This study demonstrates a successful application of Wavelet Analysis to fracturing pressure data across various conventional and unconventional formations to evaluate post treatment data and enhance future stimulation practices. This methodology was compared to the proven Moving Reference Point (MRP) technique developed by Pirayesh et al (2013), to improve the understanding of wavelet analysis. As a fracturing diagnostic tool, the wavelet analysis technique can also be used as companion diagnostic tool alongside previously published methods (such as MRP etc.)

Wavelet analysis of a signal is the mathematical decomposition of that signal into orthogonal wavelet components. The level of decomposition is chosen to discern high and low-resolution parts of the signal. The process represents the signal as a sum of translations and scalings of the chosen wavelet to obtain coefficients of each wavelet.

Fracturing treatment pressure signals occur at various frequencies with finite durations that makes it possible to divide the pressure signals into many components and analyze them individually by wavelet transformation. Discrete Wavelet Transformation by Daubechie wavelets was implemented on fracture propagation pressure to various resolution levels to reveal necessary information within the data. The detail coefficients were analyzed by examining the anomalies at various resolution levels.

Wavelet analysis was performed on various shale and conventional fracturing data. Some interesting patterns are readily discernable from the wavelet detail coefficients. For instance, during the injection of proppants, there is an amplitude change in the detail coefficients at the exact moment when the proppant contacts the formation surface. This is expected because wavelet analysis is sensitive to any discontinuity in the system. Furthermore, such amplitude changes are also observed in the analyzed pressure data corresponding to tip screen-out and near wellbore sand-out events. Comparing such events along-side the MRP method paves the way for early detection of screen-out events. A comparison with the MRP technique is also provided in this study. This method reduces the uncertainty in analysis of Nolte-Smith and MRP method by providing an independent estimate of fracture propagation characteristics.

There have been publications discussing wavelet transformations of various formation and reservoir parameters (permeability, reservoir pressure, etc.), and discussing the application of wavelets for noise reduction and data smoothing. However, this is the first study mainly about wavelet analysis of fracture injection pressure data to understand and detect anomalies during various completion treatments. Ultimately, this technique helps to improve treatment designs and efficiency by analyzing fracture and formation behavior of the treatment and enhance decision making during execution, by providing early screen-out detections.

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