This paper focuses on an automated way to generate multiple history-matched
reservoir models with the inclusion of both geological uncertainty and varying
levels of trust in the production data, using wavelet methods. As opposed to
previously developed automated history-matching algorithms, this methodology
not only ensures geological consistency in the final models but also includes
uncertainty in the production data.
A data distribution, such as a permeability field, can be (reversibly)
transformed into wavelet space in which it is fully described by a set of
wavelet coefficients. It was found that different subsets of the collection of
wavelet coefficients can be constrained separately to (a) the production
history and (b) the geological constraints. This means that the history match
need be performed only once, after which multiple realizations can be generated
by adjusting only the second subset of coefficients.
The ability to include both geological and production-data uncertainty into
the reservoir model automatically is of great consequence to reservoir modeling
and, hence, to reservoir management, risk analysis, and making key economic
decisions. A more complete and realistic reservoir model will lead to better
reservoir production and development decisions.
Reservoir modeling is an important step in forecasting the performance of a
reservoir, forming the basis for reservoir management, risk analysis, and
making key economic decisions. A history match, however, is not a sufficient
condition for a reservoir to make better predictions for future production. The
model should at least conform to all the available data and the geologist’s
prior conception of the reservoir. Thus, the purpose of reservoir modeling is
to use all available sources of information to develop such a reservoir model.
This model then can be used to forecast future performance and optimize
It is essential to integrate all the different sources of data to provide
the most complete reservoir model or models (Landa and Horne 1997; Landa 1997;
Wang 2001). Our model certainty is always limited by the data available to us.
As such, it is never possible to infer or develop a reservoir model with full
certainty. However, the optimal use of all consistent data available will yield
reservoir models that are less and less uncertain. Herein lies the significance
of methodologies that can realistically and efficiently integrate different
sources of reservoir information.
Reservoir data are, generally speaking, divided into two categories:
production data (e.g., pressure and water-cut histories from wells) and all
other sources of data (e.g., core samples, seismic, and well logs). This second
category of data depends on reservoir properties like porosity and permeability
in a relatively direct way. Core samples can be used to provide porosity and
permeability measurements at specific locations (well locations);
semivariograms (Deutsch and Journel 1998; Isaaks and Srivastava 1989) obtained
from outcrops, for example, act as spatial statistics information, and seismic
surveys may provide 3D impedance distributions that can be inverted and used as
“soft-conditioning data” at the corresponding locations. These different
sources of data can be combined together with different approaches (e.g.,
Bayesian probability techniques) to give a single set of probabilities.
© 2006. Society of Petroleum Engineers
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- Original manuscript received:
7 June 2004
- Revised manuscript received:
6 March 2006
- Manuscript approved:
16 March 2006
- Version of record:
20 June 2006