Scaling of hydraulic conductivity in porous and fractured media for continuous models: A review

Hydraulic conductivity exhibits a high spatial variability due to the heterogeneity and discontinuity of the geologic environments and their constituent materials. Representing such variability is problematic when implementing groundwater flow models, especially in geological media such as fractured rocks, fractured porous media, and karstic media, where the scale of observation is important when defining the heterogeneity of the media. In those cases, hydraulic tests performed locally in the fractures measure hydraulic conductivity at a fine scale. Nevertheless, groundwater flow models usually deal with problems involving a regional scale, with a grid cell size much greater than the cell in the fine scale. Modeling groundwater flow in fractured media using the Discrete Fracture Network (DFN) method at the regional scale is still challenging due to the difficulty of hydraulically characterizing the entire fracture network using the limited available data. Instead, methods such as Equivalent Porous Media (EPM) represent the fractured media as a continuous media, making it more practical to represent fractured rocks as a continuous equivalent media in regional models than the DFN method. However, in approaches such as EPM, choosing the block size adequately is critical because, at large scales, it can considerably affect the simulated flow patterns. Accordingly, upscaling hydraulic conductivities of fracture networks at the fine scale into equivalent parameters at the scale of the model's block is still a relevant question in practical groundwater modeling. This paper reviews the most widely used hydraulic conductivity scaling techniques to identify methods that consistently represent fractured media groundwater flow dynamics in regional models.