Multiscale spatial analysis of fracture nodes in two dimensions

Abstract

Spatial arrangement of fractures as a function of scale is an important component of fracture quantification for inferential and predictive modeling. Available methods that analyze fracture spatial arrangement are based on one-dimensional spacing data; therefore, they are limited to semi-parallel fractures. Such methods cannot be applied to fracture networks in higher dimensions, particularly when fractures have different orientations. To characterize fracture arrangements in two dimensions, we propose using Ripley's K-function, as a method of point pattern analysis, to quantify spatial arrangement of fracture nodes. Fracture nodes, such as barycenters, intersection points, and tips, are point-based representations of fracture locations and connectivity within the fracture network. We introduce formulations for isotropic as well as directional analyses of spatial arrangement. In addition, we derive formulations for edge correction in circular and rectangular study domains. Finally, we demonstrate applications of Ripley's K-function on two natural fracture datasets. Our proposed method supports quantification and characterization of fracture spatial arrangements that allow practitioners to build representative models of fractures in the subsurface.