Transformation of Discrete Fracture Networks into Equivalent Continuum Models for Sparsely Fractured Rocks: Comparing Flow-Based and Geometry-Based Upscaling for Flow and Transport

Caroline Darcel^1*Quentin Courtois¹Urban Svensson²Romain Le Goc¹Benoît Pinier¹Jan-Olof Selroos^3,4Philippe Davy⁵

• ¹Fractory, Itasca France, Rennes, France
• ²Computer-aided Fluid Engineering AB, Karlskrona, Sweden
• ³Research and Post-Closure Safety, Swedish Nuclear Fuel and Waste Management Company (SKB), Solna, Sweden
• ⁴Department of Sustainable Development, Environmental Science and Engineering, KTH Royal Institute of Technology, Stockholm, Sweden
• ⁵Fractory, Géosciences UMR 6118, Univ Rennes, CNRS, Rennes, France

In this study, we analyze the impact of transforming a discrete fracture network (DFN) model to an equivalent continuum model (ECM) on flow and solute transport characteristics. The analysis was conducted in a setting derived from – though simplified relative to – in-situ fracturing conditions at the Forsmark site. The geometrical structure of the DFN model considered is combined successively with a highly simplified transmissivity model (single constant value) in order to isolate spatial and structural effects, and with a more realistic model in which transmissivities depend on both fracture size and orientation (indirectly reflecting mechanical stress conditions). Two upscaling methods are considered: a simplified geometry-based method and a numerical flow-based method, in which local ECM cell properties are directly informed by local flow and transport simulations. For both approaches, we quantify the impact of ECM resolution. Specifically, we assess the sensitivity of local properties as well as local and global flow and transport indicators, to both the upscaling method and the ECM grid resolution. The results demonstrate that the transformation from DFN to ECM overestimates hydraulic conductivity, underestimates the geometric porosity but to a lesser extent and overestimates the transport porosity. This also artificially reduces flow path variability and tortuosity, except at very high resolutions. Consequently, average transfer times are shorter in ECMs than in DFNs, with discrepancies increasing as grid resolution coarsens. Similar trends are observed for first arrival times and mode (the peak of the distribution), but to a lesser extent. DFNs are also more likely to have very long transport times. Finally, we show that ECMs derived from geometry-based upscaling are highly sensitive to grid resolution, whereas flow-based upscaling exhibits significantly lower sensitivity.