Are You One of 99% Engineers Who Size PSV Fire Case the Wrong Way?

Are you one of 99% engineers who size PSV fire case the wrong way? Sizing PSV fire case seems extremely easy on the surface. You use API 521 to calculate the fire heat input by calculating the wet area, then you get the latent heat from a process simulator, finally you get the reliving mass flow and you follow API 520 to size the PSV area. Sounds easy, right?
The calculation sequence seems easy, but it is actually extremely difficult when you get into the details. Common mistakes of 99% engineers are making:
-Assume constant wet area, which is not true. By the way, the wet area might increase at the beginning
-Assume an inappropriate latent heat. Latent heat is changing through the reliving period
A proper way to size PSV fire case is to use a dynamic process simulator, since the relieving process is dynamic, not steady state. In this example, VMGSim Dynamics is selected to do this demo.
As you see on the PFD, there is one vessel and one PSV. The PSV orifice size is E with a set pressure of 500 psia. The vessel is horizontal with a diameter of 5 ft and a length of 20 ft. Initially it is at 34.5 F and 400 psia, with a liquid level of 60%. Suddenly the vessel is exposed to a fire.
Let us start the simulator and see what's going to happen.
Currently two strip charts are shown. On the vessel strip chart, the black line is the liquid level percentage in the vessel. The blue line is the wet area and the red line is the fire heat input. The liquid level first increases and then drops. The reason is as the vessel gets hotter, the liquid density gets lower and it results a bigger volume in the vessel. The wet area and the heat input is following the same shape of the curve, since they are directly related to liquid level.
The PSV strip chart is a lot more interesting than the vessel strip chart. The black line is the relief valve opening percentage. The blue line is the reliving mass flow. The red line is the reliving pressure and the pink line is the reliving temperature. As expected, the vessel pressure and temperature start to rise. At about 350 seconds, the vessel pressure reaches 500 psia and the relief valve starts to open. At about 900 seconds, the vessel reaches the highest pressure of about 530 psia. At the same time, the PSV reaches the highest opening of 67% and the relief flow reaches the highest of about 6900 lb/hr. After the pressure hits the peak, it starts to decline as expected. At the same time, the relief valve opening and the relief mass flow start to decline as well.
Very surprisingly at about 2400 seconds, the relief valves starts to open more and the relief flow is getting larger as well!!! The liquid level drops, thus the fire heat input drops as well. How come the relief mass flow is getting larger? The reason is the latent heat of the fluid is getting smaller and smaller. Even with smaller heat input, the relieving mass flow still gets larger, despite smaller heat input.
At about 4000 seconds, the relief flow arrives at another peak. This is where 99% engineers might get trouble. In some cases, the relief flow at the second peak is even larger than the first peak. The reason? It is because the latent heat is getting smaller.
At about 5200 seconds, the vessel has nearly 0% liquid, thus the vessel pressure drops very quickly while the temperature remain fairly the same.
After running about 7000 seconds, the vessel pressure is at about 500 psia, which is the PSV set pressure.
Since the highest vessel pressure is only about 530 psia, the vessel is protected by this PSV.
Thanks very much for watching this video. It is brought to you by Guofu Chen. More interesting topics can be found at showcase.GuofuChen.com

[@chrisdrouganis4609]

It is incorrect to say 99% of engineers size the fire case incorrectly. API 520/521 shows that you can make a steady state approximation, the 'Normal' AND CORRECT way to size a fire you could say. Then it goes on to say that you can use a dynamic simulation. Obviously that is preferable but it is not always what you are looking for.

[@donharrold1375]

The simulation actually demonstrates that for this particular situation that the approximation in the API code is reasonably valid. The biggest area of uncertainty in this type of analysis is not usually the sophistication of the analysis method. It is the estimation of the heat flux applied to the vessel in the first place. The way in which fire events occur is extremely complex and the flux values in the various codes are approximate. Applying a sophisticated dynamic simulation might improve insight into the physics taking place within the vessel and is certainly intellectually satisfying, but given the underlying uncertainties it might not produce a more valid or reliable sizing.

[@anumqassam2963]

Are you modelling the heat flux with Stefan Boltzmann or API heat flux? If you are using the API heat flux equation, many people would argue that the wetted area should be based on the initial wetted area -- it should not change. This would be because the API heat flux equation is empirically based -- and the heat flux equation was based on the initial wetted area of the vessel's which were being tested. My only point is that all people watching this video should confirm what their own company guidelines are.

[@karlbilodeau8624]

Thanks, I learned something today :).
But as we saw on the curves, can we say that the method from API 521 is valid? You showed us that the maximum flow to be relieved will be at the first opening of the PSV. At this time, the latent heat is know, and the only exception is the very little expansion of the liquid that increase the heat input from the fire.

[@GuofuChen100]

+Karl Bilodeau It is true for this case. But it is not always true. The relief flow can get larger in some instances.

[@Soumo_b]

We know fire case Relieving pressure = 1.21 x set pr in gauge = 1.21 x( 500-14.7) = 587.2 psig = 601 psia, but here we do not see the pressure rising to relieving pressure.

[@Soumo_b]

What is the relieiving temperature you consider.

[@brian332]

You did not provide a reason as to why the liquid level rises in the first instance; I am curious of the reason why. Characteristically, the liquid level should drop as it begins to vaporise from the heat input from fire exposure. However, a rise of upto 2% in level seems a lot given the industrial vessel inventories are pretty large.

[@MS-be9wv]

That is due to liquid expansion which causes level rising before vaporisation commences