Volumetric flow rate of nitrogen through relieving pressure regulator

[Gnardude]

TL;DR

Volumetric flow rate of nitrogen through relieving pressure regulator

Hello all,

I'm having trouble figuring out the volumetric flow rate upstream of a relieving pressure regulator used on a 1/4" OD nitrogen line. Upstream of the regulator P=100 PSIG and T=70F, while downstream P=80 PSIG and T=70F with downstream consumption at q=4 L/min or 0.91 SCFM (at std. T=70F, P=14.7 psia). My thoughts are to use boyles law, P1V1=P2V2 (ideal gas law), to calculate the upstream flow rate, which would equal 3.2 LPM not taking into account the flow leaving through the vent, however, I'm not too sure if the pressure regulator would impact the flow in anyway. Does anyone have an idea of how to calculate the upstream flow or if my method is correct? I currently don't have the spec sheet for the regulator, so I'm negating the flow through the vent until I have it tomorrow.

 

[BvU]

Hello @Gnardude, !

I'm not too sure if the pressure regulator would impact the flow in anyway

That's often what it is used for !

If the vent flow can be neglected you can write a material balance and for isothermal expansion use Boyle.

Usually, though, a pressure regulator is treated as isenthalpic and the gas as non-ideal. Since the flow is small, I expect the correction is reasonably small too (do you agree @Chestermiller ?).

(PS what a horrible mixture of units !)

 

[Chestermiller]

Hello @Gnardude, !

That's often what it is used for !

If the vent flow can be neglected you can write a material balance and for isothermal expansion use Boyle.

Usually, though, a pressure regulator is treated as isenthalpic and the gas as non-ideal. Since the flow is small, I expect the correction is reasonably small too (do you agree @Chestermiller ?).

(PS what a horrible mixture of units !)

You know the mass flow rate from the problem statement 0.91 SCFM. You also know the upstream pressure and temperature, so, including the non-ideality using the z-factor, you can get the upstream density. The volume flow rate upstream is equal to the mass flow rate divided by the upstream density.

 

[russ_watters]

...a relieving pressure regulator...

vent...pressure regulator,,,

I currently don't have the spec sheet for the regulator...

What's a "relieving pressure regulator"? A safety relief valve? If so, it should have a nameplate with its relief pressure and flow rate. Yes, I think we need to know the specs of that device/what exactly it is/is doing.