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Low Flow in Pipes- posted in Ankur's blog

Two-Phase Flow Relief Header Sizing Using Omega Method.


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#1 seetheforest

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Posted 18 November 2013 - 05:41 PM

Hello,

 

For simplicity, let's assume we have two relief valves connected to a main header that discharges to atmosphere.  Each device has been sized with the Omega method and stagnation conditions have been determined.  Both relief conditions are two-phase flow and their relief is the result of a shared fire-case condition.

 

I'm somewhat confused on how to approach this problem in general and the resources that I have read have only added to that confusion.  In:

 

Leung, J.C., (1996)  Easily size relief devices and piping for two-phase flow.  CEP, 92 (12), 28-50

 

Leung suggests starting from the last piping segment for relief headers, but doesn't provide a clear description of how to determine Omega of the two-phase flow mixture in this segment.  This leads me to two basic (possibly ignorant) questions:

 

  1. If the stagnation conditions for each valve have a different Omega value, how can a combined Omega of the two streams be determined.
  2. If the quality or void fraction of a stream is known (estimated) at the relief valve, the quality will change throughout the system as the stream isenthalpically expands, right?  I don't see this taken into account in the Omega method and I'm not sure how to re-calculate Omega for each segment of pipe.

My apologies if some of these questions are rudimentary.  I'm still learning.


Edited by seetheforest, 19 November 2013 - 09:24 AM.


#2 PaoloPemi

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Posted 19 November 2013 - 01:44 AM

I assume you know how simplified HEM (Omega) works,

since Omega has several limits as alternative

you may consider a rigorous HEM,HNE,NHNE as

that available in PRODE PROPERTIES,

in HEM you assume that vapor and liquid (in equilibria) travel at same speed so,

once you know the mass flux (which, for the header, could be the total)

you are able to calculate densities and velocities at exit point,

from that you can calculate the pressure diagram in different points of header,

for that you need a model to estimate pressure drops for two phase flows,

also you must verify critical flow condition (speed of sound),

a software as PRODE can calculate both speed of sound for single phase

and two phases flow with a EOS, see the method strMSS() which works with

HEM) and pressure drop (see method PIPE()),

for a complex network you may need to iterate.



#3 Ben K

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Posted 20 November 2013 - 04:40 PM

I'm working on the same problem currently (two phase Omega method sizing). I'm working out of API 520, it's fairly complete and has examples.

 

On your specific questions,

1)  I don't see why you would want to combine the Omega calculations of the two valves.  The mass rates should be calculated individually.  The only reason you would want to is if the backpressure is high and relief falls to sub-critical flow during simultaneous relief.  There is an equation in API 520 for determining if flow is sub-critical.  If it is, you would have to alternate each valve mass calculation and iterate until the mass rates even out.

 

2)  As far as I know, the Omega method is only used in PSV mass flux calculations, not pipe pressure drop.  ...?

 

Also, to piggyback a question of my own, maybe Paolo can answer this...

 

When doing an isentropic flash for the two-point Omega method, do you consider heat transfer between the gas and liquid phases?



#4 Purnesh Meshram

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Posted 20 November 2013 - 09:13 PM

Hi seetheforest

 

You can refer to Clause 7.3.1.3.5 API 521 (use the latest issue) for two phase piping PSV relief. API 520 is only for PSV orifice.omega calculated is different for PSV and piping.

hope this will help.

thanks


Edited by chemtechiee, 20 November 2013 - 09:50 PM.


#5 PaoloPemi

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Posted 21 November 2013 - 02:05 AM

Ben,

 

'When doing an isentropic flash for the two-point Omega method, do you consider heat transfer between the gas and liquid phases?'

 

with HEM model (both rigorous and simplified as Omega method) you assume that vapor and liquid phases are in equilibria, that answers the question, there are several Non Equilibrum models as HNE, NHNE etc. which consider different conditions.

 

chemtechiee,

API 521 gives a method (ref. 36) to evaluate a 'omega' solving a flash at specified (50%) enthalpy, however I would add that when applied for evaluating the critical mass flux condition a more accurate method is that based on evaluation of two-phase speed of sound (see my previous post), nowadays the software allows that.

 

API gives a correlation for two phase pressure drop (ref. 34) but it adds "There are a number of manual two-phase flashing-flow pressure-drop correlations available (see Bibliography items under headings “Flashing flow in pipes” and “Flashing flow in valves”) so it is questionable to say which method should be preferred,

also, as commented in API, the formula (ref. 34) requires iteration and a thermo package to calculate properties, solve flash etc.

at that point one may prefer to use a library (see above) or a simulator.

 

Similar considerations for 7.3.1.3.4


Edited by PaoloPemi, 21 November 2013 - 02:41 AM.


#6 seetheforest

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Posted 21 November 2013 - 10:49 AM

Thank you all for these replies.  It's helping a lot.

 

Hi seetheforest

 

You can refer to Clause 7.3.1.3.5 API 521 (use the latest issue) for two phase piping PSV relief. API 520 is only for PSV orifice.omega calculated is different for PSV and piping.

hope this will help.

thanks

 

Thanks chemtechiee, this is nearly identical to the method used in Leung's paper.  I understand that Omega is different, but was confused on how exactly to determine Omega for each pipe segment.  I still am unsure on how to achieve this, which I will elaborate in my reply to Paolo.

 

Ben,

 

'When doing an isentropic flash for the two-point Omega method, do you consider heat transfer between the gas and liquid phases?'

 

with HEM model (both rigorous and simplified as Omega method) you assume that vapor and liquid phases are in equilibria, that answers the question, there are several Non Equilibrum models as HNE, NHNE etc. which consider different conditions.

 

chemtechiee,

API 521 gives a method (ref. 36) to evaluate a 'omega' solving a flash at specified (50%) enthalpy, however I would add that when applied for evaluating the critical mass flux condition a more accurate method is that based on evaluation of two-phase speed of sound (see my previous post), nowadays the software allows that.

 

API gives a correlation for two phase pressure drop (ref. 34) but it adds "There are a number of manual two-phase flashing-flow pressure-drop correlations available (see Bibliography items under headings “Flashing flow in pipes” and “Flashing flow in valves”) so it is questionable to say which method should be preferred,

also, as commented in API, the formula (ref. 34) requires iteration and a thermo package to calculate properties, solve flash etc.

at that point one may prefer to use a library (see above) or a simulator.

 

Similar considerations for 7.3.1.3.4

 

So just for my own personal edification, I'd like to go through Leung's Omega method as drawn out in API 521 just to see what it looks like for myself.  I'm fine with the HEM assumption for my system.  However, I think you highlight my biggest concern, which is that I don't fundamentally understand how to perform the isenthalpic calculations and the reasoning behind the structure of the calculations.

 

API 521 suggests doing a flash calculation where there is a pressure loss in piping to 50% of the relieving pressure, calling it Pr.  Then do another flash calc to 50% of Pr (25% of relieving pressure) and use these two results to calculate the Omega for the relief piping.  This leads me to a number of questions:

  1. How do I do these flash calculations?  I have general physical property data, but no enthalpy or saturated temp/pressure data for my system components.  In general I don't know of a widely available enthalpy data for the variety of fluids that I could encounter (sometimes custom thermal fluids like Syltherm)
  2. Is there physical justification or an explanation for the structure of these isenthalpic flash calcs?  They seem arbitrary.
  3. I presume if my valves relieve at different pressures there is no way to do a header, right?  I mean the assumption of these flash calcs is that regardless of what relieving device you start from you will flash consistently with the same dP.

I've attached a drawing of a representative system just to aid in simplifying the discussion.  Feel free to use it if you need to reference a point in the system.

Attached Files


Edited by seetheforest, 21 November 2013 - 10:58 AM.


#7 PaoloPemi

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Posted 21 November 2013 - 11:45 AM

a problem which you have to solve is that going from p1 to p2 the liquid fraction changes

and you have to model that, the simplifying assumption of Omega method (see ref. 36 in API)

attempts to solve that problem, for the explanation of the model see Leung's papers,

there are different solutions but I would guess that if you do not consider heat balance

(for example if you assume isothermal and calculate phase equilibria accordingly)

you may  get larger errors,

by the way it is not difficult to solve a constant enthalpy flash but you need to define

suitable correlations for phase equilibria and enthalpy,

if you plan to use a software (see above post) it requires to specify a composition but if your

fluids are not in the library you may define  your own components,

for example as pseudo with a limited number of properties,

note that the final accuracy will depend from fluid's properties.

 

"I presume if my valves relieve at different pressures there is no way to do a header, right?"

 

the valve's will relieve (backpressure) to header's pressure, you need to calculate that

pressure at some specified relieving case, the procedure suggested (start from

header end and iterate) will allow you to calculate the pressure in different segments

when relieving.

Note that according API

"The basic criterion for sizing the discharge piping and the relief manifold is that the back pressure
(which can exist or be developed at any point in the system) shall not reduce the relieving capacity of any of the pressure-relieving devices below the amount required to protect the corresponding vessels from overpressure."


Edited by PaoloPemi, 21 November 2013 - 12:00 PM.


#8 seetheforest

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Posted 21 November 2013 - 03:37 PM

a problem which you have to solve is that going from p1 to p2 the liquid fraction changes

and you have to model that, the simplifying assumption of Omega method (see ref. 36 in API)

attempts to solve that problem, for the explanation of the model see Leung's papers,

there are different solutions but I would guess that if you do not consider heat balance

(for example if you assume isothermal and calculate phase equilibria accordingly)

you may  get larger errors,

by the way it is not difficult to solve a constant enthalpy flash but you need to define

suitable correlations for phase equilibria and enthalpy,

 

Hi Paolo,

 

I'm somewhat confused.  Leung describes the Omega formula as an EOS (provides PV relationships), yet to do the flash calculations to get Omega I need to use a different EOS and develop a PV diagram from that to determine the extent of flashing from the inlet pressure to an assumed outlet pressure.  Then, I can generate Omega and use that for pressure drop, etc.

 

It just seems counter-intuitive to develop a model based on a completely separate EOS to perform flash calculations in order to then get Omega and use that EOS to analyze the system.


Edited by seetheforest, 21 November 2013 - 03:37 PM.


#9 PaoloPemi

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Posted 21 November 2013 - 04:13 PM

perhaps the confusion is about the scope of Omega method,

you may read "the Omega method for discharge rate evaluation"

by Leung or similar papers which explain origin and scope of Omega method

introduced by Leung as generalized correlation for

one-component HEM model,

the main advantage is that it is more easy to solve than rigorous HEM as

it "has the attribute of bringing out key physical parameters influencing

the compressible flow of a two phase system".



#10 seetheforest

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Posted 21 November 2013 - 05:34 PM

Yes, Omega is a correlating parameter (whose value is proven by its usefulness in an EOS).  While this is true, I'm not sure it illuminates information about the core problem, which is how to develop flash calculations to determine Omega in relief header sizing.



#11 PaoloPemi

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Posted 22 November 2013 - 01:42 AM

Omega method provides a generalized correlation for one-component HEM model,

it has been extended to HNE too (see HNE-DS),

to define Omega parameter you may utilize different methods

depending from fluid characteristics,

a EOS such as PR or SRK can provide the data (volume, enthalpy, entropy...)

to define Omega compressibility parameter but, as suggested in my first port,

the different flash operations (for equilibria + H or S...) are not easy to solve,

you may wish to adopt a library or a simulator for that.

The same if you wish to compare (for purposes of testing) results of Omega

against rigorous HEM or HNE,

a software as PRODE PROPERTIES may result useful for that.


Edited by PaoloPemi, 22 November 2013 - 02:17 AM.





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