Integrate Fracture Closure with Water Hammer Model to Estimate Hydraulic Fracture Dimensions: Field Case Studies with Microseismic Validation

Abstract

To improve the accuracy of fracture geometry interpretation using water hammer data, we propose the G-function-based resistive/capacitive/inertance (G-RCI) model to address the limitation of the traditional RCI equivalent-circuit water hammer model, which neglects closure-related pressure decline after shut-in. The G-function is integrated into the RCI framework to impose a closure-controlled pressure-decline constraint associated with leakoff and fracture stiffness. Sensitivity analysis was conducted to clarify the influence of key parameters. An automated water hammer signal identification and curve fitting algorithm combined with global optimization technology was developed, with the optimal fitting algorithm determined via orthogonal experiments. Field validation of two hydraulically fractured horizontal wells in sandstone formations shows that the model-inverted fracture half-length and height agree well with microseismic monitoring results, with relative errors of about 6% for fracture half-length and 17% for fracture height. In this study, we further demonstrate that time-lapse water hammer analyses from multiple shut-in events within a fracturing stage can be used to estimate the evolution of fracture dimensions with cumulative injection volume, providing a single-well complement to offset-well diagnostics, such as sealed wellbore pressure monitoring and fiber-optic sensing.