Fracture network modeling with graph deep learning

Most existing fracture modeling workflows rely on the generation of discrete fracture networks (DFN), which simulate fracture patches based on stochastic distributions of geometric parameters and generally neglect topological constraints. To address the DFN constraints, we propose applying graph theory and deep learning to characterize and generate coherent fracture networks from real-world datasets. Our approach broadens the range of quantitative methods available for fracture modeling; it is non-gridded and accounts for both geometry and topology in the generation of new networks. 

The generation of fracture networks based on a reference and/or analog network interpretation is useful for modeling subsurface uncertainties related to fracture positions and network intersections. This application is useful for sites where fracture interpretation is possible, but where full coverage of the study site is not available. For characterization, we integrate geometry, topology, kinematics, age relationships, and geomechanics to identify the most important connections within a network. For simulations, we combine a graph recurrent neural network (GraphRNN) for generating graph topology and graph denoising diffusion probabilistic models (DDPM) for generating node positions in space. Deep generative models learn distributions from the training fracture network data and generate new networks with a variable number of fracture lineaments, represented as edges, while intersections are represented as nodes.

Our method is applied to a real case study from the Western Helvetic Alps domain in Switzerland. The model is trained on graphs derived from the fracture network interpretation of a Cretaceous limestone aquifer. The generation of new fracture networks as graphs yields coherent topologies with statistical distributions similar to those of the training data for node degree and relative node positions (i.e., edge length and azimuth). Furthermore, the training dataset and the generated networks are compared using node centrality measures (betweenness and percolation), which help describe the network's connectivity and highlight preferential flow paths, thereby emphasizing the role of fracture connectivity in enhancing permeability and controlling flow anisotropy. The method is promising for the generation of fracture networks as an alternative approach that can be used to identify preferential fluid flow paths and to build scenarios for later flow simulation for hydrogeology, reservoir management, geothermal energy, nuclear waste disposal, and geologic sequestration.