  Many theoretical treatments of transport in heterogeneous Darcy flows
consider advection only. When local-scale dispersion is neglected,
flux-weighting persists over time; mean Lagrangian and Eulerian flow velocity
distributions relate simply to each other and to the variance of the underlying
hydraulic conductivity field. Local-scale dispersion complicates this
relationship, potentially causing initially flux-weighted solute to experience
lower-velocity regions as well as Taylor-type macrodispersion due to transverse
solute movement between adjacent streamlines. To investigate the interplay of
local-scale dispersion with conductivity log-variance, correlation length, and
anisotropy, we perform a Monte Carlo study of flow and advective-dispersive
transport in spatially-periodic 2D Darcy flows in large-scale, high-resolution
multivariate Gaussian random conductivity fields. We observe flow channeling at
all heterogeneity levels and quantify its extent. We find evidence for
substantial effective retardation in the upscaled system, associated with
increased flow channeling, and observe limited Taylor-type macrodispersion,
which we physically explain. A quasi-constant Lagrangian velocity is achieved
within a short distance of release, allowing usage of a simplified
continuous-time random walk (CTRW) model we previously proposed in which the
transition time distribution is understood as a temporal mapping of unit time
in an equivalent system with no flow heterogeneity. The numerical data set is
modeled with such a CTRW; we show how dimensionless parameters defining the
CTRW transition time distribution are predicted by dimensionless heterogeneity
statistics and provide empirical equations for this purpose.
