Sizing for Two-Phase Liquid/Vapor Relief - What to do if vapor quality is not known

[CJC0117]

Hi everyone,

I am a process engineer and I've been trying to find a method for sizing relief devices for two-phase vapor-liquid venting without the need for software/equipment like SuperChems, VSP2, or RSST (I know I would probably need these for reactive systems, but for now I am only considering nonreactive systems). The most promising methods I've seen assume homogenous flow. A problem I keep running into with every method I try is that you need to know the vapor quality for at least one (T,P) point. The Pv equation that DIERs uses to find two-phase density (which is then used to find mass flux) requires performing at least two flash calculations in order to find two parameters, a and b, used in the Pv equation. The omega method is a simplification of this method that assumes a=ω and b=0. ω can be found using a one-, two-, or three-point method. Annex C of API 520 part 1 uses a two-point omega method.

API 520 also recommends a numerical integration method for calculating maximum mass flux. Numerous flash calculations are performed at constant entropy while lowering the pressure from the peak relieving pressure, until either a maximum mass flux is reached or the the backpressure is reached. I have constructed an excel spreadsheet for performing these flash calculations. It uses the Peng-Robinson EOS and Clapeyron equation to find the entropy (relative to a reference state) for the vapor and liquid phases separately. However, I still need to know the vapor quality for one of the (T,P) points in order to find the two-phase entropy value that is held constant throughout all the flash calculations. I thought of using the initial vessel average void fraction at set conditons, α = 1 - [(liquid volume at set conditions)/(total vessel volume)], and from that calculating the vapor mass quality and then the two-phase entropy (since homogenous equilibrium methods assume the vapor/liquid ratio in the vessel is the same as in the relief device). Would this be a valid method?

Basically, I just don't know how to do this without knowing the vapor quality at any (T,P) points. Maybe there's an assumption I can make about the quality or a way around it; another way to tackle this (I've read a 1995 article called “Protection of Storage Tanks from Two-Phase Flow Due to Fire Exposure” by H.G. Fisher and H.S. Forrest that assumes the vapor wt% is less than 2%, but I'm not sure how valid this assumption is). I've hit a snag and was hoping someone here could lend their experience with two-phase sizing. Thank you. Any help is much appreciated.

 

[apetri]

why reinvent the well ?
there have been many discussions about this topic and you may find an Excel page for solving the HEM model in this thread

http://eng-tips.com/viewthread.cfm?qid=329093

out of curiosity, the iterative procedure written in VBA code runs slow and is less accurate than std. ISPF() method available in Prode Properties (see prode.com for additional info) as you know VBA code is not the best option if you need speed, but is ok to create a model and understanding how it works.

also the ISPF() method in Prode which you can access from VBA and Excel (as a macro) includes several models (four or more)

1) HEM Homogeneous Equilibrium (Solution of Mass Flux integral)
2) HNE Homogeneous Non-equilibrium (HEM with Boling Delay and Gas-Liquid Slip Contributes)
3) HNE-DS , Homogeneous Non-equilibrium
4) NHNE Non-homogeneous Non-equilibrium

every model offers some advantages in specific areas of application and you should investigate which is the more suitable in your case, there is also a page which allows to compare the results from different models

 

[apetri]

why reinvent the wheel

 

[CJC0117]

Thanks apetri. I'll take a look at the Prode programs and the excel sheet on that thread as soon as I get a chance. I know I'm trying to reinvent the wheel but I really would like to be able to understand two-phase venting and the HEM method well enough to be able to make my own excel sheet, even if I end up using a more advanced sheet I find on these forums. The problem I am currently having is that I can't figure out how to find the two-phase entropy that I must hold constant for all my flash calculations. As I mentioned in my last post, I tried using the vessel void fraction at set conditions to find the two-phase entropy, but the two-phase entropy ends up being less than both the vapor and liquid entropies at the saturation conditions used in my flash calculations. This results in nonsensical values like negative mass/volume fractions, negative two-phase densities. I should mention that I'm only looking at one component and pseudo-one-component systems right now. If I remember correctly, for a one component system in two phases, you can only specify one independent, intensive variable (in this case the saturation pressures) in order to completely specify the system. However, vapor/liquid fractions and overall properties (e.g. two-phase entropy) are extensive properties and must be specified separately. So I need to know the vapor mass/volume fraction for at least one data point in order to specify the extensive properties of all the other data points. But how can I do this? How does the Prode program do this (for one component systems at least - I don't recall whether total vapor/liquid fractions are considered intensive or extensive variables for multicomponent systems in VLE)?

 

[Latexman]

Have you looked at the DIERS book? If you can't borrow it, it's available at AICHE.

Good luck,
Latexman

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[CJC0117]

Yes, I have looked at "Emergency Relief System Design Using DIERS Technology". Namely, section 3-2-2-2 of Chapter II gives analytical equations for solving mass flux (as opposed to just using numerical integration), but still, whether I use an analytical equation or numerical integration method, the problem is the same: the equation for two-phase specific volume that is used in the mass flux equation (regardless of whether the system is described as one component, psuedo-one-component, or multicomponent) requires knowing the vapor mass fraction (or the individual vapor mass fractions found via "modified" Raoult's law for each component in the case of multiple components) for at least one data point. How, if at all, can HEM method be implemented without knowing mass fractions beforehand?

 

[Latexman]

I'm 5000 miles from my books, so I cannot look. Did they not work some examples? What did they do? IIRC, they used the vapor fraction of the vessel (vapor space volume/total volume) prior to relief as that firest data point.

Good luck,
Latexman

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[CJC0117]

Yes, there are example problems for different models in Appendix II-E. It looks like they've done exactly what my excel sheet does, except that the fluid they consider is water so they just use steam tables to find properties for each individual phase (my excel sheet used the Peng-Robinson EOS and Clapeyron equation instead). It says in the problem statement that there is 5 wt% vapor in the stream at peak relieving, stagnation conditions. The example uses this vapor fraction to find the constant two-phase entropy that is used to find vapor fractions for subsequent flash calculations at lower pressures. Perhaps there is another example somewhere that used the vessel vapor fraction before relieving, as you suggests. I had thought to use that as well but it didn't work; I'm getting negative vapor fractions and two-phase properties for many of the lower pressure data points because the calculated two-phase constant entropy is smaller than the entropy of both phase (see my 2nd post). I wonder if that has any physical meaning. Or perhaps my excel sheet has a calculation error somewhere.

 

[Latexman]

You could have multiple calculation errors, if you write programs like me! lol I also recall a DIERS graph of void fraction vs. superficial gas velocity for 2 or 3 classes of liquids for liquid swell from volumetric boiling. Does that apply to your scenarios?

Good luck,
Latexman

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[PaoloPemi]

the procedure described in thread

http://eng-tips.com/viewthread.cfm?qid=329093

requires that you solve a flash at constant entropy which is the basis of the model,
for the constant entropy flash the procedure adopts a method available in Prode Properties library,
for a single component you can easily write your own code for solving a constant entropy flash,
for mixtures things may become very difficult and that is the main reason why I prefer a process library.
So, the first thing to do is to code the flash or use the method in the Prode library (the Excel page provided as example does that).
You may calculate latent heat (for a pure component) starting from saturation pressure but the ususal approach with simulators is to calculate the departure with a EOS (in your case Peng Robinson).
You can apply HEM (homogeneous equilibrium model) in many areas, for example there are methods in Prode Properties for calculating the two phase (vapor+liquid) speed of sound with HEM assumption.

 

[CJC0117]

@ Latexman, I believe the graph you're referring to is Figure I-B1 in the DIERS book. It is a graph of average void fraction vs. dimensionless superficial vapor velocity. There are also equations for the curves on the graph; I came across them when searching for a method of predicting when two-phase venting will occur. It's a bit confusing because I've seen many types of void fractions: an entrainment void fraction, the void fraction in the swelled liquid, the total vessel average void fraction at vapor-liquid disengagement, and the vessel average void fraction. Intuitively, I feel like you'd use the total vessel average void fraction at vapor-liquid disengagement if two-phase flow is predicted, but I'm really not sure. And in any case, I've tried my excel sheet using all those vapor fractions and it doesn't work in all cases. It's because the example I'm basing my sheet off of has a liquid full vessel, so if you use the void fraction at set conditions then it's going to be very low, resulting in the two-phase entropy essentially being equal to the entropy of the liquid phase at set conditions. But then for saturation pressures above the set pressure, the entropies of each phase are both greater than this two-phase entropy, such that it is impossible for the two-phase entropy to remain constant at higher pressures without making the vapor fractions negative. Sorry if I'm not making sense. Also, I've checked my entropy calculations against NIST data and it seems to be in good agreement. And the formula for mass fraction is just simply the lever rule so I'm pretty sure I can't have messed that up.



@ PaoloPemi, I'll have to read over the user's manual before I can begin to understand how Prode Properties works, let alone how to use it. I've installed it and played around with it a bit but I really have no clue how to use it at the moment. I've already got methods for calculating the properties for each phase. My problem now is finding at least one vapor fraction for one of my flash calculations so that I can find the two-phase entropy.

 

[PaoloPemi]

The model for the nozzle applied in the procedure discussed above is

hin+1/2*vin^2 = ho+1/2*vo^2

(in = inlet, o = orifice)
where vo (for a critical flow) is the speed of sound
ho, vo calculated at vena contracta conditions

the vena contracta conditions are determined with a series of constant entropy flash operations,
to solve the constant entropy flash (i.e. given initial t,p and final p (or p) the procedure finds tout (or pout) which gives Sout=Sin), as said in previous post I prefer to use a commercial product (Prode),
you can use another product or write your code.

important advantages of this approach

-rigourous (not simplified as models based on two points evaluations)
-can be applied to all conditions including critical (gas,gas+liquid)

what surprises me is your reluctance to consider a well tested approach
when attempting (with the reported difficulties) to create your own,
the model is documented (VBA code available) and can be utilized for testing purposes,

anyway, good luck

 

[CJC0117]

Thanks for the post PaoloPemi. I've been trying to follow along with the thread you sent a link to before,

http://eng-tips.com/viewthread.cfm?qid=329093.

In the thread Latexman references a method in the FAQ section that he's based one of his own excel sheets off of,

http://eng-tips.com/faqs.cfm?fid=1293.

It looks like the same method that my excel sheet is based off of. I think the example he shows at the end is for all gas flow, which is how he was able to find the entropy without knowing a vapor fraction, and how he is able to completely specify all subsequent flash calculations at lower pressures. Now are you saying that in the case of two-phase flow I'll have to use the equation h[sub]o[/sub]+(1/2)V[sub]o[/sub][sup]2[/sup]=h[sub]n[/sub]+(1/2)V[sub]n[/sub][sup]2[/sup] in order to find the two-phase entropy to hold constant in my flash calculations? Is that right? Could you point me to a reference that uses this method or else to the specific excel sheet in that thread where I can find this code you're talking about? Thanks.