When calculating the actual resistance factor (f x L/D_h) in a setup that has fittings (valves, elbows), should I calculate the L used in this expression as the sum of the straight lengths and the equivalent lengths of the fittings? Or do I have to determine the impact of the fittings a different way?
For context, I have a nitrogen regulator that in a fail open mode will dump a lot of nitrogen into a 2" Cu tube, type L line. I’m trying to determine the required flow rate for a PSV to discharge.
f = Moody friction factor
L = system length (including fittings?)
D_h = Hydraulic diameter
The N2 regulator will probably be the biggest restriction, by far. First pass, calculate the maximum flow through just the N2 regulator (i.e. ignore pipe and fittings). N2 source pressure in regulator inlet and PSV sizing pressure in regulator outlet.
If you get a reasonable size PSV, or you don’t get an unreasonable size PSV, I’d call it a day and go with that!
The simple equivalent length or K factor method (Crane) does not handle choked flow thru multiple diameters very well. You’d need compressible flow software. Maybe, @katmar ‘s software could handle this situation rigorously.
I agree with Latexman’s approach. If you just want to determine the PSV size you can make some simplifying assumptions. To get an accurate answer you would probably need a lot of iteration, calculating each component individually until the solution converged.
Apart from the overall flow determination, also check that if the regulator fails wide open the copper header will not be overpressurised at the upstream end. The PSV must be sized to keep the pressure here safe - not only at the inlet to the PSV. This will not be important if the PSV can be mounted directly after the regulator - which would probably be a good idea anyway and would simplify the flow calculation.
Since this isn’t the simple question I thought it would be, I will expand on my situation.
Downstream of my ambient air vaporizer is the regulator station (regulator failure Cv of 60) that the gas vendor will supply for a building distribution header. The vendor states the high pressure in the failure case is 250 psig because that is what relief valves upstream within their scope would limit the system to (and that would be 2 unrelated failures to get to this point). 250 psig is within the tube spec pressure limits. The relief valve is to generally protect the header from being much higher pressure than what is used inside the building between various user groups (labs, small scale pilot labs, etc.) The PSV setpoint is 120 psig. The desired installation is to have a selector valve for this line so the PSVs can be switched between with minial disruption to the building.
I calculated a failure mode flow demand of 41,670 lbm/hr at 32°F (9546 scfm, 68°F, 14.7 psia). When I use that demand to size a PSV via the API preliminary equations, I get a 3.52 sq.in. orifice requirement which is either a 3" or 4" valve depending on which vendor catalog I look at. This leads to the question of can I have an expansion before a selector valve that has the required PSVs, assuming that an expansion before a PSV is still not good practice even with something in between them.
If I use the average density (1.05 lbm/cu.ft.) between 250 psig and 120 psig, I get Ma = 0.46. If I use the density at 120 psig (0.87 lbm/cu.ft.), Ma = 0.68. This is why I was thinking I needed to do Fanno flow type calculations due to the large density variation I could expect in a relatively short length.
I think, given where all this will be installed, there could be around 10 ft of straight pipe with additional components (I’m at an equivalent length of 72ft all things considered) between the regulator and the PSV even if I say “minimize length”. The whole run from the regulator to the PSV setup would be 2", before reducing to connect to a 1.5" header.
My other option is to see if the gas vendor will supply the relief design, but my previous experieince is that they state that is the owner’s scope since protection of downstream elements is beyond their scope.
Hi, @jari001. The flow I got was 24% less. Take a look. Maybe, I got something wrong. Do you have x(t) of the regulator?
I see now why you may want to include the pipe and fittings. A 3-4" PSV on a 1.5-2" pipe and fittings appears nonsensical, and may get rude comments from the pipe fitters and operators.
Apologies, I typed “51670” instead of “41670”, so our calcualted flows match. I have reached out to the regualtor vendor for the x_t value. I’ve typically assumed 1 for a conservative estimate but here may be where that breaks down.
I quickly looked up a Consolidated 1905, M orifice, 4" x 6", 9637 scfm capacity.
This is unreasonable for a 1.5" - 2" line. You should sharpen the pencil and rigorously analyze it, hopefully with some good compressible flow software!
P.S. - You may find it hard to get the inlet dP under 3%. Consolidated uses 60 F as standard condition.
My company has PipeFlo Advantage available on request. I’ve requested that to see if it can handle these near sonic conditions.
I’ve reached out to the regulator manufacturer to get their input on what x(t) should be for the regulator. I’ve asked the bulk gas engineer for more details on the station and if they have provided solutions for other clients for this issue.
I looked at the pictures I had of the exisitng vaporizer and regulator setup and saw there was some type of orifice upstream of the regulator. I am hoping to get a P&ID of the proposed, new station and see if they provide an orifice as a standard item. If it’s there, that orifice would be the limiting factor even for a regulator failure in terms of the possible relief load.
Not getting to the 3% inlet loss criteria was the first “oh this gets worse” realization I had when I first started on this little quest x)
