Prevalence of Fracture Spatial Clustering and Implications for Solute Transport

Abstract:

The spatial distribution of fractures is commonly assumed to follow a Poisson distribution. This assumption is based on studies that relied on 1D transects and determined that fracture spacing is exponentially distributed. Moreover, the lack of well-exposed rock outcrops of sufficient scale to display a wide range of fractures sizes have led to the wide adoption of the Poisson distribution to assign fracture locations in studies utilizing discrete fracture network (DFN) simulations. Recent advances in the use of unmanned aerial vehicles (UAVs) and image processing offer the possibility of high-resolution fracture mapping that allows for more in-depth study of fracture spatial organization. This study explores the occurrence of fracture spatial clustering in networks mapped from 2D surface exposures and utilizes numerical simulations to infer how spatial clustering may influence solute transport. Fracture networks from a compilation of 20 maps generated from UAV, manual, and aerial surveys with scales ranging from 9 to 537,000 meters are analyzed using a two-point correlation method to characterize spatial scaling between fracture barycenters. The spatial distribution of fractures in each of the networks in the compilation follows power-law trends with correlation dimensions ranging between 1.47 and 1.89. This suggests that fractures commonly exhibit spatial clustering over a continuum of scales that cannot be captured by a simple Poisson point process to assign fracture centers. Synthetic DFNs are generated using three clustering scenarios: D_c=1.6 (high clustering), D_c=1.8 (intermediate clustering), and D_c=2.0 (no clustering). For each clustering scenario, 100 statistically equivalent networks are generated, and transport is simulated according to a Lagrangian approach. Ensemble transport behavior as a function of clustering is derived by comparing breakthrough curves and two specific quantile pairs (Q₁, Q₉₉; Q₁₆, Q₈₄). Median breakthrough times, interquartile range, and inter-realization variability in particle breakthroughs is shown to increase considerably as clustering increases from D_c=2.0 to D_c=1.6. These results indicate that spatial clustering introduces substantial heterogeneity into fractured media that is not captured by studies employing Poissonian DFNs.