Evaluation Indices for the Filtration Effectiveness of Pump-Stop Water Hammer Signal in Field Fracturing

A novel fracturing diagnosis technique, known as water hammer diagnostics, is used to evaluate fracture locations. Filtering can yield clearer water hammer signals, resulting in more accurate analysis of fracture locations. The evaluation index of filtration effectiveness is the foundation of more accurate filtering and more reasonable filtering parameter optimization. In this paper, the resolution of the cepstrum response (R_C) and the signal-to-noise ratio of quefrency peak (R_QSN) are proposed as evaluation indices for filtration effectiveness. The research on the evaluation indices of filtration effectiveness is founded on the synchronization between index values and filtration effectiveness, with reliability being verified by sensitivity analysis. The results indicate a positive correlation between the R_C and R_QSN indices and the filtration effectiveness of the high-frequency (1000Hz) signals. Better effectiveness and sensitivity are demonstrated by the higher R_C and R_QSN. When the filter parameter is adjusted to a defined interval, an average change rate exceeding 15% is observed in both indices. Additionally, parameters optimization of filtering algorithm is achieved by R_C and R_QSN. The cut-off frequency (f_c) of the Butterworth low-pass filter is set within the range of 40, 50 Hz, the window length of the Gaussian smoothing filter (l_win) falls within the range of 20, 30, and the decomposition level (L) of the wavelet transform is specified within the range of 1, 4. Therefore, the filtration effectiveness of water hammer signals in field cases can be effectively evaluated by R_C and R_QSN. This study can serve as a reference for the parameter optimization of filtering algorithms and the evaluation of filtration effectiveness of filtering model in field applications.