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Author: Subject: Equations for real gases
Twospoons
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[*] posted on 18-10-2016 at 15:53
Equations for real gases


I have a problem I could use some expert help with.

I have a cylinder of oxygen, when full it contains roughly 22g of O2 at a pressure of about 300 bar.

I need to be able to calculate the remaining mass of O2, from a pressure measurement and temperature measurement. Desired accuracy of better than 5% (my sensors are ~ 1%).

It is impractical to weigh the cylinder, and I need ongoing measurements so I can control (electronically) the O2 release rate, which is on the order of 2g per day.

Critical pressure for O2 is 49 bar, critical temperature is 154K.
Operating temperature range is ~260K to 290K, and pressure from 0 to 300 bar.

I've looked at the wikipedia page on real gases, real gas equations
which has half a dozen models to choose from. And there I got lost.

If anyone has experience or advice to offer, it would be much appreciated.

BTW, I'm not adverse to creating a lookup table, but I need to know which equation is going to give me best results with minimum headache.




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[*] posted on 18-10-2016 at 16:11


Whatever you do you are going to need a volume measurement as well.
Without a whole lot of experience I would venture that the ideal gas equation will give you what you want -- to within your 5% accuracy. Intermolecular forces for O2 are not going to be high. 300bar is not ridiculously high either. You are well above the melting point. So O2 is going to be close to ideal -- probably to within your measuring ability.




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Twospoons
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[*] posted on 18-10-2016 at 16:33


Knowing initial pressure, mass and temp I can work out volume no trouble - and doing it this way will take account of the volumes in the sensor and regulator.

I guess I was really wondering how much the ideal gas law deviates from reality over the range I'm working in.

[Edited on 19-10-2016 by Twospoons]




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[*] posted on 18-10-2016 at 16:43


I thought you said you were trying to calculate the mass -- and that weighing the cylinder was impractical.

Anyway, to answer your underlying question, there are reasons to consider O2 in the range you describe as close to ideal -- for some definition of close.

Why not try calculations with a couple of the real equations and see what kind of deviation you are looking at?




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[*] posted on 18-10-2016 at 17:05


Initial mass is reasonably well known - its a one time use cylinder, so has a pre-defined mass of O2 when new and full.
Running comparisons mathematically was going to be my next step - just looking to see if anyone on the board had encountered this problem before.




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[*] posted on 18-10-2016 at 18:24


Quote: Originally posted by Twospoons  

I guess I was really wondering how much the ideal gas law deviates from reality over the range I'm working in.


Your O2 temperatures are way above the critical temperature so you will never have any liquid.

I've always handled this type of problem in college using the reduced pressure-reduced temperature correlations shown as a graph. What this graph gives you is Z, a correction factor for the ideal gas law. So PV=ZnRT.

In my textbook I found Z to be equal to 0.93 at P=300bar and T= 260°K and Z = 0.97 at P =300bar and T=300°K. So, as j_sum says, not much effect.




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[*] posted on 18-10-2016 at 18:55


Thanks for that suggestion. I've run the ideal eqn against the Redlich-Kwong eqn and I get a 'Z' of .92 at 293K. I guess if I calibrate system volume in the real world (by measuring P, T and mass) it will subsume the fiddle factor in the process and I wont know the difference. So long as everything stays reasonably linear I shouldn't have an issue.

Thanks for your comments.




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