Connectivity and Fractal Dimension of Fracture Networks

This study investigates the usefulness of fractal dimension for assessing fracture network geometry especially, in terms of connectivity in petroleum and geothermal reservoirs. We evaluated connectivity using both static and dynamic approaches and analyzed a set of fractal-fracture models and outcrop maps. The models comprise a deterministic fractal-fracture network and a set of thirty random fractal-fracture networks, all sharing the same fractal dimension. The natural dataset includes a series of nested network maps from an outcrop analog. These maps have been studied for their fractal nature, clustering behavior, and flow properties. For the “static” approach, connectivity of the fracture networks is evaluated by considering three different “nodes” in each of the networks, i.e., cross-cutting (X), abutting (Y), and isolated (I). In considering a “dynamic” approach for evaluating connectivity, the flow response is computed along with the integrated “time-of-flight” (TOF) at different time-steps. The networks are converted into simulation-ready fracture continuum models that were run in a streamline flow simulator, TRACE3D. The TOF plots thus generated provide insights into the connectivity between injection and production wells placed at diagonally opposite corners of the flow domain and are used to evaluate flow pathways and the effects of reservoir heterogeneity. They also implicitly indicate the “percolation connectivity” of a fracture network. This may be confirmed by comparing previously reported values of “percolation connectivity” of the outcrop analogs and the TOF plots. The ultimate goal of this research is to determine whether the fractal dimension can serve as a unique identifier for the connectivity of fracture networks. The results derived from both fractal-fracture models and natural maps indicate otherwise. The findings from this study can improve decision-making across various fields, including hydrogeology, resource management, and environmental engineering, leading to more effective strategies for resource extraction and risk reduction.