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This is a more practical problem than theoretical, so hopefully that's acceptable on this site.

I'm trying to fill a small tank with a gas from a larger tank at much higher pressure. The two tanks are connected by a solenoid valve, and the small tank has a pressure sensor with excellent response time. The pressure sensor is monitoring while filling the small tank for several seconds, and at a specified pressure the solenoid valve is closed.

What happens next is what I'd like to understand. The pressure in the small tank actually goes down about 3% after the valve is closed. The time constant of the pressure decay is around 7 seconds. Conversely, when gas is released from the small tank to an evacuated large tank, the pressure goes up after the solenoid valve is closed.

I'm sure this phenomenon is well known and studied, but I haven't been able to find an explanation. Is it simply a heating/cooling phenomenon as the gas is added/removed, then a return to ambient over the next several seconds? Is there any way to predict the pressure drop/increase after closing/opening the valve during filling/emptying? Or, is this comment the answer?

Here are some additional details if relevant:

  • small cylinder description: 1 l, stainless steel, pressure sensor mounted on opposite side of tank from input

  • large cylinder description: 49 l, steel, 30 psi

  • target pressure: 14 psi

  • gas: Argon

  • ambient conditions: room temperature

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  • $\begingroup$ Sorry I don't have an answer - but maybe if you address these questions, someone else will be able to help you: What is a "lecture tank"? What is the pressure in the source (larger) tank? Where/how is the pressure sensor mounted? In principle, Joule expansion should not result in the gas heating... the kinetic energy of the individual atoms going through the solenoid doesn't increase. And guessing non-ideal behavior is hard without a great deal of detail. $\endgroup$ – Floris Jul 25 '17 at 1:03
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    $\begingroup$ @Floris - Thanks for taking the time to reply. I added some details as you suggested. $\endgroup$ – Mark Uebel Jul 25 '17 at 14:14
  • $\begingroup$ Is there any way for you to control the rate of flow? A "solenoid valve" suggests a binary on/off state... perhaps there is some secondary regulator between the tanks that could be adjusted? Did you try to measure the temperature of the (wall of the) smaller tank? Do things change (in particular, the time constant) if you wrap the small tank in an insulating blanket? (that would be an easy experiment to do) $\endgroup$ – Floris Jul 25 '17 at 14:17
  • $\begingroup$ Where are the pressure sensors located? Do they have good response times? What type of pressure sensors are they? $\endgroup$ – JMac Jul 25 '17 at 14:39
  • $\begingroup$ @JMac "a pressure sensor with excellent response time." and "pressure sensor mounted on opposite side of tank from input" $\endgroup$ – Floris Jul 25 '17 at 14:41
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When gas is flowing into the small tank, the gas inside is being compressed. The pressure and temperature are going up. After the valve is closed the gas gives up heat to the walls of the tank and the pressure goes down. When gas is leaving the small tank, the gas inside is expanding. The pressure and temperature drop. After the valve is closed, the gas takes heat from the walls and the pressure rises.

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After further digging into this phenomenon, I believe the answer is demonstrated in this paper, which is also noted in this post. My simplified understanding is that there is work done on the gas in moving it from one tank to the other, and this work results in a temperature increase of the gas. In my case, the small steel cylinder has a thermal mass far exceeding that of the gas, so the energy is dissipated into the cylinder over several seconds. Presumably, I could predict the time to equilibrium with some basic heat transfer equations.

Thanks to everyone that chimed in.

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