Calculating pressure release time

[Tyler Bennett]

Hey people,

I have a pressure vessel pressurized to say 20MPa at 33C, of which I'm working with a gas (scCO2 to be exact) which will then be released into the atmosphere (standard pressure and temperature) through a release valve; I'm wondering how long it will take for the pressure to reach equilibrium? I'm assuming it'll be some sort of exponential decrease and hoping to model it to figure out how long it takes to reach 70/80/90% of pressure drop.

I'm working on getting the Cv for the release valve. My main issue is wondering how the conditions change because I'm using a gas instead of a liquid? For example, the valve says it can reach a maximum flow rate of 24ml/min. This makes sense when working with a liquid at standard pressure, but how does that change if I'm working with a gas? More precisely how does that change if the pressure differential between vessel and atmosphere is 2x, 5x, 10x, 20x?

 

[JBA]

While it does not address all elements of your problem, see the below for the basic equations for calculating gas flow relative to Cv.

 

[BvU]

Pleasant units indeed, my dear JBA !

The thing to do is make a complete pressure driven model: enthalpy balance, mass balance, physical properties, the lot. Not trivial at all.

What provides the heat to do the expansion work ? Or is this adiabatic and you let it freeze up ?

 

[JBA]

Cv is a coefficient used by manufacturers of commodity valves for basic industrial applications and not appropriate for precise gas flow applications; nor, is the sizing of such valves. Unfortunately, I have been unable to identify any available more precise conversion than that I offered for the use of Cv values. At the same time, it is rare for more precise measurements to be needed for the general industrial applications of these valves.

For precise applications flow orifices with certified flow coefficients, specific gas properties and classic gas law equations should be used. In reality, essentially all applications related to gas storage transfers are polytropic and must be treated as such to be fully accurate; which, as stated, is no trivial process.

 

[JBA]

@Tyler Bennett, to get a sense of the issues facing your calculation Google "BLOWDOWN) ]Haque et al. 1992b]" for a pdf copy of this paper and take a look at Imperial College I7 Case - N2-Co2 mixture blowdown test case on pgs 6-7