A sudden change in flow in a confined system results in the formation of a series of pressure pulses known as a water hammer. Pump shutdown or valve closure at the conclusion of a hydraulic fracture treatment frequently generates a water hammer, which sends a pressure pulse down the wellbore that interacts with the created fracture before returning towards the surface. The result is a pressure profile that consists of a series of oscillations that attenuate over time due to friction. Created hydraulic fractures have been shown to alter the period, amplitude, and duration of the water hammer signal. The goal of this study was to simulate the water hammer response of hydraulically fractured wells, and quantify how fractures affect the response.

Water hammer pressure signals were simulated in this study with a numerical model that combined the continuity and momentum equations for the wellbore with a hydraulic fracture represented by a circuit with a resistance, capacitance, and inertance (R, C, and I) connected in series. To test how each variable affected the water hammer signal, the R, C, and I variables were each individually altered through a range of values while all else was held constant. Furthermore, field data from several fractured wells were history matched with the numerical model by iteratively altering R, C, and I until an appropriate match was obtained.

Changes in the fracture resistance, capacitance, or inertance are shown to alter the simulated water hammer signature. Variations in capacitance alter the period of water hammer oscillations and the average pressure sustained by the water hammer. Variations in resistance affect the initial water hammer amplitude and the rate of oscillation decay. Variations in inertance affect the period of the water hammer. Field data from hydraulically fractured wells was successfully history matched, and R, C, and I values were obtained for each well. Fracture length, height, and width were calculated from derived expressions based on R, C, and I, and were in good agreement with other fracture parameter estimation methods.  

The results from this work indicate that the water hammer signals at the conclusion of a hydraulic fracturing treatment are affected by the created hydraulic fractures. Thus, water hammer fracture diagnostics will yield important information about the created fracture such as the relative size (derived from the calculated length, width, height) and connectivity (indicated by the resistance value, R) to the wellbore.