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Multi-physics Markov chain Monte Carlo methods for subsurface flows

Author

Listed:
  • Ginting, V.
  • Pereira, F.
  • Rahunanthan, A.

Abstract

In CO2 sequestration in deep saline aquifers, contaminant transport in subsurface, or oil or gas recovery, we often need to forecast flow patterns. In the flow forecasting, subsurface characterization is an important step. To characterize subsurface properties we establish a statistical description of the subsurface properties that are conditioned to existing dynamic (and static) data. We use a Markov chain Monte Carlo (MCMC) algorithm in a Bayesian statistical description to reconstruct the spatial distribution of two important subsurface properties: rock permeability and porosity. The MCMC algorithm requires repeatedly solving a set of nonlinear partial differential equations describing displacement of fluids in porous media for different values of permeability and porosity. The time needed for the generation of a reliable MCMC chain using the algorithm can be too long to be practical for flow forecasting. In this paper we develop computationally fast and effective methods of generating MCMC chains in the Bayesian framework for the subsurface characterization. Our strategy consists of constructing a family of computationally inexpensive preconditioners based on simpler physics as well as on surrogate models such that the number of fine-grid simulations is drastically reduced in the generation MCMC chains. We assess the quality of the proposed multi-physics MCMC methods by considering Monte Carlo simulations for forecasting oil production in an oil reservoir.

Suggested Citation

  • Ginting, V. & Pereira, F. & Rahunanthan, A., 2015. "Multi-physics Markov chain Monte Carlo methods for subsurface flows," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 118(C), pages 224-238.
    • Handle: RePEc:eee:matcom:v:118:y:2015:i:c:p:224-238
    DOI: 10.1016/j.matcom.2014.11.023
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    References listed on IDEAS

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    1. Pereira, F. & Rahunanthan, A., 2011. "A semi-discrete central scheme for the approximation of two-phase flows in three space dimensions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(10), pages 2296-2306.
    2. Ginting, V. & Pereira, F. & Rahunanthan, A., 2014. "Rapid quantification of uncertainty in permeability and porosity of oil reservoirs for enabling predictive simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 99(C), pages 139-152.
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    Cited by:

    1. Akbari, Hani & Engsig-Karup, Allan P., 2018. "Screening wells by multi-scale grids for multi-stage Markov Chain Monte Carlo simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 151(C), pages 15-28.
    2. Al-Mamun, A. & Barber, J. & Ginting, V. & Pereira, F. & Rahunanthan, A., 2020. "Contaminant transport forecasting in the subsurface using a Bayesian framework," Applied Mathematics and Computation, Elsevier, vol. 387(C).

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