The Optimal Sine Pulse Frequency of Pulse Hydraulic Fracturing for Reservoir Stimulation

Pulse hydraulic fracturing (PHF) is a key technique for reservoir stimulation. PHF can well accelerate the rupture of rock. However, the supercharging mechanism of PHF is not fully understood. The main reason is that the pressure distribution and its variation, especially the peak pressure characteristics, are unclear inside the pipe and fissure. The present research focuses on the sine pulse applied at the inlet of a pipe or fracture to reveal the variation regularity of peak pressure with the pulse frequency, amplitude, pipe length, diameter and wave speed. First, the weakly compressible Navier–Stokes equations were developed to simulate the variation of fluid pressure. The computation codes were developed using the MacCormack method validated by the existing experimental data. Then, the sine pulse effect was studied inside the pipe and fissure. Last, a new frequency model was built to describe the relationship between the optimal pulse frequency, wave speed and pipe length. The results show that there is a family of frequencies at which the peak pressure of the endpoint can be significantly enhanced and that these frequencies are the optimal pulse frequency. It is found that the optimal pulse frequency depends on the pipe or fissure length and wave speed. At the optimal pulse frequency, the peak pressure at the endpoint can be increased by 100% or more, and the cavitation phenomenon occurs. However, the peak pressure decreases when with the decrease in the pipe diameter and fissure departure due to the friction drag effect of the wall. These new landmark findings are very important for the PHF technique. In addition, a new universal frequency model is built to predict the optimal sine pulse frequency. The present research shows the variation regularity of the fluid pressure inside the pipe and develops a sine frequency-controlled method, providing a potential guide for reservoir stimulation