Once you have all of the scenarios that can cause your relief valve to open (see Part 2), and all the key fluid data for each scenario, you can size the relief valve orifice. This is the size of the opening that the fluid passes through within your relief valve. In general, a relief valve vendor will have several standard orifice sizes and you will pick the one that best fits your need.
API 520/521 has some equations to determine the minimum orifice size you need, as well as good advice and factors to put into their equations when you don't have information from the valve manufacturer yet. There are many programs and spreadsheets out there to size the orifice, so find out what your office uses. By carefully reading the standard and an example problem or two done by your office's methods, you should find the actual "sizing" of the relief valve is relatively easy.
One key factor that any calculation procedure will have you do is check for choked flow / critical flow. Choked flow is when a fluid is going so fast that it reaches sonic velocity: after that, it cannot go any faster no matter what the downstream pressure is. You should know the approximate inlet and outlet pressures of the relief valve, so you can check if you will reach choked flow. If it is choked, then that changes your results. API discusses this and gives different instructions and equations for chocked vs. non-chocked flow.
Once you have several orifice sizes calculated, you will select the relief valve orifice size just a bit higher than the maximum area that you calculated. So if you calculate 2.0 square inch for the fire case, 0.675 sq in for the cooling water failure case, and 0.5 sq in for thermal expansion, you’d probably take the L orifice which is good for up to 2.853 sq in. After that, you look at a catalog of relief valves and you can see what valve sizes are offered for that relief valve orifice size. For example, a 4 N 6 valve means a 4” inlet flange, 6” outlet flange, and a N sized orifice. I would not expect to find a 1 N 2 valve though, because an "N" orifice is relatively large and a 1"x2" relief valve is somewhat small. API 526 also has tables you can look at showing typical valve sizes for each orifice.
Accumulation: pressures over the set pressure?
You may notice some discussions of accumulation in the sizing standards: in API 520, figure 1 shows that you can have 10% accumulation in most cases with a single relief valve, 16% in most cases if there is more than one relief valve, and 21% for a fire case. What does this mean?
Well, let's say the relief valve set pressure is 100 psig. The valve you bought is going to start opening at 100 psig. But it will not fully open immediately and magically vent absolutely everything to a safe location in an instant. Instead, the pressure will probably get a little above 100 psig as the valve opens; it will open fast, but not instantaneously. An allowable accumulation (also known as allowable overpressure) of 10% means that the pressure in the vessel can get as high 110 psig at some temporary point in the process of the relief valve opening. The relief valve vendor is going to look at your set pressure, look at the flowrate for the worst relief scenarios, and then make sure the valve acts fast enough that things never ever get worse than 110 psig. (Or 121 psig for a fire).
Inlet and Outlet Piping
Design of the inlet and outlet piping of relief valves must be done carefully. For a start, you want low pressure drops. High inlet pressure drops upstream of the valve can cause pipe stress / vibration, and also a high pressure loss can “hide” the real pressure in the vessel from the valve. A high downstream outlet pressure can result in back-pressure: the high outlet pressure “pushes” your relief valve and makes it harder to open or stay open. In general, the inlet pressure drop from protected equipment to relief valve should be maximum 3% of set pressure (in gauge pressure). Meanwhile, the outlet pressure of the relief valve should be a maximum X% of the set pressure; 10% is the most typical. You will check that by starting at the final relief destination (flare stack / vent location / etc.) and doing hydraulic calculations backwards, until you determine the pressure at the outlet of the relief valve. Also, because relief scenarios can put a lot of strain onto pipes, you should work with your piping designer to minimize pipe stress and have a mechanically robust layout.
Tip: "balanced" and "pilot" relief valves are two special types of relief valves that may help if you cannot meet these rules. They have less stringent requirements.
When designing inlet and outlet piping, the flowrates you use are often NOT just the relief scenario flowrates. Rather, they are the flowrates multiplied by the actual orifice size / the calculated orifice size. This is called the "rated" flowrate.
(Example: I complete calculations for all the relief scenarios, and the largest load is from the fire case. I have a fire case generating 2000 lb/hr, and I calculate I need a 2.000 sq inch orifice using my API rules. But the actual orifice I buy is going to be the closest orifice size I can find that is equal to or greater than the calculated size; probably the closest size I can find is 2.853 sq inches. My calculations told me to buy 2.000 sq inch but I actually bought 2.853 sq inch. Therefore I design all the piping and the flare header as if there were 2000 x 2.853 / 2.000 = 2853 lb/hr at relief.
The relief valve is set at 500 psig, so I aim to keep the inlet pressure losses from the vessel/pipe to the relief valve below 500 x 0.03 = 15 psig. I need to design the inlet piping such that 2853 lb/hr will not cause a pressure drop over 15 psi. I must also design the outlet piping to ensure that relief valve outlet pressure shall be less than 500 * 0.10 = 50 psig. If I am discharging to atmosphere (0 psig), that means I can have up to 50 psig pressure drop in my outlet lines. (0 psig pressure + 50 psig line losses = 50 psi, just barely meeting my 10% rule). Because it is a fire case, as discussed in Part 2, the fire could effect several vessels simultaneously. I must check if the main flare headers may be receiving loads from several relief valves at once, because the extra fluid from several valves at once will effect the outlet pressure profile.
Lastly, all my other relief scenarios will be checked and scaled the same way, with the flowrates and minimum orifices sizes calculated by API. If a cooling water failure caused 500 lb/hr and required a 0.675 sq inch minimum orifice size, I will have to check my pressure drops against 500 * 2.853 / 0.675 = 2113 lb/hr of the relief fluid generated by a cooling water failure)
In some cases, when sizing common flare header lines that serve as a main multiple for several PSVs, it is acceptable to use the normal loads when considering multiple valves relieving at once. (But you would still consider rated flows for any scenarios where a single valve pops). Also, sometimes the "normal" load is used for non-conventional valves like pilot valves. Check API and the rules of your company. If you are dealing with a lot of PSVs interacting, like say a main flare header in a plant of some kind, it's recommended you get a commercial package specializing in these types flare/header designs. They will help you keep track of multiple relief scenarios and deal the complex hydraulics.
One last point: recall that you checked for choked flow in the orifice sizing. Choked flow is OK in the valve, but it’s a bad idea for the piping: it can increase vibrations and stresses on the pipes and the noise can be so loud it breaks safety regulations. To avoid dealing with these complexities, many companies have a rule of thumb like “keep relief valve outlet pipe velocity below X% of sonic in all relief scenarios.” Where X might be 60-80%. Larger outlet pipes will help you avoid sonic flow.
(For a fluid, Sonic velocity (ft/s) = 68.1 x root(k * P/ rho), where k, P (psia), and rho (lb/ft3) are evaluated at the actual fluid conditions. Alternatively, API 520 Part 1, Section 126.96.36.199.3 has a calculation to help you do a quick check whether your outlet line will choke or not).
Odds and Ends
Some miscellaneous thoughts to close this relief valve series and encourage further reading:
- Iteration: You notice that to size the orifice you need fluid properties at the inlet of the valve, and you don’t technically know precisely what they are until you calculate the inlet pressure drop. (So that you can know the exact inlet pressure). Sometimes you can avoid this by just assuming inlet pressure = set pressure, or inlet pressure = set pressure – 3%. That guess may be close enough. If you cannot make an assumption, you may need to iterate. Other steps may also require design iteration: doing your relief design may stimulate you to change the design of the protected process system to make the relief valve cheaper. Also, you may need to do some relief design to get scenarios and rough flowrates before you start the flare header design, and then change parts of your relief system as you run through the flare system. (Recall that normally you want to limit outlet piping pressure drop, and that the relief header can face several relief loads at once in some cases like power failures or large pool fires…sometimes in the flare header design you find reasons to go back and change the relief valves)
- Two-phase flow: Is common and makes this all more complicated. API 520 Appendix D has some advice. Information from the Design Institute for Emergency Relief Systems (DIERS) may help if you need to get into real details
- Choose the right set pressure: Don’t make the set pressure unnecessarily low “to be safe.” Each time a relief valve opens you are losing product. And now someone’s got to go make sure it closed properly, and test it...you want to design your system so that the relief valve is never used.
- Remember that relief valves are safety devices, not control devices. Use a normal control loop to control pressure during normal operation
- Chattering: You may wonder why we don’t just add really huge relief valves with huge orifices to be extra safe and to avoid a lot of designer’s grief. One reason is to save money, of course, because bigger valves cost money and also generate larger releases, which increases the size of the outlet piping. Another reason is you need to determine these loads anyway to design a flare system. A third issue is chattering: recall that relief valves will close after the pressure in the vessel drops. If you have a huge relief valve, then as soon as it opens the pressure in the protected vessel will drop rapidly and the valve will slam shut. If you had a huge relief valve popping up but the overpressure cause that rebuilds the pressure again and again after each release, then the valve will keep opening, spewing all the fluid, and slamming shut. This cycle of jolting open and slamming shut wrecks the valve. You would rather have the valve smoothly open and gradually close. I think pilot valves (a type of relief valve) may help in some cases where chattering is unavoidable.
- Multiple relief valves: Sometimes several relief valves are a good idea. Why? Maybe it is too expensive to get one giant relief valve, but you can buy two smaller valves that together provide the orifice area to do the job. In some cases you have two relief scenarios at vastly different flowrates: you can buy two relief vales, set the small valve to open first to deal with the small scenario, and the big relief valve to open at a slightly higher pressure (so that if the small valve can’t cut it, the pressure rises more, and the big valve steps in to save the day). That way when you get the small relief scenario the small valve handles it, and you don’t have some huge valve experiencing dangerous chattering.
- Offline valves/maintenance: Normally it is OK to have one valve, or one set of working valves, covering a service. But what about maintenance of the valves, you ask? Well, it is nice if the relief valve inspection and maintenance schedule syncs with the equipment maintenance schedule, then you can take the equipment and the valve(s) offline for service at the same time. If the maintenance schedules do not sync up, then normally a careful procedure can be followed where the relief valve is quickly serviced while the pressure in the vessel is carefully watched and someone is ready to take manual action in the event of a high pressure.
- Installed spares: In some critical services people like to spend more and have spare of relief valves kept "offline." This could be one valve + one spare, or if two relief valves are called for in the design, have three valves with one kept offline. Some companies are willing to spend and make spare relief valves the standard procedure to use in almost all cases - it costs more but makes maintenance easier and safer. You can easily pull a valve for maintenance and have the spare perfectly placed to take over. But remember, do not have the offline valve "in service" (connected and with the isolation valves open) while you have with the other standard valve(s) also connected, because then you risk chattering. 2 valves is not safer than 1, if 1 valve was sized to do the job. Keep the spare valve(s) closed off from the process until you need them
- Locked open (LO), locked closed (LC), Car sealed open (CSO), and car sealed closed (CSC) valves: You may see gate valves marked LO and LC on the P&ID drawings. These valves can only be opened and closed with a special key, whose use is tightly controlled. The plant will have procedures so that the key has to be signed out, and can only be taken after a formal work plan has been made. Basically, these valves are a real pain for maintenance and operations to use, which prevent someone from casually and accidentally turning these valves. Spare relief valves are a common place to use such valves: you do not want spare valves open to the process UNLESS the main valve is taken offline, and you definitely do not want to accidentally close all the gate valves so that no relief valve is connected to the system. You use LO/LC to put isolation valves around the relief valves, while minimizing the risk that people accidentally open or close them incorrectly. The isolation valves are only turned after a formal work plan has been written and people have thought through the consequences. (If there is only one relief valve, preferred practice may be to have NO isolation valves, or it may be LO/LC valves...it depends on how the valve and system will be maintained). CSO & CSC are "car sealed open/closed" valves, which are a similar idea but replaces the key with a plastic seal you have to cut open after filling out a plant paperwork procedure. One cannot turn the valves without breaking the seal. Reference.
- Boilers: They have special rules. Check ASME I or whatever the appropriate standard is for you.
- Revamp projects: Whenever an existing plant or process is modified it is called a revamp. Most revamps intend to expand the capacity of the existing plant, through a combination of installing new equipment and creatively re-using what is already there. In any modification, the relief valves have to be checked to make sure they can still be used in the new service, and this is no easy task. However, there is a big savings when an existing relief valve can handle the new service, compared to the expense of installing a new valve. Sometimes companies will invest in fancy dynamic simulators and other tools to try to re-use existing relief valves. By "sharpening your pencil" with these tools and doing very precise scenario calculations, you may find that the design margins and assumptions in the original sizing calculations were so high that the old relief valve can be reused for larger revamp flowrates. This is a big savings! Also, a warning: often in revamps the hardest part can be gathering the data: finding the original datasheets and calculations available for valves and vessels, learning the layout, waiting for the records guy to get back to you, etc. The actual calculation may be relatively easy compared to the difficulties in getting data to work with
- Relief valves in equipment packages: Sometimes vendors who sell "packages" of equipment can design relief valves for you. For example, vendors selling a pressure reducing valve or a chemical injection system may have relief valves perfectly customized to suit their equipment. This can save you time and trouble
- Relief valve vendors: The good ones are quite knowledgeable. Ask for their help and advice. Ask about things like balanced and pilot relief valves if you are worried about challenges like back pressure, chattering, etc.
Edit 2010-04-22: Minor rewrite for clarity, added note on offline valves/maintenance.
Edit 2010-11-04: Expanded example, added note on Car Sealed Open / Closed valves.
Edit 2011-04-26: Noted that in some cases it is acceptable to design some flare header lines for normal flow through several relief valves, rather than the rated (scaled-by-orifice size) flow.
Edit 2011-09-14: Edited definition of locked open/closed vs. car sealed open/closed valves.
Edit 2011-12-06: Improved description of outlet line sizing.