Need help calculation Compressed gas pressures

[Vid_She]

Hi,

I have two high pressure nitrogen tanks. Tank 1 is connected to Tank 2 using a pressure regulating valve.
Initial Condition:
Tank 1: Pressure: 1500psi ; Volume of tank: 2782.08cu in
Tank 2: Pressure: 400psi ; Volume of tank: 898.56 cu in

I set my Tank 1 regulator output at 800psi to raise the pressure in tank 2 to 800psi.

I open the needle valve and let tank 2 settle at 800psi.

What will be the final pressure in tank 1?

Please help me out, im breaking my head over this!! thanks in advance!

 

[LittleInch]

Just break it down into standard conditions

SO tank 1 contains (approx) 4.73 scm (sorry I work in metric)
tank 2 0.42 scm.
To double the presusre in the same volume requires double the amount of gas in tank 2, so another 0.42 scm. Clearly what ever the extra gasis required this will need to come from tank1
So tank 1 looses 0.42 scm = 4.31 scm left

The actual volume of the tank hasn't changed so whats left is gas at about 93.5bar = 1355 psi.

Now that's a bit approx as I haven't put in Z factors etc but I think the procedure is correct.

Basically it's all about mass or standard volumes.

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[Vid_She]

I'm sorry for asking, its a dumb question but I tried to look for the volume conversions everywhere without luck. Could you explain to me how you did the conversion from cu in to scm?
Thanks!

 

[rotw]

Working via densities (so equation of state and accounting for compressibility), I derived this formula:

Ratio = (Rho1F / Rho1I) = 1 - (V2/V1) * [ (Rho2F - Rho2I) / Rho1I ]

Where:

V1 (m3) = volume of tank 1 = 0.0456 m3 (2782.08 cu in) -> constant during the transfer process (??)
V2 (m3) = volume of tank 2 = 0.015 m3 (898.56 cu in) -> constant during the transfer process (??)

Rho1I = initial density of tank 1 = 115.434 kg/ m3 (1500 psi @ assumed 300 K)
Rho1F = final density of tank 1 = Unknown (800 psi @ assumed 300 K)
Rho2I = initial density of tank 2 = 31.076 kg/ m3 (400 psi @ assumed 300 K)
Rho2F = final density of tank 2 = 62.138 kg/ m3 (800 psi @ assumed 300 K)

Ratio = 0.913 kg/m3 -> Rho1F = 105.4 kg/m3 -> iteratively pressure of tank 1 = ~94 bar.

Is my formula wrong or is there a thinking error? I am a bit puzzled too.
Can someone help ?

 

[Vid_She]

Could you please share the source of these formulas? Or have you derived them?

Thanks!

 

[rotw]

Derived them based on mass balance and equation of state (P/rho = Z R T).

 

[LittleInch]

OK so I did it using the Ideal Gas Law P1V1/T1 = P2V2/T2

So assuming T stays the same then its simply a matter of inserting figures into the equation to solve for V2.

Note P is in absolute pressure and hence P2 is 1 bara.

Cu in is not a usual volume for this - it's usually cubic feet or cubic metres.

Note that the ideal gas law is not valid for real gases, but it's usually close enough.

There are many charts and websites which can correct this to a hjigher accuracy. e.g.

https://en.wikipedia.org/wiki/Compressibility_factor

rotw has done the same thing using mass.

Does that make sense?



Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[Vid_She]

Makes sense. Thanks a ton!

 

[rotw]

Vid_She

Would like to say that I prefer LittleInch's method here because it's more fit for purpose, less prone to error and does not require EOS. As you noticed the difference in pressure is minor.

Would also like to say that it appeared that Z factor did not change that much here, because of pressure levels but also because this is a sort of "gentle" gas (N2) that you are dealing with. If you find yourself dealing with a more difficult situation (some nasty gas mixture etc.) where, for instance, compressibility could vary significantly, and moreover vary despite small changes of pressures, it would be probably more advisable to proceed with an equation of state.