PRV Discharge Piping dP Question 1

[RVAmeche]

Hi,

I'm a pretty new mechanical engineer a couple years of college. Recently I've started getting involved in PRV sizing and piping calculations at work. I've been trying to educate myself on the requirements from ASME, API, etc.

API 520 states that the Critical Pressure is the lowest pressure possible at the nozzle exit of the relief valve and provides an equation to calculate this (below).
For an example, air k = 1.4, Set Pressure = 180 psig, Fire Scenario Relieving Pressure = 232.5 psia
P(cf) = P(1)*(2/(k+1))^(k/(k-1))
For k = 1.4, P(1) = 232.5 psia, P(cf) comes out to 122.8 psia.

For a given discharge pipe, the maximum allowable dP (lets refer to this dP as P(cf) - P(2) ) is either 10% Set Pressure or 21% Set Pressure depending on the determining the case. If P(cf), which essentially defines the starting pressure of the discharge piping, is 122.8 psia and P(2)is 14.7 psia for atmospheric discharges. How can the discharge piping dP ever fall within the allowable range?

 

[tickle]

The actual (or calculated) pressure drop is different to the available pressure drop. You have stated the available pressure drop (123 - 15 psia). I would back calculate the pressure drop in the tail pipe, based on the required capacity and atmospheric pressure at the tip, to ensure that the DP is not greater than 18 psi (10% of 180 psig). The critical pressure is used to calculate the driving differential in the PSV. The gas downstream of the PSV nozzle will quickly expand to something about atmospheric.

 

[e43u8]

RVAmeche,

In a choked flow through a PSV the critical flow pressure will exist at the exit plane of the valve flow nozzle while the back pressure is the pressure at the valve outlet flange. If the PSV outlet flange size will be low enough, most critical flow pressure can be transferred to the valve outlet flange as the point of back pressure indication. Then even with a short discharge line the back pressure might be much higher than 10% of the PSV set pressure and to overcome this excessive back pressure you may have to select a larger valve outlet size or balanced bellows valve type...

Then the critical pressure in a choked flow conditions wouldn't be a starting pressure to calculate the dP along the relevant PSV tailpipe. You can back calculate using Fanno lines/curves, describing the irreversible adiabatic flow of a gas at constant mass flow, to get the actual back pressure at the PSV outlet flange...

 

[Latexman]

Once sonic flow exists at the exit plane of the PSV flow nozzle, it is possible to have a pressure discontinuity/shock wave at the exit plane of the PSV flow nozzle. Therefore, when sonic flow exists at the exit plane of the PSV flow nozzle, in my experience P(cf) usually does NOT define the starting pressure of the discharge piping. Backpressure is always referenced at the PSV outlet flange. When sonic flow exists at the exit plane of the PSV flow nozzle, backpressure at the PSV outlet flange is usually calculated backwards from the final exit to atmosphere back to the PSV outlet flange.

So, "How can the discharge piping dP ever fall within the allowable range?" Because of the pressure discontinuity at the exit plane of the PSV flow nozzle.

Good luck,
Latexman

Technically, the glass is always full - 1/2 air and 1/2 water.

 

[RVAmeche]

Thanks all.

If I'm understanding this correctly, due to the shock wave/discontinuity inherent in critical flow, the pressure at the PSV nozzle exit would be P(cf). However, due to the pressure discontinuity, the pressure at the valve's exit flange will be substantially less, which is found by working backwards to find the back pressure built-up?

In other terms, when API 520 states that the "nozzle exit" cannot be below P(cf), this does not mean the exit flange pressure is also P(cf)? Does anyone know of a drawing/diagram depicting these pressures inside the valve so I can better picture it? The picture attached is my rough interpretation.

 

[Latexman]

You've got it! The only thing I will clarify is the exit flange pressure can be << P(cf). In my experience, it usually is << P(cf), but it doesn't have to be. It all depends on the backpressure.

Good luck,
Latexman

Technically, the glass is always full - 1/2 air and 1/2 water.

 

[RVAmeche]

Awesome! Thanks a lot for your help.

 

[Latexman]

RVAmeche,

Since you are a newbie, there is a button for that.

Good luck,
Latexman

Technically, the glass is always full - 1/2 air and 1/2 water.