Abstract
In subsurface characterization using a history matching algorithm subsurface properties are reconstructed with a set of limited data. Here we focus on the characterization of the permeability field in an aquifer using Markov Chain Monte Carlo (MCMC) algorithms, which are reliable procedures for such reconstruction. The MCMC method is serial in nature due to its Markovian property. Moreover, the calculation of the likelihood information in the MCMC is computationally expensive for subsurface flow problems. Running a long MCMC chain for a very long period makes the method less attractive for the characterization of subsurface. In contrast, several shorter MCMC chains can substantially reduce computation time and can make the framework more suitable to subsurface flows. However, the convergence of such MCMC chains should be carefully studied. In this paper, we consider multi-MCMC chains for a single–phase flow problem and analyze the chains aiming at a reliable characterization.
F. Pereira—The research by this author is supported in part by the National Science Foundation under Grant No. DMS 1514808, a Science Without Borders/CNPq-Brazil grant and UT Dallas.
A. Rahunanthan—The research by this author is supported by the National Science Foundation under Grant No. HRD 1600818.
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Acknowledgments
The authors would like to thank the Department of Mathematics and Computer Science of the Central State University for allowing to run the MCMC simulations on the NSF-funded CPU-GPU computing cluster.
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Mamun, A., Pereira, F., Rahunanthan, A. (2018). Convergence Analysis of MCMC Methods for Subsurface Flow Problems. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2018. ICCSA 2018. Lecture Notes in Computer Science(), vol 10961. Springer, Cham. https://doi.org/10.1007/978-3-319-95165-2_22
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DOI: https://doi.org/10.1007/978-3-319-95165-2_22
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