Use of Wavelet Transform in PDG Data Treatment

Abstract

Since the beginning of the 80´s, more and more Pressure Downhole Gauges (PDG´s) were installed in production and injection wells. The main purpose was well monitoring and evaluation of reservoir performance. This kind of gauge provides a large amount of data, but there are different problems that do not allow their complete use. These problems are related to quantity and quality. Most of the softwares are not able to handle with all the data available in a long recording period, the main objective of the use of PDG´s. Besides that, gauges present noise and strange data (outliers). It becomes necessary to treat the data before its use in the study of reservoir behavior. The concept of wavelet transform was developed about a century ago, but it was during the 80´s that it received practical application. Now it is used in a wide variety of applications, and, especially in data treatment, it presents two main features that make it attractive: smoothing of the signal and retention of the details. In this paper we use the wavelet transform to overcome the main problems and enhance the reliability of the information contained in the data. We tested different wavelets with several decomposition levels against actual and synthetic data. The outliers must be removed before the wavelet analysis in order to enhance its performance. We show that there is no unique "correct" wavelet transform to apply in any flow period. For example, for some datasets the Daubechies 1 wavelet at decomposition level 6 was used for flow periods, and level 3 for build up. It is important to notice that the use of high decomposition levels may cause loss of information, as it is shown in some examples. The wavelet analysis was also used to recognize transients from its ability to enhance the details. This is particularly useful to identify flow rate changes when they have not been reported, for example. Finally, we propose a methodology to treat the data before its use in posterior interpretation. Introduction Reservoir characterization has been a major research subject in reservoir engineering. The main goal is to estimate the spatial distribution of the reservoir properties, e.g., permeability and porosity, by integration of all kinds of available information1. Pressure data from pressure downhole gauges (PDG) provide more information than traditional pressure tests. The long period data can indicate how reservoir properties are changing during exploitation. The use of these instruments is very recent and a specific methodology to data interpretation is not available yet. The use of long-term data requires special handling and interpretation techniques due to the instability of in-situ permanent data acquisition systems, extremely large volume of data, incomplete flow rate history caused by unmeasured and uncertain rate changes, and dynamic changes in reservoir conditions and properties throughout the life of the reservoir2. The reservoir pressure is probably the most important information to monitor reservoir condition, to characterize the reservoir, to find best recovery methods and to determine future behavior of reservoir. The characteristics of simulated pressure transient data were investigated in the frequency domain3. Wavelet transform was introduced to accomplish the time-frequency analysis of long-term pressure transient data. A set of data can be treated as a signal. Most of the signals in practice are time-domain signals in their raw format, but frequently the information that cannot be readily seen in the time-domain can be seen in the frequency domain. Mathematical transformations are applied to signals to obtain further information from signals that is not readily available in the raw signal. There is a huge list of transforms and the Fourier Transform is probably the most commonly used. The Wavelet Transform is a kind of transform which provides time-frequency representation. It is a useful tool for analyzing time series with many different timescales or changes in variance. Wavelet Transform is now used in a wide variety of applications in the areas of medicine, biology, data compression, etc. A significant benefit provided by Wavelet Transform is its capability to provide smoothing of the basic signal, and retention or even enhancement of the details4. The Wavelet Transform is a band pass filter with a known response function. The inverse filter may reconstruct the original time series. This filter is capable to remove amplitude regions at all frequencies. Due to this property, it can be used to remove noise, isolate single events or multiply events that present varying frequency, for example.

Wavelet Filtering of Permanent Downhole Gauge Data

“…This distinctive behavior of the Haar wavelet, for drawdowns and build-ups, was previously reported by Ribeiro et al (2006). This distinctive behavior of the Haar wavelet, for drawdowns and build-ups, was previously reported by Ribeiro et al (2006).…”

Listening to the Reservoir—Interpreting Data From Permanent Downhole Gauges

“…The successful use of wavelet analysis to handle the noise and outliers has been reported by several authors, including Kikani and He (1998), Athichanagorn (1999), Athichanagorn et al (2002), Ouyang and Kikani (2002), and Ribeiro and Pires (2006). Figs.…”

“…2) from real data, in this case by use of the spline wavelet. Other families of wavelets also are used [see Ribeiro and Pires (2006) for a comparison].…”