Grant: Frozen-Ground Waste Containment
3
Table 2. Total lengths of pipe and the lengths in unsaturated and saturated soil under the revised design
for three thicknesses of the perched water table
Perched
water table
Total pipe length (m)
thickness (m)
Unsaturated soil Saturated soil
2
580.20
99.52
4
493.40
186.32
6
405.64
274.08
Table 3. Calculated thermal properties of the saturated and unsaturated soils and the attendant times to
freeze and total energy demand.
Soil
cvu
cvf
ku
kf
t
Q
MJ C m-3
◦ -1
◦ -1
-1
MJm-1
W C m
days
Unsat.
2.4813
1.8610
0.9233
1.7361
17.519
202.58
Sat.
3.8225
2.5316
1.7361
1.7361
17.121
252.70
Calculation of time and energy
other factors, inefficiencies in the refrigeration and
brine-distribution systems and pumps needed to cir-
requirements
culate the brine.
The time required to form a frozen ground wall was
calculated via:
Revised design
a2-1
R2L + ( 2 lrn ar )cuf νs
t
=
(8)
By a similar calculation, the revised design with a
4kf νs
2-m-thick perched aquifer would require 32,501 kilo-
c
.
2
R
vf νs
watt hours of energy. The 4-m-thick and 6-m-thick
)-
ln(
2-1
a
r0
perched aquifers would require 33,491 and 34,493
L + ( 2 lrn ar )cuf νs
kilowatt hours of energy. These are more than six
The energy required to form a frozen ground wall
times the energy requirement of the original design.
was calculated via:
L
(
2
a -1
cvf νs
+( r
Q = πR2
)cuf νs +
9)
R
2 ln ar
2 log( r )
Concluding remarks
0
[Sanger and Sayles, 1979]. The calculated times and
energy requirements are presented in Table 3.
The estimated capital and operating costs of the re-
vised design were roughly 6.4 times the original de-
sign. This dramatic increase in costs suggested that
Original design
the expected benefits of the revised plan should be
evaluated to determine if they were commensurate.
The original design had a total of 107.87 m of pipe
installed in unsaturated soil. Each meter of pipe
would withdraw 202.58 MJ for a total of energy re-
quirement of 4,977.5 kilowatt hours. The actual en-
ergy consumption would be higher due to, among
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