Vent pipe calculation and the expansion factor "Y"

[GasDistEng]

I'm doing a vent line calculation for 2.0 PSIG natural gas to 14.70 PSIA across several feet. The line is made up of three different lengths + many fittings.

Here is my approach:

Using a fittings chart - I converted all the fittings to equivalent lengths of pipe. Then, assuming that the piping is all one diameter (in this case the smallest diameter) + assuming a flow rate - one that will get my friction factor in the fully turbulent zone, I calculated the Re then the friction factor using the Colebrook-White method (iterated with MathCAD). I then calculated the K values for pipe + equiv lengths. Here is where it gets Harry...


My next move is to find the limiting expansion factor "Y" - using deltaP/P1 - then letting MathCAD interpolate from the CRANE A-22 table for k=1.3

Now that I have the limiting factor - I then go to the A22 graph for k=1.3 using the deltap/P1 I find "Y". If "Y" is less then the Limiting "Y" then I'm in chocked flow, if not then I'm good.

I then use the "Y" found on the graph to calculate Q in SCFH through the stack. I then take Q through the stack and plug that back into my original Q assumption and repeat until the guess Q equals the Q through the stack.

When I ran this on a very old version of Crane Companion I was getting a "Y" for each component. Now I'm confused! What happened to the limiting Y?

Finally, my deltaP/P1 is always going to be the same. Therefore my "Y" is always the same?

I guess I'm stuck here.

 

[katmar]

Maybe I'm getting old and lazy, but if I were faced with this problem where the pressure drop is fairly small relative to the absolute pressure, I would assume the density at the lower pressure (i.e. at the exit) and do the whole calculation based on incompressible flow.

I would be interested in seeing the difference between the results you get using this assumption and the rigorous result once you nail it!

Good luck
Katmar

 

[katmar]

P.S. Comparing my post with that of David Simpson in reply to your other question - yes, I am definitely getting old and lazy!

 

[GasDistEng]

Not sure what you mean by "assume the density at the lower pressure (i.e. at the exit) and do the whole calculation based on incompressible flow". It was always drilled into my head to find the "choked flow" condition then work backwards. I do a lot of pipe sizing for natural gas distribution - occasionally I run into these vent or relief stack problems. I have yet to find an easy and accurate solution.

Anyway - When using an old version of the Crane Companion software, a "Y" value for each component is calculated. If you look at the examples on PG 4-14 CRANE 410 example 4-21 they do not determine the "Y" Expansion factor for each component (i.e. entrance, exit, and pipe) crane companion does. This is a big question mark for me.

For anyone interested I used the following numbers:


Pipe Dia = 1.380 (Sched 40 1.250")

Stack Length = 70 feet

Equiv Length of fitting (in terms of 1-1/4" pipe) = 108 feet

Pipe Roughness = 0.0018 in

K_exit = 1

K_entrance = 0.5

abs viscosity = 0.0000072 lbm/ft-sec

SG = 0.6

k = 1.3

T = 60 F

Patm = 14.7

Inlet pressure = 2.0 PSIG

Pressure at outlet = 14.7 PSIA

Q. What is the maximum flow rate through the vent under these conditions? Assume an adiabatic system.

Using the method described in my original post (essentially follow example 4-21 CRANE 410) I iterated for Q through the stack so I had to keep trying an initial Q until the resultant Q was equal to my trial Q. I did this mostly to find Re and f (I could have assumed fully turbulent flow as in the example - But chose to calculate f by use of the implicit Colebrook-White equation. After several iterations on Mathcad I balanced out at 3,943 SCFH.

Re: 77186 (I have not looked on a moody diagram to see where this is - my guess is transition...

f = 0.02369

K_total = 38.16

Following CRANE-410 example 4-21 I found "Y" Limiting (by interpolation) to be 0.718 and Y(net) to be 0.9602. The question is that deltaP/P1 is not going to change - so I will always get Y = 0.9602. So K_total is the only driving factor in the Q equation since deltaP and P1 will not change, the only theoretical changes are T and SG.

What am I missing here????

 

[katmar]

All equations for pipe pressure drop involve the density of the fluid in one way or another. Some work from the SG and then calculate the density from that. I prefer to work with the density directly because there is always confusion over the definition of SG.

At the very end of your post you said "the only theoretical changes are T and SG". This is an example of that confusion. By my definition, SG is fixed for any gas as it is simply the ratio of the density of the gas to that of air AT THE SAME TEMPERATURE AND PRESSURE. Effectively, the SG of a gas is its molecular weight divided by the molecular weight of air - this is the definition I use and seems to be the one most widely accepted. The confusion comes in because in liquids the SG is always referenced to water at a fixed temperature.

The calculations you are doing using the "Y" factor assume that you are working with a compressible gas. My assumption was that the gas is behaving like a liquid and is incompressible. The main difference between calculating the pressure drop for a gas and for a liquid is that as the pressure decreases along the line the density of a gas decreases and the velocity increases. It takes energy to cause this acceleration. However, if the pressure drop is small relative to the absolute pressure the acceleration is small and can be neglected in normal plant calculations.

Thanks for giving all the pipe details. Using this information, and treating the gas as an incompressible liquid with a density of 0.046 lb/ft3, I get a flowrate of 177 lb/h, or 3865 SCFH. This compares with your 3943 SCFH. My calculation took 30 seconds and is within 2% of your number. That is why I say for normal plant calculations the incompressible assumption is good enough. If your pressure drop is more than 30-40% of the absolute pressure then it is worth checking by rigorous means.

You will never get choked flow where the pressure drop through a fitting is less that 50% of the absolute pressure. As your overall pressure drop is about 15% of the absolute pressure you do not even need to consider it - saving considerable work!

regards
Katmar

 

[GasDistEng]

Katmar-

Thank you very much!

 

[zdas04]

GasDistEngr,
I would have approached it much like Katmar did. My only reason for responding is your comment above that you should find the "choked flow" condition and work backwards. With 16.7 psia discharging into 14.7 psia, you won't have choked flow so you have to resort to itterative turbulent-flow models for decreasing pressures. I've done that calculation for pipeline blowdown times (choked flow to the critical pressure, turbulent flow to zero). When I've done that, I generally use a 5 psi step during the blowdown. Since your starting pressure is less than 5 psig you don't need to get really fancy. Katmar is right that you can treat the whole problem as constant density.

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.

 

[GasDistEng]

Thanks David and Katmar. I tried Davids approach and calculated 4001 SCFH - real close to my other calc + what Katmar calculated - I used the general flow equation with the "fanning" friction factor (calculated by means of Colebrook-White). I use the fanning friction factor (which is 4 times less then darcy) because it's easier for me to use the pipeline gas equations that I have in my mathcad models..

Still a bit confused about how to determine choked flow??

Thank again!

 

[zdas04]

Choked flow just means that the flow is limited by sonic velocity. You can find the point where you stop having choked flow by:

P(c)=P(upstream)*(2/(k-1))^(k/(k-1)

For air (k=1.4), the multiplier is 0.52. For methane (e.g., k=1.28) the multiplier is 0.54. So basically any time you have upstream pressure more than about twice (in absolute terms) downstream pressure you will have sonic velocity which is a function of upstream pressure, temperature, and gas composition. If you are just less than twice, then the above calculation will tell you which side of the cusp you are on. If downstream pressure is below P(c) then you have to use the turbulent equations which are much lower flow rates than sonic.

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.

 

[1974vet]

Another approach: ran the situation on AFT Arrow demo, got 4,087 scfh using 100% methane.

http://www.aft.com