I need a method of estimating the volume of a gas container

[Jehannum]

In the gas industry you often need to know the installation volume of a system, i.e. the amount of gas it contains in the pipework, fitting and meters.

If part of the installation is buried or inaccessible this is difficult to estimate.

My concept is to estimate installation volume by measuring the change in pressure when the system volume is increased by a known amount (i.e. by opening a valve to a smaller system of known volume). I've had a go at the maths and experimentation but the results have not yet been good.

The method is as follows:

The SYSTEM is the meter / pipework installation whose volume we wish to know.

The TESTER is a small section of pipework and a gas meter whose volume is known, which is attached to the SYSTEM by an isolation valve.

1. Ensure the TESTER is at atmospheric pressure
2. Determine atmospheric pressure
3. Ensure the SYSTEM is pressurised above atmospheric pressure
4. Close the incoming gas supply to the SYSTEM
5. Measure the absolute pressure of gas within the SYSTEM (atmospheric pressure + gauge pressure)
6. Open the isolation valve on the system to allow gas to enter the TESTER
7. Measure the absolute pressure of gas within the now-combined SYSTEM + TESTER

Some figures I got:

Atmospheric pressure = 1015 mbar
TESTER volume = 0.030 cubic metre
Absolute initial pressure of SYSTEM = 1038.4 mbar
Absolute final pressure of SYSTEM + TESTER = 1032.85

I tried using the Ideal Gas Equation, but I got a SYSTEM volume of 5.6 cubic metre, which is vastly larger than the actual size.

One problem I can see is that the TESTER does not contain a vacuum initially, so the number of molecules of gas increases when the SYSTEM and TESTER are combined. This means the simple proportionality of the Ideal Gas Equation won't work. This is showing me the limitations of my maths, and it's where I could really do with a little help.

 

[Dr. Courtney]

The idea is sound, but the accuracy will depend on what fraction of the overall volume is represented by the added volume.

 

[Jehannum]

Thanks for your input. I tried varying the TESTER size (smaller than before) and got results 20 times closer to the true value. That's a big improvement, but there's still a way to go.

Am I right in the following reasoning?

1. If the added volume (TESTER) is large then the simple inverse proportionality of pressure and volume will not hold, because the number of gas molecules changes significantly.

I believe there is no way of rearranging the Ideal Gas Equation to factor out the additional gas molecules in the TESTER.
i.e. PV = NRT
=> P1V1 = P2V2 if N remains constant

But since N increases by the number of molecules in the TESTER = n, this simple relationship doesn't hold exactly.

There are two unknowns, the volume of the SYSTEM and the number of gas molecules within it, so we can't solve it with the one equation we have.

2. If the added volume (TESTER) is small then the reduction in pressure in the system will be very small and therefore difficult to measure accurately.

PS. One thing I notice is that a very slight change in pressure equates to a very large change in volume, so accurate pressure measurement is crucial.

 

[Baluncore]

One problem you may have with any pressure change technique is a phase change of one of the contained species.
For example, if air is used, some water vapour could precipitate as pressure falls.

 

[Lok]

Atmospheric pressure = 1015 mbar
TESTER volume = 0.030 cubic metre
Absolute initial pressure of SYSTEM = 1038.4 mbar
Absolute final pressure of SYSTEM + TESTER = 1032.85

I tried using the Ideal Gas Equation, but I got a SYSTEM volume of 5.6 cubic metre, which is vastly larger than the actual size.

Please send us some of your complete calculations as:

a quick running calc => Amount of NRT change in Tester =>
Pfin*Vt-Patm*Vt=0.5355 in units of [NRT] (no need to complicate it further)
Amount of volume needed for such a change in NRT in Tester for the pressure drop in System.
Pfin*Vs-Pini*Vs=-0.5355 => V=-0.5355/(Pfin-Pini) ~=0.09648 m^3

Would that be a more reasonable volume?

 

[Baluncore]

Consider an alternative dilution method. You might reduce container pressure to 1 atm, then evacuate one litre and replace that one litre with a gas that is different to, but will mix with the existing contents without stratification. Analysis of the mixed contents for the trace gas will then give you the volume based on the dilution of the trace gas that was added.

 

[Jehannum]

Please send us some of your complete calculations as:

a quick running calc => Amount of NRT change in Tester =>
Pfin*Vt-Patm*Vt=0.5355 in units of [NRT] (no need to complicate it further)
Amount of volume needed for such a change in NRT in Tester for the pressure drop in System.
Pfin*Vs-Pini*Vs=-0.5355 => V=-0.5355/(Pfin-Pini) ~=0.09648 m^3

Would that be a more reasonable volume?

Yes, very much more reasonable. Close enough to be usable. Thank you very much indeed.

 

[Lok]

Yes, very much more reasonable. Close enough to be usable. Thank you very much indeed.

So Vs=(Vt*(Pfin-Patm)/(Pini-Pfin)) as the total number of gas molecules in both flasks, unknown as it is, does not vary during the measurement.

Before declaring a complete victory you could do the measurement again. But with a slightly different SYSTEM pressure. This way you could see what your error can be in this type of measurement, as stated above : temperature effects, phase changes etc. But IMO for such a small pressure difference there should not be a significant deviation.
Also your measurement will be as accurate as your TESTER Volume measurement, and for high volume differences (SYSTEM vs TESTER) you might measure very small pressure differences which will horribly affect your precision.

 

[Jehannum]

Thank you again for all the replies, which have added to and corrected my quarter century-old recollections of physics A Level.

The method is intended as a quick way for on-site gas engineers to estimate of installation volumes where pipework measurement is impracticable. It needs no additional equipment other than their normal toolkit (manometer). Simplicity is the key, together with reasonable accuracy (two significant figures in the range 0 to 1 cubic metre). I will test it out more before putting it into practice, but it seems workable.

EDIT: after putting it into a spreadsheet I can see its accuracy is not quite as high as I'd have liked, and is very dependent upon accurate pressure measurement and volume measurement. A good electronic manometer that reads to 0.01 mbar appears to be crucial.

 

[Jehannum]

Consider an alternative dilution method. You might reduce container pressure to 1 atm, then evacuate one litre and replace that one litre with a gas that is different to, but will mix with the existing contents without stratification. Analysis of the mixed contents for the trace gas will then give you the volume based on the dilution of the trace gas that was added.

Too complex for plumbers like us :)