(
)
where β = ρf L / Tat Tat Tf + ατI / hc
will not be a problem. However, thawing the sludge
by air convection only will not be possible. Fortunately,
(0.35 W/m C)
there is a considerable amount of solar radiation avail-
θ = fraction of settled sludge per unit depth
able during the summer months.
of thawed sludge (0.15 for aerobically
digested sludge)
Freezing depth
Pth = thawing period (hr)
The freezing depth (Df) can be predicted from
T at = average ambient air temperature during
(Martel 1989):
thaw (C)
α = solar absorptance of the sludge (0.9)
Pf (Tf Taf )
τ = transmittance of the roof material (0.9
Df =
1
ε
for fiber reinforced polyester roof)
(1)
ρf L +
hc 2Kfs
I = average insolation during the thawing
period (W/m2).
where Pf = freezing period (hr)
Tf = freezing point temperature (0C)
If the months of March through September are used
for freezing, then the remaining months (October
Taf = average ambient temperature during
freezing (C)
through February) will be used for thawing, draining,
ρf = density of frozen sludge (917 kg/m3)
drying, and removing the sludge for retrograde back
to the U.S. Most of this time will be needed for thaw-
L = latent heat of fusion (93 W hr/kg)
ing and draining, which occur simultaneously under
ε = thickness of each sludge layer (m)
normal operation. For this analysis, it is assumed that
the thawing period (Pth) will include the months of
sludge (2.21 W/m C).
October, November, December, and January (2952
hours). The average air temperature ( T at ) and insola-
tion ( I ) during this period are 8.9C and 265 W/m2,
Examination of Table 1 suggests a freezing period
respectively. Substituting these values into eq 2 gives
(Pf) consisting of the months of March through Sep-
tember, since these months have no significant solar
β = 917 93/ (8.9 0 +(0.9 0.9 265)/ 7.5)
insolation. This period is equivalent to 5136 hours. The
= 4325
average temperature ( Taf ) during this period is 23C.
Assuming a sludge layer thickness (ε) of 0.08 m, and
0.35 2
substituting the remaining values into eq 1, we
Y=
+
0.15 7.5
obtain
5136[0 - (-23)]
12
2 0.35 2952
Df =
= 8.9 m.
0.35
+
-
= 1.5 m.
1 + 0.1
917 93
0.15 4325
0.15 7.5
7.5 2 2.21
Thus, eq 2 predicts that only 1.5 m of sludge can be
Thus, eq 1 predicts that 8.9 m of sludge can be fro-
thawed during the selected thawing period. This depth
zen in the freezing bed during an average winter at
is lower than would be expected in more temperate
McMurdo, assuming that sludge will be applied in 8-
climates because of the subfreezing air temperature dur-
cm layers and that each layer would be applied as soon
ing the thawing period. Thawing in this case is achieved
as the previous layer had frozen. The equation also
assumes that the surface of the bed is kept free of
snow.
Thawing depth with supplemental heating
According to the CTE (1999) report, the sewage
Thawing depth
effluent has a temperature of 23C. If this effluent was
The equation for predicting the thawing design
used to heat the freezing bed, the thawing depth could
depth (Y) is (Martel 1989):
be increased for the October to February thawing pe-
riod. One way to do this would be to build a pipe net-
1/ 2
2K ss Pth
2
K ss
work into the concrete base of the freezing bed. Warm
K ss
Y =
+
-
(2)
secondary effluent from the treatment plant could then
θhc
θβ
θhc
be pumped through this network during the thawing
4
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