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# Steam PSV Inlet / Outlet Pressure Drop Calculation Methodology4

## Steam PSV Inlet / Outlet Pressure Drop Calculation Methodology

(OP)
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

### RE: Steam PSV Inlet / Outlet Pressure Drop Calculation Methodology

If I may.

A) Inlet Pressure Drop:

For the inlet pressure drop I will assume the opening sizing pressure of the PSV to be at set pressure plus 10% over pressure(P2) and then . . .

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 ).

You should noodle on the above some more.

Critical pressure/sonic velocity will exist at the exit of the PSV’s flow nozzle. There will probably be a shock wave with a pressure discontinuity between the critical pressure at the PSV flow nozzle exit and the back pressure at the PSV outlet flange. The pipe exit will most definitely NOT be at the critical pressure ratio of the sizing pressure.

Good Luck,
Latexman

### RE: Steam PSV Inlet / Outlet Pressure Drop Calculation Methodology

Comment regarding the statement that the inlet pressure loss "has to be less than or equal to 3%.."
- Understand that the 3% rule is not a sufficiently reliable predictor of instability/chatter. Refer to the discussion on this API 520 Pt II.

Comment regarding the statement that the PSV outlet pressure drop "has to be less than 10%.." for conventional PSVs.
- This statement is only true when the PSV is set at the MAWP and the allowable accumulation is 10%. A better (more generalized) statement is to say that the outlet pressure loss for conventional PSVs is limited to the amount of overpressure. That is, if the overpressure is 10%, then the outlet piping loss is limited to 10%. If the overpressure is 50%, then the limit is 50%. Etc.

### RE: Steam PSV Inlet / Outlet Pressure Drop Calculation Methodology

(OP)
Hi Don,

1. For the inlet pressure drop even with pressure within 3% of the set pressure chatter / PSV instability is still cannot be ruled out?.

2. The MAWP of the equipment protected is 210 psig while the set pressure is 72.5 psig. With allowable accumulation as 10% which means the maximum pressure the vessel can see is 1.1*210 = 231 psig. With this as the basis the % overpressure would be (231-72.5)*100/72.5 =218.6%. So you are saying the allowable outlet pressure drop is 218.6% of set pressure?.

Thanks and Regards,
Pavan Kumar

### RE: Steam PSV Inlet / Outlet Pressure Drop Calculation Methodology

(OP)
Hi Latexman,

How do I calculate the pressure at Pipe exit if it is not same as critical pressure ( calculated from PSV sizing pressure)?.

Thanks and Regards,
Pavan Kumar

### RE: Steam PSV Inlet / Outlet Pressure Drop Calculation Methodology

(OP)
Hi All,

Can anyone provide literature that I can use to calculate pressure drop for two phase flashing flow for Condensate flashing out at the PSV orifice in the outlet line?. Your help will be highly invaluable to me.

Thanks and Regards,
Pavan Kumar

### RE: Steam PSV Inlet / Outlet Pressure Drop Calculation Methodology

You might want to review the notes and guidance for steam safety valve piping contained in ASME B31.1 - 2020 Particularly Nonmandatory Appendix II - Rules for the Design of Safety Valve Installation. Although B31.1 is primarily a Piping Code for Power Piping, this Appendix is specific to Safety Valves and contains various formulae for piping, including outlet positions. If your steam safety valve is following ASME I, this is recommended, even for ASME VIII, but you have not stated what your application is or to what code your re working to.

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

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

### RE: Steam PSV Inlet / Outlet Pressure Drop Calculation Methodology

(OP)
Hi The Obturator,

The PSV is protecting the shell side of a kettle type reboiler which is generating 10 psig steam for process use using the LP steam in the tube side ( please see sketch attached ). The code of construction of the heat exchanger is ASME Sec VIII Div 1, so the PSV will have to sized per ASME Sec VIII Div 1 rules correct?.

Thanks and Regards,
Pavan Kumar

### RE: Steam PSV Inlet / Outlet Pressure Drop Calculation Methodology

For the exit loss, I use K = 1.

If exit velocity is > Mach 1, use a larger diameter pipe. (My company guidelines are "maximum discharge velocity should not exceed 75% of sonic velocity". Your company may be different.)

If ΔPoutlet > 10% (or > the overpressure), use a larger diameter pipe.

Good Luck,
Latexman

### RE: Steam PSV Inlet / Outlet Pressure Drop Calculation Methodology

#### Quote (Pavan)

1. For the inlet pressure drop even with pressure within 3% of the set pressure chatter / PSV instability is still cannot be ruled out?.

An inlet loss of 3% or less does not rule out the risk of instability. Research has shown, for example, that a PSV with an inlet loss of 2% may chatter, while one with an inlet loss of 7% may not chatter. The 3% rule is technically insufficient for predicting instability. Again, refer to the explanation and guidance in API 520 Pt II.

#### Quote (Pavan)

With this as the basis the % overpressure would be (231-72.5)*100/72.5 =218.6%. So you are saying the allowable outlet pressure drop is 218.6% of set pressure?.

Yes, that's exactly what I'm saying. The 218.6 % outlet loss is offset by 218.6% of overpressure. The force balance on the PSV seat is exactly the same as that for a PSV which has 10% overpressure and 10% outlet pipe loss. Engineers commonly cite a 10% limit for outlet piping loss, and that is the limit for typical cases (PSV set at MAWP and 10% allowable accumulation), but it's not an accurate way to state the limit for all cases. Saying that the outlet piping loss is limited to the amount of overpressure is the universally accurate way to state this limit.

### RE: Steam PSV Inlet / Outlet Pressure Drop Calculation Methodology

#### Quote (Pavan Kumar)

Can anyone provide literature that I can use to calculate pressure drop for two phase flashing flow for Condensate flashing out at the PSV orifice in the outlet line?. Your help will be highly invaluable to me.

Yes. Reference API 520, Part I, Appendix C.2.3 "Sizing for Subcooled Liquid at the Pressure-relief Valve Inlet Using the Omega Method"

This section is applicable to saturated liquids as well, and is designed for evaluated PSV capacity when flashing occurs either just upstream or downstream of the throat of the PSV nozzle. The caveat is that the fluid entering the PSV MUST be all liquid.

#### Quote (Pavan Kumar)

With this as the basis the % overpressure would be (231-72.5)*100/72.5 =218.6%. So you are saying the allowable outlet pressure drop is 218.6% of set pressure?.

Yes. See API 520 Part I 5.2.2.1.3. In a conventional PRV application, the allowable built-up backpressure is equal to the allowable overpressure

Just be aware of the reduction in PSV certified flow capacity with increasing backpressure.

### RE: Steam PSV Inlet / Outlet Pressure Drop Calculation Methodology

(OP)
Hi TiCl4,

API 520 Part 1 provides for the Two phase PSV sizing per Omega method you mentioned. I understood that. I need methodology to calculate PSV outlet pressure drop for flashing flow of condensate in the PSV outlet line. For the inlet side the condensate is subcooled or pressurized liquid so incompressible flow equations are applicable. The fluid is two phase in the outlet side as the saturated condensate at 79.5 psig at 120 Deg C flashes to atmospheric pressure in the outlet line. I have seen literature to calculate pressure drop for two phase flow ( gas-liquid flow) when the gas is different component than the liquid. I do not have Aspen with me to calculate and need to use equations. Any help would be highly invaluable.

Thanks and Regards,
Pavan Kumar

### RE: Steam PSV Inlet / Outlet Pressure Drop Calculation Methodology

Pavan,

Take a look at API 521 5.5.10.

Daniel
Rio de Janeiro - Brazil

### RE: Steam PSV Inlet / Outlet Pressure Drop Calculation Methodology

(OP)
Hi Latexman,

#### Quote (Latexman)

If exit velocity is > Mach 1, use a larger diameter pipe. (My company guidelines are "maximum discharge velocity should not exceed 75% of sonic velocity". Your company may be different.)

If ΔPoutlet > 10% (or > the overpressure), use a larger diameter pipe.

The critical pressure ratio for steam at 79.75 psig is 0.53 which means the critical pressure is 0.53*(79.75+14.7) = 50.2 psia = 35.5 psig. Since the atmospheric pressure is less than the critical pressure the velocity of the steam will reach sonic velocity no matter how big the line size is increased to. How do I calculate pressure drop in the PSV outlet line in this case?.

Thanks and Regards,
Pavan Kumar

### RE: Steam PSV Inlet / Outlet Pressure Drop Calculation Methodology

You are still thinking about this wrong. The flow will choke in the PSV flow nozzle. The flow passes through the PSV flow nozzle before the tailpipe, and its a lot smaller in diameter than the PSV tailpipe. You should simulate (Aspen?) the inlet line, PSV flow nozzle, and outlet line as series connected pipes in adiabatic, compressible flow to see what goes on.

If you can't do that for any reason, characterize the inlet pipe and fittings, the PSV, and outlet pipe and fittings, and I'll be glad to run it.

The tailpipe exit will probably be near atmospheric pressure. To be choked at the exit, the backpressure at the PSV outlet flange would need to be about 14.7/0.53 = 27.7 psia or 13 psig. 13/72.5 x 100 = 18% overpressure. That's way more then the 10% allowance, so the tailpipe exit will not be choked on a successful design, and, yes, the tailpipe exit will be at atmospheric pressure + 1 velocity head.

Good Luck,
Latexman

### RE: Steam PSV Inlet / Outlet Pressure Drop Calculation Methodology

(OP)
Hi Latexman,

I don't have Aspen but I have AFT Arrow that can simulate Compressible flow. I will simulate and check.

Thanks and Regards,
Pavan Kumar

### RE: Steam PSV Inlet / Outlet Pressure Drop Calculation Methodology

Latexman, can you explain your statement saying the 18% was more than the 10% allowance? Backpressure allowance is 218% due to the lower-than-MAWP setpoint.

### RE: Steam PSV Inlet / Outlet Pressure Drop Calculation Methodology

TiCl4, yes, I saw that discussion between PK and don, but in the post above mine, PK is using a sizing pressure of 79.25 psig (set pressure + 10% overpressure), so that’s what I used.

Good Luck,
Latexman

### RE: Steam PSV Inlet / Outlet Pressure Drop Calculation Methodology

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 ΔP. 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

### RE: Steam PSV Inlet / Outlet Pressure Drop Calculation Methodology

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

### RE: Steam PSV Inlet / Outlet Pressure Drop Calculation Methodology

(OP)
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

### RE: Steam PSV Inlet / Outlet Pressure Drop Calculation Methodology

(OP)
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

### RE: Steam PSV Inlet / Outlet Pressure Drop Calculation Methodology

(OP)
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

### RE: Steam PSV Inlet / Outlet Pressure Drop Calculation Methodology

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 ***

### RE: Steam PSV Inlet / Outlet Pressure Drop Calculation Methodology

#### Quote (danschwind)

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

### RE: Steam PSV Inlet / Outlet Pressure Drop Calculation Methodology

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

### RE: Steam PSV Inlet / Outlet Pressure Drop Calculation Methodology

#### Quote (Pavan Kumar)

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

### RE: Steam PSV Inlet / Outlet Pressure Drop Calculation Methodology

(OP)
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

### RE: Steam PSV Inlet / Outlet Pressure Drop Calculation Methodology

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

etc. etc.

### RE: Steam PSV Inlet / Outlet Pressure Drop Calculation Methodology

(OP)
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

### RE: Steam PSV Inlet / Outlet Pressure Drop Calculation Methodology

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

### RE: Steam PSV Inlet / Outlet Pressure Drop Calculation Methodology

(OP)
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

### RE: Steam PSV Inlet / Outlet Pressure Drop Calculation Methodology

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...

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