Oscillation Times in Water Hammer Signatures: New Insights for the Evaluation of Diversion Effectiveness in Field Cases

Diversion is a crucial technique for effectively improving shale reservoir production by creating more complex fracture networks. Evaluating diversion effectiveness is necessary to optimize the parameters in hydraulic fracturing. Water hammer diagnostics, an emerging fracturing diagnosis technique, evaluate diversion effectiveness by analyzing water hammer signals. The water hammer attenuation, as indicated by the oscillation time, correlates with the complexity of fracture networks. However, it remains unclear whether the oscillation time is associated with diversion effectiveness. This paper elucidates the relationship between the water hammer oscillation time and diversion effectiveness by taking the probability of diversion and the treating pressure response as the evaluation criteria. Initially, a high-frequency pressure sensor was installed at the wellhead to sample the water hammer signals. Next, the oscillation times were determined using the feature extraction method. Simultaneously, the probability of diversion and the treating pressure response were calculated using the cepstrum error function and treating pressure curve, respectively. Then, the relationship between the oscillation time and diversion effectiveness was analyzed. Finally, a rapid judgment method for evaluating diversion effectiveness based on the water hammer oscillation time was proposed. The results indicated a negative correlation between the probability of diversion and the oscillation time, with higher probabilities resulting in lower oscillation times. The oscillation times exhibited a negative correlation with the treating pressure response, including the treating pressure increases and diversion pressure spikes, wherein a greater pressure differential led to lower oscillation times. Drawing from the statistics of a shale gas horizontal well in Sichuan, a better diversion effectiveness is associated with fewer oscillations, demonstrating a negative correlation between the diversion effectiveness and the oscillation time in water hammer signatures. Finally, a rapid judgment method for evaluating diversion effectiveness was proposed, utilizing the 95% confidence interval of the mean oscillation time. This paper offers useful insights into evaluating diversion performance in field cases.