Summary
Nonlinear regression is a well-established technique in well-test
interpretation. However, this widely used technique is vulnerable to issues
commonly observed in real data sets--specifically, sensitivity to noise,
parameter uncertainty, and dependence on starting guess. In this paper, we show
significant improvements in nonlinear regression by using transformations on
the parameter space and the data space. Our techniques improve the accuracy of
parameter estimation substantially. The techniques also provide faster
convergence, reduced sensitivity to starting guesses, automatic noise
reduction, and data compression.
In the first part of the paper, we show, for the first time, that Cartesian
parameter transformations are necessary for correct statistical representation
of physical systems (e.g., the reservoir). Using true Cartesian parameters
enables nonlinear regression to search for the optimal solution homogeneously
on the entire parameter space, which results in faster convergence and
increases the probability of convergence for a random starting guess. Nonlinear
regression using Cartesian parameters also reveals inherent ambiguities in a
data set, which may be left concealed when using existing techniques, leading
to incorrect conclusions. We proposed suitable Cartesian transform pairs for
common reservoir parameters and used a Monte Carlo technique to verify that the
transform pairs generate Cartesian parameters.
The second part of the paper discusses nonlinear regression using the
wavelet transformation of the data set. The wavelet transformation is a process
that can compress and denoise data automatically. We showed that only a few
wavelet coefficients are sufficient for an improved performance and direct
control of nonlinear regression. By using regression on a reduced wavelet basis
rather than the original pressure data points, we achieved improved performance
in terms of likelihood of convergence and narrower confidence intervals. The
wavelet components in the reduced basis isolate the key contributors to the
response and, hence, use only the relevant elements in the pressure-transient
signal. We investigated four different wavelet strategies, which differ in the
method of choosing a reduced wavelet basis.
Combinations of the techniques discussed in this paper were used to analyze
20 data sets to find the technique or combination of techniques that works best
with a particular data set. Using the appropriate combination of our techniques
provides very robust and novel interpretation techniques, which will allow for
reliable estimation of reservoir parameters using nonlinear regression.
© 2011. Society of Petroleum Engineers
View full textPDF
(
1,601 KB
)
History
- Original manuscript received:
29 March 2010
- Meeting paper published:
27 May 2010
- Revised manuscript received:
6 August 2010
- Manuscript approved:
18 August 2010
- Published online:
29 March 2011
- Version of record:
15 September 2011
View Cart
