Improved Understanding of Dynamic Fracture Behavior in Unconventional Horizontal Wells Using Wavelet Transformation
Authors: Unal Ebru , Rezaei Ali , Siddiqui Fahd , Likrama Fatmir , Soliman M. , Dindoruk Birol 
Published: September 2019

abstract
In the last decade, technical advancements have greatly improved the design and execution efficiency of well completions, leading to improved recovery from unconventional reservoirs. However, analyzing fracture diagnostic tests in unconventional plays are still challenging due to high uncertainty in predictive capabilities in the context of fracture dynamics during treatment. The main objective of this study is to identify fracture behavior during injection and pressure fall-off periods in hydraulic fracturing treatments and diagnostic fracture injection tests (DFIT), respectively.
In this study, discrete wavelet transformation (DWT) was used to analyze real field injection and fall-off data in the wavelet domain. The analyzed data are from multi-stage hydraulic fracturing operations and DFIT in unconventional horizontal wells. DWT coefficients reveal very crucial information related to the nature of the events within recorded signals; they also reveal various patterns that are hard to recognize otherwise. The high-frequency components of the pressure and rate signals (detail coefficients) that are calculated by the wavelet transformation determine localization and separation of various events. We compared the identified events for injection and fall-off periods with moving reference point (MRP) and G-function analysis, respectively.
The main advantage of our proposed approach is that it is based on real-time data and does not require any assumptions related to existing or created fractures. Also, it is very sensitive to physical changes in the system; thus, it reveals hidden information related to those changes. Consequently, the energy of detail coefficients represents several events at different frequencies. We used pseudo-frequency of wavelet coefficients as a diagnostic tool for an accurate comparison of fracture propagation and fracture closure events to determine similarities and differences between them. For example, the signal energy of detail coefficients from the wavelet transformation of hydraulic fracturing data demonstrates abrupt frequency changes during dilation or fracture height growth during fracture propagation. Therefore, we were able to identify those events by energy density analysis in both time and pseudo-frequency domains in an objective manner, which otherwise was not possible with conventional methodologies such as G- function derivative analysis.
This paper details the successful methodology for effective implementation of a new fracture diagnostic technique for fracturing operations or DFITs in unconventional horizontal wells. This new fracture diagnostic method does not require any reservoir or fracture pre-assumptions; it mainly relies on the pressure behavior, which is a result of various events at different frequencies. Pressure fall-off behavior of a DFIT gives essential information related to closure event of the created mini-fracture. Identification of these events at different pseudo-frequency ranges improves the understanding of the dynamic fracture behavior also the characteristics of the reservoir. Unlike many other diagnostic techniques, this data-driven approach requires minimum input/data for analysis. This approach also lends itself to real-time application quite easily.