Fracture size inversion method based on water hammer signal for shale reservoir

Hydraulic fracturs size inversion plays an important role on evaluating hydraulic fracturing efficiency. Fracture size can be calculated by microseism events or all the pressure data generated by hydraulic fracturing stimulations. These methods are time-consuming. However, the sudden shutoff of pumping can induce a special data known as the water hammer signal. The size of this data is much fewer than others so using it to calculate fracture size is efficient. This study proposes a method of using water hammer signal to work out the hydraulic fracture size. The numerical simulation model is proposed based on the transient flow model to describe the water hammer behavior. The impacts of fracture on water hammer behavior are represented by three parameters (R,C and I). Through these parameters, the fracture size can be calculated. The accuracy of this method is validated by comparing fracture size inversion results between different methods. The results show that the parameter C and R have obvious impacts on water hammer signal and they can cause the amplitude of water hammer signal alternate from 5 to 2 MPa. In addition, this method is accurate for fracture size calculation and the overall error between its results and ones from normal methods is about 6.28%. This method is more suitable for fractures away from horizontal well toe than ones near to well toe. The mean error of fractures away from well toe is only 3.49% but it is 12.75% for fracture near well toe. It is because that the fracture structure is complex near well toe. It indicates that the more accurate relationship between fracture size and parameters (R,C and I) is required for fracture with complex structure.