Blowdown Valve Sizing for time 2

[AndrewTravers]

Good Morning All,
I've been working on a customer request to determine the time it will take to vent a vessel we've supplied down to near atmospheric pressures using a blowdown valve. I've been sizing valves for about a decade, including blowdown valves, but have never seen any resources for this subject. I'm wanting to bounce the following methodology off you fine folks, and see if anyone has refinements.

Here's my method, step by step:
1) Work out the volume of gas to be vented. (In this case, it's about 2000 ft3)
2) Work out the density of the gas at the initial point, and from this the mass of the gas contained.
3) Calculate the gas flow rate over the blowdown valve at the initial conditions (this actually takes iteration, as the valve DP is a function of flow). I'm using mass flow units, as it simplifies things later.
4) Reduce the pressure by an increment (say 5-10% of the absolute pressure) and recalculate 2 and 3, repeating until down to the final pressure.
5) For each increment, work out the time it takes by taking the difference in volume contained, and dividing by the average mass flow rate between steps. Time=(mass1 - mass2)/(average mass flow).
6) Sum the times per increment to come up with the approximate total time.

The biggest concern is that I find that I get very long blowdown times, although my time per increment remains nearly constant until the pressure drop gets below the outlet pressure.

Any thoughts or references to printed methods would be greatly appreciated.

 

[btrueblood]

Sounds like the right approach, but you wrote:

"5) For each increment, work out the time it takes by taking the difference in volume contained, and dividing by the average mass flow rate between steps. Time=(mass1 - mass2)/(average mass flow)."

Substitute 'mass' where you wrote 'volume'. The equation is correct.

 

[AndrewTravers]

Thanks for spotting that btrueblood. It is supposed to be the difference in mass, not volume.

 

[Latexman]

Take a look at this:

http://www.air-dispersion.com/feature2.html

It's not exactly what you are looking for, but it's closely related. Plus, Mr. Beychok comes in ET from time to time.

Good luck,
Latexman

 

[btrueblood]

Hmm. " my time per increment remains nearly constant until the pressure drop gets below the outlet pressure" doesn't sound right. Flow rate should go roughly proprotional to sqrt(tank pressure), so the time per increment should increase in a smooth, nonlinear fashion as the blowdown progresses.

You might search the posts in the pipeline/piping engineering forum also, member zdas has posted an article about blowdown calculations recently, IIRC.

 

[AndrewTravers]

Thanks, I'll look for that.
The constant time increment appears to be tied into the dp/P1 ratio for the valve sizing, which is near constant in the same run. This is a result of the increase in pressure losses at higher flows I think.

 

[maddocks]

Keep in mind that the times become proportionally longer the lower the outlet pressure. We usually use 100 Psig as our blowdown lower threshold - in theory, it could take an infinite time to reach 0 pressure as the driving force is decreasing every second.

You basically have to integrate the valve equation over time from P0 to P1. Write a spreadsheet and you can create the increments as necessary.

 

[zdas04]

Guys, this is a choked flow problem until pressure is below about 160% of atmospheric pressure. As long as pressure is above critical, flow out the vent is at sonic velocity. Multiply that times the flow area of the valve and you have volume flow rate at actual conditions (which is a constant). Multiply that times the density at each pressure increment and you have mass flow rate. Flow that for a fixed time (I usually use about a minute, but longer doesn't really change the results much). Calculate the remaining mass using the real gas equation (you have to iterate because you need to know pressure to get compressibility). That gives you a new density to flow for the next time increment. Repeat until you are below choked flow.

There are a bunch of equations that will let you calculate the incompressible-flow portion, I attached the one I use. You'll see on page 3 that there is a disconnect between the volume flow rate at standard conditions (a surrogate for mass flow rate) between the two equations at 1.0 Mach. I generally say the incompressible flow equation starts being relevant around 0.6 Mach and the period between the two equations is called the "transonic region". Basically no generally-applicable equation works in this region. I drew it as a straight line, and I usually calculate it as a straight line, but that assumption introduces a pretty big error. I can calculate the time to critical pressure within a few seconds, but the time to zero psig is a lot tougher and I've never been within a few minutes (sometimes I'm off by tens of minutes).


David Simpson, PE
MuleShoe Engineering

http://www.muleshoe-eng.com

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.

"It is always a poor idea to ask your Bridge Club for medical advice or a collection of geek engineers for legal advice"

 

[btrueblood]

"in theory, it could take an infinite time to reach 0 pressure as the driving force is decreasing every second."

Err, no. That's an example of the old fallacy, that if you run a race, it takes a finite time to go 1/2 the distance, and a finite time to go 1/4 of the remaining distance, etc., and because you can keep summing the fractions to infinity, it will take infinite time to get there.

There is a closed-form, integral solution to the time problem when the delta-p drops the flow into the low subsonic range.

 

[DRWeig]

By the way, that was Zeno's second paradox -- always gotta go halfway first, so you'll never arrive.

Good on y'all,

Goober Dave

 

[AndrewTravers]

Thank you all for your help on this.
Your collective guidance has helped me greatly in working this through, as well as raising a few points I had not considered sufficiently.
The infinite low pressure blowdown time is, of course, erroneous, but at the same time, on the system I have in front of me, it's going to seem like it takes forever. I'm going to let them worry about it below 10 psig, and let them deal with Zeno.

Thanks again
Andrew Travers

 

[btrueblood]

Thanks DRWeig, it was bugging me that I couldn't remember the name.

 

[JLSeagull]

Some blowdown valves for safety shutdown use fixed chokes. These often apply to streams in Class 600 or above. Many blowdown valves are NPS 2; some at NPS 3 with the choke downstream of the blowdown valve. Different calculations apply to the required fixed chokes in lieu of adjustable chokes. Choke calculation sets may be available on the web or obtained from vendors. The choke orifice selections are sold in 64th inch sizes with many compatable components among peddlers throughout the globe.

 

[AndrewTravers]

JL
I've never run into those. Usually in my small part of the industry, they are using a snap acting plug style control valve (such as a Fisher D2 or D3, or a Norriseal 2275, or a host of other small valves) that is more commonly installed on a liquid dump line. In this case, though, there is so much back pressure that I had to actually enter in the ISA Valve sizing formula into the spreadsheet and iterate with piping losses.

Zdas / btrueblood
As an interesting footnote to Zeno's Blowdown valve, the customer has pointed out that, per API 520, we only need to do the calculation down to 100 psig. On this little problem, since the vessel only operates at 130 psig, it simplifies things greatly.

Thanks

 

[maddocks]

True enough - in fact, I'd even wonder if a vessel at 130 Psig requires an automated blowdown system. We don't usually blowdown fuel and propane refrigerant systems that operate at higher pressures - perhaps this one can be exempted as well.

I still have to think that blowing down to atmospheric pressure will take (theoretically)an infinite time according to the valve equation. As P1 reduces, the flow reduces, the upstream volume has reduced, the pressure drops again, and so on and so on.... In reality this is not the case, but in theory....?

 

[AndrewTravers]

Maddocks
Linear algebra and infinite series were never my strong suit in school, but I seem to recall that is what the math club used to put Zeno in his place. I suspect it would take longer to work out the math than it would to vent the vessel though, especially with all the minor effects in play that get disregarded under normal circumstances. There's going to be flashing at low pressure, for example, as well as aerodynamic effects from other flow in the vent line that go past the opening in the pipe.

The automated blowdown is mostly to have the plant fail-safe, and the decision to put one in is several levels above me.

Thanks