Pressure Matching for Hydrocarbon Reservoirs: A Case Study in the Use of Bayes Linear Strategies for Large Computer Experiments
In the oil industry, fluid flow models for reservoirs are usually too complex to be solved analytically and approximate numerical solutions must be obtained using a ‘reservoir simulator’, a complex computer program which takes as input descriptions of the reservoir geology. We describe a Bayes linear strategy for history matching; that is, seeking simulator inputs for which the outputs match closely to historical production. This approach, which only requires specification of means, variances and covariances, formally combines reservoir engineers’ beliefs with data from fast approximations to the simulator. We present an account of our experiences in applying the strategy to match the pressure history of an active reservoir. The methodology is appropriate in a wide variety of applications involving inverse problems in computer experiments.
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- Craig, P.S., Goldstein, M., Seheult, A.H. and Smith, J.A. (1996). Bayes linear strategies for matching hydrocarbon reservoir history. In Berger et al., editors, Bayesian Statistics 5. Oxford.Google Scholar
- Goldstein, M. (1996). Prior inferences for posterior judgements. In M.L.D. Chiara et al., editors, 10M International Congress of Logic, Methodology and Philosophy of Science. Kluwer, to appear.Google Scholar
- Statistical Sciences Inc. S-PLUS Reference Manual, Version 3.2 StatSci, a division of MathSoft Inc., Seattle, 1993.Google Scholar
- Mattax, C.C. and Dalton, R.L. (1990). Reservoir Simulation. Society of Petroleum Engineers.Google Scholar
- Goldstein, M. (1988). The Data Trajectory, in Bayesian Statistics 3, ed. Bernardo, J. M., et. al., Oxford University Press.Google Scholar
- Zellner, A. (1996). Bayesian Methods of Moments/Instrumental Variable (BMOM/IV) Analysis of Mean and Regression Models, in Prediction and Modeling: In Honor of Seymour Geisser, eds. Lee, J. C., A. Zenner, W. O. Johnson, Springer-Verlag.Google Scholar