It’s well known that SCUBA tanks heat up during filling, and that filling a tank too quickly can damage it from overheating. I like physics, and wanted to try to calculate how hot the inside of a cylinder can get if filled instantly.
TL;DR: It depends on the ratio between the current pressure and the final fill pressure. If a SCUBA tank is nearly empty, it can get very hot during filling, and needs to be filled slowly. If a tank is already half full, it’s impossible for it to heat up much during filling, and can be filled quickly without causing damage.
How hot is too hot? I had a hard time finding an answer online, but I got a chance to ask Mark Gresham of PSI-PCI last week at DEMA. He told me steel cylinders can be damaged above 600 F / 315 C, and aluminum cylinders can be damaged as low as 265 F / 130 C.
Filling a cylinder quickly means there isn’t much time for heat to escape through the cylinder walls. This means the cylinder’s temperature after filling can be calculated with one of the adiabatic compression formulas (and not the ideal gas law like I expected). Since oxygen and nitrogen gas are both diatomic gases, the formula to use is P^(-2/5) T^(7/5) = constant.
For aluminum cylinders:
(3000 psi)^(-2/5) (265 F)^(7/5) = (1001 psi)^(-2/5) (70 F)^(7/5)
For steel cylinders:
(3442 psi)^(-2/5) (600 F)^(7/5) = (303.9 psi)^(-2/5) (70 F)^(7/5)
As long as aluminum cylinders start with at least 1000 psi, or steel cylinders start with at least 300 psi, it’s impossible to overheat them by filling too quickly. Of course, if a tank leaves the shop hot, it won’t have a good fill once it cools down.
(Fill station operators should be aware of these limits, because tanks can absolutely be damaged if they’re exceeded. I also wouldn’t be comfortable quickly filling a tank with anything but air – gases with more oxygen are still dangerous.)
Why does any of this matter? Because quickly filling a cylinder to service pressure, then topping it off as it cools down is the fastest way to get a good fill. Getting a good fill means getting rid of all the heat from filling, and the total energy transferred is the same whether the tank is filled quickly or slowly. However, when a tank is filled quickly, it gets hotter, which means heat transfer to the surrounding environment is faster.
Want to test it? Start with two identical cylinders at at least 1000 psi. Fill the first cylinder to service pressure slowly over 10 minutes. Fill the second cylinder to service pressure as quickly as possible, then continue topping it off as it cools for the remainder of the 10 minutes. Stop filling and come back when both cylinders have cooled to room temperature (give it a few hours) – the cylinder that was filled quickly will be at a higher pressure.