Bayesian uncertainty quantification for flows in heterogeneous porous media using reversible jump Markov chain Monte Carlo methods

A. Mondal, Y. Efendiev*, B. Mallick, A. Datta-Gupta

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

43 Scopus citations

Abstract

In this paper, we study the uncertainty quantification in inverse problems for flows in heterogeneous porous media. Reversible jump Markov chain Monte Carlo algorithms (MCMC) are used for hierarchical modeling of channelized permeability fields. Within each channel, the permeability is assumed to have a lognormal distribution. Uncertainty quantification in history matching is carried out hierarchically by constructing geologic facies boundaries as well as permeability fields within each facies using dynamic data such as production data. The search with Metropolis-Hastings algorithm results in very low acceptance rate, and consequently, the computations are CPU demanding. To speed-up the computations, we use a two-stage MCMC that utilizes upscaled models to screen the proposals. In our numerical results, we assume that the channels intersect the wells and the intersection locations are known. Our results show that the proposed algorithms are capable of capturing the channel boundaries and describe the permeability variations within the channels using dynamic production history at the wells. © 2009 Elsevier Ltd. All rights reserved.
Original languageEnglish (US)
Pages (from-to)241-256
Number of pages16
JournalAdvances in Water Resources
Volume33
Issue number3
DOIs
StatePublished - Mar 2010
Externally publishedYes

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