The water hammer signatures, which can be observed after pump shutdown at the end of a hydraulic fracture treatment, have proven to contain useful information about the geometry of generated hydraulic fractures. This paper presents a novel hydraulic fracture diagnostics approach using the water hammer data. A water hammer model that describes the pressure transient in hydraulically fractured horizontal well is established. In the model, a new multi-cluster hydraulic fracture boundary condition is derived by considering the perforation friction and leak-off in fractures. The method of characteristics is applied to efficiently solve the water hammer model. The water hammer signals can be effectively reproduced under different fracture characteristics. The MCMC method is applied to construct the posterior statistics of fracture parameters (e.g., width, length, height). The proposed approach is first verified by a series of synthetic models, and then applied to a real field case of a multi-stage hydraulic-fractured horizontal well in a shale gas reservoir to demonstrate its applicability and efficiency.


Hydraulic fracturing has been the commonly used stimulation technique for the economic development of shale/tight gas and oil reservoirs. Although rapid progress has been made in fracturing technology, accurate characterization of hydraulic fracture is a great challenge which hinders the evaluation of fracturing efficiency and prediction of well productivity.

Various techniques have been developed to characterize hydraulic fractures, which can be divided into two categories, i.e., direct monitoring methods and indirect interpretation methods. Direct monitoring methods mainly include micro-seismic monitoring (Le Calvez et al. 2007; Zhu et al. 2017), fiber-optic sensing (Liu et al. 2020; Liu et al. 2023), coring observation (Maity et al. 2018), and downhole imaging (Roberts et al. 2018a; Roberts, et al. 2018b). These methods are usually characterized by their high accuracy, but limited by the high cost and limited observation range. Instead, indirect interpretation methods, including flowback analysis (Chen et al. 2018; Liu et al. 2019), pressure transient analysis (He et al. 2017; Wang et al. 2021), and water hammer analysis (Carey et al. 2015; Hu et al. 2022), are commonly used low-cost fracture diagnosis techniques. However, flowback analysis and pressure transient analysis usually require the production data after the well completion, which can hardly provide the real-time fracture information during hydraulic fracturing. The water hammer analysis has the advantages of short testing time, low-cost and real time.

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