We use homogenization theory to investigate the asymptotic
macrodispersion in arbitrary nonuniform velocity fields, which show
small-scale fluctuations. In the first part of the paper, a
multiple-scale expansion analysis is performed to study transport
phenomena in the asymptotic limit epsilon << 1, where epsilon
represents the ratio between typical lengths of the small and large
scale. In this limit the effects of small-scale velocity fluctuations
on the transport behavior are described by a macrodispersive term, and
our analysis provides an additional local equation that allows
calculating the macrodispersive tensor. For Darcian flow fields we show
that the macrodispersivity is a fourth-rank tensor. If
dispersion/diffusion can be neglected, it depends only on the direction
of the mean flow with respect to the principal axes of anisotropy of
the medium. Hence the macrodispersivity represents a medium property.
In the second part of the paper, we heuristically extend the theory to
finite epsilon effects. Our results differ from those obtained in the
common probabilistic approach employing ensemble averages. This
demonstrates that standard ensemble averaging does not consistently
account for finite scale effects: it tends to overestimate the
dispersion coefficient in the single realization.