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Abstract

AAPG Bulletin, V. 107, No. 7 (July 2023), P. 1169-1189.

Copyright ©2023. The American Association of Petroleum Geologists. All rights reserved.

DOI: 10.1306/11062222008

Characterization of spatial relationships between fractures from different sets using K-function analysis

Mahmood Shakiba,1 Larry W. Lake,2 Julia F. W. Gale,3 and Michael J. Pyrcz4

1Hildebrand Department of Petroleum and Geosystems Engineering, The University of Texas at Austin, Austin, Texas; [email protected]
2Hildebrand Department of Petroleum and Geosystems Engineering, The University of Texas at Austin, Austin, Texas; [email protected]
3Bureau of Economic Geology, Jackson School of Geosciences, The University of Texas at Austin, Austin, Texas; [email protected]
4Hildebrand Department of Petroleum and Geosystems Engineering, The University of Texas at Austin, Austin, Texas; Bureau of Economic Geology, Jackson School of Geosciences, The University of Texas at Austin, Austin, Texas; Department of Geological Sciences, Jackson School of Geosciences, The University of Texas at Austin, Austin, Texas; [email protected]

Abstract

Fractures within rocks commonly appear in multiple sets. Characterization of spatial relationships between fracture locations from different sets is important for accurately describing fracture pattern and for building representative subsurface models. Although analysis of fracture arrangement in a single set is common, statistical tools for analysis of spatial relationships between multiple fracture sets are underdeveloped. We propose novel spatial data analytics using Ripley’s K-function to compare different fracture sets to each other to identify whether they exhibit attraction (i.e., overlap of fracture locations) or repulsion (i.e., segregation of fracture locations) inside the study domain. In addition, we introduce a method to quantify the degree of similarity between fracture arrangements in each set. We deploy both the random relabeling and the random shift approaches to quantify the statistical significance of spatial relationships between fracture sets at each length scale. We apply Ripley’s K-functions to various synthetic one-dimensional data sets for demonstration. In addition, we use Ripley’s K-functions to characterize the spatial relationships between two size fractions of fractures in a one-dimensional data set from a limestone outcrop. Results indicate that fractures with larger aperture sizes are more clustered than fractures with smaller aperture sizes. Although clusters of both fracture groups overlap, a repulsion is observed between fractures with different aperture sizes within the clusters.

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