Use of hydraulic tests to identify conceptual models of heterogeneity for fractured rock aquifers

Important aquifers, petroleum reservoirs, geothermal reservoirs, and waste disposal sites throughout the world are located in fractured rock formations. Responsible management of these resources and sites requires appropriate field characterization studies and modeling techniques to assess the impact of management alternatives. Characterization and modeling of aquifers is particularly challenging in fractured media, where flow is concentrated into channels and thus violates the assumptions of traditional analysis approaches. The General Radial Flow (GRF) model is an alternative method for hydraulic test interpretation that infers an additional parameter, the flow dimension n, to describe the flow geometry. Previous studies have reported non-integer flow dimensions for a number of aquifers and reservoirs of various rock types, suggesting that flow is dominated by a series of fractal channels [Acuna and Yortsos, 1995]. Typically, the information carried by the flow dimension is ignored in subsequent modeling studies. The present work is a Monte Carlo analysis of numerical models of aquifer tests in two-dimensional fractured media, with the objective to identify stochastic models of aquifer heterogeneity that consistently produce stable apparent flow dimensions in agreement with those inferred from aquifer test conducted in fractured rock aquifers. The flow dimension is examined first for three conventional stochastic models of the transmissivity field: multivariate log Gaussian (mvG), Fractional Brownian Motion (fBm), and Site Percolation Network (SPN). Then, the more realistic discrete fracture network (DFN) model, with fracture lengths distributed as a power-law is analyzed. The study is focused on the relationships among the parameters of a DFN, the flow dimension, and the regime of diffusion of pressure transients of aquifer tests (e.g., Fickian or non-Fickian). Results demonstrate that the DFN model is the best candidate to represent the heterogeneity of fractured rock aquifers. In particular for the DFN model, the apparent flow dimension and anomalous diffusion 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 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