The ensemble Kalman filter (EnKF) is a subject of intensive investigation
for use as a reservoir management tool. For strongly nonlinear problems,
however, the EnKF can fail to achieve an acceptable data match at certain times
in the data assimilation process. Here, we provide two iterative EnKF
procedures to remedy this deficiency and explore the validity of these
iterative methods compared to the standard EnKF by considering two examples. In
both examples, we are able to obtain better data matches using iterative
methods than with the standard EnKF.
The simplest derivation of the EnKF analysis equation "linearizes"
the objective function by adding the vector of predicted data to the original
combined state vector of model parameters and dynamical variables. We show that
there is no assurance that this trick for turning a nonlinear problem into a
linear problem results in a correct sampling of the pdf one wishes to sample.
However, we show that augmenting the state vector with the data results in a
correct procedure for sampling the probability density function (pdf) if, at
every data assimilation step, the predicted data vector is a linear function of
the combined (unaugmented) state vector. Without this assumption, we know of no
way to show EnKF samples correctly.
© 2009. Society of Petroleum Engineers
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- Original manuscript received:
29 July 2007
- Meeting paper published:
11 November 2007
- Revised manuscript received:
11 December 2008
- Manuscript approved:
12 December 2008
- Published online:
23 July 2009
- Version of record:
28 September 2009