Multi-physics Markov Chain Monte Carlo Methods for Subsurface Flows . Ginting, V., Pereira, F., & Rahunanthan, A. Mathematics and Computers in Simulation , 118:224-238, 2015. ![Multi-physics Markov Chain Monte Carlo Methods for Subsurface Flows [link]](https://bibbase.org/img/filetypes/link.svg "link")
Paper doi abstract bibtex Abstract In \CO\ 2 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.
@article{Ginting2015224,
title = "Multi-physics {M}arkov {C}hain {M}onte {C}arlo {M}ethods for {S}ubsurface {F}lows ",
journal = "Mathematics and Computers in Simulation ",
volume = "118",
number = "",
pages = "224-238",
year = "2015",
issn = "0378-4754",
doi = "http://dx.doi.org/10.1016/j.matcom.2014.11.023",
url = "http://www.sciencedirect.com/science/article/pii/S0378475414003231",
author = "V. Ginting and F. Pereira and A. Rahunanthan",
keywords = "MCMC",
keywords = "Porous media",
keywords = "Multi-physics",
keywords = "Multi-stage ",
abstract = "Abstract In \{CO\} 2 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. "
}
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