A modified node-based measure for estimating the connectedness of fracture patterns

Connectivity is a key factor governing the permeability and flow behavior of fracture networks. Topological graph theory has recently been applied to quantify connectivity, where topological connectivity (CL) is defined by the relative proportions of ‘X’, ‘Y’, and ‘I’ nodes—representing cross-cutting, abutting, and isolated nodes, respectively—without accounting for their spatial distribution. As a result, fracture maps with very different spatial arrangements may yield the same CL values, making this parameter inadequate for predicting percolation properties. To overcome this limitation, we propose a modified parameter, S-connectivity (Sc), which integrates both node abundance and spatial distribution. Spatial distribution is captured using the statistical measure lacunarity. Sc is defined as the product of CL and a weighting factor (κ), where κ is derived from the normalized lacunarity of the combined ‘X’ and ‘Y’ nodes (termed ‘XY’-nodes).We evaluated Sc using synthetic fracture maps with identical CL values but different node distributions. Sc successfully distinguished between these maps. Numerical flow simulations further demonstrated that Sc correlates positively with equivalent permeability, providing better predictive accuracy than CL alone. Analysis of natural fracture patterns from a fault damage zone confirmed the consistent positive relationship between Sc and equivalent permeability. These findings highlight S-connectivity as a more robust and distinctive measure of fracture network connectivity, offering valuable applications for modeling and engineering tasks in fractured petroleum reservoirs and aquifers.