Summary
In this paper, ensemble-based closed-loop optimization is applied to a
large-scale SPE benchmark study. The Brugge field, a synthetic reservoir, is
designed as a common platform to test different closed-loop reservoir
management methods. The problem was designed to mimic real field management
scenarios and, as a result, is by far the largest and most complex test case on
closed-loop optimization. The Brugge field model consists of nine layers with a
total of 44,550 active cells. It has one internal fault and seven rock regions
with different relative permeability and capillary pressure functions. There
are 20 producers and 10 injectors in the field. Noise corrupted production data
are provided monthly. Each well has three different completions that can be
controlled independently. The producing life of the reservoir is 30 years, and
the objective of optimization is to maximize the net present value (NPV) at the
end of 30 years.
Because of the complexity of this test case, several advanced techniques are
used in order to improve the solution of the ensemble-based closed-loop
optimization. First, covariance localization was used to obtain good model
updates with a relatively small ensemble of reservoir models. Localization
alleviated the effect of spurious correlations and made it possible to
incorporate large amounts of data. Second, covariance inflation was used to
compensate for the tendency of small ensembles to lose variability too quickly.
When covariance inflation was used together with localization, variability in
the ensemble was maintained. Third, regularization was also used in the
ensemble-based optimization to reduce the effect of spurious correlations and
to smooth the optimized control parameters. Fourth, normalized saturations were
used in the state vector because different rock regions had different relative
permeability endpoint saturations. Finally, the addition of global parameters
such as relative permeability curves and initial oil/water contact (IOWC)
reduced the tendency for overshoot. The resulting combination of ensemble-based
data assimilation and optimization performed very well on the benchmark study,
achieving an NPV within 1% of the value obtained by the test organizers with
known geology.
© 2010. Society of Petroleum Engineers
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History
- Original manuscript received:
31 October 2008
- Revised manuscript received:
20 February 2009
- Manuscript approved:
27 February 2009
- Published online:
11 February 2010
- Version of record:
24 February 2010
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