Wavelets in Petroleum Industry: Past, Present and Future

Abstract

TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractWavelet is first introduced by Alfred Haar in 1910, but the development of wavelet was very slow until the middle of 1980s. In 1984, Jean Morlet made the wavelet rebirth by developing a new way of analyzing the seismic signals to overcome the deficiencies in the Fourier method. Since then, the new developments of wavelets have fascinated the scientific and engineering communities.A wavelet is a waveform of effectively limited duration that has an average value of zero and wavelets are a family of basis functions, which can separate a signal into distinct frequency packets that are localized in the time domain. Thus, wavelets are well suited to analyze nonstationary data. They can smooth the basic signals and keep the details of basic signals. Therefore, they provide a multiresolution framework for data representation.Wavelet analysis is a rapidly developing area in many disciplines of science and engineering and it is used in a wide variety of applications in the areas of medicine, biology, data compression, etc. In recent years, wavelet analysis has found its application in the petroleum industry. This paper reviews the recent application of wavelet analysis in the industry.Various application examples are discussed, especially the examples in the areas of reservoir characterization, geological model upscaling, and well testing. simple digital filter ideas, shown in Fig.1. Thanks to Daubechies' work, wavelet transform has been widely used in many fields such as pattern recognition, image compression, mechanical fault diagnostic, signal de-noising, signal compression, earthquake diction, and other areas since 1990s.

Development of Marginal/Mature Oil Fields: A Case Study of the Sinclair Field

“…During the screening of production data analysis techniques (8)(9)(10)(11)(12)(13)(14)(15)(16)(17) , which can help derive useful information (interwell connectivity in particular), this method was chosen because of its ability to manage non-stationarity issues. This ability is very important in obtaining meaningful correlations for wells that were started at different dates and have considerable production and complex shut-in history.…”

Stochastic History Matching and Data Integration for Complex Reservoirs Using a Wavelet-Based Algorithm

“…The algorithm described in previous papers (Sahni, 2003, Sahni and Horne 2003, 2004, 2006 used the two-dimensional Nonstandard implementation of Haar wavelets (see Appendix A). The underlying basis function for the Nonstandard Haar wavelet implementation is square thus the methodology based on it was limited in scope to the description of reservoir property distributions for which the number of gridblocks in the x coordinate equaled those in the y coordinate.…”

“…In the context of reservoir parameter estimation a more detailed description of the Haar wavelets and their implementations can be found in Lu (2001), Lu and Horne (2000), Sahni (2003), Sahni and Horne (2003, 2004, 2006. Here we present briefly the implementation of the one-dimensional Haar wavelet transform, followed by a description of their two-dimensional extensions.…”

“…Wavelets have been used in the petroleum industry (Guan 2004) mostly for the analysis of temporal data and more recently for two or higher dimensional reservoir description (Jansen 1998, Panda 2000, Lu 2000. The data-integration algorithm (as described in Sahni 2003, Sahni and Horne 2005, 2006 uses multiresolution wavelet analysis for the efficient integration of different data into the reservoir model at appropriate scales.…”

Singularity spectrum of hydrocarbon fluids in synthetic seismograms

“…Spectral decomposition involves the frequency analysis of the seismic data. Hydrocarbon reservoirs are detected at low frequencies [3][4][5][6][7][8]. The analysis of seismic model and real seismic data indicates that the holder exponent spectrum obtained from spectral decomposition is sensitive to changes in lithology and pore fluid types and therefore can be used to estimate reservoir properties [7].…”