Automatic calibration of wellbore pressure wave velocity using perforation-induced shock waves

Conventional wellbore wave velocity estimation mainly relies on water hammer oscillation signals. These signals have a limited frequency range and long oscillation periods. Under complex wellbore conditions, they are easily affected by noise and changes in boundary conditions, which limits the accuracy and stability of wave velocity characterization. To address this limitation, this study focuses on staged hydraulic fracturing in horizontal wells and proposes an automatic method for calibrating wellbore pressure wave velocity using impact pressure waves generated during perforation operations. The impact pressure waves produced during perforation have high frequencies, short pulse durations, concentrated energy, and clear propagation paths. These characteristics provide a signal source with strong physical advantages for detailed wellbore wave velocity characterization. Based on these properties, this study introduces a peak to peak detection approach. This approach shifts wellbore pressure wave velocity calibration from a dependence on overall oscillation features to a physical description based on transient echo time scales. A complete automatic calibration workflow is therefore established. Numerical simulation results show that, for synthetic pressure waves generated by a convolution model, the extracted time intervals between adjacent waves agree well with theoretical values. For individual perforation clusters, the mean absolute error ranges from 1.6 to 1.8 ms, and the root mean square error does not exceed 2.4 ms, indicating millisecond level time extraction accuracy. In addition, simulations based on a water hammer model show that the relative errors of pressure wave peak amplitudes are all below 0.2%. This result confirms the high accuracy of the proposed method from both the time and amplitude perspectives. Field applications indicate that the average wave velocities calculated for individual perforation clusters are mainly concentrated between 1530 and 1555 m/s. The coefficients of variation within clusters are generally below 5%, and the differences in average wave velocity between different stages are less than ± 15 m/s. These results demonstrate good overall consistency and stability. Further statistical analysis shows that the wave velocity distribution at the perforation cluster scale exhibits stable multimodal characteristics. This behavior reflects the possible existence of multiple propagation paths for perforation induced shock waves within the wellbore. The results demonstrate that the proposed method can achieve stable identification of perforation reflected waves and reliable wave velocity calibration under complex wellbore conditions. It provides an effective approach for the quantitative analysis of wellbore acoustic characteristics.