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# PSV Sizing for Two Phase Flashing Flow using Direct Integration Method

## PSV Sizing for Two Phase Flashing Flow using Direct Integration Method

(OP)
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 2.1.1.3. 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.

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.

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
.
.
. 

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

### RE: PSV Sizing for Two Phase Flashing Flow using Direct Integration Method

Hi,
Sounds good to me!
Pierre

### RE: PSV Sizing for Two Phase Flashing Flow using Direct Integration Method

Hi Pavan ,
This link is an alternative to the HDMI method :
https://www.hydrocarbonprocessing.com/magazine/202...
note : People love to comment in this forum, not much to review or share documents!

Pierre

### RE: PSV Sizing for Two Phase Flashing Flow using Direct Integration Method

(OP)
Hi pierreick,

Thank you so much for sharing so many documents. I very grateful to you for sharing the documents which are difficult to get. I will read Leung's paper this weekend.

Thanks and Regards,
Pavan Kumar

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