Multiple Markov Chains Monte Carlo Approach for Flow Forecasting in Porous Media*

Ginting, Victor; Pereira, Felipe; Rahunanthan, Arunasalam

doi:10.1016/j.procs.2012.04.076

Cited by 10 publications

(4 citation statements)

References 17 publications

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“…In this subsection we discuss Karhunen-Loève (KL) expansion [28,33] to reduce dimension of uncertainty space for permeability and porosity. This reduction technique has been applied within a Bayesian statistical framework in [11,17,18,20,19,21]. Here we reproduce the technique for the sake of completeness of the discussion.…”

Section: Parametrization Of Uncertaintymentioning

confidence: 99%

“…The quality of the characterization of the underlying formations was accessed through the prediction of future fluid flow production. They also considered parallelizing the generation of MCMC chains to speed-up the posterior exploration in [18,21]. In [18] the authors addressed this issue using several parallel MCMC chains for flow prediction.…”

Section: Introductionmentioning

confidence: 99%

“…They also considered parallelizing the generation of MCMC chains to speed-up the posterior exploration in [18,21]. In [18] the authors addressed this issue using several parallel MCMC chains for flow prediction. In [21] the authors parallelized single MCMC chains using a prefetching technique implemented on GPUs and showed that the parallelization can make the Bayesian approach computationally tractable for subsurface characterization and prediction of porous media flows.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Multi-physics Markov chain Monte Carlo methods for subsurface flows

Ginting

Pereira

Rahunanthan

2015

Mathematics and Computers in Simulation

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Section: Parametrization Of Uncertaintymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Multi-physics Markov chain Monte Carlo methods for subsurface flows

Ginting

Pereira

Rahunanthan

2015

Mathematics and Computers in Simulation

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“…MCMC methods have been applied in several areas of science and engineering, and have attracted the attention of many research groups [19,33]. There are many recent and important developments related to gradient-based MCMC procedures.…”

Section: Introductionmentioning

confidence: 99%

Conditioning by Projection for the Sampling from Prior Gaussian Distributions

Ali¹,

Mamun²,

Pereira³

et al. 2021

Preprint

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In this work we are interested in the (ill-posed) inverse problem for absolute permeability characterization that arises in predictive modeling of porous media flows. We consider a Bayesian statistical framework with a preconditioned Markov Chain Monte Carlo (MCMC) algorithm for the solution of the inverse problem. Reduction of uncertainty can be accomplished by incorporating measurements at sparse locations (static data) in the prior distribution. We present a new method to condition Gaussian fields (the log of permeability fields) to available sparse measurements. A truncated Karhunen-Loève expansion (KLE) is used for dimension reduction. In the proposed method the imposition of static data is made through the projection of a sample (expressed as a vector of independent, identically distributed normal random variables) onto the nullspace of a data matrix, that is defined in terms of the KLE. The numerical implementation of the proposed method is straightforward. Through numerical experiments for a model of second-order elliptic equation, we show that the proposed method in multi-chain studies converges much faster than the MCMC method without conditioning. These studies indicate the importance of conditioning in accelerating the MCMC convergence.

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