of 2D marked point process stochastic Discrete Fracture Network models (DFN) or 3D simulations if properly upscaled to its volumetric equivalent (P32). Given the heterogeneous nature of fracture networks, P21 calculation is inherently scale and position dependent, meaning that its value changes depending on the scan area size and its position within the outcrop boundary. For this reason, P21 calculation cannot be separated from the concept of Representative Elementary Volume (REV) or Area (REA), in case of 2D outcrop studies. Depending on the field of application, REV or REA size definition changes, adapting to the different sampling strategies and parameters specific to that research field. We propose a novel approach to define the REA for the P21 parameter as a range bounded by a lower and an upper limit. The upper limit, often overlooked but nonetheless theorized, identifies the largest representative domain, which is crucial for optimizing computational efficiency. To determine the REA range, we evaluate the shape, mean, and variance of P21 value statistical distributions across scan areas of increasing radius. Each statistical parameter is assessed by combining formal statistical tests and diagnostic plots. Within a multi-parametric framework, the method enables a detailed analysis of the statistical behavior of the dataset, facilitating more objective and informed decisions when defining the REA range.