ANISOTROPY IN FRACTURE CLUSTERING: A LACUNARITY STUDY

The clustering of fractures can lead to preferential flow pathways influencing the equivalent permeability of a network. Quantification of the directional variability in clustering within a network is important for understanding its anisotropy. Lacunarity, L is a parameter that can quantify the clustering of spatial patterns at different scales, r. We have recently employed L(r) to quantify clustering along the NS and EW directions of a set of synthetic and natural fracture maps and compared the results to the anisotropy in equivalent permeabilities. The present study provides a more robust computation of lacunarity for finding the clustering anisotropy of fracture maps.

A scanline passing through the center of a square map was rotated every 15° and the lacunarity at each orientation was calculated. Rotating the scanline changes its length. Furthermore, the number of fractures encountered at different orientations will vary. To accommodate these two factors, a normalized value for the lacunarity, L*, was employed, and the weighted mean of this value, wmnl, was computed, the weights being the normalized scale, r*. The normalization was such that the values of both L* and r* varied between 0 and 1. A circular plot was constructed from the computed wmnl values in order to delineate the clustering anisotropy for any given map.

A set of 7 nested natural fracture maps from the Devonian Sandstone, Hornelen Basin, Norway were analyzed using the circular wmnl plots. The results bring forth two important observations. First, distinct sets of fractures can be delineated when the maps are differentially clustered. Secondly, clustering anisotropy appears to decrease at larger scales suggesting that large scale fracture networks are more isotropic. This is because fractures become more randomized at these scales as observed in a previous study by our group. Finally, comparing circular wmnl plots with permeability (1/√K) anisotropy plots may delineate if anisotropy in clustering implies anisotropy in flow.