Solution to GLY 414/514 In-Class Example on Dispersion

Using these plots of variance (s²) in the direction of flow versus time, determine the longitudinal coefficient of dispersion and the dispersivity for these three media of increasing disorder. Which of these media would be considered statistically homogeneous (stationary)?

K = random, with mean 1 m/d
dh/dx: 0.02
porosity: 0.20

We will need average linear velocity for these calculations. We apply Darcy's Law where:

The longitudinal variance is related to the longitudinal coefficent of dispersion by:

which is the equation of a straight line:

so the slope of a plot of s2 versus time is

we note that the dispersivity is related to the coefficient of dispersion by:

Now we can calculate D and a for each plot

Here we have two slopes so the medium is statistically inhomogeneous or non-stationary. We could pick two slopes: