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 = T_{dewar} = V_{dewar}/R_{dewar} ,
where V_{dewar} = total storage capacity of dewar
R_{dewar} = 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 
R_{big}  R_{small}  R_{Wess}  R_{250}  R_{100}  R_{ASTRO}  R_{SPARO}  R_{SPIFI}  R_{ACBAR}  R_{NOAA} 
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:
R_{big }t_{big }+ n_{small }R_{small }t_{small }+ n_{250}R_{250 }t_{250 }+ n_{100 }R_{100 }t_{100 }+ R_{ASTRO }t_{ASTRO }+ R_{SPARO }t_{SPARO }+ R_{SPIFI }t_{SPIFI }+ R_{NOAA }t_{NOAA} = V_{total}
Each winter of operation can be laid out as a spreadsheet:
The winter of 1995 was a success, and a demonstration that winterover 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 semidisastrous. 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 boiloff rate. Cutting AST/RO operations to one receiver dewar, and an improved boiloff 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 CH4000, for a total of 11460 liters onstation 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 onsite 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 onsite 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 onstation 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 holdtime dewars (the 250 liter dewars have a hold time of about 90 days) from a longer holdtime 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 onstation at base closing. The CARA plan
called for unmodified dewars with a slightly lower boiloff 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 nondeployment 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 