Relieving temperature PSV

[Dulli2000]

There are some older threads about this, but I did not find answer to my question:
For gas relief, by the way.
In adiabatic processes we use T1/p1=Tn/pn (as also API521 says). I calculated a backpressure of 1,37 bara at PSV discharge and have relieving pressure of 7bara (121% set-pressure). Upstream PSV we have saturated conditions so that I get the corresponding temperature from the saturation curve which is 287K. The calculated relieving temperature seems way off in my eyes. Do I use the right variables here for the relieving temperature?
Am I right when we talk about relieving temperature is on the discharge side of the PSV at relieving pressure equal to backpressure?

 

[pierreick]

The relieving temperature for a pressure safety valve (PSV) is the temperature of the fluid at the time the valve is expected to open due to an overpressure event.

Pierre

 

[goutam_freelance]

Assuming you want the temperature at the outlet of PSV, where the pressure is 1.37 bar(a). The process is adiabatic(isenthalpic). Using the steam table software in Excel, the required temperature at the exit of PSV is 144.5 deg C.

 

[shvet]

relieving T&P&composition are referenced to PSV upstream conditions when a PSV's seat is in an open position

API 520-1-2020
3.1.49 relieving conditions
The inlet pressure and temperature on a pressure-relief device during an overpressure condition. The relieving pressure is equal to the valve set pressure (or rupture disk burst pressure) plus the overpressure. ...

 

[Latexman]

Assuming you want the temperature at the outlet of PSV, where the pressure is 1.37 bar(a). The process is adiabatic(isenthalpic). Using the steam table software in Excel, the required temperature at the exit of PSV is 144.5 deg C.

I don’t think the OP’s fluid is steam. I assume relieving conditions = 7 bar_a and 287 K (14 C).

OP, does the 287 K correspond to 7 bar_a?

 

[goutam_freelance]

Upstream PSV we have saturated conditions s

@Latexman , I thought he is using steam.

 

[Snickster]

In adiabatic processes we use T1/p1=Tn/pn (as also API521 says).

The above equation is based on a totally gas filled constant volume vessel (no liquid) operating at a given pressure and temperature with a fixed mass and composition. In this case when heat is added from external fire the pressure and temperature increase follows the ideal gas equation P2/P1=T2/T1. This is not an adiabatic process as heat is added to the gas in the vessel. Note that this equation only applies to vessels without any liquid inventory - only gas.

I calculated a backpressure of 1,37 bara at PSV discharge and have relieving pressure of 7bara (121% set-pressure). Upstream PSV we have saturated conditions so that I get the corresponding temperature from the saturation curve which is 287K.

For a partially liquid filled vessel with vapor space, the relieving temperature WILL correspond to the saturation vapor pressure of the liquid at relieving pressure P1. With heat input to the vessel the liquid will vaporize to gas at a temperature corresponding to the pressure in the vapor space. As vaporization occurs the pressure keeps rising in the vapor space, and so does the saturation temperature, until relieving pressure is reach at which time the temperature of vaporization equals the saturation vapor pressure of the liquid phase at P1.

The calculated relieving temperature seems way off in my eyes. Do I use the right variables here for the relieving temperature?

As discussed there are two different cased above - one with a totally gas filled vessel and one with partially liquid filled vessel with vapor space.

Am I right when we talk about relieving temperature is on the discharge side of the PSV at relieving pressure equal to backpressure?

No - relieving pressure refers to pressure on inlet of relief valve.

 

[Dulli2000]

Thank you all for very helpful replies.
Right, it is not steam, I am sizing for a vessel filled with liquid NH3 with vapour cushion. It is a very unlikely scenario to get the vessel emptied completely of liquid so that only gas is left. It is more likely that the vessel is filled to 95% for a while. Is there a definition where partially filled stops and completly filled begins?

@Snickster:
1) During evaporation under fire case liquid goes to gas phase. In case of low liquid level in vessel in fire-case, is it still the same scenario if relieving pressure is not reached before all liquid has been evaporated? I am just wondering if this could happen.

2) Also or scenario of partially filled with liquid, is it correct then that the process is still isenthalpic?
For downstream line sizing I need pressure and temperature at PSV outlet in order to get the right density. As written before, I calculated the backpressure at PSV outlet at 1,37bara which is in my eyes equal to PSV outlet pressure. Expansion leads to temperature changes per Joule Thomson effect. But do you still assume saturation? This would simply lead to -27C at PSV outlet.

 

[goutam_freelance]

@Dulli2000

Thank you for letting the cat out at last!

1. If your PSV set pressure is above the saturation vapor pressure at the particular temperature inside the vessel, it is possible that relieving pressure will not be reached just when all the liquid has vaporized. Pressure will increase subsequently on continued heating till the set pressure is reached.

2.

scenario of partially filled with liquid, is it correct then that the process is still isenthalpic?

If the expansion happens after the PSV, i.e., without heat input, the process is isenthalpic. It is difficult calculate the combined effect of Joule-Thompson effect along with the pressure drop etc. So use of a database like Peace software is
helpful.

https://www.peacesoftware.de/einigewerte/calc_nh3.php7
Using the above and assuming 7 bara inlet (saturated) and 1.37 bar a outlet the outlet temp is -6 deg C.

 

[Dulli2000]

I know the peacesoftware, but I do not figure out how to use it for isenthalpic processes. I get the same temperature (around -6C) from the pH diagram, though. If thats the way its fie. Thanks a lot.

 

[Snickster]

1. I agree with goutam. It has been a while since I did a fire calculation but I believe the worse case for relieving requirements is if the vessel was partially filled with liquid as this configuration absorbs the most heat per API 521. Per API 521 a vessel with all gas absorbs relatively small amount of heat. If there is a very little amount of liquid it is possible that all the liquid will vaporize before the relief valve pops. You should be able to calculate approximately if this will occur knowing the mass of original liquid and the mass of gas required to fill the vapor space to reach a certain pressure and temperature using the ideal gas equation. If you do both calculations for partially filled vessel and a totally gas vessel then use the highest orifice area calculated.

2. Also or scenario of partially filled with liquid, is it correct then that the process is still isenthalpic?
For downstream line sizing I need pressure and temperature at PSV outlet in order to get the right density. As written before, I calculated the backpressure at PSV outlet at 1,37bara which is in my eyes equal to PSV outlet pressure. Expansion leads to temperature changes per Joule Thomson effect. But do you still assume saturation? This would simply lead to -27C at PSV outlet.

Partially filled or not, the process is not isenthalpic. Heat is added in both cases that raise the temperature. As a partially filled vessel vaporized it does at a constant temperature given for a given pressure in the vapor space. However due to vaporization the pressure in the vapor space keeps increasing and so does the temperature at which the liquid vaporizes. Therefore at relief the pressure is at the corresponding vapor/saturation temperature of the liquid assuming there is liquid left in the vessel upon relief. If all the liquid vaporizes and still the relief pressure has not been reached then then from that point on the temperature will increase in accordance with the ideal gas equation, not per the vapor pressure of the liquid as there is no more liquid.

For a gas filled vessel the heat added causes an increase in temperature in accordance with the ideal gas equation PV = mRT considering volume of tank and mass contained is constant. In reality there is a combination of the two types of heat transfer it just that API considers the worse case is if you have a partially filled vessel and you design for such a case using the partially filled vessel wetted surface equations.

I don't think you can calculate the actual true resulting temperature as it is really a combination of heat transfer to liquid evaporating plus heat transfer to any gas vapor space even though the calculation for a partially filled vessel ignores any heat transfer directly to the gas vapor space above. I think if you have conditions of a very partially filled vessel you just need to do both calcs and see which one gives you the highest relief valve flowrate and temperature and use that in you discharge pressure drop calculations. The higher the temperature will give you the highest velocity and pressure drop in your discharge pipe.

 

[goutam_freelance]

I do not figure out how to use it for isenthalpic processes.

First, you calculate the enthalpy at 7 bara saturated. Then do iterations to match the enthalpy at 1.37 bara by successively changing the temperature and getting the enthalpy from the software.

 

[Snickster]

Oh you mean the temperature of the discharge considering a constant enthalpy expansion across the relief valve?

Ideally the temperature upstream of the relief valve equals the temperature downstream of the relief valve adjusted for the Joule Tompson Effect cooling, and for increase in velocity such that an increase in velocity kinetic energy causes a equivalent decrease in enthalpy in accordance with the equation:

dH = dKE

Cp (T1-T2) = (V2^2 - V1^2)/(2g(778))

Rearranging:

To = T1 = T2 + V2^2/(2g(Cp)(778))

or T2 = T1 - V2^2/(2g(Cp)(778))

Where T1 is upstream temperature assuming low enough that can be considered the stagnation temperature To, and T2 is downstream temperature, Deg R
Cp is specific heat BTU/lb deg R
V = velocity ft/sec
g is gravity constant 32.2 ft/sec^2
778 = conversion factor from BTU to Ft-Lb

Note that ideally the minimum downstream temperature occurs if/when the velocity in the downstream pipe reaches sonic where:

T2 = (2/k+1)To Temperature at sonic velocity based on the stagnation temperature

So if you have an upstream fire relief temperature corrected for the Joule Tompson Effect in accordance with the lower pressure of the discharge say to 1000 deg F (1460 deg R) and a ratio of specific heats k = 1.4 of the vapor, then the minimum temperature possible in the downstream piping will be:

2/2.4 (1460) = 1216 deg R = 756 deg F.

Therefore the outlet temperature will range between 1000 F for lower subsonic velocity and 756 F for velocities closer to sonic.

If you are doing a pressure drop using the constant temperature gas equation then choose which temperature to use above based on the approximated velocity you actually have in the pipe or worse case is you just choose the higher temperature to be conservative.

See following recent post on PSV relief calculations:

Thread 'PSV Inlet and Outlet Pressure Drop Calculation Question'

Jun 9, 2025

Hi All,

I sized a PSV downstream of a Control Valve for its wide-open failure case and got a 6"Q8" PSV. The required relief rate is 254107 lb/hr with Oxygen as the fluid. The rated capacity of the PSV is 294,851 lb/hr with 10% overpressure. I tried to size the inlet/outlet lines to this PSV. The PSV inlet line is 2 ft long and the outlet pipe is 4 ft long with an elbow. The PSV is to be installed on the 6" line downstream of the control valve with option to move it to the 12" line.


View attachment 10578

My questions:

1. The PSV Inlet pressure drop should be calculated from the source of...

• Pavan Kumar
• Replies: 29
• Forum: Safety Relief Valve engineering (PSV)

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