Summary
In this study, we show significant improvements over conventional
pressure-transient analysis on the basis of nonlinear regression by using total
least squares (TLS), which minimizes errors in both pressure and time
simultaneously. To our knowledge, TLS has not been applied to
pressure-transient analysis before in this sense.
TLS regression is not an easy problem to solve mathematically, especially
for nonlinear pressure-transient-model functions. In this work, we compare four
different versions of TLS. We formulate a robust approximation of the TLS
solution, which can handle a variety of tests and reservoir models yet does not
compromise the performance of the analysis. We show that our technique reduces
ambiguity in the estimation of parameters to a large extent, especially in the
presence of noise in time. Using our TLS algorithm, we obtain much narrower
confidence intervals on the parameter estimates of a variety of real data sets,
compared to the conventional least squares (LS) approach. For synthetic data
sets, we observe that the TLS estimates are often closer to the true values
than estimates made with LS, especially for poorly determined problems. When
the deviation is in pressure only, TLS and LS results are comparable. However,
in the presence of deviations in time in addition to pressure, the performance
of TLS algorithms is substantially better. We, therefore, expect that our
technique will provide more accurate estimation of reservoir parameters,
allowing for better forecasting of reservoir performance.
© 2010. Society of Petroleum Engineers
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History
- Original manuscript received:
3 August 2009
- Meeting paper published:
5 October 2009
- Revised manuscript received:
22 March 2010
- Manuscript approved:
6 April 2010
- Published online:
5 August 2010
- Version of record:
24 August 2010
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