Pressurized Air Bottle release rate 3

[rcontractor]

Hello,

I am looking to do a simple calculation. I have an air bottle, pressurized to 3000psi, and am going to draw 80psi @ 0.5 cfm from it. I need to know how long this bottle is going to last.

Its been a while, so I am drawing a blank. Any help would be appreciated.

Thank you

 

[israelkk]

What is the bottle volume?

 

[rcontractor]

It is variable. I have some freedom to play with time and volume, but we can say 400 cubic feet for the large air bottle.

 

[zeusfaber]

you're going to expand the gas about 3000/80 = 37.5 times ("about" because I don't suppose it will be truly isothermal)

If you draw 0.5 cfm at 80 psi, that means a v cubic foot (i.e. water capacity of v cubic feet) cylinder will deliver for about (v x 73) minutes.

A.

(Silly I know, but this one feels so much easier if you do it in bar and litres!)

 

[rcontractor]

zeusfaber,

Is there anyway that you can explain what you did a little more? Because it would seem as though this bottle would last for 60 8-hour shifts.
But where did the magic 73 come from? 37.5/0.5 would be 75 so i am thus confused.

Thank you very much,

Ras

 

[israelkk]

I believe zeusfaber forgot to multiply the 73 by 400.

However, air does not behave as an an ideal gas at 3000psi therefore, the correct way is to calculate the air mass inside the bottle and devide it by the air mass flow rate at 80psi. Since I do not have in hand the air specific volume data I will demonstrate with Nitrogen which is very close to air. The Nitrogen info was taken from NIST at

http://webbook.nist.gov/chemistry/fluid/

. The specific volume of Nitrogen gas at 3000psi and 25 Celsius degrees is 17.759 lbm/cubic feet and at 80psi is 0.38952 lbm/cubic feet. Therefore, the mass in the bottle is 17.759*400=7103.6 lbm. The mass flow rate at 80 psi is 0.5*0.38952=0.19476 lbm/minute. Division of 7103.6/0.19476=36473 minutes which is 607.9 hours.

 

[israelkk]

Just need to correct that not all the mass in the bottle will flow out. The mass at 80psi will stay in the bottle which is 400*0.38952=155.808 lbm. Therefore the time will be (7103.6-155.808)/0.19476=35673.608 min = 594.56 hours

 

[zeusfaber]

Couple of clarifications:

First of all, be wary of your "400 cu ft" cylinder. In my earlier post, I specified the "water capacity" of the cylinder (which is what we use in this part of the world). In other places (and since you're using imperial units, I suspect that you may live in one of them), the cylinder size is specified in terms of what volume of free air (i.e. at 1 bar) you'd get out if you expanded the contents after it had been charged to working pressure. To convert from one to the other for an ideal gas, divide by whatever 3000 psi is in bar (off the top of my head, I think it's 207).

If you're not sure which currency you're using, think of an aqualung cylinder. A standard 232 bar (3400ish psi) 12 litre WC cylinder delivers about 100 Cu Ft of free air. Is what you've got just a bit bigger than that, or something that would hold a couple of thousand gallons of water?

IsraelKK - the "multiply by 400" was in the "v x ..." (when I typed it, I didn't know the cylinder capacity - these bits crossed in the post). I take your point about the gas being non-ideal at this pressure. I wonder if that gets swallowed up in practice in the conversion between the two ways of specifying cylinder capacity (it would if 400 Cu Ft is genuinely what you'd get out if you expanded it to atmosphere - do they take account of non-ideal behaviour when sizing cylinders in US? Not sure: perhaps someone can clarify).

What about the difference between (73 x v) and (75 x v)? About 80 psi. For the last (2 x v) minutes, the pressure in the cylinder is going to be below 80 psi, so the system will no longer deliver the output you specified. Suppose it depends on your application.

Assuming a cylinder just four times aqualung size, I get (400 x 73 / 207) = about 140 minutes.

With the big tank, I make it about (400 x 73) = about 29000 min or 487 Hr.

Final thought: This isn't a breathing application is it? Converting sizes, delivery pressures and flow rates into metric, it ocurs to me that they're all in the ball-park for for a trolley-based BA system - in which case you need to ask whether you're taking 0.5 cfm at the 80 psi IP (which is what the calculations above assume), or at the mask at 1 bar (in which case it'll last a lot longer).

A.

 

[quark]

My approach presuming the bottle water volume as 400cu.ft and considering isothermal process, will be

400cu.ft bottle contains 400x(3000+14.7)/14.7 = 82032.65cu.ft at atmospheric pressure.

As you are not willing to use pressures below 80psig, the volume that can't be removed from the bottle is 400x(80+14.7)/14.7 = 2576.87 cu.ft.

Total volume of gas you are using is 82032.65-2576.87 = 79455.78cu.ft at atmospheric pressure. This volume, at 80psig, becomes 79455.78x14.7/(80+14.7) = 12333.68cu.ft. Extract at a rate of 0.5cu.ft/min and it takes 12333.68/0.5 = 24667 minutes or 411 hours.


Regards,

 

[israelkk]

The method used by quark and zeusfaber is a simplified way assuming ideal gas. To their method there is no difference between compressed Hydrogen with a very small mulecular weight to Air/Nitrogen with a molecular weight 14 times larger. The correct way is to use the gas mass and specific volume (mass per volume) properties at the bottle and outside the bottle.

 

[quark]

There is a deviation in the data when I checked the NIST website. Though the density at 80PSI is same at 0.3895lb/cu.ft, it is 13.759lb/cu.ft at 3000psi for an isothermal process.

But the actual values should be taken at psia(not psig) so corresponding densities at 94.7psia and 3014.7 psia will be 0.46069lb/cu.ft and 13.817lb/cu.ft respectively.

Total mass in the bottle = 400*13.817 = 5526.8lbm. Mass flowrate = 0.5*0.46069 = 0.230345lbm/min. But you can't draw out mass equal to 400*0.46069 = 184.276lbm.

So time taken will be (5526.8-184.276)/0.230345 = 23193 minutes or 386.55 hours.

As we are considering both volume in tank and volume flowrate out at specific temperature and pressure, density compensation is inherent.

Further, at 3000PSIg and 25⁰C compressibility factor of air is close to 1(lessthan 1.01). This indicates ideal behaviour of air.

Regards,

 

[aviat]

I think you will need pressure regulator(s) to bring down the pressure down, and some means to control the flow etc. All of which will put restrictions on system and you will not be able to go down to 80 PSI.

 

[arto]

How about
P1*V1^n = P2*V2^n


n =k (specific heat ratio = 1.4 for air)Adiabatic, n=1 isothermal [which one? - depends on how fast the discharge is]


see the Accumulator sizing equations:

http://www.parker.com/accumulator/cat/english/1630007.pdf

 

[zeusfaber]

What a depressing selection of different answers to a simple question - most of them right! I thought I'd try to understand the differences.

First of all, the massive 140 min versus 300-400 Hr. This is simply down to what "a 400 Cu Ft" cylinder means - which I think is probably explained to death in the thread above.

Quark (originally) and I have both used the same "ideal gas" simplification, but used different assumptions about what the original question meant by 80 psi and 3000 psi. I made the quick and dirty assumption that this was psia - giving 487 Hr, quark assumed you meant psig giving 411 Hr(and although the question could mean either, quark's interpretation is more likely to be correct). The difference is about 20%, so it's worth giving a bit of thought to what you're measuring.

israelkk has gone for the more precise science of correcting for the fact that gases become less compressible at higher pressures, and has worked it out by conservation of mass. The theory is sound, although one of the constants is wrong, giving an inflated duration. I agree with Quark's rework of this method (386 Hr which assumes all pressures stated in psig) - To complete the picture, I think the corresponding duration for psia (the figure israelkk was aiming for) would be 458 Hr.

How much error do you get if you assume an ideal gas? In this case, the difference between comparable results is about 6%, which explains why in 15 years of calculating gas supply durations by assuming ideal gas behaviour (mainly for divers) I've never noticed enough of a difference beween subsequent reality and expectation to question the method - the last couple of days have been a bit of an eye-opener in that respect.

Other observations.

rcontractor started the thread by quoting four variables, each to one significant figure - and here we all are quoting answers to three or four SF. Apart from the cylinder volume, all these variables are likely to be pretty unstable.

We've all (except arto) assumed isothermal expansion. Whether this assumption is fair depends a lot on the application - not just on rate of discharge, but on things like quality of heatsinking.

Been interesting so far - made me think about some things I'd never considered before.

A

 

[rcontractor]

I think I owe it to you all to give you a little more specific information on the application. I really appreciate all the thought and help that went into this, but is just how engineers are eh?

I have an high pressure air tank (like a scuba tank, only 400 cu ft) that is being used as a substitute to a compressor to provide air at 80psi and 0.5 cfm to a "filter unit for extraction of solder Fumes". The air consumption is right off of the manual for the filter.

I basically wanted to find out whether it is feasible to get an air bottle to replace a compressor in terms of time to empty the bottle, since we are limited by noise levels.

Cheers,

rcontractor

 

[zeusfaber]

What happens when the cylinder is empty? Were you planning to buy air from an industrial gas supplier, or to refill the bottles yourself?

Buying air in looks a bit like an exercise in military logistics - four bottles per shift, each about the size and weight of a man (guessing a bit here, the largest single air bottle our local supplier does is an N, (1460*230 mm, 82 kg gross, 230 bar, fill volume 8.86 Cu m - a tad over 300 Cu Ft).

Filling to 3000 psi needs a high-pressure compressor - a machine that makes much more noise than a small low pressure that would drive your filter direct, and takes substantially more maintenance and operator skill.

I don't use low pressure compressors myself, but I bet there are some very good hush kits out there.

A

 

[zdas04]

The noise levels of an electric motor driven dry screw compressor to take 0.5 CFM of air from atmospheric to 80 psig (6 ratios, call it 1 hp) would be about the same as a refrigerator compressor. If noise is your big concern zeusfaber is right, there might be a better way to skin this duck.

David

 

[rcontractor]

The air bottle is 8" in diameter and 4 ft high. The plan is to contract a company (I believe it will be Praxair) to bring in air bottles ever time it runs out. There are a number of other applications, but this one will draw the most from the bottle. I agree the best way to approach the situation would be to buy a silent compressor, but that is a bit out of the budget for this application.

we have compressor to fill these bottles to 3000psi but as you say it is extremely loud and we have nowhere to run the compressor in our new office. Thus the idea of either a silent compressor (costly) or contracted air supply (costly but over time).

 

[zeusfaber]

rcontractor,

One of the problems with quoting cylinder sizes in terms of the volume of free gas you might be able to extract from them is that this figure is only meaningful if the cylinder starts off filled to its designed working pressure.

Just multiplying up the outside dimensions of your cylinder (and taking no account of wall thickess!) I don't see how a cylinder that small can possibly hold 400 Cu Ft at 3000 psi.

I wonder if you've got a bottle with a specified WP of 300 bar (about 4400 psi) - which is all very well if the supplier charges it to that pressure and your valve gear will withstand that pressure (it sounds like its beyond the capability of your own compressor). Fill them only two-thirds full, and you're looking at nearer six bottles a shift. How does that affect the economics?

A.

 

[sailoday28]

rcontractor (Mechanical) Feb 16, 2005
STATES
"I have an high pressure air tank (like a scuba tank, only 400 cu ft) that is being used as a substitute to a compressor to provide air at 80psi and 0.5 cfm to a "filter unit for extraction of solder Fumes". The air consumption is right off of the manual for the filter."

Is this a safety problem? Does the original compressor discharge the air at a specified or known temp thereby giving more meaning to SCFM rather than cfm.

Clearly, the process in theory is between isothermal and adiabatic. If the blowdown is in hours (quark ) as I've seen from responses, then the cylinder process is more like isothermal.
zeusfaber (Military)STATES
"israelkk has gone for the more precise science of correcting for the fact that gases become less compressible at higher pressures, and has worked it out by conservation of mass."

Other engineers perform calcs with high pressure gases. I believe that israelkk has gone for a better engineering solution. For example, what type of analysis should have been done for safety purposes on the air blowdown/ballast system of the submarine "Thresher" ?