Flow Dimension and Anomalous Diffusion of Aquifer Tests in Fracture Networks

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Characterization and modeling of aquifers is particularly challenging in fractured media, where flow is concentrated into channels that are poorly suited to traditional approaches to analysis. The generalized radial flow model is an alternative method for hydraulic test interpretation that infers an additional parameter, the flow dimension n, to describe the flow geometry. This study was a Monte Carlo analysis of numerical models of aquifer tests in two-dimensional fractured media, with the objective of understanding the relationships between the parameters of a discrete fracture network (DFN) with lengths distributed as a power law, the flow dimension, and the regime of hydraulic diffusion (e.g., Fickian or non-Fickian). The diffusion regime of each realization was evaluated using 〈R²〉 ∼ t^k, where t is time, 〈R²〉 is the mean squared radius of hydraulic diffusion, and an apparent value of k = 1 indicates normal (Fickian) diffusion and k < 1 indicates anomalous (non-Fickian) diffusion. For the DFN model, the apparent flow dimension and exponent k depend on both the density and the power of the fracture length distribution, and thus also on the connectivity regime of the fracture network system. Depending on the connectivity regime, the apparent flow dimension stabilizes to less than the Euclidean dimension and the apparent value of k < 1 indicates that hydraulic diffusion is non-Fickian. These results suggest that the flow dimension and the exponent k may be useful for characterizing flow and transport in fractured media.