A little OT: flow calculation of nitrogen

[ELake20]

I'm attempting to calculate flow of nitrogen gas. I have a fixed volume but due to the discharge pressure and temperature will be changing. I've started with pV=nRT, here are the values I came up with for that.

p= pressure of gas, starting at 1000psi converted to atmostphere (atm) 68.04596

V= volume of gas, which is 23 cubic feet converted to liters 651.2875

n is what I'm solving for, which with my current parameters works out to 1870.69 moles

R= gas constant, which is .082057. I've converted my values to ATM, Liters & Kelvin for temperature due to this constant.

T = absolute temperature, 60 degrees converted to kelvin 288.7056.

Solving for n: (p*V)/(R*T)

I feel confident in the ideal gas equation, but when it comes to calculating density I'm lost.
The formulas I'm using for determining density of the gas are: mass = moles * molecular weight so mass = PV(MW)/RT
density = mass/volume so D=PV(MW)/RTV

My goal is to develop this to calculate the CFM of nitrogen through a pipe. I have a high response thermocouple mounted in the flow stream to detect the temperature change and will be plotting the values in excel during the discharge.

Once I have the density I'm that much closer to getting there. Am I atleast on the right track??

 

[leitmotif]

What are you doing with the gas ie what is the process?
What is your allowable error?
Flow meter? Orifice plate and DP gage or sensor?

All these calculations may already have been worked out for you by an instrument mfr.

you can use PRT = PRT
measure cylinder pressure at To and pressure at T1. Knowing cylider volume and time you now can easily calc flow
assuming flow was constant and there was not a large ie 3000 to 0 psi pressure change.

Wont be exact but will get you close.

Dan Bentler

 

[ELake20]

The gas is being expelled through a 40ft 1.5" pipe. The process is to test an air-shut off valve. The valve will trip at a determined CFM and close.

I realize there will be some error due to the condensation of the nitrogen but I would like it as accurate as possible. I'm not using a flow meter, I have a .25% accuracy transducer mounted in the nitrogen 'bottle' (its actually a converted hydraulic accumulator with the piston shoved forward) and a high response thermocouple to measure the temperature. You make a great point about mounting one downstream of the cartridge valve, DP can be easily calculated. The plan is to energize a 50mm cartridge valve downstream to start the acquisition and discharge for the duration of 5 seconds. The purpose of the test is to verify that this valve works as advertised and closes at the correct flow rate.

 

[leitmotif]

Interesting
Is this a single installation single test or are you testing as a valve manufacturer for a sample of a produciton run?

If production you could also consider a critical orifice where once air hits speed of sound no matter the pressure velocity (thus cfm) are same.
Takes some tinkering to find the right size hole and great precision but can be done.

Provided one side or other is at ambient a ball type flowmeter could be used - not sure if you can get what you need in the range of precision you need but worth a thought see the guys at Dwyer.

As an aside as an industrial hygienist we calibrate sampling pump flow rate using a graduated buret and a soap bubble - measure displaced volume and time and you have flow - in our case lpm. Dont think you are going to be able to do that in this case. but it was considered a primary standard for our ball type flowmeters.

Dan Bentler

 

[SCADA_Dude]

I don't know what your budget allows, but what about installing a flow meter? Something like this perhaps.
http://sierrainstruments.com/products/220.html

Not cheap..

 

[jamesau]

OK, so I'm still a little confused by your description of what you're doing. Assuming you want to do a leak test of a 'closed' system, the ideal gas law may be well-suited. (At your conditions, the deviation from ideal behavior will be small).

Consider a timed leak test:
1) Charge cylinder
2) close cylinder, allow x seconds for T and P to stabilize.
3) record pressure and temperature at time 0: P0, T0
4) Wait y seconds
5) record pressure and temperature at time 1: P1, T1
6) calculate molar leak rate (mols/ sec) with ideal gas law: (P0/T0 - P1/T1)*V/(R*y)

Since I'm still not clear of your problem, I can't say if the above is your solution.

 

[leitmotif]

Subject to correction by E Lake (it is his project)

I believe:
He is testing to ensure that a valve shuts off at a specific flow rate. I believe these are called velocity fuse valves. The reason for them is to shut off air to hose with break in it to prevent whipping and knocking someones head in.

What he is going to need is an accurate indication and measurement and ideally recording of CFM (or velocity?) of nitrogen thru valve before and at the time the valve shuts. To simulate real world he has to let the valve discharge to ambient pressure.

Based on this I think
- using changes in a tank pressure
- he is going to have a hard time setting up to ensure constant flow rate or controllable flow rate
- and able to show near instantaneous flow readings .
Tank dP would only give him total cubic feet which divided by time only gives him average flow.

Dan Bentler

 

[leitmotif]

Subject to correction by E Lake (it is his project)

I believe:
He is testing to ensure that a valve shuts off at a specific flow rate. I believe these are called velocity fuse valves. The reason for them is to shut off air to hose with break in it to prevent whipping and knocking someones head in.

What he is going to need is an accurate indication and measurement and ideally recording of CFM (or velocity?) of nitrogen thru valve before and at the time the valve shuts. To simulate real world he has to let the valve discharge to ambient pressure.

Based on this I think
- using changes in a tank pressure
- he is going to have a hard time setting up to ensure constant flow rate or controllable flow rate
- and able to show near instantaneous flow readings .
Tank dP would only give him total cubic feet which divided by time only gives him average flow.

Dan Bentler

 

[ELake20]

Dan - That is exactly it. I'm trying to get things around now because normally these projects tend to sneak up on us. It is just a trial - I think we have six valves to test. The customer purchased these valves from another manufacturer and they cannot test the products they sell (go figure).


I'm planning on using the nitrogen pressure to determine my flow rate. As the pressure decays, flow will drop with it. Engineer has done simulations but we all know how much to trust those..

I'm thinking of sampling at 100hz, response time of thermocouple is around 5ms it *should* be fast enough.

 

[mellis]

I don't believe you can measure flow of a gas with a single thermocouple. The "classic" method of measuring gas flow is to use a volumetric flowmeter and correct it with temperature and pressure to obtain a mass flow.

I believe that with a critical flow orifice and fast temperature and pressure sensors, you may be able to pull this off.

Another way to approach it is to measure the mass of the cylinder and do a loss-in-mass flow calculation. No need for pressure and temperature compensation. Simply difference in mass over sample time.

 

[jamesau]

Why not just spare everyone any lingering uncertainty by doing the following:
1) Ask manufacturer of a recommended test.
2) Assuming this is a reputable manufacturer with a proven product, test the valve in-place at the customer's site.
3) If the test environment is a confined (or even semi-confined) space, use compressed air so no one gets asphyxiated.

 

[leitmotif]

Granted you are doing only six valves - this time!! Sounds like you are a testing calibration and QC lab. I think this will not be the last time so you may as well setup a flow bench that will adapt easily to other valve etc testing.

I still think if you are trying to determine and control flow you should be using a direct reading and ideally real time flow meter. The thermocouple jogged by thoughts - Kurz makes thermo anemometers - they may have some good options. Another may be Vasaila.

The point about using nitrogen vs compressed air is a good one. Oxygen deprivation is a definite risk in this setup. Good ventilation and a good ambient percent oxygen indicator will go a long ways to reduce/prevent this. OSHA allowable oxygen is 21.5 to 19.5% - submarine operations allow for much more tolerant lower level. Depending on employees' health it will not become dangerous until 14 or 15 and maybe lower which is why OSHA is conservative at 19.5.

Dan Bentler

 

[Tom Jenkins]

The classic flow measurement method for this type of test is the orifice plate. ASME has standards for doing this, and you will need the plate, a differential pressure transmitter, a prssure transmitter, and a temperature transmitter to get the mass flow rate.

Kurz, FCI, Sage Metering, and others make thermal mass flow meter. If you want good accuracy you will want NBS (NAtional Berueau of Standards) certification. These units give direct mass flow rate if you have them calibrated in the same gas you are using - nitrogen is common.

If you want volumetric flow rate instead of nass flow then you need to use temperature and pressure measurements to correct using Boyles(?) law - volume is proportional to the ratio of absolute pressures and temperatures. Your flow meter supplier can give you the equation - I don't have them at hand.

You cannot measure flow with just a temperture measurement.

 

[kdcui]

I believe Boyle's Law just takes in to account the relationship between pressure and volume. If you want to correct for temp, then I think the combined gas law is what you want:

( P * V ) / T = k

where k is a constant. If you know enough about the conditions of your gas then:

(P1 * V1) / T1 = (P2 * V2) / T2

which can also be derived by taking a ratio of the Ideal Gas Equation when the amount of gas, n or M depending on the gas constant you use (moles or some unit of mass), is assumed to be constant.

 

[robertkjonesjr]

I'm planning on using the nitrogen pressure to determine my flow rate. As the pressure decays, flow will drop with it. Engineer has done simulations but we all know how much to trust those..

I'm thinking of sampling at 100hz, response time of thermocouple is around 5ms it *should* be fast enough.

If your approach is pressure decay, why the focus on a thermocouple for measuring temperature? A pressure transducer would be the instrument. I have modeled control volumes and estimated flowrates of leaks and other flows from pressure decay tests, but it requires calculus and some assumptions to derive the model equations.

The flowrate will vary as the pressure drop changes as you describe - at reasonable pressures so the mass flow isn't choked. If you need a valve to blow at a certain flow, I am not sure how to 'up' the flow slowly until the trip point is reached - almost by definition you will start above that flow and the valve would instantly trigger. I suppose you could constantly re-run at a decreased starting pressure until you found one that didn't make it trip. But at that point, how about just buy a rotameter or other flow measurement device? I prefer thermal mass flow meters (which use two temperature measurement devices, if I recall) or Coriolis Effect (very accurate, but $$$).


Here is some info on choked flow. I would think this would be important in setting up your test - too high a starting pressure and you won't see the drop in flow with a drop in pressure that you are expecting.