  We present a numerical simulation study of advective-diffusive scalar
transport in three-dimensional high-contrast discontinuous permeability fields,
generated with a truncated pluri-Gaussian geostatistical approach. A range of
permeability contrasts, correlation lengths, and P\'eclet numbers are studied
to characterise the transition to non-Fickian transport behaviour. This is
triggered by high permeability contrasts between different zones and is
enhanced by the presence of connected higher permeability channels, which are
characterised by high advective flow velocities. In this case, the overall
transport behaviour deviate from the macroscopic advection-dispersion model
based on a Fickian analogy. The numerical experiments are run with an Eulerian
approach using a novel unified numerical framework based on the finite-volume
library \of, for i) generating random pluri-Gaussian porous media, ii) solving
the steady state Darcy-scale flow, iii) solving the advection diffusion
equation, iv) computing post-processing quantities such as first order
statistics, spatial probability density functions and breakthrough curves. We
identify a hierarchy of non-Fickian transport triggering factors, the strength
of permebility contrast being the pivotal driver. The P\'eclet number and the
characteristic length at which facies transitions are observed as secondary
factors. Transport remains Fickian when the facies conductivities differ by up
to one order of magnitude. Greater permeability contrasts act strengthen the
emergence of fast flow channels leading to non-Fickian transport.
