Application of Wavelet Transform to the Analysis of Pressure-Transient Data

Abstract

Summary Although the mathematical concept of "wavelet transform" was developed in the early part of the 20th century, it did not receive practical application until the 1980s. Wavelet transform is now used in a wide variety of applications in the areas of medicine, biology, and data compression, among others. A significant benefit provided by wavelet transform is its capability to provide two functions: Smoothing of the basic signal. Retention or even enhancement of the details. In data analysis, these characteristics allow the user to recognize hidden signals quickly. In well testing, these capabilities can enhance signals that can be masked by other events or by the data frequency itself. Because the derivative techniques currently used in well testing tend to smooth data and conceal certain events, the use of the wavelet transform to analyze the raw data could prove to be very valuable as a major step in enhancing the techniques of modern data analysis. This paper briefly reviews the application of the wavelet transform methodology to data analysis in general and shows why its application to well-testing data in particular is important. It also provides guidelines for the application of this technology to well testing. Several field examples are provided to demonstrate the application of the wavelet transform to well testing and to show how the qualitative and quantitative uses of the method determine wellbore anomalies, boundary effects, and other well-testing phenomena.