  We study the distributions of traveling length l and minimal traveling time t
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) 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 for correlated geometries take values intermediate between
the uncorrelated and homogeneous limiting cases.
