A Simple Formula To Estimate 2D Fracture Connectivity

Summary A simple expression is derived for average fracture intersections per fracture, λ, as the product of fracture density, average length, and angular standard deviation in 2D fracture models. The calculated λ value quite accurately estimates the observed λ values for a variety of cases including one- or two-fracture sets, truncated or not-truncated fractures, and log-normal or power law length distribution. The formula fails to estimate the number of fracture intersections accurately when fractures are clustered. Fracture clusters could either be fault-related fracture corridors or highly fractured layers. In either case, it is necessary to calculate λ for each fracture corridor or each fractured layer with a different fracture density. The relationship between λ and fracture connectivity was investigated using several stochastic fracture models. λ seems to be a reasonably good estimator of fracture connectivity, which we define as the percentage of fractures within the largest interconnected fracture aggregate. The relationship between the number of fracture intersections and percolation threshold is, however, weak because percolation threshold is dependent on the relative length of fractures with respect to the distance between two opposite ends of a fractured medium.