Dispersivity
The dominant mechanism of subsurface mass transport is groundwater advection. Geologic
heterogeneity contributes significantly to advective transport because it creates variations
in velocity that influence patterns of groundwater flow. As a result, advective transport
is extremely sensitive to how subsurface geologic heterogeneities are distributed in space.
When heterogeneities are distributed uniformly in space, and when the scale of prediction is
much larger than the scale of the heterogeneities, dissolved mass will migrate through and
around heterogeneities in much the same way as molecules diffuse through liquid under the
influence of a concentration gradient. This spreading phenomenon is referred to as mechanical
mixing. While it arises from an entirely different mechanism than that governing molecular
diffusion, at practical scales the two processes produce the same outcome, and
can be described using Fick's law:
M =  D dC/dx
where M is mass flux per unit length squared per unit time [M/L^{2}T],
D is the diffusion coefficient in units of L^{2}/T, C is concentration [M/L^{3}],
and x is coordinate location. Extension to two and three dimensions is fairly straightforward.
Field scale transport described by this model of molecular diffusion is often
referred to as Fickian transport, and its corresponding diffusion coefficient is called
dispersivity (a) to reflect the fact that dispersion, rather
than molecular diffusion, is the actual mechanism responsible for spreading.
Dispersitivities are generally orders of magnitude larger than diffusion coefficients
because, while diffusion is caused by random molecular motion due to thermal
kinetic energy, mechanical mixing is a consequence of porescale variations in
fluid velocity. Instantaneous concentration breakthrough curves for dissolved mass
that spreads according to Fick's law exhibit bellshaped, or gaussian, behavior.
The rate of spreading can be related to the variance of the gaussian curve via
the equations:
a_{L} = v*s^{2}_{tL}/2t
a_{T} = v*s^{2}_{tT}/2t
where s^{2}_{tL} and s^{2}_{tT}
are variances from instantaneous breakthrough curves (C vs. time) in the longitudinal and transverse directions, v is velocity (constant over
time), t is time since displacement, and x is plume displacement distance in the longitudinal direction.
Note that, if breakthrough curves in the transverse direction are not available, empirical evidence suggests that
a_{T} is roughly onetenth of a_{L}.
Classical Fickian Dispersivity From Breakthrough Curve Data


