Air loss calculation

[dkhayes117]

Hi all, I'm trying to determine CFM loss from change in PSI and known storage. We have an Ingersoll rand r75n screw compressor rated at a maximum of 457 CFM, 75kw/100hp. The compressor runs at approximately 114psi. The compressor is tankless, the only storage is the piping, which comes out to about 6000 cubic feet volume. The pressure drops from 114 psi to 84 psi in 1.55 minutes with compressor off. How much CFM is being lost?
What I've tried so far....
114psi/14.7psi = 7.755 atmospheres x 6000 cubic feet = 46530 cubic feet
84psi/14.7psi = 5.714 atmospheres x 6000 cubic feet = 34284 cubic feet

46530-34284 = 12246 cubic feet difference/1.55 minutes = 7900CFM which cannot be right, what am I missing?

also tried
leakage rate = (volume x (Pressure intial - Pressure final))/14.7 x time

(6000cuft x 30psi)/14.7psi x 1.55min = approx. 7900CFM???

there must be a difference between the compressor's cfm rating and the cfm I'm calculating???

 

[BigInch]

Assuming an ideal gas and a constant temperature, that's what I get.
Leak rate doesn't have anything to do with compressor rating.

 

[LittleInch]

You don't describe your system very well, but on the assumption that there is a compressor, a non return valve, quite a lot of piping ( can you describe how you got to 6000 cubic feet please) and presumably some sort of usage.

So does your compressor normally maintain the pressure at 114 psi no problem??

If yes then when you stop the compressor in 1.55 minutes the pressure falls from 114 psig to 84 psig?

Then either there is a lot of gas now going somewhere else ( back through the compressor??) or
Your volume is incorrect ( by factor of 10)
Your pressure readings are inaccurate
There is a pressure regulating valve somewhere in the system

Your system is very small bore and very long and hence the average pressure in the piping isn't 114 psig but something much lower.

What happens after 1.55 minutes (I minute 55 seconds or 1 minute and 32 seconds?? Does pressure keep falling?

Bit more info required.....

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

 

[dkhayes117]

Thanks for the replies!
There are two 100 hp compressors, only one runs at any given time. 2" diameter main line goes from compressor to air dryer then out with 2"dia into a 3" main distribution line(about 72 ft long). From here it is necked down to five 2"dia lines about 240ft each. Out of the 2" piping runs 3/4" short runs of 40ft or less ending with 3/8dia, 10ft long whip hoses. There are some off shoots of longer 3/4dia lines feeding other lines, basically I estimated total storage volume by multiplying lineal footage by cross section area of each diameter. This may have been a little short sighted not taking into account pressure drop on the lines, etc. Really I'm just trying to get a good ball park idea of my cfm loss from leaks. Any who, The compressors are continuous running, so they never stop running until turned off(it feeds upholstery manufacturing lines). When running they maintain the 114-116 PSIG. I also just found out that the compressors have a capacity, or duty cycle, meter. I do not know the % capacity while the plant is wide open, I will check tomorrow. The pressure drops from 114psig to 84psig in 1.55 minutes with NO USAGE and with the air lines open.....Yes there are many, many system leaks. The system leaks all the way down to 0 psig with the compressors off, but the psi decay rate falls off. I didn't time it, but I believe it took 15-20 minutes to reach 0 psig. What if I have the compressor running with no line usage and note the duty cycle of the compressor than multiply that times the total cfm capability to calculate the cfm loss? For example, at 100% duty cycle the compressor can produce 457 CFM, and if the compressor runs at 40% duty cycle with no usage to maintain the 114 psi, then
40% x 457 CFM = 182.8 CFM system loss. If this is correct, I'd still like to know if you can figure it with the psi drop over time. Thanks again!

 

[LittleInch]

Your idea of running the units with no loads is much better to establish some idea of leakage rates, though this may be higher as other parts of the network will be at a higher pressure then they normally operate and hence have a higher mass flow leakage.

This seems like a complex network with many pressure drops and areas where the start pressure when you turn off the compressors will be a lot lower than 114 psig, hence I would say a large percent of your "loss" in the initial minute or two is actually just the air equalising all over the system.

I would add some more pressure gauges at points along your network to understand what is happening.

At the end of the day, the leakage simply must be less than the amount of air you're pouring into this network minus the amount leaving at the end doing useful work. It isn't coming from nowhere.

It would be interesting though to see a detailed plot of air pressure versus time for your shutdown situation. Whilst there is some reduction in leakage with lowering air pressure, the decay curve should be smooth - my guess is the initial drop is quite high compared to what happens after once it's all equalised. Also plot the air pressure drop over time at other points in the network, especially the far end point.

114 psig is a bit of an odd pressure - make sure their aren't any relief valves wrongly set at 100 psig or busy passing. Ditto isolate the compressor when you turn it off.

Can you isolate different sections to check pressure drop / leakage rate at no usage in smaller sections?

Let us know what you find.

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

 

[dkhayes117]

Again, thanks for the prompt reply. I wrongly typed 114pisg, It is 100 PSIG! It'll take me a few days or so to get more detailed info for analysis. I will reply though.



Engineer's motto
If it isn't broken, take it apart and fix it!!

 

[LittleInch]

Ok, but you use 114 in a lot of places so at least consistently wrong....

While you're at it please double check your distances and volumes.

For a 2" pipe I get approx. 40 cubic inches per linear foot.
Your 600 cubic FEET is about 1 million cubic inches = approx. 26,000 (thousand) linear FEET of pipe.

I didn't add up all your distances and different sizes, but only came up with about 2000 equivalent feet of 2" pipe.

Therefore your volume figure seems be out by a factor of over 10??

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

 

[dkhayes117]

Actually its is 114-115 PSIG, I got a little confused when thinking about PSIA, PSI, and PSIG. I think that the PSIG is 114 so that you get 100PSIG at the end of the air lines after pressure drop and losses. I rigged me up a pressure gauge with a male coupling adaptor so I can plug it in to any female coupling and determine end pressure. I'm also in the process of drawing out the air line layout for better analysis. Stay tuned!

ENGINEER"S MOTTO
If it isn't broken, take it apart and fix it!!

 

[BigInch]

"G" means you read it from a guage. "A" means not.
PSI means none of the above.

 

[dkhayes117]

Wow what a stupid mistake, yes LittleInch, you are right. I mixed inches and feet like a dummy. I didn't list all of the pipe that is in the system, I'm measuring it more accurately now, but I think I should end up around the 100 cubic ft mark total. That might make a small difference lol. Updated measures will be posted, hopefully tomorrow! Thanks guys

ENGINEER"S MOTTO
If it isn't broken, take it apart and fix it!!

 

[BigInch]

Wow. A little more than ... a scuba tank.
I'd suggest that the next time you do a calculation that you have some idea of the number you should get before you ... do the math. It will be kind of a self-check.
You know what was the best thing about slide rules. You at least had to keep track of the decimal point in your own head.

 

[LittleInch]

Errr a scuba tank volume is about 0.4 cubic feet. At full pressure it holds about 80 scf, but that's not the same thing.

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

 

[BigInch]

72 SCF. More or less the same with respect to 6000.

 

[LittleInch]

dkhayes,

A couple more points come to mind.

If someone asks why you're bothering, its probably worth calculating how much say 1000 cubic feet of air ( or some other volume) is actually costing you to pressurise to then just let it leak away for no benefit.

I can't understand how you're operating this system without an air receiver. Compressors of the size you're using normally work on a load and unload operation between certain set pressures (high and low). If you have no receiver, then I suspect your compressor is constantly loading and unloading between your high and low pressures ( any idea what they're set at?)

This won't be doing your compressor any good and will also be difficult to control air pressure .

Unless you've accidently exactly matched compressor output to usage plus leaks you really need to think about installing a reasonable sized receiver to smooth out your air supply.

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

 

[dkhayes117]

I've run the numbers, correctly this time, and I have 2749 feet of .75" pipe, 1223 feet of 1" pipe, 1080 feet of 1.5" pipe, 715 feet of 2", and 325 feet of 3" pipe. I also found an air exchange tank, I'm new to this company, Therefore....
.75" OD pipe = 3.682 cubic inches per lineal foot x 2749' divided by 1728 = 5.858 cubic feet
1" OD pipe = 7.216 cubic inches per lineal foot x 1223' divided by 1728 = 5.107 cubic feet
1.5" OD pipe = 17.819 cubic inches per lineal foot x 1080' divided by 1728 = 11.137 cubic feet
2" OD pipe = 33.134 cubic inches per lineal foot x 715 divided by 1728 = 13.710 cubic feet
3" OD pipe = 77.902 cubic inches per lineal foot x 325' divided by 1728 = 14.652 cubic feet
30" diameter x 80" tall air exchange = 32.725 cubic feet

Grand Total = 83.189 cubic feet

Also, The compressor runs loaded the whole time, whether it should or not I am not completely sure. At full work load, compressor 1 runs at 82% capacity, while compressor 2 runs at 77% capacity. Note that only one compressor runs at any time, they usually alternate day by day. There are 2 other plants in the business, and I checked their loads to compare. Granted they are slightly smaller plants, but they were running at 47%(plant 3) and 40%(plant4) capacity with same compressor. I don't see there being but maybe 10% compressor capacity difference in theory. I see at least 20% waste in this system. I won't be able to run my leak down tests until Friday. I also did do a pressure drop test....Plant 1 runs 114psig at compressor with no regulator it ends up at 88-90 psig at the business end every single hose I checked. Plant 3 ran 110psig regulated to 95psig, and finished at 88psig. Plant 4 ran 120psig unregulated, and finished at 118-119psig. Plant 4 has newer run lines and is by far the best system.

ENGINEER"S MOTTO
If it isn't broken, take it apart and fix it!!

 

[LittleInch]

Well done - See what proper data does for you?

On your run down tests see if you can get pressure / time readings from the compressor end AND business end at the same time or do two tests.

Then you can estimate a settle out start pressure for the entire system.

Looks like you're loosing a lot of air in plant 1 alright.
Still think you need an air receiver to make it really work better, but that's your call

Let us know how it turns out.

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

 

[dkhayes117]

Okay, I finally got to do my leak test with no workers on the lines Friday evening. I did a pressure decay analysis at the compressor first, then built the system back up and tested at the end of a hose next. Another note, I finally got to talk to the head maintenance tech, and he showed me all of the air exchange tanks on the system. There were two more for a new FINAL total of 140.189 cubic feet of storage.
I attached a link to the results at the bottom, it wouldn't let me insert a photo for some reason. Also, I used wolfram alpha to create a quadratic fit equation.

ENGINEER"S MOTTO
If it isn't broken, take it apart and fix it!!

 

[dkhayes117]

I did a quick calculation and got an average of 140 CFM loss over a minute, however this calculation assumes that the pressure can drop over that minute. Less pressure equals less CFM leakage. The compressor keeps itself at a near constant of 114psig at 50% capacity with no work related usage. This means that since the compressor is rated at about 454 CFM times 50% equals 227. This means that roughly 227 CFM is being lost constantly. I plugged this into an excel sheet I made for calculating the yearly cost of this and it comes out to $9144.47 per year, not to mention the extra wear on the compressor itself. Thanks for the help guys, and let me know if I missed something.

ENGINEER"S MOTTO
If it isn't broken, take it apart and fix it!!

 

[LittleInch]

Great.

so by my reckoning going back to your OP you're loosing approx. 100 scfm you've paid good money to pressure up to 114 psig. That's quite a bit of air / cash over a week or month.

Might be very slight, but the graphs indicate that the losses are more towards the compressor end than the hose end because as the compressor pressure falls to equalize the pressure, it over shoots - indicating more losses at that end of the system.

you've learnt a lot about your system!

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

 

[dkhayes117]

Thanks again to all that replied

ENGINEER"S MOTTO
If it isn't broken, take it apart and fix it!!