Helium Liquefier - Numbers at Hand
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                                         Initial Rev.  8-Feb-2022
                                         Current Rev. 11-Aug-2023


1.  High Pressure Gas Cylinders:

    AirGas  Ultra High Purity Helium 99.999%   HE UHP300
    cylinder size 300,  291 cubic feet of Helium gas per
    cylinder,  2640 psi when full

    One of these full helium cylinder costs about $ 250

    The internal volume (aka water volume) of the cylinder
    is  49 L  or  2990 cubic inches  or  1.73 cubic feet

    Other companies call this cylinder size:
    049, 49, T, and K,   These cylinders are about
    9.3" dia and  about 59" tall to the top of the valve.

    Lots of high pressure gas cylinder folks seem to call
    the internal volume of a cylinder its water volume.


2.  Recovery System Storage Tanks:

    Our 400 psi Storage Tanks are about  40" tall  (for the
    equivalent purely cylindrical shape)  and  about  29.9"
    in outside diameter  giving an internal volume of about
    16.2 cubic feet per storage tank.

    Our 400 psi Storage Tanks   may be   a standard commercial
    size call "1/2 Ton"  typically used for storing propane at
    110 psi at 70 deg F.


3.   1 cubic foot = 28.317 L


4.  Helium Gas to Liquid Volume Ratio:

    Liquid Helium density is about  125 g/L   at boiling point
    Helium Gas density is about  0.1785 g/L   at STP
    This is a volume ratio of right about 700

    I have also seen a Helium liquid to gas ratio
    stated as 757.


5.  Pumping a full Recovery Bag into the Storage Tanks
    causes about a  65 psi  rise in the storage tank
    pressure.


6.  The Liquid Helium Dewar has a capacity of  150 L.


7.  Storage Tanks - HP Cylinders - Liquid  Equivalents:

    A full high pressure cylinder of Helium gas can
    make about  10 L  of liquid Helium.

    The 4 Storage Tanks when full at 400 psi hold a total
    of about  1750 cubic feet stp of helium gas.  This is
    about the same amount of helium as is held in the
    6 full high pressure cylinders.

    This 1750 cubic feet stp of helium gas is enough
    to make about  68 L  of liquid helium.


8.  Value of the Overall Helium Inventory:

    If you consider our Helium Inventory to be:  150 L of
    liquid in the dewar  plus  1750 cubic feet stp of gas
    in the storage tanks,  and  if the cost of helium gas
    is about $250 for a standard 291 cubic foot stp high
    pressure cylinder,  then the value of our helium
    inventory is about:  $ 4,800

    This overall helium inventory is about 19 high
    pressure cylinders.


9.  Watts of Heat to Cooling Water Temperature Rise:

    4184 Joules will raise the temperature of 1 kilogram
    of water by 1 deg C.   or   4184 Joules is 1 k Calorie,
    1 kilogram of water is 1 L.   Put things together and:

       1 k Watt   is   14.34  L per minute - degrees C

    If you need this in gpm recall:   3.785 L = 1 gallon

    Recall that the little calorie is the heat to raise
    1 gram  or  1 cc,  or  1 mL  of water by 1 deg C.  


10.  Heat generated by the main power consuming items:

       Liquefier Pulse Tube Compressor   about  9.9 k Watts
       Helium Gas Purifier               about  3.1 k Watts
       Storage Tank 400 psi Compressor   about  5.5 k Watts

     Because the Storage Tank Compressor runs only about
     20 minutes a day it does not add very much to the
     overall heat load to the building.


11.  Height of Water Head vs psi of Water Pressure:

        2.31 feet of water head  is  1 psi of water pressure


12.  Power used / dissipated by the Air Chiller:

        The name plate on the air chiller has these numbers:

           Compressor    6.9 Amps
           Fan           0.8 Amps
           Pump          2.6 Amps

        This is a 480 Volt 3 phase unit.   10.3 Amps at
        480 VAC 3 phase is about  8.56 kWatts  for unity
        power factor.  Given a typical power factor and
        assuming that the pump is operating at only a
        fraction of its full load capacity,  the heat
        load is probably something like  5 kWatts.


13.  Required air flow rate 

        To hold the temperature rise of the air to  1 deg C
        you need a flow rate of about   5.6 cubic feet per minute
        per Watt of heat that you add to the air.

        This value is obviously a function of atmospheric
        pressure and the water content of the air.


14.  Recovery Tank Pressure Drop  per  Liter of Liquid Helium Produced

        The pressure in the Recovery Tanks drops by about
        5.35 psi  for every Liter of liquid Helium produced
        by the liquefier.