Time to Fill Receiver with ACFM at PSI

[2easyg]

Hello All

I have been challenged on my knowledge of compressed air systems which has caused me to pause and consider that I might be blindly following consensus without adequate understanding.

The question is relatively simple, calculate the time to fill the following receivers:
I have 2, 400 gallon receivers that I need to fill to 175 PSIG from empty (0 PSIG) with a reciprocating air compressor rated at 26 ACFM at 175 PSI, with a sub note indicating the ACFM is FAD tested in accordance with ISO 1217.

In the past, I have assumed that the 26 ACFM is the amount of free air entering the compressor to deliver 175 PSI. I would convert the ACFM to SCFM from the estimated location the compressor was tested and then SCFM to ACFM to where the compressor will be operating.

I would then apply the formula:
t = (V(total receiver) * (Psig(final) + Psi(atm))) / (Psi(atm) * ACFM)
t = ((107 Cu Ft) * (175 + 14.7 - 14.7)) / (14.7 * 26) = ~ 50 mins.

However, I have recently been asked why include the pressure ratio when the definition of ACFM is the CFM at the tested environmental conditions at the outlet of the compressor, as defined on engineeringtoolbox.com. If the compressor rating is indeed pushing 26 CFM at 175 PSI, then indeed there is no reason to include the pressure ratio and since the pressure of the tanks are the same as the pressure rating of the compressor. The time to fill would neglect the pressure and just be Receiver Volume / Volumetric flow. Essentially, filling up a bucket.

Additionally, I have been told that to use the above formula, I would have to convert the ACFM to "free air" conditions, i.e.:
Free Air Flow = 26 CFM * (175 + 14.7) / 14.7 = 335.52 CFM
then
t = ((107 Cu Ft) * (175 + 14.7 - 14.7)) / (14.7 * 336) = ~ 3.8 mins.

I guess that I haven't previously questioned the idea that all compressors are rated from a standard ambient condition. Are different types of compressors rated differently? Could the same type of compressor be rated different ways for different applications?

So if someone with air compressor expertise could give me a hand with clearing out the confusion, it would be most appreciated. Perhaps suggesting a good text on the subject?

Cheers,

 

[georgeverghese]

Yes, the delivery flow for a compressor is influenced by both suction and discharge pressure and temperature conditions. For a fixed suction pressure, the discharge flow varies to suit the displacement volumes for each stage and even the interstage pressures and temperatures will vary.

The computation for the new delivery flow for this compressor requires information on the net displacement volume for each stage and the volume not swept out, in addition to the compression polytropic eff for each stage also for a recip machine or an oil free screw. So it is more complicated than the expression you have here. While I have no idea how this is done for an oil flooded screw.

Ask the machine vendor to tell you to give you a rough plot of the delivery flow profile is for the 0-175psig discharge range. If there is an aftercooler, there may be temperature effects also due to changes in mass flow, operating pressure and feed temp to the cooler, but it may be possible to ignore this to get a rough idea of fill time.

 

[zdas04]

2easyg
You've fallen into the trap that too many people fall into, these calculations only have meaning in mass flow rate or the excellent surrogate for mass flow rate that is volume flow rate at standard conditions. Trying to work in ACF will always give you problems. Convert the ACFM rating of the air compressor to SCFM and never think of ACFM again. Your "free air" calculation has reversed the numerator and denominator.

Your compressor has enough power to produce 26 ACFM into 175 psig, but it is only producing 2.01 ACFM at discharge conditions (at sea level). This means that the equation you provided should have been
q_acfm*[rho]_suction=q_acfm*[rho]_discharge
terms cancel and it becomes q_discharge=q_suction*P_suction/P_discharge=26*14.7/189.7=2.01 ACFM, but if you work in ACFM you are sure to get messed up.

If your local atmospheric pressure is 12 psia (like it is here in Farmington, NM) then your 26 ACFM becomes 26 ACFM*(12/14.7)=21.2 SCFM (using STP equal to 14.7 psia and 60F).

To fill your 400 gallon (53.5 cu ft times two) vessel to 175 psig you need (107*(175+12)/14.7)=1361 SCF of air. So it should take 64.2 min to fill at my elevation. At sea level it would take 52 minutes (since suction ACF is at standard pressure at sea level).

[bold]David Simpson, PE[/bold]
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist

 

[georgeverghese]

My previous response applies only when there is no backpressure PCV to hold the recip compressor discharge pressure constant at 175psig while filling these vessels.

 

[2easyg]

Thanks @zdas04. I think you and I are on the same page.

@georgeverghese, I think your explanation is a bit more in depth for my application, but by diving into the depths of compressor mechanics, I am very intrigued by the different types, particularly screw compressors. I will contact my vender and ask for a sample flow profile. Thanks