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# PSV Outlet Line Pressure Drop for Two Phase Flow

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## PSV Outlet Line Pressure Drop for Two Phase Flow

(OP)
Hi All,

The PSV that I am sizing has subcooled liquid at the PSV inlet and flashes at the PSV orifice. I referred to the guideline in API 521 5.5.10 to calculate the pressure drop in the PSV outlet line for two phase flow. The procedure is for a single line size that is horizontal. In my case the line size is 4" and is NOT horizontal. The line is 45.9 ft long with that ends up 34.5 ft below the PSV outlet flange at the grade. Now I want to know if I can still use API 521 Sec 5.5.10 or is there another guideline that I can use. Kindly suggest. There are some papers which talk about DIERS methodology but is that one applicable for non-horizontal flow?. If yes could anyone of you provide a copy of the document if it is not copyrighted.

I finished PSV sizing per API 520 Part 1 C2.3 assuming a back pressure of 10 psig ( PSV set pressure = 72.5 psig), but now I need to replace this number with the correct back pressure.

Thanks and Regards,
Pavan Kumar

### RE: PSV Outlet Line Pressure Drop for Two Phase Flow

for additional details about the correlation proposed in API 5.5.10 you may refer to the paper "The Discharge of Two-phase Flashing Flow in a Horizontal Duct" by Leung and Grolmes
as alternative you may consider the method based on HEM approach discussed in Emergency Relief System Design Using DIERS Technology (DIERS Project manual),
DIERS manual includes reports comparing HEM with Lockhart-Martinelli Slip and other methods, HEM gives conservative results but is quite a standard.
Take care to verify the limit due to sound velocity (critical mass flux), I utilize the method StrMSS() in Prode Properties which returns the sound velocity for vapor, liquid and (vapor+liquid) calculated with HEM method and selected thermodynamic model but any equivalent rigorous procedure should be ok.

### RE: PSV Outlet Line Pressure Drop for Two Phase Flow

(OP)
Hi PaoloPemi,

Would it possible to share the relevant pages of the DIERS manual in this thread. Also is the DIERS method applicable to NON-HORIZONTAL pipeline flow?. Besides is Prode Properties a freely downloadable software?.

Thanks and Regards,
Pavan Kumar

### RE: PSV Outlet Line Pressure Drop for Two Phase Flow

if I remember correctly they proposed different versions, the oldest being quite simple.
The homogeneous model treats the two-phase mixture as a single fluid at phase equilibrium (no slip).
The (homogeneous) volume is defined as vm = X*vg + (1-X)*vl where X is the weight-flow fraction for vapor
The two-phase frictional pressure drop is calculated (for each segment) from the Fanning Equation
dP/dL = 2*f*G*G*vm/D
where
f is the Fanning friction factor
G is based on the total mass flow (liquid plus vapor)
D is the actual pipe i.d

given P1 (inlet) you can integrate (forward) from P1 to P2 or backward, in principle you can apply the method to non-horizontal pipes (including dH).
I can't share the pages from my paper copy of the manual but you should be able to find some examples in the net.
Finally, yes there is a free version of Prode Properties for students and non commercial applications (note that it has a limited database of fluids)

### RE: PSV Outlet Line Pressure Drop for Two Phase Flow

The proper selection of 2-phase methods for horizontal, vertical up flow, and vertical down flow is quite time consuming. There's even some correlations for the vapor and liquid being co-current and countercurrent flow. I have used HEM for everything for past 20-ish years. It is conservative, but not overly conservative, IMO. It sure does simplify the tasks. It's also RAGAGEP in the relief sizing field.

Good Luck,
Latexman

### RE: PSV Outlet Line Pressure Drop for Two Phase Flow

(OP)
Thank you PaoloPemi and Latexman.

Thanks and Regards,
Pavan Kumar

### RE: PSV Outlet Line Pressure Drop for Two Phase Flow

(OP)
Hi PaoloPemi and Latexman,

If I can't get hold of DIERS' equations for calculating the two phase PSV outlet line pressure drop then can I use the API 521 Sec 5.5.10 and still be reasonable. I was able to get this paper ( attached), from the internet, which mentions the DIERS's equations but that is all.

Thanks and Regards,
Pavan Kumar

### RE: PSV Outlet Line Pressure Drop for Two Phase Flow

as far as I know API formulation adopts an approximate analytical approach based on isenthalpic approximation and omega one parameter equation (see Leung papers for details),
as alternative you can adopt numerical integration (solving many small steps) with the formulations in my previous post.
An advantage of numerical integration is that you can include your preferred methods to estimate dP ,
nowadays with the help of process simulators or thermodynamic libraries you can solve quickly all the basic steps required by these procedures,
you can compare Omega method with Direct Integration in API Sizing for Two-phase Liquid/Vapor Relief to see the difference
(the VBA code in previous thread adopts the Direct Integration of the Isentropic Nozzle Flow procedure discussed in API)

### RE: PSV Outlet Line Pressure Drop for Two Phase Flow

Try for these:

Simpson, L. L., “Estimate Two-Phase Flow in Safety Devices” Chem. Eng., 98 (8), pp. 98–102 (Aug. 1991).

Simpson, L. L., “Navigating the Two-Phase Maze” in International Symposium on Runaway Reactions and Pressure Relief Design, G. A. Melham and H. G. Fisher, eds., Design Institute for Emergency Relief Systems (DIERS), AIChE, New York, meeting held in Boston, MA, pp. 394–417 (Aug. 2–4 1995).

Good Luck,
Latexman

### RE: PSV Outlet Line Pressure Drop for Two Phase Flow

(OP)
Hi pierreick,

I had downloaded the paper you suggested earlier and read it. I wanted to confirm if the equations for the HEM method mentioned in the paper match with the equations that PaoloPemi and Latexman have used for calculating two phase pressure drop. I thought it would be better to get confirmation. If I can't then I will stick with the API 521 Sec 5.5.10 method.

Thanks and Regards,
Pavan Kumar

### RE: PSV Outlet Line Pressure Drop for Two Phase Flow

the method in API 5.5.10 is based on the (simplified) omega formulation, these formulations dates back to 1980 when not many computer codes were available (see attached paper)
In recent editions API suggests a procedure based on numerical integration for nozzles (see my previous post with the link to VBA code which adopts Prode for solving flash operations), probably they'll include the equivalent for piping in next editions.
if you wish to follow DIERS procedure I would suggest to purchase the Emergency Relief System Design Using DIERS... the DIERS Manual, mainly because there are several details to consider, for example reducers etc. anyway, they propose a method similar to that mentioned in my previous post
"the approach favored in the DIERS work is to integrate back up the duct from a trial value of assumed pressure at the end of the duct... More steps are required for slip flow..."

Hoping this helps,

Paolo

### RE: PSV Outlet Line Pressure Drop for Two Phase Flow

(OP)
Hi PaoloPemi and Latexman,

I have a question regarding how to correctly perform isenthalpic flashing. As per API 5.5.10 for PSV outlet line pressure drop calculation the first step is detailed as follows:

1. Assume back pressure of the PSV as 10%, 30% of 50 % as the back pressure(PB) depending on the type of the PSV. Consider this pressure as the reference pressure PR. In my case the the PSV is a balanced bellows type so I took PR=PB=0.30*Pset, where Pset is the set pressure of the PSV

Perform isenthalpic flash from relieving pressure P1 to PR. Estimate the two phase mixture density as ρR

in my case Pset = 72.5 psig
so PR=PB = 0.30*72.5 = 21.75 psig = 36.45 psia

As per Step 1 : I need to flash from P1 = 94.45 psia (=1.1*72.5+14.7) to PR = 36.45 psia

The following is the flash data:

Condition 1:

Pressure = P1 = 94.45 psia
Temperature = T1 = 248 Deg F
Fluid Condition = Subcooled Liquid
Specific Enthalpy of liquid (hf1) = 216.517 Btu /lb

Condition 2 :

Pressure = PR = 36.45 psia
Saturation Temperature TR = 261.652 Deg F
Fluid Condition = Two Phase
Specific Enthalpy of Saturated liquid ( hf9) = 230.254 Btu/lb
Specific enthalpy of vaporization ( hfg) = 937.511 Btu/lb
Specific Enthalpy of Saturated Vapor(hg) = 1167.76 Btu/lb

If you observe the specific enthalpy subcooled liquid hf1(=216.517 Btu/lb) at condition 1 and specific enthalpy of saturated liquid at condition 2, hf9(=230.254 Btu/lb) . hf9 is greater than hf1 which is my question as to how is it possible and how to perform isenthalpic flash using Steam Tables and Mollier Diagram to determine the density and quality at Condition 2.
I don't have access to Process simulator like Aspen or Hysys nor do I have access to Prode properties.

Thanks and Regards,
Pavan Kumar

### RE: PSV Outlet Line Pressure Drop for Two Phase Flow

@ 248oF you will not get flashing until less than 29 psia.

Good Luck,
Latexman

### RE: PSV Outlet Line Pressure Drop for Two Phase Flow

(OP)
Hi Latexman,

So the fluid will remain subcooled liquid at PR=36.45 psia, so the temperature will still be 248 Deg F.
The fluid will not flash until the pressure drops to below 29 psia. Thanks for pointing it out as I was too focused to see a flash and I missed this out.

Thanks and Regards,
Pavan Kumar

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