PSV Sizing for Two Phase Flashing Flow using Direct Integration Method

Hi All,

I performed sizing of the PSV for Two phase with subcooled condensate water at the PSV inlet and flashing through the orifice using the Direct Integration method proposed in API 520 Part 1 C As per this method I performed successive isentropic flashes from the pressure at the PSV inlet(P1) to the back pressure acting on the PSV. My PSV vents to atmosphere through a 45 feet long pipe that leads to the grade. Since I did not know the built-up back pressure. I performed isentropic flashes from P1 to atmospheric pressure( Patm=14.7 psia).

My question is whether I have performed the isentropic flashes correctly since I did not use a process simulator as I don’t have access to it. Instead I used the steam tables, the procedure is described below.

  1. From the steam tables for subcooled water I determined the specific entropy of water at relieving pressure P1 = 94.45 psia and relief temperature T1 = 248 Deg F. The specific entropy is s1=0.364867 Btu/lbm-Deg F.

  2. For subsequent pressures which are a decrement by 1 psia, I determined the specific entropy just by changing the pressure by keeping the temperature constant. I found that the specific entropy values increased but by a very very small value ( in the 4 decimal). I considered this is essentially constant as the specific entropy is changing infinitesimally. Ideally I should have decreased the temperature to keep the specific entropy constant but found it too cumbersome to do especially for the number of steps I have to do this for. Is this acceptable?. I determined the fluid density at this pressure and temperature. I did this until I reached the pressure where the water started to flash. At this point I determined the liquid and vapor specific entropies and determined the vapor mass fraction ( quality ) by equating the mixture specific entropy to the value at P1 and T1. I determined the liquid and vapor densities and the mixture density using the vapor mass fraction.

For example

Step Pressure Temperature Specific Entropy
(psia) (Deg F) ( Btu/lbm-Deg F)
1 94.45 248 0.364867
2 93.45 248 0.364869
3 92.45 248 0.364869
4 91.45 248 0.364872

  1. I then performed the numerical integration of the mass flux integral and determined the maximum mass flux which occurred exactly at the pressure where condensate started to flash. I calculated the required orifice area using

A = 0.04 W / (Kd Kb Kc Kv . G)

where W is required relief rate, lb/hr
Kd = 0.65
Kb, K, Kv =1
G = Maximum Mass flux

I would be grateful if any one of you can review my calculation and let me know if I did my calculations correctly ( procedure wise). I have attached my calculation spreadsheet with this thread.

Thanks and Regards,
Pavan Kumar

66PSV Sizing for Two Phase Flow Using Direct Integration Method.xlsx (52.1 KB)

Hi Pavan,

I just saw this. I’ll look at your spreadsheet in more detail later today, and revert by EOB, but I wanted to pass on some advice our fluid flow/relief expert has in our design manual. Isentropic flashes, as you have done, are technically the proper choice, but he said if you use isenthalpic flashes, which are much easier, you’ll get essentially the same answer. There is not much difference. As such, he advises always use isenthalpic flashes, and save the time. My quick $0.02.

Hi Pavan,

Keeping the temperature constant in the subcooled region is acceptable; changes are very small there. Your calculation procedure looks good. The cells that had cell math looked good. The input data and calculated data looked good and reasonable. And, you got the same general results that I have always gotten with a subcooled liquid PSV that flashes in the discharge. That is, you can size the PSV based on liquid properties (Kd=0.65) right before it starts flashing, then calculate the discharge pressure drop using two-phase methods, which for me means HEM.

I think you are good to go! Good job!

Hi Latexman,

Thanks for your time in reviewing my calculations. I did the PSV sizing with Omega Method too and got the same orifice area.

One thing I assumed in my calculations is the back pressure, which I assumed it to be atmospheric. I should replace the back pressure of 14.7 psia with the calculated back pressure for two phase flow. The mass flux maximized at 29.45 psia( the pressure very close to flash of 28.53 psia). But if the back pressure was say 33 psia then the mass flux I should use for PSV sizing would less than 5954.2 lbm/ft2-sec which would result in a larger required orifice area. I did a calculation using API 521 5.5.10 and getting a result which is not making sense to me. I am getting a back pressure of 37.22 psia. This is not making sense to me because the calculated choke pressure is 26.37 psia which means that the condensate is not flashing within the orifice. Flashing should happen in the orifice or before the orifice correct?. Can I post this question here?. If Yes I can upload the spreadsheet in my next message.

Thanks and Regards,
Pavan Kumar

Sure, you can post that here, and I’ll look at it.

Or after, it depends on BP (and the diameter of discharge line selected).

Personally, I think it will end up flashing right at the PSV nozzle exit and be 2 phase to the pipe exit. Work from the pipe exit (atmospheric) backwards to the PSV discharge flange. If the pressure at the PSV outlet flange < 29.45 psia, then it will flash from 29.45 to the pressure at the PSV outlet flange, That’s reasonable. I’d increase the outlet pipe diameter to make the pressure at the PSV outlet flange < 29.45 as long as it did not get unreasonable.

Is it conventional PSV? If so, dP < 10% of set pressure anyway.

Hi Latexman,

Attached with this message please find the excel spreadsheet with the tab " PSV Outlet DP" which shows the calculation I did for PSV Outlet DP for Flashing flow using the method mentioned in API 521 7th Edition Section 5.5.10. Using this method I am getting a back pressure of 37.22 psia while the choke pressure calculated as part of the calculation is 26.37 psia. So the pressure at PSV outlet pipe inlet is 37.22 psia and pipe exit is 26.37 psia while the pressure outside of the pipe P3 is 14.7 psia. As per PSV Sizing using Direct Integration method the mass flux, “G” to be used for orifice area calculation is the one at the pressure where the mass flux is maximum for at the back pressure which ever pressure is greater. If the calculated back pressure of 37.22 psia is correct then the condensate will flash in the outlet pipe and not in the PSV nozzle. The PSV is balanced bellows type.

The problem is with the API 521 5.5.10 method as the calculation is heavily dependent on the back pressure we assume as the initial value for the reference pressure required by the calculation. I used a value of 30% of PSV set pressure as my PSV is a balanced bellows type. I repeated the calculation by taking the reference pressure as 50% of PSV pressure I get different outlet DP. I tried repeating the calculation with reference pressure as 10% of PSV set pressure then I could not converge the equation. This inaccuracy is the actual cause of my concern. The results are summarized as below:

#        Reference Pressure     P1                     P2                    
                    (psig)                  (psia)               (psia )         
1                   21.75                 37.22               26.37        
2                   36.25                 33.67               14.7           
3                   7.25                   Could not converge

I have been struggling with this problem for quite some time. Your help in resolving this issue will be a great help to me.

Thanks and Regards,
Pavan Kumar

PSV Outlet Pressure Drop Calculation.xlsx (91.2 KB)

I’ve been spoiled being in a megacorp. Our triple PhD’s codified the HEM for us BS guys. So, I’m really not familiar with the manual API 521 method, since I have a HEM program. Unfortunately, I’m at our FL condo and my laptop is at the office in NC. I’ll be back in the office Nov. 22 and will look at it then.

Here’s something to noodle on. In our HEM program we do not include an exit loss. They tell us not to. When I read the API method I see no mention of that, so . . . maybe that needs to be researched.

It seems at the rated flow there needs to be enough back pressure to keep the flow one phase through 4” pipe and fittings. Thus the 10% BP calc did not converge.

Btw, what is the elevation difference between the PSV outlet flange and the end of the tailpipe?

Hi Latexman, the elevation difference is 34.5 ft.



Are you designing for a certain sizing flow, or are you evaluating an existing 3J4 PSV to see what it will do? (I suspect the latter is the case.)

Hi Latexman,

I am validating the existing PSV by re-analyzing the overpressure scenarios.
The existing PSV is 3L4 but as per my calculations I find a 3J4 orifice is sufficient. We do not need an oversized PSV.

As per my study the closed liquid outlets and Failure of Liquid Level control valve + By pass valve are the two applicable scenarios. Both these scenarios lead to two phase relief and the Control valve failure scenario is the sizing case. The fluid is subcooled condensate at PSV inlet but two phase in the PSV outlet. I need to evaluate if the fluid is flashing across the orifice or in the downstream outlet line which is were I am stuck right now and need help. I will try and alternate method based on the paper “Discharge of Two Phase Flashing Flow in a Horizontal Duct” - JC Leung & MA Grolmes as attached at the earliest and check the result against the API 521 Section 5.5.10 method.Discharge of Two Phase Flashing Flow in a Horizontal Duct - JC Leung & MA Grolmes.pdf unless you have some better suggestions. (258.1 KB)

Thanks and Regards,
Pavan Kumar

What’s the sizing case flow rate? 124,525 lb/hr? Knowing this will help once I’m back in the office next week.

The basis for my HEM program is:

  1. Simpson, L. L., Chem. Eng., pp 98-102, Aug. (1991).
  2. Simpson, L. L., Navigating the Two-Phase Maze, “Proc. of International
    Symposium on Runaway Reations and Pressure Relief Design,” G. A. Melhem and H. G. Fisher eds., AIChE/DIERS, New York (1995).

Hi Latexman,

The required relief rate for the sizing case ( Control Valve scenario ) is 119362 lb/hr. The mass flux assuming there is no back pressure is Gmax=5954.2 lbm/ft2-sec. With 3J4 orifice the rated capacity is 124525 lb/hr. But this will be different if the back pressure is more than the pressure of 29.45 psia which is the pressure at which the mass flux maximized. Once I determine the back pressure I will re-evaluate the mass flux and required orifice area which in-turn will lead me to the different rated capacity and different back pressure. After a couple of iterations I will be able to get the correct PSV size.

Thanks and Regards,
Pavan Kumar

Great. I think about the only thing missing is a characterization of the inlet pipe and fitting to evaluate the inlet pressure drop. What’s the diameter (3" Sch. 40?), length, and fittings in the inlet line. My program will evaluate that too.

Hi Latexman,

The inlet pipe is 3" Sch 40 with a length of just 2’10" with no fittings except for the sharp edged pipe entrance. I evaluated the inlet pressure loss using Darcy Equation as the condensate is subcooled water at the PSV inlet and got a DP = 0.4 psi which is 0.55% of PSV set pressure of 72.5 psig. It will be great if you can verify all the calculations with your software, especially the outlet DP.

Thanks and Regards,
Pavan Kumar

Okay, sounds good. My plan next week is to run my PSV program, which detects 2-phase transitions and gives warnings, but does no 2-phase dP calculations, and, then, run my HEM program on two separate components, the PSV nozzle and the outlet pipe/fittings. Depending on what happens between the PSV nozzle and the tailpipe, I’ll converge between them, and let you know what I find. This shouldn’t take too long; the programs crunch most of the numbers. I just have to characterize the water properties at 2 or 3 data states (probably 3 with subcooled liquid) so the HEM program can interpolate while it is integrating. So a little isethalpic steam table work on my part.

That will be great. But are you going to verify the PSV outlet line pressure drop for two phase flashing flow?.

Thanks and Regards,
Pavan Kumar

Yes, yes. That’s what HEM does.

Hi Latexman,

I can send my Excel workbook which I used to analyze my scenarios and the PSV sizing which has all the information that you may need for the calculation. Do you want me to send it?.

Thanks and Regards,
Pavan Kumar

I have the two spreadsheets you uploaded to the site in the thread above. If it’s different from those, please do. If not, no need.