Quantitative Analysis of Hydraulic Fracture Geometry and Its Relationship with Key Water Hammer Pressure Features

Hydraulic fracturing technology is crucial for promoting oil and gas resource development. In recent years, water hammer fracture diagnostic techniques, derived from the water hammer effect in hydraulic fracturing, have garnered significant attention due to their low cost and ease of operation. The characteristic parameters of water hammer pressure are closely related to fracture geometry parameters. Monitoring the characteristics of water hammer pressure at the wellhead allows for rapid assessment of fracturing effectiveness. This study comprehensively considers wellbore friction, perforation friction, and the fluid loss effect within hydraulic fractures, establishing a mathematical model for the evolution of water hammer pressure during multi-cluster staged fracturing in horizontal wells. Based on field-monitored water hammer data from multiple stages, this study employed water hammer fracture diagnostics to inversely determine the geometric parameters of fractures in different fracturing stages. Characteristic parameters of the water hammer pressure, including the initial amplitude, number of oscillations, oscillation duration, and attenuation rate, were calculated for different well sections. Furthermore, the correlations between these water hammer characteristics and the fracture geometric parameters were analyzed. The correlation analysis between characteristic parameters of water hammer pressure and geometric parameters of hydraulic fractures indicates that under conditions of longer fracture half-length and smaller fracture height, the generated water hammer pressure exhibits a higher initial amplitude, fewer oscillations, a shorter oscillation duration, and a larger attenuation rate. The research findings can facilitate rapid estimation of fracture geometry using water hammer pressure, thereby optimizing fracturing design and enhancing fracturing effectiveness.