Suppose a 5 ml slug of water having a NaCl concentration of 100 grams/liter were injected into the medium depth piezometer on the up-gradient (left) side of the "ant farm" model shown below, and that the model extends a great distance into the computer screen.



What concentration of salt would we expect in the shallow down-gradient piezometer after 1.5 minutes? Assume the following:
hydraulic conductivity (K) =200 m/day.
Gradient (i) = 0.25 ft/ft.
effective porosity (NE) = 0.23
dispersivity () = 0.36 in
dispersivities in the y and z directions are 1/10th that in the x direction
molecular diffusion (D*) = 1.55 x 10-6 in2/sec
distance between piezometer nests = 8 in
vertical distance between shallow and medium depth piezometers = 3 in

For your convenience, I include the appropriate expression here:

where:
C = concentration [M/L3]
x, y, z = are orthogonal distances from the initial position of the mass
X, Y, Z = are orthogonal distances from the center of mass
= average linear velocity of ground water [L/T ]
t = time since mass was released [ T ]
M = mass introduced at time 0 at x=y=z=0
Dx, Dy, Dz = dispersion coefficients in the x, y, & z directions [L2/T ]
Note: dispersivity varies with scale of plume migration, as well as, direction and each dispersivity is multiplied by the velocity in the x direction

Calculate your answer, being extremely careful with respect to using consistent units, then check yourself by deciding whether the answer is reasonable, and visiting the key. If you want to know if your answer is correct before viewing the key, click answer for the value.

KEY TO EXERCISE FOR EXPLORING 1D CONTAMINANT TRANSPORT, SLUG SOURCE