Traveling time and traveling length for flow in porous media

Youngki Lee; Jose S. Andrade Jr.; Sergey V. Buldyrev; Nikolay V. Dokholyan; Shlomo Havlin; Peter R. King; Gerald Paul; H. Eugene Stanley

arXiv · cond-mat/9903066

Traveling time and traveling length for flow in porous media

Youngki Lee·Jose S. Andrade Jr.·Sergey V. Buldyrev·Nikolay V. Dokholyan·Shlomo Havlin·Peter R. King·Gerald Paul·H. Eugene Stanley

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Abstract

We study traveling time and traveling length for tracer dispersion in porous media. We model porous media by two-dimensional bond percolation, and we model flow by tracer particles driven by a pressure difference between two points separated by Euclidean distance $r$. We find that the minimal traveling time $t_{min}$ scales as $t_{min} \sim r^{1.40}$, which is different from the scaling of the most probable traveling time, ${\tilde t} \sim r^{1.64}$. We also calculate the length of the path corresponding to the minimal traveling time and find $\ell_{min} \sim r^{1.13}$ and that the most probable traveling length scales as ${\tilde \ell} \sim r^{1.21}$. We present the relevant distribution functions and scaling relations.

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Youngki Lee, Jose S. Andrade Jr., Sergey V. Buldyrev, Nikolay V. Dokholyan, Shlomo Havlin, Peter R. King, Gerald Paul, H. Eugene Stanley. 1999-08-18. Traveling time and traveling length for flow in porous media. https://arxiv.org/abs/cond-mat/9903066

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