Calibration of Continuous Wavelet Transform for Dynamic Hydraulic Fracture Propagation with Micro-Seismic Data: Field Investigation

Abstract

Abstract The aim of this study is to investigate the potential of the Continuous Wavelet Transform (CWT) as a mathematical tool for improving the understanding of hydraulic fracture propagation mechanisms and evaluating interactions between fractures and formation. The study examines one of the CWT techniques: the normalized scalogram technique for understanding fracture propagation. However, the implementation of these techniques requires calibration using observed measured variables, such as microseismic events. To overcome this obstacle, micro-seismic events, and pressure data recorded in wells are used to calibrate the normalized CWT scalogram. The objective of this study is to validate the effectiveness of these approaches as cost-effective techniques for understating the fracture propagation modes in scenarios where micro-seismic events are not available. The Continuous Wavelet Transform (CWT) is a powerful mathematical technique that can be used for analyzing hydraulic fracturing data. It involves convolving a short wavelet signal with the measured pressure data in a smooth and continuous manner, applying various dilation and translation operations to produce a scaled representation of the pressure data. This process acts as a local microscope, enhancing the high-frequency information in the pressure signal. The resulting CWT scalogram is normalized to represent fracturing pressure data, which can provide valuable insights into treatment propagation. However, a major challenge in implementing these techniques is the need for calibration using observed measured variables, such as microseismic events. To address this issue, microseismic data recorded in the Bakken was used to calibrate the normalized CWT scalogram. The objective of this study was to validate the effectiveness of this approach as a cost-effective alternative for dynamic fracture events detection in cases where microseismic events are not available. The validation of the normalized CWT scalogram was carried out by calibrating against microseismic events recorded in the Bakken. This confirmation was established by assessing the correlation between fracture events detected by microseismic events and those observed using the normalized CWT scalogram. This paper validates the application of normalized CWT scalograms for understanding fracture propagation modes. These techniques offer a cost-effective approach to optimizing hydraulic fracturing in unconventional reservoirs.