Reciprocating Piston Pump Air/N2 SCFM Flow

[Harveylanc]

Hello Everyone. I am new to the forums so I hope I am posting this in the best section.

I am looking to buy a gas booster that is electrically powered. The factory cannot give me any sort of flow chart so that I can determine how long it would take to boost air or nitrogen from a lower pressure to a higher pressure. The supply pressure would be constantly decreasing while the outlet pressure would be increasing.

After days of research I found that to get a flow curve I would need the volumetric efficiency of the pump, volume per cycle, number of cycles per minute, the starting inlet pressure and the outlet pressure. I understand that the inlet gas temperature and the outlet gas temperature would cause changes in the compressibility but I am looking more at just calculating the flow if at all possible. Although I am not sure if this is all that would be needed, I was able to get the volume per cycle, .455 cubic inches of displacement per cycle. The booster will cycle 618 times per minute and has a volumetric efficiency of 78.89%. The maximum booster pressure is 6000 psig.

I would like to calculate the scfm flow rate at different pressures such as 250 psig inlet with 2400 psig outlet, 250 psig inlet with 3000 psig outlet, 500 psig inlet and 4500 psig outlet and 1000 psig inlet and 6000 psig outlet to get a good feel for the flow rates it is capable of and how long it would take to achieve different pressures.

There may be a spreadsheet or a calculator online that would allow for the calculations however I have not found one and I would like to be able to do the calcculation and create a chart for this information. I am really unsure where to turn for assistance for something of this nature. I am not looking for someone to do all the work but I cannot figure out the caculation so if anyone on the forums would be willing to help me to understand how to create the calculation that would give a flow rate with a decreasing inlet pressure and an increasing outlet pressure I would be very thankful.

 

[jrmichler]

It would help if you provided more information on the gas booster - make, model, web site, etc.

Flow rate is cubic inches per cycle times cycles per minute when the inlet pressure is at standard temperature and pressure (STP - search the term). That will give you flow rate in SCIM (standard cubic inches per minute). Divide by cubic inches per cubic foot to get SCFM (standard cubic feet per minute).

Since the inlet pressure varies over a wide range, you need to correct for inlet density. Assuming everything starts at normal room temperature, just multiply by the ratio of inlet absolute pressure to STP. For example, if the inlet pressure is 250 PSIG, the inlet absolute pressure is 264.7 PSIA. The flow would then be 0.455 X 0.789 X 618 X 264.7 / 14.7 = 3995 SCIM = 2.3 SCFM.

It's possible to derive an equation for flow rate vs time when pumping from a vessel of known volume to a vessel of known volume, but it is much easier to numerically simulate it. A numerical simulation can be done with a spreadsheet.

There is a practical reality that you have to be aware of. The flow rate will decrease below the calculated rate at high compression ratios. When the ratio of outlet absolute pressure to inlet absolute pressure is high, the flow rate will be less than calculated. That is because there is always some dead volume between the piston and the outlet check valve.

This should be enough to get started. Take it as far as you can, then come back.

 

[Harveylanc]

Hello jrmichler,

Thanks for your assistance in this calculation. The volume per cycle is in liquid, would this need to be converted to a gas volume before the calculation is made or does it matter? I have read online it doesn't matter but I would rather ask to make sure.

 

[jrmichler]

Hello jrmichler,

Thanks for your assistance in this calculation. The volume per cycle is in liquid, would this need to be converted to a gas volume before the calculation is made or does it matter? I have read online it doesn't matter but I would rather ask to make sure.

Quoted, and added a PM from the OP:
I have been studying what you sent me yesterday in regards to calculating the flow rate of the reciprocating piston pump and have been researching the STP and I am now very confused. I understand by researching that the STP = Standard Temperature (273.15 Kelvin) and Pressure (760 Torr) and have looked at many examples, some are saying to use the Ideal Gas Law to make the calculation others refer to using the Z Factor to include compressibility. I have seen the use molecular weight (lb/lbmol) and a number of other possibilities.
Could you please help me to understand what is actually required to correct for inlet density? Maybe I am just not fully understanding what you mean by the phrase "multiply by the ratio of inlet absolute pressure to STP":

"Since the inlet pressure varies over a wide range, you need to correct for inlet density. Assuming everything starts at normal room temperature, just multiply by the ratio of inlet absolute pressure to STP. For example, if the inlet pressure is 250 PSIG, the inlet absolute pressure is 264.7 PSIA. The flow would then be 0.455 X 0.789 X 618 X 264.7 / 14.7 = 3995 SCIM = 2.3 SCFM."

I apologize if this may be of any inconvience to you, I would really like to understand how this works and know that I am doing it correctly. Any assistance you could provide would be greatly appreciated.

With gases, volume is volume. It is NOT like liquids, where you have fluid ounces and weight ounces.

Forget compressibility and Z factors for now.

Compressed gases can be confusing because you have to keep track of both actual volume and standard volume. My experience is with industrial compressed air systems, where the units are in cubic feet, so that's what I will use here. If an air compressor sucks in 100 cubic feet of air from the room, it has sucked in 100 standard cubic feet. If it sucks that much air in every minute, the rate is 100 standard cubic feet per minute (100 SCFM).

Assume that that air is compressed to 100 PSIG (pounds per square inch gauge pressure). The absolute pressure is 114.7 PSIA (pounds per square inch absolute). The air compressor is producing 100 SCFM of air at 100 PSIG, with inlet pressure 0 PSIG. That air is cooled after compression in an aftercooler, so is at room temperature. The volume is 100 SCF X 14.7 / 114.7 = 12.8 actual cubic feet (ACF). You can say that the compressor is delivering 12.8 ACFM or 100 SCFM. Either is correct, but you need to keep track.

Now increase the inlet pressure from 0 PSIG (14.7 PSIA) to 14.7 PSIG (29.4 PSIA) and keep the discharge pressure constant. The compressor is still sucking in 100 ACFM, but because the inlet air is at double atmospheric pressure, it is sucking in 200 SCFM. It is delivering 200 SCFM (25.6 ACFM) at 100 PSIG. The power consumed by the compressor also doubled.

When working these type of calculations, it is helpful to keep track of the numbers using a table. The table headings would be something like the following: Inlet gauge pressure, inlet absolute pressure, inlet ACFM, inlet SCFM, plus similar for the discharge. If temperatures differ from room temperature, add inlet and outlet temperatures to the table.

I use 0.075 lb/ft^3 for the density of air at room temperature and normal atmospheric pressure. The actual density will vary with atmospheric pressure, temperature, and humidity, but 0.075 works for most normal calculations. For other gases, just multiply by the ratio of molecular weights. CO2, for example, is 0.075 X 44 / 29 = 0.11 lbs per ft^3 at room temperature and pressure. Get your head around all of this before looking at compressibility and Z factors.

At high pressures, and 6000 PSI is high pressure, other factors enter the calculations. Start by looking a phase diagram for your gas. Then seek help from others on this forum, because that is beyond my sphere of competence.