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Multiscale flow and transport model in three-dimensional fractal porous media

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Abstract

This paper proposes a multiscale flow and transport model which can be used in three-dimensional fractal random fields. The fractal random field effectively describes a field with a high degree of variability to satisfy the one-point statistics of Levy-stable distribution and the two-point statistics of fractional Levy motion (fLm). To overcome the difficulty of using infinite variance of Levy-stable distribution and to provide the physical meaning of a finite domain in real space, truncated power variograms are utilized for the fLm fields. The fLm model is general in the sense that both stationary and commonly used fractional Brownian motion (fBm) models are its special cases. When the upper cutoff of the truncated power variogram is close to the lower cutoff, the stationary model is well approximated. The commonly used fBm model is recovered when the Levy index of fLm is 2. Flow and solute transport were analyzed using the first-order perturbation method. Mean velocity, velocity covariance, and effective hydraulic conductivity in a three-dimensional fractal random field were derived. Analytical results for particle displacement covariance and macrodispersion coefficients are also presented. The results show that the plume in an fLm field moves slower at early time and has more significant long-tailing behavior at late time than in fBm or stationary exponential fields. The proposed fractal transport model has broader applications than those of stationary and fBm models. Flow and solute transport can be simulated for various scenarios by adjusting the Levy index and cutoffs of fLm to yield more accurate modeling results.

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Acknowledgements

This study was financially supported by the National Science Council (NSC) of Taiwan under grant NSC96-2628-E-006-089-MY3. Part of this research was sponsored by National Cheng-Kung University (NCKU) under grant R046.

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Authors and Affiliations

  1. Department of Resources Engineering, National Cheng-Kung University, Tainan City, Taiwan, ROC

    Kuo-Chin Hsu & Kuan-Chih Chen

  2. Research Center for Soil and Water Resources and Natural Disaster Prevention, National Yunlin University of Science and Technology, Douliou, Yunlin, Taiwan, ROC

    Kuan-Chih Chen

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  1. Kuo-Chin Hsu
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  2. Kuan-Chih Chen
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Correspondence to Kuo-Chin Hsu.

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Hsu, KC., Chen, KC. Multiscale flow and transport model in three-dimensional fractal porous media. Stoch Environ Res Risk Assess 24, 1053–1065 (2010). https://doi.org/10.1007/s00477-010-0404-1

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