Info Real gas - the real deal

[WarthogARJ]

Hi,
Please take this comment as being constructive, but I question the overall advantages of using a EOS like GERG for diving applications.
As compared to one of the other MUCH SIMPLER EOS like VDW or virial equations.

There's a trade-off in whatever EOS you use that's governed by the accuracy you get vs the complexity. GERG is several orders of magnitude more complex than VDW or virial approaches.
Which means much greater risk of coding errors, amongst other things.

From an engineering point of view, one needs to decide what accuracy is needed, and try to follow KISS: Keep It Simple Stupid.

GERG (and the related NIST codes) were developed for COMPLETELY different reasons than the diving industry case.
GERG is intended to be used with a VERY complex "soup": often >20 hydrocarbon gases along with water and hydrogen.
The idea was to be able to accurately quantify natural gas mixtures that are being transfered by pipeline or LNG tank in VERY large quantities: in order to make the payments for it more accurate/consistent.

Air liquide or Lurgi might see advantages in using GERG at the high end of things: millions of tonnes of gas processed. But Joe Blender? I don't buy it.

Alan

 

[goldfishtornado]

As compared to one of the other MUCH SIMPLER EOS like VDW or virial equations.

I think I have advocated that using an ideal gas approximation was fine for most practical diving applications. It's not really a question of quantities of gas but of required accuracy of blends.

If you're going to use some other equation of state, I think I would argue for either GERG or an empirical interpolation like that used in subsurface. I think that GERG is more or less (obviously more) an extension of a virial approach. It should be straight forward to validate the output of a GERG based model for the limited cases of the few gases of interest to divers.

Van der Waals is much worse. Worse than ideal gas approximation in some regions of interest for diving. This is discussed here with a plot showing that z-1 has the wrong sign for Van der Waals for dry air at 200 bar! Obviously, you could object to the VDW coefficients I used for the plot. But if you are going to pick different coefficients to better fit to empirical data, rather than theoretical, you might as well have started from an empirical description. And since you would have to validate anyway, I don't see a major advantage over validating GERG over the limited phase space of interest here.

 

[WarthogARJ]

Hi Herr GoldFish,
Yes, I agree with you.

It's a case of "horses for courses" wrt to which Equation of State (EOS) you use for diving applications.

Van der Waals is still useful for teaching non-specialists about the limitiations of the ideal gas law, but for any actual use, as you say, you should use a cubic (3-component) virial EOS: for very little increased complexity, you get a big increase in accuracy.

My only point was that GERG 2004 (and its later variants) is indeed more accurate, but....the point is you pay for that (usually very slight accuracy improvement) with a lot of extra complexity. And it's in many cases, overkill, compared to using a 3-parameter virial cubic type.

It is not straightforward to use GERG 2004 in a DIY/Excel based set-up, as you can see by looking at the VBA Macro routine written for this Excel spreadsheet.

If you program a GERG-2004 based model for 3 components (O2, N2 & He: without water vapour) you need a LOT of constants in multiple functions that need to be called properly in whatever iterative search routine you use to solve with (it's not a direct solution like vDW etc):
- Common: 18 constants
- O2 and He: each gas needs 12 constants each
- N2: needs 24 constants
So that's 66 constants (for only THREE components).
Lots of places to screw up.

If someone wants to use davidem's Excel/VBA macro as a "black box" to calculated compressibility factors there's no real danger. But modifying it to do other things is not straightforward: you really need to be very careful.

GERG-2004 is based on a thermodynamic semi-rigorous approach. It uses the Helmholtz energy to do some very accurate combinations of very accurate correlations to experimental data for the gases it models: in particular for complex MIXTURES of non-ideal type gases used in natural gas mixes.

To quote from Oliver Kunz's PhD thesis (the developer of GERG-2004):
"These models use equations of state in the form of fundamental equations for each mixture component along with further correlation equations to take into account the residual mixture behaviour.
The equations are explicit in the Helmholtz free energy. The basic principles for the development of these mixture models are strongly related to the development of empirical equations of state for pure substances. The models enable the accurate description of the thermodynamic properties of mixtures in the extended fluid region for wide ranges of temperature, pressure, and composition"

The real advantage of using a Helmholtz Energy (GERG-2004 etc) based approach is it means you can derive many other properties important to pipeline use: viscosity, density, thermal properties etc.