Filling Scuba Cylinders/Cascade filling

Inrtoduction
Cascade filling is a procedure used to transfer compressed gas between storage cylinders. There is no work input, and transfer is purely due to pressure difference.

This procedure is useful when filling scuba cylinders from bulk storage cylinders when no compressor is available, and for transfer of oxygen and helium from bulk cylinders to the scuba cylinder when partial pressure blending Nitrox, Heliox, amd Trimix.

Cascade filling can also be done in conjunction with the use of a booster pump, which is used to continue the transfer when the pressure differential has been exhausted, and allows the filling of cylinders to pressures higher than the equilibrium pressure between the two connected cylinders.

The concept of equilibrium pressure between two cylinders is central to cascade filling, and it is necessary to be able to calculate the final pressure when decanting between two cylinders. This is the pressure when gas from the high pressure cylinder has transferred to the low pessure cylinder and the pressure drop of the supply cylinder meets the pressure rise in the receiving cylinder. When this happens, flow stops. If the transfer is slow or the cylinders are left to return to ambient temperature, the calculation follows the general gas equation for ideal gases with temperature constant.

Calculation of equilibrium pressure
The ideal gas law:


 * $$PV = nRT \,$$

where


 * P is pressure
 * V is volume
 * n is the number of moles
 * R is the universal gas constant with a value of .08206 (atm∙L)/(mol∙K).
 * T is temperature (K)

This can also be written PV/RT = n for any specific quantity of gas, and when two quantities of gas are combined, the number of moles must be added.
 * n1 + n2 = n3

Therefore, when decanting from one cylinder into another, with no loss to leaks, P1V1/RT1 + P2V2/RT2 = P3V3/RT3


 * and at a constant temperature T1 = T2 = T3, this will reduce to:

P1.V1 for the first cylinder plus P2.V2 for the second cylinder equals P3.V3 for the combination of both cylinders, or:


 * (P1.V1 + P2.V2)/V3 = P3

and since the final volume is the volume of the two cylinders combined, V3 = V1 + V2. so:


 * P3 = (P1.V1 + P2.V2)/(V1 + V2)

This can be expanded for any number of cylinders connected and allowed to reach equilibrium with no loss of gas.


 * Pn = (P1.V1 + P2.V2 + ... + Pn.Vn)/(V1 + V2 + ... + Vn)

Clearly the maximum pressure possible in the filled cylinder is the equilibrium pressure. To fill to a higher pressure would require another transfer from a cylinder with a higher pressure, and this would be limited by the equilibrium pressure of the second combination.

What may not be immediately obvious, is that the final pressure in the receiving cylinder will be higher if gas is decanted from the lowest higher pressure supply first.

Order of transfers
To get the most out of the storage cylinders, start with the one with the lowest pressure, and transfer to the receiving cylinder with the highest pressure that will transfer gas the right way, and repeat this until no more transfers are possible.