Traveling time and traveling length for flow in porous media

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.

4 pages including 9 figures, Minor corrections in text