Investigating spatial heterogeneity within fracture networks using hierarchical clustering and graph distance metrics

Abstract

Abstract. Rock fractures organize as networks, exhibiting natural variation in their spatial arrangements. Therefore, identifying, quantifying, and comparing variations in spatial arrangements within network geometries are of interest when explicit fracture representations or discrete fracture network models are chosen to capture the influence of fractures on bulk rock behaviour. Treating fracture networks as spatial graphs, we introduce a novel approach to quantify spatial variation. The method combines graph similarity measures with hierarchical clustering and is applied to investigate the spatial variation within large-scale 2-D fracture networks digitized from the well-known Lilstock limestone pavements, Bristol Channel, UK. We consider three large, fractured regions, comprising nearly 300 000 fractures spread over 14 200 m2 from the Lilstock pavements. Using a moving-window sampling approach, we first subsample the large networks into subgraphs. Four graph similarity measures – fingerprint distance, D-measure, Network Laplacian spectral descriptor (NetLSD), and portrait divergence – that encapsulate topological relationships and geometry of fracture networks are then used to compute pair-wise subgraph distances serving as input for the statistical hierarchical clustering technique. In the form of hierarchical dendrograms and derived spatial variation maps, the results indicate spatial autocorrelation with localized spatial clusters that gradually vary over distances of tens of metres with visually discernable and quantifiable boundaries. Fractures within the identified clusters exhibit differences in fracture orientations and topology. The comparison of graph similarity-derived clusters with fracture persistence measures indicates an intra-network spatial variation that is not immediately obvious from the ubiquitous fracture intensity and density maps. The proposed method provides a quantitative way to identify spatial variations in fracture networks, guiding stochastic and geostatistical approaches to fracture network modelling.

Cement Deposits in Opening-Mode Fractures in Sandstone: Implications for Size, Spacing, Connectivity, and Erosion

“…For opening-mode fractures, size, spatial arrangement, and connectivity are essential elements defining fracture patterns. For fluid flow and rock strength, the specific pattern that is present -the sizes and arraignments of fractures-can have a profound effect of rock behavior (e.g., Olson et al 2007;Prabhakaran et al 2021). A review of sandstone opening-mode fracture size, spatial arrangement, and connectivity is beyond the scope of this note.…”

Using fractured outcrops to calculate permeability tensors: implications for geothermal fluid flow and the influence of seismic-scale faults

“…Interpreting and utilizing analogues is therefore vital for understanding the fractured networks at depth. For reservoir analogues, scan lines (1D) and fractured pavements (2D) are the most used data techniques and, whilst scan lines can provide statistical information on fracture arrangement, they are not useful for developing further models (Priest and Hudson, 1976;Dershowitz et al, 1992;Prabhakaran et al 2021). Two-dimensional pavement and fracture trace analysis allow for the interpretation and modelling of geometric and topological data (fracture orientation, length, intersections, aperture) from the fracture networks using advanced techniques of data acquisition, e.g.…”