Bayesian Reservoir History Matching Considering Model and Parameter Uncertainties

This paper presents a consistent Bayesian solution for data integration and history matching for oil reservoirs while accounting for both model and parameter uncertainties. The developed method uses Gaussian Process Regression to build a permeability map conforming to collected data at well bores. F...

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Bibliographic Details
Published in:Mathematical geosciences 2012-07, Vol.44 (5), p.515-543
Main Authors: Elsheikh, A. H., Jackson, M. D., Laforce, T. C.
Format: Article
Language:English
Subjects:
Bayesian analysis
Chemistry and Earth Sciences
Computer Science
Earth and Environmental Science
Earth Sciences
Earth, ocean, space
Exact sciences and technology
Geotechnical Engineering & Applied Earth Sciences
Hydrocarbons
Hydrogeology
Inverse problems
Markov analysis
Monte Carlo simulation
Normal distribution
Physics
Sedimentary rocks
Statistics for Engineering
Uncertainty
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Summary:This paper presents a consistent Bayesian solution for data integration and history matching for oil reservoirs while accounting for both model and parameter uncertainties. The developed method uses Gaussian Process Regression to build a permeability map conforming to collected data at well bores. Following that, an augmented Markov Chain Monte Carlo sampler is used to condition the permeability map to dynamic production data. The selected proposal distribution for the Markov Chain Monte Carlo conforms to the Gaussian process regression output. The augmented Markov Chain Monte Carlo sampler allows transition steps between different models of the covariance function, and hence both the parameter and model space are effectively explored. In contrast to single model Markov Chain Monte Carlo samplers, the proposed augmented Markov Chain Monte Carlo sampler eliminates the selection bias of certain covariance structures of the inferred permeability field. The proposed algorithm can be used to account for general model and parameter uncertainties.
ISSN:1874-8961
1874-8953
DOI:10.1007/s11004-012-9397-2