A new method of data inversion for the identification of fractal characteristics and homogenization scale from hydraulic pumping tests in fractured aquifers

SummaryHydraulic interference pumping tests are widely used for identifying mid-to large-scale aquifer hydraulic parameters. Fractured reservoirs often behave as fractal media for which classical interpretations may fail because of the decrease in permeability and fracture porosity (or, equivalently, transmissivity and storage capacity) with the pumping time and the extent over which the pumping stress has propagated. A solution to hydraulic interference tests in fractal media is developed in dimensional variables, which allows for a very rapid and unique fitting to data. Hydraulic parameters, their scale exponents and the fractal dimension of the medium can be determined for each pressure draw-down curve without any prior information or other calculation. The method is applied to a large series of tests completed on the calcareous fractured aquifer of the experimental site in Poitiers (France). Even though data of pressure draw-downs are various and show a fractal behavior, permeability seems to rapidly homogenize for distances of 100–200 m. On the other hand, the fracture porosity shows a much progressive decrease with distance and homogenization is reached for scales beyond 300–500 m. It is also shown that the classical Cooper–Jacob interpretation of pressure draw-downs may yield artifacts in the identification of permeability and fracture porosity. Orders of magnitude are comparable to that from fractal interpretation but their evolution with respect to time or distance (scaling laws) may strongly differ.