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Stochastic flow simulation in 3D porous media

Author

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  • Kolyukhin Dmitry

    (1. Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, D – 10117 Berlin, Germany)

  • Sabelfeld Karl

    (1. Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, D – 10117 Berlin, Germany)

Abstract

Stochastic models and Monte Carlo algorithms for simulation of flow through porous media beyond the small hydraulic conductivity fluctuation assumptions are developed. The hydraulic conductivity is modelled as an isotropic random field with a lognormal distribution and prescribed correlation or spectral functions. It is sampled by a Monte Carlo method based on a randomized spectral representation. The Darcy and continuity equations with the random hydraulic conductivity are solved numerically, using the successive over relaxation method in order to extract statistical characteristics of the flow. Hybrid averaging is used: we combine spatial and ensemble avergaing to get efficient numerical procedure.We provide some conceptual and numerical comparison of various stochastic simulation techniques, and focus on the prediction of applicability of the randomized spectral models derived under the assumption of small hydraulic conductivity fluctuations.

Suggested Citation

  • Kolyukhin Dmitry & Sabelfeld Karl, 2005. "Stochastic flow simulation in 3D porous media," Monte Carlo Methods and Applications, De Gruyter, vol. 11(1), pages 15-37, March.
    • Handle: RePEc:bpj:mcmeap:v:11:y:2005:i:1:p:15-37:n:6
    DOI: 10.1515/1569396054027292
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    References listed on IDEAS

    as
    1. Kurbanmuradov O. & Sabelfeld K. & Smidts O.F. & Vereecken H., 2003. "A Lagrangian Stochastic Model for the Transport in Statistically Homogeneous Porous Media," Monte Carlo Methods and Applications, De Gruyter, vol. 9(4), pages 341-366, December.
    2. Kurbanmuradov O. & Sabelfeld K. & Koluhin D., 1997. "Stochastic Lagrangian Models for Two-Particle Motion in Turbulent Flows. Numerical Results," Monte Carlo Methods and Applications, De Gruyter, vol. 3(3), pages 199-224, December.
    3. Sabelfeld Karl & Kolyukhin Dmitry, 2003. "Stochastic Eulerian model for the flow simulation in porous media," Monte Carlo Methods and Applications, De Gruyter, vol. 9(3), pages 271-290, September.
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    Cited by:

    1. Kolyukhin Dmitriy & Sabelfeld Karl K., 2015. "Stochastic small perturbation based simulation technique for solving isotropic elastostatics equations," Monte Carlo Methods and Applications, De Gruyter, vol. 21(2), pages 153-161, June.

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