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# Temperature Drop of Compressed Air Tank

## Temperature Drop of Compressed Air Tank

(OP)
Hello all,

I'm busy calculating the time taken to fill a tank to a certain pressure. With the data from the compressor supplier, I've been successful in determining the time taken in IDEAL conditions.

What I'm a little stumped on is the temperature of the tank while the compressor fills it to its desired pressure. In reality, the compressor being used right now leaves the 1 gallon tank in question somewhere near 140-160 Fahrenheit after compressing the tank to 300 psi.

My theoretical calculations leaves the tank at 205 Fahrenheit.

How can I make a reasonable model to mimic the realistic case?

I have a numerical iteration for the theoretical calculation, it would be ideal if I can incorporate a temperature drop within it. What's my best method to approach this?

Thanks!

### RE: Temperature Drop of Compressed Air Tank

Your "theoretical" calculations are somewhat at odds with thermodynamics. If I'm filling a space with 160F air (let's say through a flow restriction so I have nearly full discharge pressure upstream of the restriction and tank pressure downstream, you don't need this restriction, but it makes the explanation easier to follow). When the tank is empty I'll get some amount of J-T cooling. Late in the fill the incoming gas will not get any J-T effect, but the incoming gas will be compressing the gas already within the tank. You want to apply the adiabatic heat of compression calcs to this, but they are not valid. That equation only works when there is trivial heat lost to the "environment". But the environment includes the gas doing the compression which absorbs considerable heat. In short, there is no mechanism to heat the gas in the tank from your supply temp of 140-160F up to 205F.

I've filled a lot of vessels with gas in my career. Many times I've seen frost form on the vessel wall at the start of the fill. The frost stops growing when the tank pressure reaches some number around the critical pressure for choked flow (somewhere around half the supply pressure in absolute units for air). Somewhere around half way between the critical pressure and the supply pressure the frost will all be gone, but the temperature of the tank will still be well below the supply temperature. For the last (about) 10% of the fill the temperature of the tank will rise closer to the supply temperature, but cannot exceed supply temp.

David Simpson, PE
MuleShoe Engineering

Law is the common force organized to act as an obstacle of injustice Frédéric Bastiat

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