Calculating venting capacity of a vessel under choked flow

[chusker15]

I have a multi-stage centrifigual compressor. Natural gas (approx 85% methane) is being compressed from 700 to 1300 psig. Lubricated labyrinth seals are used in the compressor. The lubrication comes from a lube oil tank with a MAWP of 15 psig. The lube oil tank has a 3" NPS line venting to the atmosphere. I need to calculate if the 3" vent line would be adequate in the case of a 1/4" seal leak. I use 1/4" as an example to understand the calculation, I will use additional values later.

The flow will obviously be choked through the 1/4" hole. I have calculated the choked flow rate, outlet temperature and outlet pressure.

I would like to just do a pressure drop calculation for the vent piping, but I don't know what to use for an upstream pressure. I do not have a good understanding of what happens just downstream the point of choked flow. For example, in this case, 1300psig gas flows through a 1/4" hole and choked flow occurs. The gas flow into an atmospheric storage vessel. The pressure of the gas after flowing through the 1/4" hole is approximately 600psig. What happens to the pressure at the outset of the choked flow region?

Sorry if any of this is unclear.

Thanks

 

[Eltron]

I'm a bit confused. You said that the pressure of the gas after the 1/4" hole is 600psig, but then you said that it flows into an atmospheric storage tank. It seems like you would be pressurizing your storage vessel, unless I'm missing something.

 

[djack77494]

chusker,
I agree with Eltron. The situation is not fully and accurately described. Assuming there is no other significant restriction in your line between the seal and the L.O. tank, then the downstream side of the orifice will be at essentially the tank's pressure (not 600psig I hope). With choked flow, decreases in the downstream pressure do not change the flowrate, so the downstream pressure will decrease to the point where it is tank pressure + (presumably small) line losses. The absolute highest pressure than can be allowed to develop would be 16.5 psig (1.1*design pressure). When this occurs, your flowrate will be the gas you are pushing through a 1/4" orifice with 1300psig upstream and 16.5psig downstream. (I am making no suggestions that your design basis is reasonable. Check with folks knowledgable about seal performance and failure modes to determine how to approach the problem of what relieving flowrate to use. Please!)
Doug

 

[rbcoulter]

Theory tells us that after the gas exits the choke point suddenly to a much greater flow area, (which appears to be your case) that the gas suddenly expands and the pressure drops rapidly (usually with shock waves). So I tend to agree with the other respondents that your pressure after the choke point is low and approaches the vent tank pressure.

Fortunately, in your case, because this is critical flow, then the flow through the 1/4" hole is independent of the downstream pressure. You can calculate the discharge of natural gas using an adiabatic flow equation at critical flow.
You could probably use the methods in API RP 520 to estimate the flow. Once knowing the flow through the 1/4 " orifice, you can then calculate the pressure drop through your 3" vent pipe on the tank to see if you exceed its rating.

 

[zdas04]

You can do a first approximation that the head of the vent pipe is at atmospheric pressure. Then using that flow rate, calculate the pressure drop in the vent pipe. If it is high, then you have to verify that you really have choked flow through the 1/4 inch hole (taking the dP down the vent pipe into consideration).

One of the most common choked-flow errors that I see in PSV calculations is not taking the pressure drop down the vent pipe into consideration.

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.

The harder I work, the luckier I seem

 

[chusker15]

Thanks for the good information. I'm sorry the original post wasn't clear enough, but the information provided gives me enough information to solve my problem.

 

[mechprocess]

You have a piping system with a restricting point such as the 1/4 inch and piping there after to an exit. You need to calculate the maximum flow through your piping system which includes an inline restriction (1/4 inch opening.

Known:

3 inch inlet loss = 0.78 for inward projecting
1/4 inch restricted flow area. K = f (A1/A2)
3 inch piping K = f(fl/d)
3 inch piping with an exit loss K = 1
Supply pressure

Sum up your K loss coeff for the entire flow path.
You can use the Crane TP-410 formula for mass flow rate

W = 1891Yd^2SQRT(DP/KV1)

K = total loss coeff
V1 = upstream specific volume
DP = Upstream pressure - downstream pipe exit choked pressure

For a given upstream pressure your flow will choke based on the total K loss of the entire system which includes the restricting area. Yes the flow may reach a Mach number of 1 at the throat where the 1/4 inch area is located but it will recover and be choked at the exit. Don't worry about that. This is a code relief calc.

A typical code relief calculation stipulates that you add all your loss coefficients and determine the available DP/P1
that can be used in equation 3-22 Crane 410 for you total K value. The more K you have, the lower your downstream exit pressure has to be in order to have choked flow. I know that sounds crazy but its true.

Theoretically, your system will experience near isentropic expansion through the 1/4 in restriction and then static regain to the 3 inch vent pipe and then fanno flow through the 3 inch piping(adiabatic) to the exit.