No compensation for ideal gas law deviations

[magicfx]

The following texts are from SW Teric manual p.53:

No compensation for ideal gas law deviations
Note that all SAC and GTR calculations assume that the ideal gas law is valid. This is a good approximation up to about 207 Bar (3000 PSI). Above this pressure, the change in gas compressibility as pressure increases becomes a noticeable factor. This is mainly an issue for European divers using 300 Bar cylinders. The end result is early in the dive, when pressures are above 207 Bar/3000 PSI, the SAC is over-estimated, resulting in under-estimation of GTR (although this is the good way to err, as it is more conservative). As the dive progresses and pressure drops, this problem rectifies itself and the numbers become more accurate.

==
How can we say 3000psi is the limit of applying ideal gas law to breathing gas?

 

[wnissen]

The following texts are from SW Teric manual p.53:

No compensation for ideal gas law deviations
Note that all SAC and GTR calculations assume that the ideal gas law is valid. This is a good approximation up to about 207 Bar (3000 PSI). Above this pressure, the change in gas compressibility as pressure increases becomes a noticeable factor. This is mainly an issue for European divers using 300 Bar cylinders. The end result is early in the dive, when pressures are above 207 Bar/3000 PSI, the SAC is over-estimated, resulting in under-estimation of GTR (although this is the good way to err, as it is more conservative). As the dive progresses and pressure drops, this problem rectifies itself and the numbers become more accurate.

==
How can we say 3000psi is the limit of applying ideal gas law to breathing gas?

The answer is always in what you're using the data for. Don't be fooled by the "law" part of the name; no gas perfectly follows it. Even at "standard temperature and pressure" (STP, 20C / 68F, 1 atm) there's a small (typically less than 1%) deviation.

Molecular nitrogen follows the ideal gas approximation very closely (less than 5%) up to about 200 bar. From there it goes far off relatively quickly. At 400 bar it's about 30% off.

Deviations from the Ideal Gas Law

So if you need to know your accurate SAC at the beginning of the tank to the level where 5% is important, then you need to use a better approximation, which is in that link. If you were doing a huge amount of deco with a dozen tanks, it might make a difference. For your typical recreational dive where the tank is drained down to 50 bar, it's literally a rounding error.

 

[Angelo Farina]

What matters to me is the following.
My old Faber steel tank contains 15l at 200 bar, hence it holds 3000 liters (in reality the capacity is around 2920 liters).
Modern tanks available here in Europe (Eurocylinder) contain 10l at 300 bar. In theory, they should have the same total content, 3000 liters.
Instead, due to the imperfect behaviour of air, they hold only 2700 liters.
Furthermore, the number of charging stations which actually fill them to 300 bar is very limited...
Current standard charging pressure here, in most stations, goes up to 232 bars maximum. Only a few are equipped for charging at 250 bar.
So, whenever I will change my tank, the new one will be 15 liters, 232 bars. But the old one is good enough, also because in most places they fill it at 232 bars...

 

[tursiops]

How can we say 3000psi is the limit of applying ideal gas law to breathing gas?

Because the answers for N2 and O2 are the same within a few percent. If you want better than that, go to lower pressures or use the corrections.

 

[Storker]

For air, or moderate EAN mixes, the ideal gas law is a Good Enough model up to some 232-250 bar (3350-3600 psi). Both for diving and for mixing. Throw in some He, and the picture becomes seriously muddled and the ideal gas law isn't very valid.

If you go above those limits, there's always the vdW equation.

 

[lowwall]

How can we say 3000psi is the limit of applying ideal gas law to breathing gas?

Because an "ideal gas" is a hypothetical construct, not an actual physical thing. The construct assumes gas particles occupy a negligible fraction of the total volume of the gas. It also assumes that the force of attraction between gas molecules is zero. (quote from @wnissen linked article above. I'll give the link again because it directly answers the question in much greater detail: Deviations from Ideal Gas Law Behavior:).

Neither of these assumptions are valid for actual gasses. But they are reasonably close until you compress them a couple hundred atmospheres.

 

[elmo]

If you go above those limits, there's always the vdW equation.

Unfortunately, and somewhat surprisingly, van der Waal's equation isn't very helpful at the pressures and temperatures we care about.
@atdotde wrote a very good post on this Equalizing real gases – The Theoretical Diver

 

[Storker]

Unfortunately, and somewhat surprisingly, van der Waal's equation isn't very helpful at the pressures and temperatures we care about.
@atdotde wrote a very good post on this Equalizing real gases – The Theoretical Diver

I'm using the vdW equation. Not with the tabulated constants, but with constants I've fitted from data in the P-T range we are operating in.

Works surprisingly well.

 

[Bernie_U]

It's always fun to see Mr. van der Waal pop-up in SCUBA forums from time to time. Apart from educational purposes and approximations for compact equations, no-one else is using vdW as equation of state for real gases. But yeah, why not? I would drive a Ford T model just for fun, but not to carry my SCUBA equipment to the dive site. And the Ford T is younger than the vdW equation ...

 

[Storker]

It's always fun to see Mr. van der Waal pop-up in SCUBA forums from time to time. Apart from educational purposes and approximations for compact equations, no-one else is using vdW as equation of state for real gases. But yeah, why not? I would drive a Ford T model just for fun, but not to carry my SCUBA equipment to the dive site. And the Ford T is younger than the vdW equation ...

Cool story, bro. So what do you use?

I believe that Newton's law of gravity is quite a bit older than the vdW equation. It still works pretty well on most occasions.