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.