Computational Geosciences

, Volume 18, Issue 5, pp 661–675

A prefetching technique for prediction of porous media flows

ORIGINAL PAPER

DOI: 10.1007/s10596-014-9413-3

Cite this article as:
Ginting, V., Pereira, F. & Rahunanthan, A. Comput Geosci (2014) 18: 661. doi:10.1007/s10596-014-9413-3

Abstract

In many applications in flows through porous media, one needs to determine the properties of subsurface to detect, monitor, or predict the actions of natural or induced forces. Here, we focus on two important subsurface properties: rock permeability and porosity. A Bayesian approach using a Markov Chain Monte Carlo (MCMC) algorithm is well suited for reconstructing the spatial distribution of permeability and porosity, and quantifying associated uncertainty in these properties. A crucial step in this approach is the computation of a likelihood function, which involves solving a possibly nonlinear system of partial differential equations. The computation time for the likelihood function limits the number of MCMC iterations that can be performed in a practical period of time. This affects the consistency of the posterior distribution of permeability and porosity obtained by MCMC exploration. To speed-up the posterior exploration, we can use a prefetching technique, which relies on the fact that multiple likelihoods of possible states into the future in an MCMC chain can be computed ahead of time. In this paper, we show that the prefetching technique implemented on multiple processors can make the Bayesian approach computationally tractable for subsurface characterization and prediction of porous media flows.

Keywords

GPU MCMC Prediction in porous media Pre-fetching Two-phase flow Two-stage MCMC Uncertainty quantification 

Mathematics Subject Classifications (2010)

62F15 65C40 65N06 68M07 68U20 68W10 76T99 

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of WyomingLaramieUSA
  2. 2.Departments of Chemical and Petroleum Engineering and Mathematics, and School of Energy ResourcesUniversity of WyomingLaramieUSA
  3. 3.Department of Mathematics and Computer ScienceEdinboro UniversityEdinboroUSA

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