Most studies in percolation theory assume a random infinite medium,
while natural porous media are neither random nor infinite. A few
studies have examined the impact of short-range correlation structure on
the percolation threshold, but not its broader influence on fluid
transport. Furthermore, there have been no investigations of
longer-range correlation structures such as fBm. We investigate the
impact of exponential and fBm random field connectivity structures on
pore accessibility and tortuosity. In particular, we examine the
porosity fraction which is accessible from the edge of the porous medium
(e.g., a fracture face) but is not part of the infinite cluster. Near
the percolation threshold, this portion of the porosity may have
important contributions to long-term diffusion behavior in the presence
of oscillating boundary conditions, such as intermittent wet/dry cycles
inside Yucca Mountain.