| Abstract |
In geothermal reservoirs, the relationship between fluid flow and fracture networks remains poorly understood due to the geometrical complexity of the fractures. This lack of understanding makes it challenging to identify thermally significant flow paths directly from structural data. As a result, conventional simulation approaches typically perform fluid flow calculations across the entire fracture domain in a sequential manner, ultimately identifying preferential flow paths only after extensive computation. This approach imposes a heavy computational burden and offers limited insight into the essential structural features governing flow behavior. To address this issue, we present an analytical approach that provides a new way to describe flow behavior directly from fracture geometry. Our method leverages Topological Data Analysis (TDA) to extract meaningful structural information from complex fracture networks. Specifically, we use the Mapper algorithm (one of the tools in TDA) to convert complex fracture structures into simplified graph representations known as the Mapper graph. This graph preserves the essential topological features of the original structure while translating them into a form that is more interpretable and tractable. This transformation enables the application of graph algorithms such as shortest-path search to identify thermally dominant flow paths based solely on structural information, without requiring fluid simulations. By focusing on these structurally significant pathways, our method greatly reduces the model complexity and parameter space while maintaining predictive accuracy. This framework offers a structural descriptor that bridges the gap between geometry and flow, advancing geothermal reservoir modeling and promoting more efficient and sustainable geothermal energy utilization. |