South Pole station is closed to cargo shipments for approximately 270 days each year.
It is desirable to maintain a LHe supply at the Pole during the period of closure. In recent years, this has been accomplished by shipping into Pole one or more LHe storage dewars, and transferring LHe from those dewars as needed during the winter. There has never been a transfer of LHe between storage dewars (although this has been extensively discussed), simplifying the analysis.
An assumption which further simplifies the analysis of the problem is this:
Each storage, temporary transport, or experimental dewar which uses or stores LHe causes the LHe in it to evaporate at a constant rate during the time that dewar is in use. |
This is approximately true because the internal construction of a dewar conducts heat inwards to the LHe it holds at a roughly constant rate. (This rate is affected by temperature, and the temperature of the dewar's internal parts changes depending on how full it is, but this is a minor effect which is neglected here.) LHe is also evaporated in the process of transfer from storage to transport dewar and from transport dewar to experimental dewar; this loss is included below as part of the average loss from each dewar, since the transfers occur at regular intervals.
Under this assumption, each dewar has a "hold time" defined by:
hold time = Tdewar = Vdewar/Rdewar ,
where Vdewar = total storage capacity of dewar
Rdewar = rate of evaporation from dewar.
Here are evaporation rates for some of the dewars used at the Pole:
3000 Gallon | 1000 Gallon | Wessington 3820 l | temporary store 250 l | temporary store 100 l | AST/RO | SPARO | SPIFI | ACBAR | NOAA |
Rbig | Rsmall | RWess | R250 | R100 | RASTRO | RSPARO | RSPIFI | RACBAR | RNOAA |
17 to 33 liters/day | 12 to 25 liters/day | 6 to 8 liters/day | 3 liters/day | 2 liters/day | 7 liters/day | 5.5 liters/day | 50 liters/day | 10 liters/day | 5 liters/day |
Each dewar uses R liters each day it is in use. Assume that each dewar is in use for t days, and that the number of dewars is n. Then the total volume of LHe consumed is the sum:
Rbig tbig + nsmall Rsmall tsmall + n250R250 t250 + n100 R100 t100 + RASTRO tASTRO + RSPARO tSPARO + RSPIFI tSPIFI + RNOAA tNOAA = Vtotal
Each winter of operation can be laid out as a spreadsheet:
The winter of 1995 was a success, and a demonstration that winter-over LHe at Pole is possible.
Winter 1995 | ||||
n |
R (liters/day) |
t (days) |
n*R*t (liters) |
|
3000 gallon |
1 |
17 | 270 | 4590 |
1000 gallon | ||||
temp 250 |
3 |
3 | 270 | 2430 |
temp 100 | ||||
AST/RO | 1 | 7 | 270 | 1890 |
NOAA | 1 | 5 | 270 | 1350 |
total on site at closing = 10260 |
The winter of 1996 was a failure, because the 3000 gallon dewar was unavailable and the two 1000 gallon dewars only lasted until August 8:
Winter 1996 | ||||
n |
R (liters/day) |
t (days) |
n*R*t (liters) |
|
3000 gallon |
|
|||
1000 gallon |
2 |
12 | 160 | 3840 |
temp 250 |
2 |
3 | 170 | 1020 |
temp 100 | ||||
AST/RO | 1 | 7 | 170 | 1190 |
NOAA | 1 | 5 | 170 | 850 |
total on site at closing = 6900 |
The winter of 1998 was essentially identical to the winter of 1995:
Winter 1998 | ||||
n |
R (liters/day) |
t (days) |
n*R*t (liters) |
|
3000 gallon |
1 |
17 | 270 | 4590 |
1000 gallon |
|
|||
temp 250 |
3 |
3 | 270 | 2430 |
temp 100 | ||||
AST/RO | 1 | 7 | 270 | 1890 |
NOAA | 1 | 5 | 270 | 1350 |
total on site at closing = 10260 |
Winter 1999 | ||||
n |
R (liters/day) |
t (days) |
n*R*t (liters) |
|
3000 gallon |
1 |
30 | 250 | 7500 |
1000 gallon |
1 |
20 | 90 | 1800 |
temp 250 |
2 |
3 | 270 | 1620 |
temp 100 | 3 | 2 | 30 | 180 |
AST/RO | 1 | 7 | 270 | 1890 |
SPARO | 1 | 8 | 60 | 480 |
SPIFI | ||||
NOAA | 1 | 5 | 270 | 1350 |
total on site at closing = 14820 |
Winter 2000 has been semi-disastrous. Only one of the two 3000 gallon containers was found to contain helium after base closing, and that remaining 3000 gallon container had not been properly maintained and therefore has a high boil-off rate. Cutting AST/RO operations to one receiver dewar, and an improved boil-off rate for SPARO allowed observations to continue through July.
Winter 2000 | ||||
n |
R (liters/day) |
t (days) |
n*R*t (liters) |
|
3000 gallon |
1 |
40 | 120 | 4800 |
1000 gallon |
|
|||
temp 250 |
3 |
3 | 150 | 1350 |
temp 100 | 3 | 2 | 60 | 360 |
AST/RO | 1 | 3 | 150 | 450 |
SPARO | 1 | 5.5 | 150 | 825 |
ACBAR | 0 | 10 | 0 | 0 |
NOAA | 1 | 5 | 150 | 750 |
total on site at closing = 8535 |
Plans for 2001 call for three Wessington storage dewars, 3820 liter model CH-4000, for a total of 11460 liters on-station at base closing.
It is likely that the three Wessington dewars would be
"staged" through the winter, emptied in succession to reduce the total
storage loss. Even so, the plan is inadequate:
Winter 2001 staged Wessington dewars | ||||
n |
R (liters/day) |
t (days) |
n*R*t (liters) |
|
3000 gallon |
0 |
|||
Wessington 1 |
1 |
7 | 90 | 630 |
Wessington 2 |
1 |
7 | 180 | 1260 |
Wessington 3 |
1 |
7 | 270 | 1890 |
temp 250 |
2 |
3 | 270 | 1620 |
temp 100 | 3 | 2 | 60 | 360 |
AST/RO | 1 | 7 | 270 | 1890 |
SPARO | 1 | 5.5 | 90 | 495 |
SPIFI | 0 | 50 | 60 | 0 |
FTS | 1 | 7 | 90 | 630 |
ACBAR | 1 | 10 | 180 | 1800 |
NOAA | 1 | 5 | 270 | 1350 |
total needed for season = 11925 |
||||
actual amount on site = 11460 |
Additional helium is needed on-site at base
closing. This can be accomplished by the delivery of additional helium, to
be stored in other dewars. Suppose that six 250 liter dewars were full, in
addition to the three Wessington dewars. These six 250 liter dewars would
be used for the first 90 days after base closing, until their helium is gone:
Winter 2001 staged Wessington dewars + helium in smaller dewars | ||||
n |
R (liters/day) |
t (days) |
n*R*t (liters) |
|
3000 gallon |
0 |
|||
Wessington 1 |
1 |
7 | 180 | 1260 |
Wessington 2 |
1 |
7 | 270 | 1890 |
Wessington 3 |
1 |
7 | 270 | 1890 |
temp 250 |
6 |
3 | 90 | 1620 |
temp 250 | 2 | 3 | 180 | 1080 |
temp 100 | 3 | 2 | 60 | 360 |
AST/RO | 1 | 7 | 270 | 1890 |
SPARO | 1 | 5.5 | 90 | 495 |
SPIFI | 0 | 50 | 60 | 0 |
FTS | 1 | 7 | 90 | 630 |
ACBAR | 1 | 10 | 180 | 1800 |
NOAA | 1 | 5 | 270 | 1350 |
total needed for season = 14265 |
||||
actual amount on site = 12960 |
Having helium on-site in dewars which have a short hold time does not help very much, as the above example shows. The total consumption goes up by an amount which consumes nearly all of the additional helium.
If instead the three Wessington dewars are supplemented by the
3000 gallon dewar, and it works better than it did in 2000, arriving at Pole
half full with an improved evaporation rate, there will be a total of 16914 liters on-station at base closing.
This plan is marginally compatible with a successful season, but still leaves
some single points of failure. Staging of the dewars would provide some
backup and margin.
Winter 2001, Wessington + 3000 gallon | ||||
n |
R (liters/day) |
t (days) |
n*R*t (liters) |
|
3000 gallon |
1 |
30 | 100 | 3000 |
Wessington |
3 |
7 | 270 | 5670 |
temp 250 |
2 |
3 | 270 | 1620 |
temp 100 | 3 | 2 | 60 | 360 |
AST/RO | 1 | 7 | 270 | 1890 |
SPARO | 1 | 5.5 | 90 | 495 |
SPIFI | 0 | 50 | 60 | 0 |
FTS | 1 | 7 | 90 | 630 |
ACBAR | 1 | 10 | 180 | 1800 |
NOAA | 1 | 5 | 270 | 1350 |
total needed at closing = 16815 |
||||
total available at closing = 16914 |
A comparison of the two examples above shows the futility of attempting to preserve helium by transferring it to short hold-time dewars (the 250 liter dewars have a hold time of about 90 days) from a longer hold-time dewar (the 3000 gallon dewar has a hold time of 200 to 350 days, depending on how well it is working). It is crucial that the helium be stored in dewars that have intrinsically long hold times, the longer the better. The Wessington dewars have the best hold time of any dewars available to us.
The original CARA plan for 2001 reqested four Wessington dewars,
for a total of 15280 liters on-station at base closing. The CARA plan
called for unmodified dewars with a slightly lower boil-off rate. This
plan would have also worked.
Winter 2001, 4X Wessington | ||||
n |
R (liters/day) |
t (days) |
n*R*t (liters) |
|
3000 gallon |
0 |
|||
Wessington |
4 |
6.5 | 270 | 7020 |
temp 250 |
2 |
3 | 270 | 1620 |
temp 100 | 3 | 2 | 60 | 360 |
AST/RO | 1 | 7 | 270 | 1890 |
SPARO | 1 | 5.5 | 90 | 495 |
SPIFI | 0 | 50 | 60 | 0 |
FTS | 1 | 7 | 90 | 630 |
ACBAR | 1 | 10 | 180 | 1800 |
NOAA | 1 | 5 | 270 | 1350 |
total needed at closing = 15165 |
||||
total available at closing = 15280 |
These plans for the winter of 2002 are at present woefully
inadequate, since SPIFI will be deployed after two seasons of non-deployment due
to insufficient support.
Winter 2002 | ||||
n |
R (liters/day) |
t (days) |
n*R*t (liters) |
|
3000 gallon |
0 |
|||
Wessington |
3 |
7 | 270 | 5670 |
temp 250 |
2 |
3 | 270 | 1620 |
temp 100 | 3 | 2 | 60 | 360 |
AST/RO | 1 | 7 | 210 | 1470 |
SPARO | 1 | 5.5 | 90 | 495 |
SPIFI | 1 | 30 | 60 | 1800 |
FTS | 1 | 7 | 90 | 630 |
ACBAR | 1 | 10 | 180 | 1800 |
NOAA | 1 | 5 | 270 | 1350 |
total needed for season = 15195 |
||||
actual amount on site = 11460 |