No compensation for ideal gas law deviations

[Angelo Farina]

I use the real gas formula:
pv=kRT
If the gas is perfect, k=1.
Above 100 bar, at ambient temperature, k increases with pressure.
The chart (or table) of k(p) is easily found on the Internet...

 

[tursiops]

The chart (or table) of k(p) is easily found on the Internet...

Can you provide a link? I'm not finding anything very useful. Thanks!

 

[Storker]

Can you provide a link? I'm not finding anything very useful. Thanks!

Perry's Chemical Engineer's Handbook has compressibility tables for air, real experimental data. You can also look up "Compressibility factor" on Wikipedia. For He mixes, you have to dig quite a bit deeper.

 

[wnissen]

Can you provide a link? I'm not finding anything very useful. Thanks!

I would be skeptical of anything you find that hasn't been vetted. It's very easy to produce an "equation of state" that gives a value for any material, at any pressure, at any temperature. So-called "analytic" equations of state like the ideal gas law or Van der Waals are useful tools, but need to be calibrated to get very accurate answers. Even if you can find "real" data for your particular gas mix, there's always the question of whether the data themselves are were taken accurately. It's a whole field unto itself.

 

[Storker]

I would be skeptical of anything you find that hasn't been vetted

The cite I gave above (Perry's) has been thoroughly vetted.

So-called "analytic" equations of state like the ideal gas law or Van der Waals are useful tools, but need to be calibrated to get very accurate answers.

The ideal gas law is never accurate, but often accurate enough (tm). I totally agree that the vdW equation has to be "calibrated", or iow, its predictions have to be checked against real world data. If it doesn't fit, just adjust the constants. They are empirical and just numbers chosen to make the predictions fit reality. If reality doesn't agree with the predictions, it's time to re-draw the map (or, IOW, adjust the constants in the prediction formula). For any empirical model, the constants are just fitted to the reality that the formula tries to predict.

 

[Bernie_U]

Fully agree with wnissen. I do not blend breathing gasses, so I cannot provide an alternative here.

At work, I can use simulation software from Aspentech or Simsci that has variety of thermodynamic models. For simple problems, i use them out-of-the box and do not really care - still good enough. The complex problems I leave to the colleagues who are more familiar with thermodynamics. For best results, we still rely on datasets obtained from experiments. That is similar to your own fitting of the parameters.

Two years ago, I wrote a program just for fun to calculate trimix blends based on the Soave-Redlich-Kwong (SRK) equation with binary parameters. The binary parameters I simply reverse-engineered from an example on www.techgasblender.com. So yeah, I would recommend that to start with. The guys on techgasblender.com prefer a modified Benedict-Webb-Rubin approach. To be honest, I don't have a clue what that might be.

The question is: Who does research on helium gas mixes nowadays? I only found the helium manufacturers, i.e. natural gas producers. There is indeed research going on to model the properties of gas mixes with helium an nitrogen (and methane, of course) in that area. If I had money to spend, I would buy a software license from them.

 

[Storker]

I do not blend breathing gasses, so I cannot provide an alternative here.

I do (albeit without He). Works like a charm, especially when I use my own spreadsheet. Hits the target plusmimus one half to one percentage point every time. Even at 300 bar (cold) end pressure, when non-ideality has long kicked in.

 

[stuartv]

@scubadada Post #1 may answer a question you had about why the Shearwater GTR is so off in the early part of a dive.

 

[scubadada]

@scubadada Post #1 may answer a question you had about why the Shearwater GTR is so off in the early part of a dive.

Hi Stuart,

Thanks for the post. Nearly all my dives are with AL80s, 3000psi, 207 bar. I don't think this relatively small difference would make a significant change in the GTR calculation. I didn't know that SW accounted for variations in the ideal gas law compared to Oceanic, is that right?

 

[stuartv]

Hi Stuart,

Thanks for the post. Nearly all my dives are with AL80s, 3000psi, 207 bar. I don't think this relatively small difference would make a significant change in the GTR calculation. I didn't know that SW accounted for variations in the ideal gas law compared to Oceanic, is that right?

The OP says that Shearwater does not compensate for gas non-compressibility. I.e. Shearwater is being simplistic (and, thus, less accurate). I don't know if Oceanic does compensate for non-compressibility, but if they do, then that would explain a scenario where, early in the dive, Shearwater shows a shorter GTR and Oceanic shows a greater GTR.

The difference, at 3000 psi, is relatively small. But, the small difference is being extrapolated over the whole rest of the tank. So, if you are consistently seeing a lower GTR on Shearwater and bigger on Oceanic, I would strongly suspect that that is why.