Relieving Rate from Infinite Compressible Flow Reservoir? 3

[KernOily]

Hi guys. Once again life is a cruel teacher; it makes us take the exam before we've had a chance to study. Such is life in the oil patch these days. I should know how to do this but I'm stumped.

I need to size a PSV. Therefore I need to specify the required relief rate. The problem is the source is essentially an infinite compressible flow reservoir.

The scenario is blocked discharge for the tubeside of a S/T HX. The system consists of the following: a very large 70% quality 800 psig steam header of essentially infinite capacity and a steam lateral coming off the header feeding the HX. In the lateral, in series, are an ESD valve, a restriction orifice, a letdown valve, a second ESD valve, and finally a temperature control valve. This PSV is located just downstream of the TV.

The PSV relieves to atmosphere therefore the dP across the PSV is 800 psid. The scenario is blocked discharge with all the upstream control valves stuck in the wide open position. OK that means my Cv's are all known.

Q is a function of dP and Cv. I have two unknowns so I'm stuck. Do I assume choked flow at each of the control valves using the critical pressure ratio of 0.545 for steam, and therefore that fixes the dP across each device in the lateral?

Thanks guys!! Pete

 

[zdas04]

The infinite reservoir assumption just says that pressure will not decrease with flow. Source pressure will be 800 psig at the start. An infinite time later (probably taken to be an hour) it will still be at 800 psig, (i.e., you can't expect any help from drawdown). If your set pressure is 800 psig then regardless of the capacity, as soon as it opens the upstream pressure will be something less than 800 psig (due to friction and valve losses in the control valves) and the PSV will go shut. This scenario can't do anything but chatter, regardless of the orifice size.

Now if the PSV set point was less than source pressure it gets a lot more difficult to calculate. For that I would start with the setpoint of the PSV and assume that it has an infinite flow rate (i.e., no build up in the upstream piping above the setpoint). Assuming that the difference between the PSV setpoint and the source cannot give me critical flow in any of the intermediate restrictions I'd set up a series of equations where P(down) of the first restriction equals P(up) of the second restriction, etc. (basically disregarding friction in the pipe at this time). That gives you a maximum mass flow rate. You can either use that (conservative) or use that mass flow rate to calculate friction in the pipe to determine if it is material (it will be if the PSV setting is well below the source pressure). Use either the mass flow rate from the valves or the mass flow rate represented by both friction and valve losses to pick a PSV size and orifice.

David Simpson, PE
MuleShoe Engineering

"Belief" is the acceptance of an hypotheses in the absence of data.
"Prejudice" is having an opinion not supported by the preponderance of the data.
"Knowledge" is only found through the accumulation and analysis of data.
The plural of anecdote is not "data"

 

[LittleInch]

Zdas04 is totally correct here and when I read it first I thought there was something not right, but couldn't put my finger on it.

You have an 800psig supply, but a relief valve set at 800 psig downstream of three restriction devices, just doesn't make sense. If you said 400 psig then you have something to work with. Given that most spring reliefs are no more accurate than 10% on set pressure it might not go off.

Before I go much further, can you sort this issue out for us please.

My motto: Learn something new every day

Also: There's usually a good reason why everyone does it that way

 

[zdas04]

I thought about it some more and the solution to the problem as stated is--set a TINY PSV at 840 psig. Since you have a source that cannot be over 800 psig and you have to size safety devices to stay below 110% of MAWP, just set the PSV less than 110% (but greater than 100%) and get on with your life.

David Simpson, PE
MuleShoe Engineering

Law is the common force organized to act as an obstacle of injustice Frédéric Bastiat

 

[KernOily]

Ugh. I left out one very important detail. This is what happens when I try to multi-task, run projects, and supervise green engineers, all at the same time...

The required PSV set pressure is 200 psig. Thanks guys! Pete

 

[Latexman]

What's the MAWP of the protected piping/equipment? Doesn't that set your dP? dP = 800 - MAWP.

Good luck,
Latexman

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

 

[KernOily]

MAWP of protected equipment is 200 psig and it relieves to atmosphere. Steam header pressure is 800 psig. So the total dP across the entire system (header to atmosphere) is 800 psid which includes the orifice inside the PSV.

 

[zdas04]

No, the steam header dP that matters to the PSV is 600 psig. You could easily have choked flow in one or more of the various control valves. I'd solve it for incompressible flow first and see if any of the chokes are approaching choking. This is not a trivial problem.

David Simpson, PE
MuleShoe Engineering

Law is the common force organized to act as an obstacle of injustice Frédéric Bastiat

 

[LittleInch]

Ok, that makes a bit more sense. With three main regualtiing / throttling items in series (, it would be easier to do this in an analysis program, but otherwise I would first check choked flow by looking at each of the main items and working out which of them has the lowest mass flow at choked conditions. The end one you have your relief presusre, the firat one you have th eupstream presusre, the middle one you might need to guess a bit.... Then find the pressure drop through the other two at that mass flow and then see if the total pressure drop is less than 600 psig. If it is you have choked flow and can use then iterate a bit to increase DP accross your choked flow to get the max mass flow until the sum of the pressures equals 600.

If its more than 600 then you won't have choked flow and then iterate backwards to find the same mass flow which has the sum of the pressure drops equaling 600, based of course on which item follows which so you use the right pressure and density. ZDAS04 sets it out better than me.

Difficult to do manually so I think you need an analysis program.

My motto: Learn something new every day

Also: There's usually a good reason why everyone does it that way

 

[Latexman]

Find the steam flow for 800 psig in header to 220 psig (10% OP) just upstream of the PSV. With the right software, it'll be easy. Without the right software, it's at least a 2 martini problem.

Good luck,
Latexman

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

 

[zdas04]

I want to find that "right program". 3 chokes in series is a tough problem for any software to get right. I've never had my hands on a program that I would have any confidence would get it right enough. Even the big guns (like Hysys, or OLGA) start getting a bit squirrelly as you move into transsonic flow. It is kind of like the Transition region on the Moody Diagram where the Colebrook Equation goes crackerdog, but worse (weaving between compressible and incompressible flow and back results in some major energy transients). If I was guessing, I'd expect this flow to be transonic from the entrance to the second choke to the entrance of the PSV. You might be able to program it in a really flexible CFD engine, but I wouldn't want to try to do it in a plant or piping simulator.

David Simpson, PE
MuleShoe Engineering

Law is the common force organized to act as an obstacle of injustice Frédéric Bastiat

 

[LittleInch]

Then perhaps the thing to do is find the lowest choked flow from any of the three main restrictions and use that?

My motto: Learn something new every day

Also: There's usually a good reason why everyone does it that way

 

[KernOily]

Guys thanks for the great help - it is much appreciated. I am using Pipephase. As David said, it goes ga-ga at choked flow conditions. So I will go ahead and, as you all suggested, manually set the pressure drop across each device at the critical flow ratio for steam (0.545) and start with that and run the iterations. Pipephase will be used to account for the property changes along the pipe lengths between the control valves and at the exit of the control valves.

 

[Latexman]

The problem is you won't know the lowest of the three chokes in series until all are calculated together. You could pick the most restrictive using some criteria and just use that. That would be very conservative and easier.

I've used SiNet (EPCON) for more complex than average flow problems. But like zdas04 my past experiences with it lead me to believe that on a compressible flow case with three successive chokes, first, I'd be surprised if it converged, and second, I'd be very skeptical if it did!

My company has an in-house program that would make short work of it. It assumes ideal gas behavior, but the flow equations are rigorous for high speed gases, and I've never seen it go crazy on choked flow conditions or multiple chokes. You have to know what you are doing so the right "fudge factors" (flow coefficients) are used when needed, but I believe it would do it. This doesn't really help sshep, but the right program's do exist, they just may not be in the public/mainstream domain.

Good luck,
Latexman

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