Analysis of periodic pumping tests in a fractured rock mass based on the generalized radial-flow model

Summary We evaluated periodic pumping tests carried out in boreholes penetrating fractured gneiss in the research mine “Reiche Zeche”, Freiberg, Germany, employing a fractional diffusion equation, known as the generalized radial-flow (GRF) model. Water was injected into three borehole intervals, successively isolated by a double-packer probe. The three intervals correspond to distinct hydraulic conduits: (i) an induced axial fracture, (ii) a stimulated pre-existing radial fracture, and (iii) a fault zone intersecting the borehole at a near-normal angle. Pressure responses were monitored in sections of up to four monitoring boreholes. We evaluated the collected data by two spectral methods, injectivity analysis and interference analysis. The former exploits flow rate and pressure of the injection interval, whereas the latter relies on pressure records only, namely that of monitoring sections and of the injection intervals. In the GRF-framework, interference analysis yields a unique pair of flow dimension and hydraulic diffusivity, while the two observables of the spectral injectivity analysis, amplitude ratio and phase shift, only constrain admissible ranges of the three involved unknowns, flow dimension, hydraulic diffusivity, and conductivity. We addressed this under-determinateness by two combinations of spectral parameters from injectivity and interference observations. Even when accounting for the effects of finite length, storage capacity, skin, and non-parallelism of injection intervals and monitoring sections on the spectral parameters, it seems difficult to reconcile the bulk of our observations with the predictions of the GRF model. In cases, however, the gained fractal flow dimensions may bear geometrical significance, as for the likely anastomosing fault zone. The decrease in fractional flow regime with increasing mean interval pressure observed for two hydraulic paths between injection intervals and monitoring sections points towards a role of hydromechanical coupling in flow localization.