Steam PSV Inlet / Outlet Pressure Drop Calculation Methodology 4

[Pavan Kumar]

Hi All,

I am performing the inlet and outlet pressure drop for a Steam PSV ( sketch attached) set at 72.5 psig and wanted to discuss the methodology of calculating them using adiabatic compressible flow equations. Your inputs shall be valuable to me.

A) Inlet Pressure Drop:

For the inlet pressure drop I will assume the opening pressure of the PSV to be at set pressure plus 10% over pressure(P2) and then back calculate the pressure(P1) in the equipment protected using adiabatic compressible flow equation for the rated capacity of the PSV ( back calculated using the selected orifice area and vendor kd ). The pressure difference P1-P2 is the inlet pressure drop and has to be less than or equal to 3% of the PSV set pressure.

B) Outlet Pressure Drop Calculation:

The PSV vents to atmosphere through a pipe that is 23 ft long. Since the PSV vents to atmosphere the flow will reach critical pressure and since the velocity cannot exceed sonic velocity, critical pressure would achieved at the pipe exit ( P4 ). I then back calculate the pressure the PSV outlet flange(P3) using the adiabatic compressible flow equation. The difference in these pressures that is P3-P4 is the PSV outlet pressure drop and has to be less than 10% of PSV set pressure for conventional PSVs.

Please let me know what you all think.

Thanks and Regards,
Pavan Kumar

 

[Latexman]

The flow is known; it's the rated capacity. The pressure just outside the tailpipe exit is atmospheric pressure. The pressure just inside the tailpipe exit is atmospheric pressure + 1 velocity head (K = 1). The tailpipe velocity cannot exceed Mach 1; some companies limit this further by policy. From previous post with OP = 10%, velocity also is limited by [Δ]P. Select a pipe diameter that satisfies the velocity contraints. Then, work backwards along the 23 feet of pipe and calculate the pressure rise. Check this backpressure at the PSV outlet flange against the OP constraint. If OK, the pressure discontinuity of the shock wave = the critical pressure at the exit of the PSV flow nozzle - the backpressure at the PSV outlet flange.

Good Luck,
Latexman

 

[danschwind]

Latexman,

AFAIK there are some recommendations not to include K=1 to pipe exits for PSV outlet piping discharging freely to atmosphere. I think this is based in some comments made by Hooper or Darby (can't recall) in a paper.

Daniel
Rio de Janeiro - Brazil

 

[Pavan Kumar]

Hi danschwind,

You are correct. Per Darby's book page 194, there is no loss factor associated with a free jet that issues into an unconfined space because the velocity of the fluid exiting the pipe is same as the the velocity of the fluid inside the pipe. If the fluid were to exit into confined space the fluid existing the pipe mixed with the same fluid in the vessel and experiences deceleration and the kinetic energy is dissipated as frictional loss bring the fluid's velocity to zero. Hence a loss factor of K=1 is applied in this case.

Thanks and Regards,
Pavan Kumar

 

[Pavan Kumar]

Hi Latexman,

Thanks for the guidance provided. I will work on it and get back to you with the results. Per your previous post that per your company guideline the PSV exit velocity is restricted to a Mach Number of 0.75. Is that guideline for PSVs venting to atmosphere?. I think for PSVs venting to Flare the PSV exit pipe velocities are limited to 0.4 Mach number.

Thanks and Regards,
Pavan Kumar

 

[Pavan Kumar]

Hi All,

Can anyone share the following paper by J.C Leung if that is good material that I can use excel to complete my calculations. If not kindly suggest a better reference. I need to size the PSV for two phase flashing flow with pressurized condensate at the PSV inlet and flashing flow across the orifice.

"Easily Size Relief Devices and Piping for Two-Phase Flow", Chemical Engineering Progress, December 1996

Thanks and Regards,
Pavan Kumar

 

[The Obturator]

You might want to review the various Leung influenced formulae contained within the Emerson PRV Engineering Handbook which is freely available. In the early days folks writing this were involved also in the DIERS Committee.

*** Per ISO-4126, the generic term 'Safety Valve' is used regardless of application or design ***

*** 'Pressure-relief Valve' is the equivalent ASME/API term ***

 

[Latexman]

AFAIK there are some recommendations not to include K=1 to pipe exits for PSV outlet piping discharging freely to atmosphere. I think this is based in some comments made by Hooper or Darby (can't recall) in a paper.

I have heard debate whether this is true or not, but I have not been convinced yet to abandon the (conservative) K = 1 approach that Crane TP410, "Handbook of Hydraulic Resistance", Perry's ChE Handbook, and my old textbook, McCabe and Smith, recommend.

Now, I do have some software where the exit loss has already been baked into the methodology/calculations. I do exclude the exit loss when using those. They usually have a note saying, exit loss is included; do not include K = 1 for an exit loss.

Good Luck,
Latexman

 

[danschwind]

Yes, I realized I used a word (recommendation) that I did not mean to. I agree there is some debate revolving around that and that your approach is at least the most conservative one (therefore, it guarantees that it will function as expected).

This is a very interesting topic by the way. Wonder if there are any papers with experimental data to indicate what approach should be taken?

Daniel
Rio de Janeiro - Brazil

 

[Latexman]

Per your previous post that per your company guideline the PSV exit velocity is restricted to a Mach Number of 0.75. Is that guideline for PSVs venting to atmosphere?

Yes.

Good Luck,
Latexman

 

[Pavan Kumar]

Hi All,

I am sizing PSV for two phase with subcooled condensate at PSV inlet and flashing across the PSV orifice using Omega Method given in API 520 Part 1 C 2.3. The PSV set pressure is 72.5 psig and relief temperature(T) is 248 Deg F. Per Omega method I need to calculate the specific volume of the fluid ( fluid mixture) at two pressure points.

1. The first pressure (P1) is is PSV inlet pressure which is PSV set pressure + % overpressure +
atmospheric pressure.
2. The second pressure P9 is 90% of the saturation pressure Ps at the relieving temperature T.

The specific volume should be determined at the P1 and P9 by isentropic or isenthalpic flash. My question is on how to perform an isentropic or isenthalpic and determine the specific volume?. I flashed the subcooled water at P1 = 94.45 psia (= 1.1*72.5+14.7) to P9 = 25.93377 psia (= 0.9*Ps = 0.9*28.8153 psia),where Ps= 28.8153 psia the saturation pressure at T=248 Deg F. The specific enthalpies are as given below.

Condition 1:

P1 = 94.45 psia
T1= 248 Deg F
hf1 = 216.517 Btu/lb ( Specific enthalpy )

Condition 2:

P9 = 25.93377 psia
T2= 242.369 Deg F
hf2 = 210.367 Btu/lb ( Specific enthalpy)
hfg = 950.678 Btu/lb ( specific enthalpy of vaporization)

Fraction of Flash F = (hf1 - hf2) / hfg

F = (216.517 - 210.367) / 950.678 = 0.00646 = 0.646 %

That means quality (x) at P9 = 0.00646

Now per Omega method I am supposed to flash the stream isentropically or isenthalpically. From the data you see above the enthalpy has fallen down. If I understand it correctly if I perform a flash between pressure P1 and P9 by keeping the enthalpy same between the subcooled liquid at P1 and the total enthalpy of the liquid and vapor mixture. The ratio of the vapor and liquid mass fractions ( quality ) has to be adjusted till the enthalpies ate same. Is this process correct?.


Thanks and Regards,
Pavan Kumar

 

[PaoloPemi]

The Omega method proposed by Leung adopted a single point (pressure vs volume) to determine a compressibility coefficient ω "found to be a unique function of the stagnation pressure for a given fluid", note that first part of process is isentropic, second part is isenthalpic and one can integrate directly to find the solution,
API adopted two points (p.stagnation and 0.9 * p) to estimate Omega
finally DIERS adopted a Direct Integration method to determine the mass flux through the relief valve which is the method proposed in last versions of API.
You can find several threads discussing the different methods in Eng-Tips forum, you can utilize a thermodynamic library or a process simulator for solving the different flash operations and estimate the required fluid properties,
a EXCEL VBA code for direct integration method is available in this thread

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

etc. etc.

 

[Pavan Kumar]

Hi PaoloPemi,

I don't have a process simulator with me. I can only use the steam tables as my fluid is water. I wanted to know how to calculate the vapor mass fraction and the fluid mixture ( liquid and vapor combines) when the flash is done iso-enthalpically. For the direction integration method too I need to flash isentropically for decreasing pressure intervals of 1 psi. I need a correct way to calculate the mixture density after each isentropic / isenthalpic flash. That is my problem.

Thanks and Regards,
Pavan Kumar

 

[PaoloPemi]

which is the purpose of your work ?
If you wish to learn how it works probably the numerical examples included in standards / books / etc. could help,
differently, if you wish to code a procedure a thermodynamic library (see my previous post) or a process simulator could help by solving the most difficult parts

 

[Pavan Kumar]

Hi PaoloPemi,

The purpose if my questions is to size a PSV that has subcooled water at the PSV inlet ( blocked liquid outlet scenario) and is two phase at the PSV outlet as the outlet pipe is open to atmosphere. I need to size the PSV and calculate the inlet and outlet pressure drop for my project. When you say Thermodynamic library which application are you referring to specifically?.

I shall calculate the PSV sizing using both API Omega method and Direct Integration method but I should be able to calculate the fluid mixture properties after every isentropic or isenthalpic flash. I will try with the steam tables and post the results shortly.


Thanks and Regards,
Pavan Kumar

 

[PaoloPemi]

with sub-cooled liquids HEM model could give conservative results (compared for example with HNE-DS which includes a boiling delay), depending from operating point,
anyway you should be able to solve with the help of steam tables.
Another possibility, as said, could be to use a thermodynamic library (the EXCEL VBA code utilizes Prode Properties) or a process simulator,
both these tools would allow to solve flash operations and estimate fluid properties...