Summary
It is demonstrated that a method for multiscale history matching can be used
to improve efficiency and/or quality of the solution when achieving a
fine-scale match as compared to history-matching directly on the fine scale.
Starting from a given fine-scale realization, coarser models are generated
using a global upscaling technique in which the coarse models are “history
matched” with respect to the solution at the fine scale. Conditioning to
dynamic data is performed by history matching a coarse model, and this model is
then successively refined using a combination of downscaling and history
matching until a model that matches dynamic data is obtained at the finest
scale. Bias in predicted data because of upscaling errors may be taken into
account. The advantage of this procedure is that the large-scale corrections
are obtained using fast models which—combined with proper downscaling
procedures—provide a better initial model for the final adjustment on the fine
scale. Coarse-scale history matching also provides a regularization of the
fine-scale match, making the process less dependent on a correct prior model.
With the proposed methodology, a series of models with varying degrees of
complexity—all being consistent with both static and dynamic data—may be
generated without additional cost. Effects of including a priori information
and different initial downscaling techniques, such as sampling or block kriging
with sequential Gaussian simulation (BKSGS), are investigated using two
synthetic reservoir models.
Introduction
In Aanonsen and Eydinov (2006), a multiscale method was proposed for
more-effective history matching of petrophysical properties. Starting from a
given fine-scale realization, coarser models are generated by use of a global
upscaling technique in which the coarse models are “history matched” with
respect to the solution at the fine scale. Conditioning to dynamic data is
accomplished by history matching a coarse model, and this model is then
successively refined using a combination of downscaling and history matching
until a model that matches dynamic data is obtained at the finest scale. It was
demonstrated through some simple examples that this procedure may reduce the
computational effort and/or improve the quality of the match as compared to
history matching directly on the fine scale. In this paper, the technique is
taken further, by taking into account bias in the coarse-scale solution. Also,
effects of including a priori information and different initial downscaling
techniques, such as sampling and BKSGS, are investigated.
In traditional multiscale estimation, a series of estimations is performed
in which the resolution of the zonation is increased for each step in the
sequence for examples, see Liu (1993); Chavent and Bissel (1998); and Yoon et
al. (1999). This approach reduces both the computational effort and the
overparameterization problem. The multiscale estimation was improved by Ben
Ameur et al. (2002); Grimstad et al. (2003); and Grimstad and Mannseth (2004),
who introduced a method for adaptive multiscale estimation in which the
resolution is increased only in some regions of the reservoir of each stage in
the sequence. Other types of multiscale approaches include updating a fine
model on the basis of simulations performed on a coarse model (Mezghani and
Roggero 2001).
Common for all of the above-mentioned multiscale techniques is that the
computational grid is kept the same while the parameter resolution is changed.
In the method used here, the forward problem is also computed on grids of
varying resolution. The main challenge with the method is that it requires an
efficient way for tuning the properties in every grid cell in the model. We
have used commercial software in which the number of parameters (which, with
this method, is equal to the number of active grid cells) is limited to 500.
However, with software based on the adjoint method (Li et al. 2003; Gao and
Reynolds 2006), this procedure may be applied to much larger cases—up to real
field-model size.
© 2008. Society of Petroleum Engineers
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History
- Original manuscript received:
7 December 2004
- Meeting paper published:
31 January 2005
- Revised manuscript received:
8 February 2007
- Manuscript approved:
30 May 2007
- Version of record:
25 February 2008
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