Calculating Cooling Effect in Gas Cylinder Expansion

[OG63]

I'm building a gas supply system that will dump half the contents of a compressed gas cylinder of nitrogen in 10 minutes. I need to ensure the output delivery pressure doesn't fall below a certain limit because of cooling during the gas expansion. If the cooling effect is excessive, I will need to heat the cylinder to compensate for it and prevent excessive pressure drop. But if the cooling effect is relatively small, the thermal mass of the steel cylinder might be sufficient to prevent excessive cooling of the contents in the 10-minute time frame that matters. (I'm hoping for the latter, of course.)

Cylinder volume: 49.3 L
Initial cylinder pressure: 1250 psi
Final cylinder pressure: 625 psi
Initial cylinder temperature: 20 C
Final cylinder temperature: ?
Cylinder weight: 42 kg
Cylinder material: steel

I've included the cylinder weight and material for anybody who wants to look at the entire system. However, since this is a risk mitigation exercise, I'm willing to make any sort of simplifying assumptions that lead to a "worst-case scenario" answer for the gas alone (i.e., the maximum possible cooling).

For what its worth, I tried using an online thermodynamic calculator but got hung up when I couldn't decide what type of process this was. In one sense, it seems like an isochoric process (constant volume) because the cylinder volume doesn't change. But that didn't seem right because the volume of the initial gas charge certainly changed when half of it expanded into the open atmosphere. I also considered solving this as an isothermal process problem, with the idea that I might be able to calculate the amount of energy required to keep the temperature constant. But here again, I'm tripped up by the question of whether I should consider the system to be the initial amount of gas in the cylinder or just the half that's left in the bottle after dumping.

I should have paid more attention in Physics class, and so now must humbly request assistance from those who did.

 

[Philip Koeck]

I'm building a gas supply system that will dump half the contents of a compressed gas cylinder of nitrogen in 10 minutes. I need to ensure the output delivery pressure doesn't fall below a certain limit because of cooling during the gas expansion. If the cooling effect is excessive, I will need to heat the cylinder to compensate for it and prevent excessive pressure drop. But if the cooling effect is relatively small, the thermal mass of the steel cylinder might be sufficient to prevent excessive cooling of the contents in the 10-minute time frame that matters. (I'm hoping for the latter, of course.)

Cylinder volume: 49.3 L
Initial cylinder pressure: 1250 psi
Final cylinder pressure: 625 psi
Initial cylinder temperature: 20 C
Final cylinder temperature: ?
Cylinder weight: 42 kg
Cylinder material: steel

I've included the cylinder weight and material for anybody who wants to look at the entire system. However, since this is a risk mitigation exercise, I'm willing to make any sort of simplifying assumptions that lead to a "worst-case scenario" answer for the gas alone (i.e., the maximum possible cooling).

For what its worth, I tried using an online thermodynamic calculator but got hung up when I couldn't decide what type of process this was. In one sense, it seems like an isochoric process (constant volume) because the cylinder volume doesn't change. But that didn't seem right because the volume of the initial gas charge certainly changed when half of it expanded into the open atmosphere. I also considered solving this as an isothermal process problem, with the idea that I might be able to calculate the amount of energy required to keep the temperature constant. But here again, I'm tripped up by the question of whether I should consider the system to be the initial amount of gas in the cylinder or just the half that's left in the bottle after dumping.

I should have paid more attention in Physics class, and so now must humbly request assistance from those who did.

You should look at an adiabatic expansion as the gas leaves through the valve.
You have a sudden pressure drop there from whatever the pressure is inside the cylinder to the outside pressure.
This will cool mainly the valve since it's in direct contact with the cold expanded gas.
The cylinder should cool mainly due to conduction from the warmer cylinder to the now colder valve.
So it's important what's between the opening of the valve and the cylinder, steel or a rubber tube?

One question is also whether and how quickly the expanded gas is transported away from the cylinder.

Inside the cylinder the pressure drops because the amount of gas decreases so this is not directly connected to a temperature change.
I'm clearly idealizing here, but in principle I think that's the way to analyze the problem.
Technical details are note my strength, I'm afraid.

 

[OG63]

Thanks for sharing your insights, Philip!

In my current project, adiabatic expansion will primarily occur inside a pressure regulator attached to the cylinder valve. In past projects involving similar gas releases, I've seen regulators frost up. However, thermal conduction from the cylinder to the frosted regulator has not appeared to be significant within the short time frame of the gas release.

I understand that the main factor affecting cylinder pressure after the release will be the amount of gas left in the cylinder. Boyle's Law tells me that if I release half the gas from a fixed volume, I should be left with half the pressure. But Boyle's Law is for isothermal processes, and I'm worried that my releases aren't isothermal. Specifically, I'm concerned tat the release of the gas from the cylinder will remove energy from the gas remaining in the cylinder, which will cool the remaining gas and leave me with less pressure than Boyle's Law might suggest.

I'm just not sure how to calculate the amount of energy removed from the remaining gas, or even how to bound the problem with some simplifying assumptions so I can be reasonably assured that the cooling effect isn't going to decrease my gas delivery pressure by too much toward the end of the release.

 

[Philip Koeck]

Thanks for sharing your insights, Philip!

In my current project, adiabatic expansion will primarily occur inside a pressure regulator attached to the cylinder valve. In past projects involving similar gas releases, I've seen regulators frost up. However, thermal conduction from the cylinder to the frosted regulator has not appeared to be significant within the short time frame of the gas release.

I understand that the main factor affecting cylinder pressure after the release will be the amount of gas left in the cylinder. Boyle's Law tells me that if I release half the gas from a fixed volume, I should be left with half the pressure. But Boyle's Law is for isothermal processes, and I'm worried that my releases aren't isothermal. Specifically, I'm concerned tat the release of the gas from the cylinder will remove energy from the gas remaining in the cylinder, which will cool the remaining gas and leave me with less pressure than Boyle's Law might suggest.

I'm just not sure how to calculate the amount of energy removed from the remaining gas, or even how to bound the problem with some simplifying assumptions so I can be reasonably assured that the cooling effect isn't going to decrease my gas delivery pressure by too much toward the end of the release.

Details are always tricky, I'm afraid.

Probably you can safely assume that the gas in the flask has roughly constant T.
Even if it cools by for example 20 degrees the temperature in Kelvin is not very different, 270 instead of 290 for example, so the pressure won't change very much (according to the ideal gas law, which is a bit dodgy in this case).