Looking for help. Thank you! High-level radioactive waste is buried in a cavern
ID: 119206 • Letter: L
Question
Looking for help. Thank you!
High-level radioactive waste is buried in a cavern in an unfractured shale at the depth of 1,000 m below ground surface. The burial zone is separated from the nearest overlying aquifer by a vertical thickness of 100 m of shale. The shale has a hydraulic conductivity of 1012 m/s and a vertical hydraulic gradient of 102 directed upward. In the shale, the effective diffusion coefficient (D*) for the radionuclides is 1010 m2/s. After 1,000 years the waste will start to move out into the shale. Will the radioactive plume remain within the shale layer after 100,000 years?Explanation / Answer
Since shale is a low permeability medium, the coefficient of mechanical dispersion would be negligible. Therefore, the diffusion is the only mechanism to be considered to check whether the plume remains within shale or not.
The waste starts to move out into shale in 1000 years and we need to check the distance covered by the plume after 100000 years. Therefore the time period (t) is 99000 years.
We know Darcy's law:
q/A = k.( h/L)
where q= quantity, m3/s
A = area. m2
k= hydraulic conductivity, 10-12 m/s
( h/L) = hydraulic gradient, 10-2
Now, since we have the diffusion coefficient, D*, we can determine the area using,
A = D* x t = 10-10 * 99000 * 365 * 24 * 60 * 60 = 312.2 m2
Also, q = D* x d
where d = vertical diffusion height
Therefore, q=10-10 *d
Substituting values in Darcy's law,
q/A = k.( h/L)
10-10 *d/312.2 = 10-12 * 10-2
d = 312.2 * 10-14 / 10-10 = 0.0312 m
Therefore, even after 100000 years the plume will not go out of the shale as the distance it will travel is only 3.12 cm.
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