Abstract
We study the distributions of traveling length l and minimal traveling
time t(min) through two-dimensional percolation porous media
characterized by long-range spatial correlations. We model the dynamics
of fluid displacement by the convective movement of tracer particles
driven by a pressure difference between two fixed sites (''wells'')
separated by Euclidean distance r. For strongly correlated pore networks
at criticality, we find that the probability distribution functions P(l)
and P(t(min)) follow the same scaling ansatz originally proposed for the
uncorrelated case, but with quite different scaling exponents. We relate
these changes in dynamical behavior to the main morphological difference
between correlated and uncorrelated clusters, namely, the compactness of
their backbones. Our simulations reveal that the dynamical scaling
exponents d(l) and d(t) for correlated geometries take values
intermediate between the uncorrelated and homogeneous limiting cases,
where l*similar tor(l)(d) and t(min)*similar tor(t)(d), and l* and
t(min)* are the most probable values of l and t(min), respectively.
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