Multiscale spatial analysis and modeling of fracture arrangements
Creators: name: Shakiba, Mahmood
Publisher: name: The University of Texas at Austin
Year: 2021
Subjects: Spatial arrangement
Fracture arrangement
Fracture network
Ripley's K-function
Spatial analysis
Simulated annealing

description: Fractures can strongly affect fluid flow, mass transport, and rock strength in the subsurface. In general, direct measurements of fracture abundance (intensity), their spatial arrangement, size, and connectivity are exceedingly challenging. Therefore, methods that improve characterization and modeling of fractures are of paramount importance in petroleum reservoir development, geothermal energy exploitation, water resources management, CO₂ sequestration, and mining. When fractures are evaluated as a network, their spatial arrangement becomes very important. Spatial arrangement describes how arrays of objects are placed in a space based on the sequence of and the distances between the objects. Fracture arrangement has been increasingly recognized as a critical attribute in understanding spatial distribution of fractures. In this dissertation, novel formulations and methods are developed for multiscale spatial characterization and simulation of fracture arrangements. Ripley’s K-function, as a method of point pattern analysis, is deployed to describe and quantify spatial arrangements. Ripley’s K-function takes length scale as a primary variable in the spatial analysis, which makes it well suited for studying multiscale characteristics of fractures. The K-function analysis classifies arrangements into clustered, anticlustered, or indistinguishable from random. Novel approaches are developed to calculate the confidence intervals for spatial randomness and spatial independence to test statistical significance. In addition, new methods of edge correction are implemented for one-dimensional study intervals as well as two-dimensional circular and rectangular study domains. Several one- and two-dimensional fracture datasets are used in this work to demonstrate the application of the K-function analysis. In one dimension, fracture spacings are used to classify fracture arrangements across various length scales. In addition, a new method is introduced to study the changing nature of fracture arrangement over the study interval. This method provides a tool for objectively quantifying the location and size of fracture clusters. In two dimensions, the spatial analysis is applied to fracture nodes extracted from fracture trace maps, including fracture intersection points, abutments, tips, and barycenters. Each node type exhibits a unique multiscale spatial arrangement. Finally, new algorithms are introduced for pattern reconstruction and simulation of fracture arrangements. The simulation algorithms are formulated as optimization problems and are solved by simulated annealing. The simulated fracture arrangements exhibit spatial characteristics similar to those of the original fracture dataset. For the two-dimensional simulations, flow behaviors of the generated fracture network realizations are compared against those of the original dataset using numerical flow models. They match closely, which indicates that the spatial arrangements of fracture nodes can be considered as flow surrogates in model calibration. Such modeling tools expand and improve our capability in predicting flow performance in naturally and hydraulically fractured reservoirs.