Determining an equiv. scfm value for leaks 3

[IntrepidLearner]

After pressuzing my air receiver to 120psi, I turned off the two air compressors and watched how quickly the receiver pressure dropped:

- after ~0:35 (35 secs), pressure had dropped to 80psi;
- after ~1:10, pressure had dropped to 60psi;
- after ~2:20, pressure had dropped to 40psi.

Note, this was done during a period when there was no demand. Hence, air loss/consumption can be wholely attributed to leaks.

I'm trying to determine an equivalent scfm value of the air consumption. Does anyone know of a formula for this?

Air receiver capacity = 500L.
Inlet and outlet are both 2".

 

[zdas04]

SCF is a really effective surrogate for mass. I would approach your problem by determining the SCF in the system at each point, then the difference divided by the elapsed time is the SCF/unit time. If the "system" is the 500 l vessel then:

vol=17.6573 ft^3

SCF = vol*((P(actual)T(std)Z(std))/(P(std)T(actual)Z(actual)

At these pressures Z(std)=Z(actual), and I'm assuming that the vessel is at 60F and temp cancels also. Your starting point is 161 SCF.

Point 1 113.6 SCF so your first rate is 82 scfm.

Point 2 is 89.6 SCF so the rate from the start is 61.2 scfm, rate from point 1 is 41.1 scfm.

Point 3 is 65.6 SCF so the rate from the start is 40.8 scfm and, rate from point 2 is 20.6 scfm.

I'm sure there is a more elegant way to do this arithmetic, but I've never found it. This arithmetic is based on the entire system being the receiver. If you had that kind of a leak in the receiver it would be really obvious. For a real-world answer you would have to include the volume of piping, filters, and traps.

David

 

[25362]

If you know the temperature of the air at the end of each period, you can easily estimate the remaining gas of air by use of:

mass = PV/RT, assuming air behaves ideally.

For example,

120 psig = 134.7 psia
V = 500 L = 17.7 ft³
T = 80^oF = 540^oR

mass = (134.7)(144)(17.7)[÷][(53.3)(540)] = 11.9 lb

If the process were isothermic, the amounts of remaining air after each period would be:

(94.7)(144)(17.7)[÷][(53.3)(540)] = 8.4 lb
(74.7)(144)(17.7)[÷][(53.3)(540)] = 6.6 lb
(54.7)(144)(17.7)[÷][(53.3)(540)] = 4.8 lb

Taking 13.6 cf/lb_m at atmospheric (29.92 in Hg) pressure, as the density of dry air, it would result in losses:

First, 35-s period: ~ 82 scfm
Second, 35-s period: ~ 42 scfm
Third, 70-s period: ~ 21 scfm

Saturated moist air at the same conditions would have a specific volume of 14.1 scf/lb_m, and the results would change a bit.

 

[quark]

Like David suggested, it is better to check the overall system leakage. If you know the total system volume, you can use the procedure given by David to exactly estimate the leakage. However, it is difficult to arrive at a common numerical when you deal with leakages at various pressure intervals.

You can use compressor loading and unloading times to check the leakage as percentage of compressor capacity under no load conditions. You should close of all the user valves but receiver shut off valve to header should be open. Once you reach the set pressure at the receiver, compressor unloads and note the time duration of unloading. As the system leaks air from receiver and distribution network, there is a drop in pressure and compressor loads up. Now check the loading time.

Percentage leakage can be expressed as T_L*100/(T_L+T_UL)

(T_L, T_UL) are loading and unloading times respectively (preferrably in minutes but does't matter)

 

[25362]

13.6 scf/lb is density^-1, not density as I typed.

 

[Ashereng]

I have some thoughts and questions, they may be dumb (warning), but, here goes.

When you turned the compressors off, did you also shut the inlet valve to the I/A receiver? Is all the losses from the I/A receiver and downstream?

Secondly, when you say no demand, how do you know? Are all of your valves on/off? Control valves with I/P and positioners usually have a constant bleed (the newer positioners have drastically reduced constant bleed, but it's still there).




"Do not worry about your problems with mathematics, I assure you mine are far greater."
Albert Einstein
Have you read FAQ731-376 to make the best use of Eng-Tips Forums?

 

[IntrepidLearner]

Hi Ashereng,

I didn't shut off air reciever inlet valve. There are leaks upstream as well as down.

You are right, there are I/P positioners with a constant bleed. However, I have identified them all (approx 10), and have attributed an scfm consumption to them.

I appreciate the input/questions.