Choked flow through a PRV with an vertical stack

[hanafyaa]

Hello, I have read several eng-tips forums over the past year and they are very helpful, recently I have read choked flow related questions and answers.
I have been trying to determine the effect of stacks on a large propane tank pressure relief valve(s) (2 inch relief valves and stacks: API equivalent relief valve size is smaller than 2 inches).
I am curious as to what happens with a spring PRV that is combined with a stack.

Without the stack, I know there will be choked flow. During a relief situation psia is >265 and is relieved to atmosphere.
With the stack I believe there will still be choked flow, but I am unsure exactly where this is happening and what effect the stack may have. The main goal is to determine if the stack reduces flow rate by any significant amount. Let's define significant as about 1%.

My guess is that with the stack there will be choked flow across the PRV and what happens in the stack has no effect. However, the problem I have is when I try to think of velocities and pressures throughout the flow:

as I understand it, the pressure from the tank can only drop by about 50% maximum through a choked flow. If that is the case, then the pressure in the stack is still well above atmospheric. If this is the case the pressure in the stack would be about 130 psia and could not decrease by much without increasing the velocity of fluid (which I believe is not allowed to be greater than Mach 1). This would mean that at the exit of the stack, the pressure drop would again be great enough as to induce choked flow again.

Overall, I think that the PRV is the limiting factor and that putting the stack on has little if anything. However, I cannot seem to explain why.
If anybody can explain to me what exactly would be happening and explain the pressure at the different points in the system I would greatly appreciate it.

Thanks

 

[Latexman]

Of course, the outlet piping (i.e. "the stack") must meet the pressure drop constraints that apply to the type of PRV (conventional, bellows, pilot operated) being used.

I suspect there would be two choke points. At the end of the PRV nozzle, and at the end of the stack.

Good luck,
Latexman

 

[don1980]

Hanafyaa - There's an error in your logic. The downstream pressure isn't necessarily 50% of the upstream pressure. The downstream pressure is entirely a function of the resistance in that downstream piping. In your particular case, the backpressure on the PRV will be some value between 0-265 psia. Almost all gas/vapor PRVs have choked flow at the valve orifice, and in some cases it will choke again at the tailpipe outlet. Whether or not it chokes at the outlet depends on the properties of the gas, the flowrate, and the tailpipe size.

The bottom line is that you have to calculate the pressure drop in the outlet line. One can't estimate the outlet line loss based on the PRV upstream pressure.

 

[hanafyaa]

Thanks Latexman and don1980,
but I think I need someone to hold my hand through this.

My guess was that the backpressure from the stack was not going to be enough to prevent choked flow from the PRV. I believe what you are both saying is that if this is the case, then whatever comes after the PRV has zero effect on the flow rate?

However, the other situation is that the stack creates enough backpressure such that my PRV is not choked flow? If so, then I can calculate my flow rate from my choked flow through the stack exit?

For case 1 I need to make sure that my backpressure is sufficiently low through a regular compressible fluid calculation in the stack? This backpressure is dependent on the stack exit which is possibly choked. I do not know if it is choked however unless I know the pressure feeding the stack.

For case 2 I need to calculate the pressure drop from the PRV so that I can calculate the inlet pressure to my stack choked flow? But my PRV pressure drop depends on my backpressure, up to a maximum pressure drop beyond which the backpressure doesn't matter.

I guess my question is how do I start - do I just start assuming certain situations and see which ones work?
Thanks

 

[rutherford703]

The starting point is from the exit of the stack - following API521 and backward calculation to your PSV.

 

[hanafyaa]

Thanks to everyone, I think I'm getting an answer!