2-phase flow thro' orifice: any comments? 2

[Leclerc]

I would appreciate any polite comments on what I am doing.

My scratch-built method for calculating 2-phase flow through a given orifice brought about by a given differential pressure consists of the following steps:

1. Determine the flash of a multicomponent system.Calculate the ratio of gas to liquid phases.

2. Assign a fraction,x, of the existing orifice area for flow of gas: This immediately gives the fraction of orifice area for liquid flow, 1-x.

3. Calculate flow of gas through an orifice x.A, where A is area of existing orifice.

4. Calculate flow of liquid though orifice of area (1-x).A. Assume an involatile liquid and incompressible flow.

5 Obtain ratios of flows obtained in steps 3 and 4 above.

6. Vary the value of x and repeat steps 3-5 until the ratio obtained in step 5 is equal to the ratio of the flash (step 1).

7. 2-phase flow through the given orifice is equal to the sum of flows obtained in steps 3 and 4.

 

[SooCS]

The method you have just explain is more or less as recommended in API RP 521 which is a reabonably conservative method. This is what we do vent sizing relief valves for two phase flow.

If you want a more accurate but very complicated method refer to "Leung method" in the Lost Prevention in the Process Industries by Frank Lee.

Best of luck

 

[pleckner]

To SooCS and others:

The method given in API RP521 is no longer the recommended approach for sizing relief valves for two-phase flow. Obtain a copy of the latest edition of API RP 520 (January 2000, 7th edition) which outlines the Leung procedure for two-phase relief valve sizing. You can also get Leung's great article on the topic from CEP, December 1996. In my opinion, this article should be the bible on two-phase flow design.

However, there is a problem in applying this to a plate orifice. Contrary to popular belief, and the fact that we in engineering call the opening within a relef valve an "orifice", it is not. A relief valve opening is really a nozzle and the derivation of the formulas are based on this fact (it is considered an isentropic nozzle, adiabatic and frictionless). An orifice plate is not a nozzle nor is it isentropic but is considered isenthalpic.

For Leclerc:

For an orifice, you may be able to use the same approach one would use to size a control valve for two-phase flow. You can contact Fisher to get their control valve sizing handbook (you may have to pay for it) or look for articles on the subject from Chemical Engineering Magazine or CEP in a good library. The major problem with this method is that they use a valve Cv and what you need is a coefficient of discharge. You might consider using the coefficient of discharge given in CRANE Technical Paper No. 410 but use the values for liquids.

Another possibility is to use the equations for two-phase flow in pipe from the Leung article I mention above. This is probably as close as you will get to an orifice as pipe flow is also isenthalpic. The only difference here is instead of using fl/D, you would use the coefficient of discharge.

Still one more idea, which is rather hairy but if you are good in math...you can derive the equations yourself, following Leung's procedure for the nozzle but substitue the equations for the orifice instead.

Perhaps someone else will have a better idea because I know of no good way of doing a two-phase orifice calculation other than what I mention above. I feel the best you will accomplish with your method (and even using the control valve route) is an answer that is no more accurace than a SWAG (Scientific Wild Ass Guess). My advice, unless this is an academic exercise, stay away from a two-phase orifice like the plague.

 

[d23]

Leclerc:

For what it’s worth in my personal experience dealing with multi phase flow the best you can hope for is a “SWAG” as defined by pleckner. With Bernoulli's equation

DP = ((r(Vo)^2)/(2(Cv)^2) * (1-(Do)^2)/((Di)^2))

a change in fluid density you should leave a little room for error in your design / calcs. If you’re dealing with day one on the design it would offer you a little more accuracy to design with a choke. Multi phase choke calculations are available from the SPE manual.

Good Luck!

 

[Leclerc]

many thanks for all the comments. I'll spend the next few days trying them out.

SooCS; I am using the method to calculate flow into a blocked-outlet system so that I can specify a relief valve for the system. I guess that if the method of API RP 521 is reasonably conservative for a relief valve, then it will predict conservatively low flows, forcing a higher size valve. I need to be careful, because I seem to need the opposite, that is, a conservatively high flow. I suppose I am OK if I use the method for both flows into and out of my system.

Peckner; Coincidentally, I already use the control valve method as decribed in Fisher Emerson's Control Valve handbook, which I was given free for asking! I calculate the Cv from the K by means of formula:

Cv = 29.9*d^2/sqrt(K) ... Perry et al.
where d is size of my pipe system, not the orifice.

I have put the equations into a simple spreadsheet and goal seek the Cv by varying the flow.

d23; What is the SPE manual?

 

[d23]

Leclerc

Society of Petroleum Engineers (SPE) has a printed manual that is a good reference for the petroleum industry both downhole and surface installation / applications.

Sorry for the confusion.

After testing please let me know if your formula works very well.

 

[pleckner]

Leclerc:

If I now read you correctly (and correct me if I am wrong), you are talking about sizing a relief valve and NOT trying to calculate a two-phase flow through a plate orifice. If this is indeed the case, DO NOT use the procedure in API RP521. Use the procedures given in the sourece I stated in my previous thread.

 

[Leclerc]

Pleckner:
I am sorry: I haven't made myself clear. I am rating an orifice for flow into a closed system from a higher pressure source.

Previously,
1. I have identified a system which can be blocked in and can be overpressured.

2. I have identified, among others, a higher pressure source connected to the system which can, potentially, overpressure the system.

Now,
1. I am calculating the maximum flow from the higher pressure source to the system. the pipework connection contains an orifice plate. This calculation is the subject of my thread.

2. I will calculate maximum flows from the other higher pressure sources.

Next,
1. I will specify and size relief device(s) for the system having regard for the maximum flows, states, calculated above, plus other means of overpressuring.

 

[pleckner]

Can you be more specific as to what is the contents of the high pressure source and is this a pumped liquid, vapors, what? Also, the temperature and pressure we are talking about.

 

[dbevil]

For what it's worth, most two-phase flow calculations thru orifices are only accurate if the two phases are in one of the homogeneous flow regimes (i.e., mist flow or distributed bubble) thru the orifice. For all the other flow regimes (stratified, wavy, annular, plug, or slug flow)two-phase flow pressure drop is a function of which phase is trying to get thru the orifice. Depending on the flow regime and the ratio of gas to liquid, almost any length of either may be present at the orifice. The conservative approach would be to calculate the orifice based on gas, if it can be present at the orifice long enough to over-pressure your closed system.