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Reservoir Characterization Integrating
Well Observations, Seismic Data and
Production History
Bj rn Kare Hegstad and Henning Omre
Department of Mathematical Sciences
Norwegian University of Science and Technology
Trondheim, Norway
September 1998

This is the nal report from the project "Reservoir characterization integrating well, seismic
and production data".
The goal for this project is to establish a stochastic model integrating all kinds of information
in reservoir characterization and to specify a corresponding sampling procedure. A synthetic
test case is used to explore the model and how much di erent sources of information increase
accuracy and reduce uncertainty.
We would like to thank Alfhild Eide for allowing us to use here work on integration of
seismic data as a base for the current work. Without her results we would not have a ying
start. We are also grateful to Hakon Tjelmeland and Alfhild Eide for allowing us to use
their software for fast generation of large Gaussian elds. Also our contacts in Norsk Hydro,
Charlotte Tj lsen and Eivind Damsleth, have been giving us valuable feedback and help on
how reservoir characteristics are related.
The project is nanced by Norsk Hydro A.S.
September 1998
Bj rn Kare Hegstad and Henning Omre.

A stochastic model for a 3D reservoir integrating well observations, seismic data and production history is presented.
A true reservoir, not constructed by generating a realization from the prior model, is dened. Data are observed from this reservoir and various simulation studies including di erent
amount of data is performed.
The stochastic model is illustrated by a directed graph. This graph is used to illustrate
the relations between the variables involved. These relations could be physical relations,
empirical relations between reservoir characteristics, the relation between observations and
reality, and conditional independence. Simplifying assumptions are discussed and utilized to
de ne a sampling algorithm. The algorithm is de ned by sequential sampling of Gaussian and
log-Gaussian elds, and a accept-reject step where Markov chain Monte Carlo or rejection
sampling can be used. The time consuming part in the algorithm, is the evaluation of a uid
ow simulator.
The simulation study demonstrates that seismic data adds valuable global information on the
reservoir characteristics and reduce the number of uid ow simulation runs for each accepted
realization. In some cases the ratio of accepted r...
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