Volume Approximation of Pressure Vessel Using Mass Flowmeter

[Jack B]

Hi, first post! So forgive me if this is posted in the wrong place.

I work in lithium ion battery chemistry R+D. As part of a safety test, we want to approximate the volume of the inside of a pressure vessel with a porous structure inside.

I have a mass flowmeter hooked up to a pressure controller which has compressed N2 gas fed to it. The mass flowmeter is in line with my pressure vessel. My mass flowmeter is calibrated to N2 gas with dynamic parameter correction. I figured that I could use this setup in combination with ideal gas law to compute the volume of my pressure vessel with the porous structure inside.

I did a few trials at a few different pressures and got results that were very linear (R^2 > .999 for grams N2 vs psia). Though when I computed V = nRT/P I got results that increased with pressure, so I think I’m doing something wrong. Perhaps my theory that this would work was incorrect?

I appreciate any help and could supply the data if it is of interest.

Regards,
Jack

 

[georgeverghese]

Would this mass flowmeter be a Coriolis meter? If so, it would typically have density correction, and it would measure N2 injected into the pressure vessel on mass basis correctly.
So, may be there is some error with the units used in the V = nRT/P computation? If you were to use SI units, V=m3, n=kgmoles, R=8.3143kJ/kgmole/degK,T=degK, P=kpa abs. Strictly speaking, V=znRT/P,with z=1.0 at low pressure. ambient temp range.
If this calc is done correctly, and the anomaly persists, this porous medium in the pressure vessel may have residual adsorbed N2 in the pores? How do you ensure the media is completely devoid of N2 before you start each test run?

 

[hacksaw]

from you equation n=PV/RT, so the kg-moles capatured for a fixed volume is linearly proportional to pressure, to first order, as you have reported,

So what is the concern?

 

[Jack B]

Hi, thank you for responses.

I am not sure if I am approaching the problem in the correct way. I initially thought that measuring the amount of air required to pressurize the vessel to a specific pressure and fitting that a linear function would allow me to compute volume of air in the fixture at atmospheric pressure. I was mistaken, as this would give me a volume of 0, naturally. I feel like there’s an obvious solution I’m missing, e.g. volume of air required to reach 2x room pressure in fixture perhaps.

George- Yes, these are the units I’ve used and the assumptions I’ve made. I’m not sure if the flowmeter is a coriolis, but here is the link. I don’t have a way to verify that the inside of the pressure vessel is vacated of N2 before the start of the experiment. The pressure controller I was using isn’t set up to pull vacuum but I can get that set up if needed. Perhaps I pull the fixture to some suitable vacuum pressure, zero the flow meter, and vent to atmospheric, I could get a correct volume.


hacksaw- I apologize for being unclear. I think the issue, as described in the beginning of this response, is the way I’m going about this experiment. Things are behaving as I should, but I’m not looking at them in a way that allows me to obtain what I am looking for, the volume of the fixture.

 

[georgeverghese]

I dont see what type of meter this meter from the linked docs - it could be an ultrasonic meter also. It does appear to apply density correction, but I would call up these people to confirm.

If you are starting at atmospheric pressure, then V = nRT/(P-Po), where Po is the starting pressure of 101.3kpa abs. In this case, there is no need to vacate the vessel down to vacuum, since you are always starting at 101.3kpa abs for each test.

 

[btrueblood]

So...you are integrating the output of a flowmeter to obtain total volume? That works ok with a relatively constant flow rate that is within the calibrated range of the meter. But you are filling a closed volume, so the flow rate is a decaying exponential curve, which means at some time after starting the fill the flow rate will drop below the calibration range of the meter, and you will be integrating noise.

An alternate method to do what you want would be to drive a piston in a cylinder to displace the air volume and fill your vessel. Measure the cylinder displacement to know the volume change. Calibrate the device against closed volumes of known proportions. You could also run similar calibrations of the flowmeter setup against known closed volumes, and vary the integration time, or stop the fill and integration when the pressure drop across a known orifice drops below some value, or when the flowmeter signal drops below a certain value. Bottom line is the sanity check of calibrating against a known volume...

 

[Jack B]

Thanks again for replies.

George - I have confirmed with the manufacturer that the meter does account for dynamic compressibility, viscosity, and density.

btrueblood - The meter is fitted with a totalizer, which integrates flow rate over time at dt = 1 ms. I’ve been getting very consistent results at n=5 across multiple pressures (stdev of .002g @ 5, 10, and 15 psig) which rules out noise somewhat. Once I get the chance I agree that calibrating against a known volume is a good idea, especially since I just jumped into this method without validating it.

 

[LittleInch]

How exactly are you doing this?

If you're pressurising a fixed volume with a fixed pressure but restricted flow then at some point you are presumably getting a gradual fall off in mass flow so makes it tricky to get good total ass as the flow rate falls as you approach your end pressure?

Also not sure if you are using absolute pressure or not.

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

 

[btrueblood]

Coming back to this, I think you should expect some pressure driven variation - i.e. the absorption of gas by a porous substrate may be a diffusion limited process, i.e. occurs slowly but at a rate defined by the concentration difference, which at least initially is roughly proportional to pressure difference. So filling at higher pressure would drive faster internal diffusion, more gas gets absorbed before you stop the fill. Would be interesting to lock off the container after your fill, then monitor internal pressure and temperature over hours or days, a drop might indicate continuing absorption of gas by the porous material.