A cubic underground storage tank (1 meter thick x 10 meters square) with its top at a depth of 10 meters below the ground surface and generally even with the water table surface was leaching a contaminant at a concentration of 700 mg/L from its down gradient face into ground-water flow at the prevailing flow velocity. The aquifer had the following properties:
K = 3.0 x 10-5m/s
dh/dl = 0.002
effective porosity = 0.23
dispersivity () = 10m
dispersivity in the y is 1/5th that in the x direction
dispersivity in the z is 1/10th that in the x direction
D* = 1 x 10-9m2/s
let us now assume that the contaminant:
has a half-life of 0.5 years, and
sorps to the solids with a distribution coefficient of 1x10-4 ml/mg
while the soil:
has a total porosity of 0.27
has a particle density of 2.65 g/cc



Calculate the contaminant concentration at the same time and location, i.e.:
in a ground-water sample collected from a well 15 meters down gradient after 1 year. The well has a total depth of 14 meters and is screened from 13 to 14 meters depth. The well is offset laterally from the center of the tank by a distance of 5 meters. When you want to confirm your answer, click answer for the value.

For your convenience, I include the appropriate expression here:

(Domenico 1987 - An analytical method for multidimensional transport of a decaying contaminant species - Journal of Hydrology, v. 91, p. 49-58)

where:
Co = source concentration [M/L3]
C = concentration [M/L3]
x = distance from the source in the direction of flow
y, z = orthogonal distances from the center of the plane source
= average linear velocity of ground water [L/T ]
t = time since continuous concentration release began [ T ]
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

erf = the error function ERF
erfc = the complimentary error function ERFC


FOR DOWNWARD SPREADING ONLY, substitute Z for Z/2

FOR NO SPREADING IN THE z DIRECTION, increase CO/8 to CO/4 and omit the erf terms for z.


Calculate your answer, being extremely careful with respect to using consistent units and noticing how the answer is expressed (e.g. as Concentration or relative Concentration, then check yourself by deciding whether the answer is reasonable, by visiting the key.


Calculate your answer, being extremely careful with respect to using consistent units and noticing how the answer is expressed (e.g. as Concentration or relative Concentration, then check yourself by deciding whether the answer is reasonable, and visiting the key.

KEY TO EXERCISE FOR EXPLORING 3D CONTAMINANT TRANSPORT, CONTINUOUS SOURCE with SORPTION and DECAY