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4

# Air Receiver Filling Time Calculation

7 replies to this topic
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### #1 raman123

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Posted 06 December 2017 - 01:26 PM

Im trying to calculate the filling time of an air receiver. Air receiver will not be supplying air when its filling.

I was trying to use following formula:

T = Vr (P2 – P1) Po (Acfm)

Where: T is time required – min. Vr is tank (or system) volume-cu ft. (cu ft = gal/7.48) Po is atmospheric pressure – psiA P1 is initial tank pressure – psiA (*) P2 is final tank pressure – psiA (*)

Acfm is CFM air delivered by the compressor during the pump-up pressure change

I wanted to know this Acfm value will be Actual ft3/min at compressor suction?

Or at the point where it enters receiver. Actual ft3/min values will differ. Do we use

Acfm or scfm for this formula. Kindly advise?

### #2 Art Montemayor

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Posted 06 December 2017 - 03:09 PM

Raman123:

As a future engineer you should never try to apply so-called “equations” to resolve your engineering problems.  Equations are useless - and potentially dangerous - as a potential tool towards a solution unless you absolutely know:

• where the equation came from;
• who derived the equation and how;
• the specific basis and conditions for its application; and
• the limitations to its application in the specific problem.

I cite the above guidelines based on over 50 years of engineering practice and I have cited these obvious and practical guidelines for many years - not only in our Forums, but in the field to those young engineers who worked under me.  It is folly to blindly employ any equation unless you take into consideration the above basic information.

The absolute best “equation” you can use is one that is the product of your own ingenuity, learnings, and common sense.  I will offer you the following example:

If you are taxed with finding out how much air is needed to fill an empty pressure vessel, then the best thing for you is to sit down and ponder the basic data of your problem and concentrate on how the solution can best be arrived at.  For example:

1. You know that the “empty” vessel is not really “empty”.  It initially contains a quantity of atmospheric air.  If it were truly empty, it would have to have a perfect vacuum.
2. Therefore, you should calculate or find the volume inside the vessel.
3. You also know that if you can apply the equation of state (EOS) for a gas - PV = ZnRT - then you can calculate the moles of air in the vessel when it is at the pressurized condition.  (you know all the information about the EOS for gas from your studies)
4. From the difference in volumes in the vessel from initial to full, you know the amount of compressor filling volume you require.
5. From the compressor’s capacity you know the filling rate of the vessel.  (I am assuming this is a reciprocating, positive displacement compressor - and not a centrifugal type)
6. Voila!  You should easily calculate the filling time.

• The compressor has a steady, constant filling capacity since it is a positive displacement machine.
• The compressor’s capacity does not change or vary while its discharge pressure slowly increases during the filling.
• The compressor has an aftercooler that cools the discharged air to atmospheric temperature (or the temperature you set for the filled vessel).

Learn what the terms “Standard” conditions, “Actual” conditions, or any other type of temperature/pressure conditions apply to the problem.  Always identify a gas condition by stating its temperature and pressure conditions.

I hope this helps you work out and correctly resolve this problem in a logical, common sensical manner.

### #3 breizh

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Posted 06 December 2017 - 05:45 PM

Hi ,

Good pointers in this pamphlet issued by Atlas Copco .

Breizh

### #4 raman123

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Posted 07 December 2017 - 06:47 PM

Hi Art and breizh

Thank you for your valuable responses.

My air receiver has to be filled with air from 0 psig /atmospheric pressure to 160 psig pressure

I am following this approach:

1.       I know the volume of air receiver in ft3

2.       For initial atmospheric pressure / 0 psig, I can workout the density (density = Pressure x Mol Wt / R x Temperature)

3.       From density and knowing volume of vessel, I can calculate mass initially in vessel

4.       Now under pressurized conditions, 160 psig, I can similarly calculate mass

5.       Now the delta or change in mass has to be supplied, I assume

6.       I assume I want to fill in 10 minutes, so change in mass/10 minutes is the mass rate I need

7.       Calculating density at standard conditions (P=14.7 psia, T= 60F / 460R), I can use mass rate and density to get Standard cubic ft per minute.

Does my approach sound logical. I will appreciate any comments and advice.

Thanks

### #5 fallah

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Posted 08 December 2017 - 12:31 AM

Raman123,

Supposing there is standard conditions at compressor suction within filling time; appears your approach is logical...

### #6 raman123

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Posted 08 December 2017 - 12:46 AM

Hi Fallah,

So, if the compressor inlet conditions are not std. conditions. I just use the flow i get from my solution

and can convert it to an actual flow using ideal gas equations i.e. P1 V1 / T1 = P2 V2 / T2?

### #7 fallah

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Posted 08 December 2017 - 12:53 AM

Raman123,

Yes, you can; and anyway the basis for your calculation should be the compressor suction flow conditions because the conditions at compressor discharge would be variable within filling rate  .

### #8 raman123

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Posted 08 December 2017 - 03:41 PM

Dear fallah

thank you