The relative dispersion framework for the non-reactive and reactive
solute flux in
aquifers is presented in terms of the first two statistical moments. The
solute flux is
described as a space–time process where time refers to the solute
flux breakthrough
and space refers to the transverse displacement distribution at the control
plane. The
statistics of the solute flux breakthrough and transversal displacement
distributions
are derived by analysing the motion of particle pairs. The results indicate
that
the relative dispersion formulation approaches the absolute dispersion
results on
increasing the source size (e.g. >10 heterogeneity scales). The solute
flux statistics,
when sampling volume is accounted for, show a flattened distribution for
the solute
flux variance in the space–time domain. For reactive solutes, the
solute flux shows
a tailing phenomenon in time while solute flux variance exhibits bi-modality
in
transverse distribution during the recession stage of the solute breakthrough.
The
solute flux correlation structure is defined as an integral measure over
space and time,
providing a potentially useful tool for sampling design in the subsurface.