Comprehensive model for multi-fracture localization based on water hammer signals: Evaluation and field application

Determining fracture locations in hydraulic fracturing is essential for diagnostic purposes. Water hammer waves generated during pump shut-in in hydraulic fracturing create pressure fluctuations as they pass through fractures. The pressure signals collected at the wellhead contain valuable information about subsurface fracture positions. This study, based on the water hammer equation, establishes an internal flow model within pipelines, considering both the pump shut-in process and subsurface fracture boundary conditions (fracture permeability, fracture storage, and fracture inertia effects). The method of characteristics (MOC) is employed for numerical discretization to simulate the wellhead pressure fluctuations during pump shut-in. A novel fracture localization method is proposed, combining comprehensive filtering, cepstral analysis, and velocity conversion. Comprehensive filtering effectively removes various noises present in the collected signals. Subsequently, cepstral analysis identifies negative peaks in the cepstral domain generated by pulse functions at fracture locations. This information is then used to determine the propagation time of pressure waves from fractures to the wellhead, which is converted to depth by wave velocity. Through numerical simulations and field experiments, the method's effectiveness is validated, demonstrating its capability to efficiently filter out signal noise, identify cepstral negative peaks from pulse functions at fractures, and provide precise inversion of fracture locations. This method holds significant guidance for practical field applications.