Bayesian uncertainty quantification for flows in heterogeneous porous media using reversible jump Markov chain Monte Carlo methods
KAUST Grant NumberKUS-C1-016-04
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AbstractIn 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.
CitationMondal A, Efendiev Y, Mallick B, Datta-Gupta A (2010) Bayesian uncertainty quantification for flows in heterogeneous porous media using reversible jump Markov chain Monte Carlo methods. Advances in Water Resources 33: 241–256. Available: http://dx.doi.org/10.1016/j.advwatres.2009.10.010.
SponsorsWe would like to acknowledge NSF CMG 0724704 This work is partly supported by Award Number KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).
JournalAdvances in Water Resources