Deterministic linear Bayesian updating of state and model parameters

O. Pajonk*, B.V. Rosić, H.G. Matthies

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

Abstract

Bayesian estimation has become an important topic for inverse problems in the context of hydrocarbon recovery. The conceptual and computational advantages due to direct integration with uncertainty quantification workflows are appealing. Especially, linear Bayesian techniques like the ensemble Kalman filter (EnKF) have been successfully used in numerous cases. However, such techniques have difficulties in some applications which are often caused by sampling errors, a limited ensemble size, or the sometimes large number of required samples. In this work we present and discuss a closely related linear Bayesian technique which is based on orthogonal expansions of the stochastic spectrum of the involved random variables and random fields. Basically being a family of fully deterministic implementations of the well-known projection theorem of Hilbert spaces, the technique is conceptually simple, yet powerful. Since they are fully deterministic, these methods avoid all sampling errors. First combined parameter and state estimation results with a low-dimensional chaotic model are presented, using a specific choice of orthogonal expansion. These are compared to results obtained with EnSRF, since it is a close relative to these spectral estimation methods. Challenges and opportunities for applications to the inverse problem of identification for hydrocarbon reservoirs are discussed.

Original languageEnglish
Title of host publicationConference Proceedings, ECMOR XIII
Subtitle of host publication13th European Conference on the Mathematics of Oil Recovery, Sep 2012,
PublisherEuropean Association of Geoscientists and Engineers
ISBN (Print)978-90-73834-30-9
DOIs
Publication statusPublished - 2012
Externally publishedYes
Event13th European Conference on the Mathematics of Oil Recovery, ECMOR 2012 - Biarritz, France
Duration: 10 Sep 201213 Sep 2012
Conference number: 13

Conference

Conference13th European Conference on the Mathematics of Oil Recovery, ECMOR 2012
Abbreviated titleECMOR 2012
CountryFrance
CityBiarritz
Period10/09/1213/09/12

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