Poroelastic modeling of borehole-based periodic hydraulic tests in non-fractured and fractured porous rocks

Characterizing fluid transport and pore pressure diffusion is key for understanding and monitoring many natural (e.g., seismically active zones and volcanic systems) and engineered environments (e.g., enhanced geothermal reservoirs and CO₂ underground storage). Borehole hydraulic testing allows to infer relevant properties of the probed sub-surface volume, such as, for example, its transmissivity and diffusivity, for assessing the governing flow regime as well as for detecting the presence of hydraulic boundaries. Periodic hydraulic tests (PHT) achieve these objectives using a time-harmonic fluid injection procedure while measuring the fluid pressure response in monitoring boreholes. The relevant information on the pressure diffusion process occurring in the probed formation is retrieved from the phase shifts and amplitude ratios between the injected flow rate and the interval pressure. In general, the interpretation of PHT data relies on the assumption that the pressure diffusion process is uncoupled from the solid deformation of the probed rock volume. We present a poroelastic numerical approach to investigate the role played by hydromechanical coupling (HMC) effects during PHT and to assess whether and to what extent additional mechanical information can be extracted from these tests. We focus on (i) the influence of the borehole wall deformation on the wellbore storage coefficient S_w, which quantifies the difference between the injected flow rates and those actually entering the porous formation; and on (ii) the HMC effects associated with the presence of fractures in the formation. Following the commonly taken approach, we also interpret the synthetic data from the numerical poroelastic approach using the uncoupled diffusion solution. For different rock physical properties, we demonstrate that, in homogeneous formations, the uncoupled diffusion solution reproduces the poroelastic results. In this scenario, neglecting the effect of the deformation of the borehole wall on S_w upon injection can lead to an underestimation of both the transmissivity and diffusivity, which becomes worse for shorter oscillation periods. We also show that the effective values of S_w depend on the shear modulus of the formation and do not change with the oscillatory period. Based on this evidence, we present a methodology to obtain the effective S_w along with the hydraulic properties using observations at various oscillatory periods. Next, we consider formations containing hydraulically open and compliant fractures intersecting the borehole perpendicularly. Here, a single uncoupled diffusion model is not able to fully describe the poroelastic response of the medium at different periods. Furthermore, the presence of fractures significantly affects the effective value of S_w: it increases with respect to the one associated with the intact homogeneous rock, and the HMC effects associated with the compressibility contrast in the formation result in a period dependence of S_w. The characteristic period of the latter is primarily related to the diffusivity and size of the fractures. This result is particularly relevant for the planning and interpretation of monitoring experiments, in which the mechanical properties of the formation are expected to evolve, such as, for example, hydraulic stimulation procedures, seismic and/or volcanic regions, and injection of wastewater and CO₂ for subsurface storage.