Summary
Since the beginning of the 1980s, more downhole pressure gauges (DPGs) 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 various problems that do not allow their
complete use. These problems are related to quantity and quality. Most software
is not able to handle the main objective for using DPGs with all the data
available in a long recording period. 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 (WT) was
developed about a century ago, but it was during the 1980s 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 WT 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” WT to apply in any flow
period. For example, for some data sets the Daubechies 1 wavelet at
decomposition Level 6 was used for flow periods, and Level 3 for buildup. It is
important to notice that the use of high decomposition levels may cause loss of
information, as 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 information (Lu and Horner 2000).
Pressure data from DPGs 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 for data interpretation is not available yet. The use of
long-term data requires special handling and interpretation techniques because
of the instability of in-situ permanent data-acquisition systems, the extremely
large volume of data, the incomplete flow rate history caused by unmeasured and
uncertain rate changes, and dynamic changes in reservoir conditions and
properties throughout the life of the reservoir (Athichanagorn et al.
2002).
The reservoir pressure is probably the most important information to monitor
reservoir condition, to characterize the reservoir, to find the best recovery
methods, and to determine the future behavior of the reservoir. The
characteristics of simulated pressure-transient data were investigated in the
frequency domain (Kikani and He 1998). WT 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 seen readily 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 are many transforms, and the Fourier transform (FT) is probably the
most commonly used. The WT is a kind of transform that provides time-frequency
representation. It is a useful tool for analyzing time series with many
different time scales or changes in variance.
The WT is now used in a wide variety of applications in the areas of
medicine, biology, and data compression. A significant benefit provided by the
WT is its capability to provide smoothing of the basic signal, and retention or
even enhancement of the details (Soliman et al. 2003).
© 2008. Society of Petroleum Engineers
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History
- Original manuscript received:
25 September 2006
- Meeting paper published:
24 September 2006
- Revised manuscript received:
9 May 2007
- Manuscript approved:
1 June 2007
- Version of record:
20 February 2008
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