This depends on what is contained in the vessel protected by the PSV. Is it a liquid-full vessel, is it a mixture of liquid and vapor, or the vessel contains gas only?
If this is a liquid-full vessel, hydraulic expansion will be instantaneous and you won't see any significant temperature change before the PSV pops open. Liquids are incompressible (speaking in practical terms). If you expose such vessel to a fire, liquid will essentially expand at its operating temperature and this will be the relieving temperature at the same time.
If this is a vapor-liquid containing vessel, addition of heat will cause liquid phase to start vaporizing. Vaporization will cause pressure rise. Ultimately, when the vessel pressure reaches set/relieving pressure of the PSV, liquid phase will be at its boiling temperature at the set/relieving pressure. For pure components this is a straightforward calculation. For liquid mixtures (e.g. gas condensate, petroleum fractions) there is a correlation between distillation points (temperatures) at atmospheric pressure and at any other pressure - assuming no thermal degradation will occur. This needs to be reviewed on a case to case basis. In some instances, you may get the entire liquid phase vaporized before the vessel pressure reaches the PSV set pressure and this moves the case to the next scenario.
If the vessel is vapor/gas filled, here comes the tricky part. Normally one would consider isochoric (constant volume) process and calculate relieving temperature from the gas equation of state (p[sub]1[/sub], T[sub]1[/sub], z[sub]1[/sub] --> p[sub]2[/sub], T[sub]2[/sub], z[sub]2[/sub]). What usually happens in these cases is that the calculated relieving temperature is far above the design temperature of a vessel, which means that the vessel will likely rupture much before the actual pressure reaches the PSV set pressure. Protecting the vessel with a PSV does not have any meaning under those circumstances. If this is your case, you should consider other ways of protection - API 521 recommends vapor depressuring (blowdown) which would be automatically triggered by Fire & Gas detection system (F&GS trip signal to the SIS). Other options are insulation and cold quenching (water deluge or sprinklers).
This was just a generic description of various cases. For detailed and specific analysis, all other details (fluid inventory, composition, operating and relief pressures, operating temperature etc.) would have to be known.
for vapor phase (no vapor-liquid equilibria) you do not need a simulator,
you may estimate temperature inside vessel assuming constant Z
Pin*Vin=Zin*R*Tin
Prel*Vrel=Zin*R*Trel
and since Vin = Vrel
Trel = Tin * Prel / Pin
where in is initial condition and rel is release condition
this method is discussed in API and it is good when Zin ~ Zrel
this method solves a V-P flash operation and it is applicable to both vapor-liquid and vapor cases
By the way you can do the same with another simulator (for example iterating in t to find Vrel=Vin) but Prode is capable to solve directly the V-P flash (as well as many other flash operations) and it can do that directly in Excel.
Dejan,
reading your post it seems that you consider the constant volume procedure applicable to vapor state only,
but the blog shows an application of the method for vapor + liquid,
in fact Prode solves the V-P flash operation with multiphase equilibria, note that a free version is available for non commercial applications from prode.com
Anyway, since Guri77 says he hasn't a software the information in above posts can be useful for solving the problem.
Volume is constant in all 3 cases. What I'm practically saying is that if you end up with 2,000 degC relieving temperature in a gas filled vessel designed for max 150 degC, the whole calculation is meaningless. As well as the PSV.
Guri77 - You didn't state whether or not this vessel has a liquid, and whether that liquid will boil at a resonable temperature (T below the yield T of the vessel). If this vessel has no such liquid, or an insignificant quantity of it, then this is just an academic exercise that has no safety value. As stated by EmmanualTop, the PSV won't do any good. That's true regardless of its size or how you design it (what T you choose). PSVs protect vessels from fire by removing heat which is transferred from the fire>vessel wall>liquid. If there's no liquid (no Hvap), then even the largest PSV is only removing a trivial amount of heat. That is, there's no cooling of the vessel wall and the wall T continues to rise unabated. If there are no other protection measures (auto-depressurization, fire resistant insulation, water-spray) the wall T will quickly reach the yeild point.
I am not 100% sure that the PSV can be classified as pointless for a gas filled vessel. I remember reading a post, maybe by one of the Inches or Morten (?), that states that the PSV provides inventory reduction, particularly when the starting pressure is close to PSV set pressure. Without alternative protection (depressurising) I would be including a PSV if there is a credible risk of fire, it is fairly well mandated in the code.
tickle, you are correct when saying that the PSV will provide certain level of protection if the PSV set pressure is close to the operating pressure (i.e. the relief temperature will be fairly close to the operating temperature and definitely well below the maximum wall temperature). However, it should be noted:
- Pressure-relief devices protect a vessel against overpressure only; they do not protect against structural failure when the vessel is exposed to extremely high temperatures such as during a fire. (API 520/I, Section 1)
- Temperature rise of the vessel metal cannot be assumed equal to the temperature rise of the fluid (gas) inside the vessel, due to very low heat transfer coefficients. Hence the calculated relief temperature of the gas inside the vessel will occur significantly after the vessel wall reaches the same (relieving) temperature. A characteristic of a vessel with an unwetted internal wall is that heat flow from the wall to the contained fluid is low as a result of the heat transfer resistance of the contained fluid or any internal insulating material. Heat input from a fire to the bare outside surface of an unwetted or internally insulated vessel can, in time, be sufficient to heat the vessel wall to a temperature high enough to rupture the vessel. (API 521, Section 4.4.13.2.3)
- An unwetted steel plate 25 mm (1 in.) thick takes about 12 min to reach 593 °C (1100 °F) and 17 min to reach 704 °C (1300 °F) when the plate is exposed to a typical open fire (Figure 1 and 2, API 521). This does not mean that the fluid inside the vessel will have the same temperature at the same time. As the fire continues, the vessel wall temperature and the contained-gas temperature and pressure increase with time. The PSV opens at the set pressure. With the loss of fluid on relief, the temperatures further increases at the relief pressure. If the fire is of sufficient duration, the temperature increases until vessel rupture occurs. (API 521, Section 4.4.13.2.4)
- Where a PSV alone is not adequate, additional protective measures should be considered, such as water sprays (see 4.4.13.2.6.2), depressuring (see 4.6 and Annex A), earth-covered storage (see 4.4.13.2.6.3), and diversion walls (see 4.4.13.2.6.4). Where there is insufficient time for operator reaction, then automated actuation of depressuring, water spray, or isolation should be considered. Obviously, where fire fighting facilities do not exist, depressuring is likely the only effective way to prevent from vessel rupture.
Installing fire case PSV on a vessel containing gas only or high boiling point liquid - while mandatory by the Codes - in most of the cases cannot protect the vessel from the rupture scenario. If we are interested in preventing from this actually happening, secondary measures must be provided.
for fire case with vapor only, under certain conditions (predicted stress above critical values) a simple rupture disc (burst disc) may result a relatively inexpensive and reliable solution.
In relief design discussions the most misused phrases that I hear are “you’re required to...”, “you have to....” Pressure relief codes are clear in saying that you must protect vessels from overpressure, but they’re also very clear (and correct) in saying that it's the user's responsibility to determine the sizing basis for the relief device. That includes the decision of whether the relief valve should be sized for fire exposure. Speaking globally, I know of only one instance in which there is a mandatory requirement to size a relief device for fire. That is in the US. OSHA 1910.106 requires a fire-sized relief device for storage tanks containing a liquid that has a flash point of less 200F (or a liquid that is operated within 30F of its flash point). Aside from that exception, it’s the owner’s responsibility to decide whether or not to design the relief device for protection against fire exposure.
In my view there’s an active hazard in proceeding with sizing PSVs for fire when there’s no boilable liquid in the vessel. Doing so gives the false impression that the PSV will, in fact, provide meaningful protection from fire exposure. The engineer and the equipment owner are left thinking that they’ve addressed the hazard when in reality they’ve only swept it under the rug. Rather than focusing their time, money, and attention on protective measures that are effective, they’ve wasted it on a forlorn belief that they’ve done something beneficial.
Rupture disks, unlike PSVs, can provide effective protection from fire exposure by depressuring the vessel. However, that’s not a good solution for most process vessels because it introduces another risk (disk bursting unexpectedly) which is generally intolerable.
I give a star to rense for suggesting rupture disks,
while, as noted by don1980, they may be not suitable for liquid service due to high sensitivity to pressure spikes (a rupture disc may begin to open in less than 1 millisecond)
with compressible fluids (gases) this problem is much less important,
and in addition to economical advantage,s rupture disks allow to vent the system until pressure equals downstream pressure reducing the risk in case of fire.
