Empirical scaling of formation fracturing by high-energy impulsive mechanical loads

Recent technological advances to trigger high-energy seismic waves from within the wellbore have spurred interest in their potential application to induce fracturing within deep subsurface formations. Although a considerable body of experimental observations at the bench scale (on the order of 1 cubic foot) show promise, there remains considerable uncertainty in how the process may scale to the field. This work characterizes the relationship between the extent and intensity of fracturing and the duration and strength of the dynamic load. Our approach uses a direct numerical simulation of the elastodynamic equations while accounting for nonlinear fracture mechanics. A hybrid Finite-Discrete Element Method (FDEM) is applied whereby cohesive (elastoplastic) laws hold mesh elements together until complete failure. Beyond failure, elements act as deformable free bodies that can interact via contact constraints, including friction. The consistency of the model is first verified and it is validated with observations from previously reported physical experiments. Subsequently, we apply the model to conduct a numerical exploration of the dimensionless parameter space that defines plausible loading waveforms. We model an infinite domain that contains a spherical inclusion within which various impulsive loads are applied. The dynamic loading waveform is parameterized by its rise time to peak stress, followed by a decay period, and occurring within micro-to milliseconds. The dimensionless parameter space is sampled by varying loading characteristics (rise time, peak pressure, and impulse) to reveal the stimulated damaged bulk volume and crack intensity. Consistent with reported experimental observations, the model reproduces a nearly linear trend between the radius of damage and the maximum stress on the bench scale. Beyond that scale, however, the model predicts that this scaling slows considerably to a fractional power law between the damaged radius and the peak stress. This limitation coincides with a geometric increase in the intensity of damage within the stimulated volume. We present loci curves of the expected damage radii as functions of the loading waveform properties.