12 replies to this topic

[Fr3dd]

Good Morning,

 

Once again I would like to have some of your thoughts about a specific matter I'm dealing with now.

 

-The System:

In a production site offshore, fluids from subsea facilities are being transferred to and from a floating vessel. The flowlines are routed throug a structure that has a fixed part and a rotating part that is capable to rotate freely. Of course, since rotating parts are involved, some seals are used. With time, this seals will eventually leak, that's why several lines will be installed to collect this leakage and route it to a recovery vessel or flare (depending if they're liquid or gas). Since leakage rates are enormously smaller than production rates, small tubing is used (1/2") for collecting the leakages.

 

-The Problem:

In the case of a seal rupture, a leakage flowrate much higher than expected will be flowing across the tubing at a high pressure. The tubing will act as a sort of Restriction Orifice and will limit the flow since its diameter is small. I made some estimations based on choked flow (since it determines the maximum flowrate that can flow through the tubing; however, I find the resulting flowrate too high. 

 

Is the Choked flow equation a good approach for this problem? I would like to have your opinion on this.

 

Please find more details about the problem:

 

Main Piping:

P= 353 bara

Cp/Cv= 1.8

MW= 23.2

Z= 0.65

T=50 C

 

Tubing Data:

d= 15.8mm

 

I'm getting a choked flowrate (thus, a maximum possible flowrate) of about 13.5 kg/s (approx. 48700 kg/h). Is there something I'm missing?. Thanks in advance.

 

Fr3dd

[latexman]

Attaching your calcs would have been useful.  Was the tubing treated as an orifice or long pipe?  If long pipe, was isothermal or adiabatic used?

Edited by latexman, 27 May 2014 - 08:01 AM.

[katmar]

Yes, your predicted flow rate is much too high.  Looking for the choking point (or sonic velocities) is the right way to go, but it is not going to choke at the inlet where you have the conditions that you have listed.  The line will choke at the downstream end where the pressure is much lower and the lower density results in the highest velocities.  I suspect that your compressibility (Z) will also increase towards 1 as the pressure decreases, making the velocities even higher.  I guess you are looking at around 1.0 to 1.5 kg/s, but you need to calculate it properly.

[breizh]

Fr3dd,

 

Consider this resource to support your work:

http://www.engsoft.c...team_flow_e.htm

 

Breizh

[Fr3dd]

Thank all of you for your replies.

 

Breizh, I'm on my way to check the information you posted. It looks interesting and I want to carefully read it. Thanks.

 

In the mean time, Katmar, I'm really interested to know about your statement:

 

 

...but it is not going to choke at the inlet where you have the conditions that you have listed.  The line will choke at the downstream end where the pressure is much lower and the lower density results in the highest velocities.

 

i can understand that; however, I'm having a hard time trying to think how to determine the point where the choked flow it's going to happen; is it at the very end of the line?.

 

I'm asking this because, for some other leak lines, an restriction orifice is foreseen to deal with the possibility of a high pressure seal failing; of course, this orifice will be installed in the header after the tubing: do i need to account the choked flow effects of the tubing itself in order to size the orifice?.

 

Latexman, my calculations are not big deal, is basically the input I already gave and the choked flow equation. I attached a print screen of the equation I'm using.

 

Thanks again for your insights.

 

Regards,

 

Fr3dd

 

 

 

[katmar]

Choking will occur at the first point where the velocity becomes sonic.  For a simple pipe this will be at the outlet because that is where the density is lowest.  If you have orifices or valves in the line then they could be the choke if the decrease in diameter is sufficient to increase the velocity to sonic levels.

 

You have to consider the whole system to find the choke point.  This will probably involve a bit of trial and error unless you have powerful simulation software - which will perform the trial and error behind the scenes and just present you with the answer.

[latexman]

What is the length or typical length of the 15.8 mm tubing?

[Fr3dd]

Hello Guys,

 

I took out a few days for a well deserved vacation.

 

I'll first answer the easy question: Latexman, I made a conservative estimate of the lenght of the tubing and it should be around 6m.

 

Katmar: I will have at least a ball valve and a check valve on the way (as well as several elbows and bends). If I understand you well, this trial and error would be trying different flowrates and calculating the velocity at different points on the system until I find a flowrate which choke point (flow velocity = sonic velocity) is not before the end my estimated lenght?

 

Thanks again guys!

 

Regards,

[PingPong]

You should read Perry chapter 6. Note especially Figure 6-21

 

Based on the tube length, diameter, number of bends and fittings, you first determine the number of velocity heads N to be used in formulas and graphs.

[Fr3dd]

Hello Everyone,

 

Following PingPong recommendation, after reading part of Chapter 6 of Perry's Handbook (and using the procedure outlined there) for the full line I've got around 6kg/s. However, I still think it's high (and according to Katmar's ballpark estimate, it is).

 

Also, I have extra difficulty since I don't have a material balance yet, I only have the fluid properties at the main piping conditions and its hard to estimate them for lower pressures (no compositional data is available). I can fix that by investing some time; however, I wanted to define the procedure to follow before start working with that,

 

Any additional thoughts you may have regarding this issue is highly appreciated. Thanks.

 

Fr3dd

[PingPong]

If you do not have compositional data, then how do you know value of M, Z and Cp/Cv ?

 

How exactly did you calculate that 6 kg/s ? What value did you use for N ?

 

Example 8 in Perry gives the procedure, so it would be clearer to outsiders if you would use the same format for your problem.

Note that f in Perry is Fanning Friction factor (not Moody).

 

 

The problem with theotretical formulas in textbooks or websites is that they are for ideal gases, which is not the case here.

The formula in Perry does not even include Z because it assumes it is 1.0 however you stated that Z = 0.65

If Z were included in the formula it would be in the denominator with RT, so it would be ZRT, which makes flowrate G* higher.
 

Because Z and Cp/Cv will change with P and T you would have to split the pipe up in parts to calculate G* and G more accurately.

Edited by PingPong, 05 June 2014 - 05:49 AM.

[katmar]

The difference between my 1 to 1.5 kg/s and your 6 kg/s is mainly because I had assumed the pipe was "very long".  It always goes wrong in the assumptions.  With a length of 6 m your estimate of 6 kg/s is probably not far off the mark.  Another assumption I have made is that the seal rupture is large enough that the pressure in the housing can be taken as 353 bara (and that the housing can contain this pressure without rupturing itself!).

 

My calculations are all based on isothermal flow (to avoid the difficulty pointed out by PingPong in requiring data for Z, Cp/Cv, downstream T etc etc) and therefore I would expect calculations based on the adiabatic model to give slightly higher mass flow rates. 

[breizh]

Fr3dd and others

Consider this resource (yellow book) , in particular chapter 2 .

Hope this helps

 

Breizh