Abstract

Connectivity estimated by simply considering the relative number of nodes in fracture networks, i.e., cross-cutting (X), abutting (Y), and isolated (I), without regard to their spatial distributions, is often not a unique identifier of fracture geometry. This research proposes a modified, lacunarity based estimate of connectivity which considers both the spatial distribution of such nodes in a network and also their abundance. We compare three pairs of natural fracture maps from different sources, each pair with the same connectivity but very different visual appearances. A study of the flow properties of these maps using a streamline simulator and invoking the fracture continuum model showed that pairs of maps with same connectivity but different visual appearances yield distinct recovery curves and time-of-flight (TOF) plots. A MATLAB toolbox, FracPaQ, is used to identify and spatially map the three different X, Y and I-nodes in fracture networks. The spatial clustering of nodes that facilitate conductivity (X, Y) and those that hinder flow (I), are calculated separately by implementing a log-transformed lacunarity summed over a range of scales as: <LXY> and <LI> respectively. The values are then used for generating a multiplier, κ = <LXY> / <LI>, which is incorporated into a new connectivity index, L-connectivity. The results show that pairs of fracture maps that have the same apparent connectivity, but with differences in visual appearances and hence, flow properties, can be distinguished based on this new lacunarity-based connectivity index. This parameter may therefore, prove to be a unique identifier of the connectivity of fracture networks. L-connectivity may be potentially utilized for estimating the network connectivity and, as a first pass for evaluating fracture network geometry by modelers and engineers who deal in fractured petroleum reservoirs and aquifers.

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