longitudinal dispersion in nonuniform isotropic porous media

shows a histogram of 10000 particle locations after a time t * = V tId
s g
= 100, with Peclet = 10000. The number of steps required before the
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asymptotic dispersion coefficient applies is 2.6xl0 6 , while n = 150 for
Figure 3.3. The dispersion coefficient at this point is only 54% of
its asymptotic value, but the coefficient of determination between the
histogram and the standard Gaussian profile is 0.965. Thus, no
exaggerated skewness of the tracer profile is expected from this
theory, even in the extreme near field.
The change 1n the dispersion coefficient during the initial stages
of longitudinal transport has not been observed experimentally and is
apparently not significant over the length scales important in
laboratory measurements (Haring and Greenkorn, 1970). Figure 2.5 shows
that the experimentally determined longitudinal dispersion coefficients
match the asymptotic theory fairly well (within 50%) even under
extremely high Peclet number conditions when the column lengths were
clearly not long enough to reach the asymptotic limit. The simulation
is computationally time-consuming for calculation of the asymptotic
longitudinal dispersion coefficient since the particle trajectories
must be carried out for a sufficient distance downstream. At high
Peclet numbers this downstream distance becomes too large for practical
calculations. The analysis of the random walk as given by Saffman
(1959) for the asymptotic longitudinal dispersion coefficient provides
a direct method for calculating the asymptotic dispersion coefficient
and requires only trivial modification to be used for a nonuniform
medium.