Introduction to Pressure Relief Valve Design Part 3 – Sizing Orifices and Piping

This is the third in a set of articles introducing the basics of pressure relief valve design from a process designer’s viewpoint. Read Part 1 here and Part 2 here.

Orifice Sizes

Now that you have the scenarios and all the fluid data for them, you can size the orifice. API 520/521 has some equations for this, as well as good advice and factors to put into the equations. There are many programs and spreadsheets out there, so find out what your office uses. You will be better off just reading the design standard you have to use, rather than I trying to explain something that may not apply to you.

One key factor that any calculation procedure will have you do is check for choked flow / critical flow. http://en.wikipedia.org/wiki/Choked_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.

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 1 square inch for the fire case, 2 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 catalogue of relief valves and you can see what 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.

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 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 max 3% of set pressure (in gauge pressure), and the outlet pressure drop from relief valve to the final destination (flare stack / vent location / etc.) should be maximum 10% of set pressure. Tip: “balanced” relief valves, a special type of relief valves, may help if you cannot meet these rules.

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.

When designing inlet and outlet piping, the flowrates you use are NOT just the relief scenario flowrates. Rather, they are the flowrates multiplied by the actual orifice size / the calculated orifice size.

(ex: 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. All my other relief scenarios will be scaled the same way)

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. Many companies have a rule of thumb like “keep relief valve outlet pipe velocity below X% of sonic in all cases.” Where X might be 60, 70, 75%. 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).

Odds and Ends

Some miscellaneous thoughts to close this post 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 them until you calculate the inlet pressure drop. (So that you know the exact inlet pressure). Sometimes you can avoid this by just assuming inlet pressure = set pressure, or inlet pressure = set pressure – 3%. If you cannot, you may need to iterate. Other steps may also require design iteration: doing your relief design may stimulate you to change the 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) http://www.aiche.org/technicalsocieties/DIERS/index.aspx 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. For similar reasons, 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 have the overpressure cause happening again and again, then the valve will keep opening, spewing all the fluid, and slamming shut. It wrecks the valve. You would rather have the valve smoothly open and gradually close. I think pilot valves can help in some cases of chattering.
• 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 valves for service. It is nice if the relief valve inspection schedule syncs with the equipment maintenance schedule. If not, 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. In some critical services people like to have sparing of relief valves with a valve kept “offline.” Or maybe if two relief valves are called for in the design, have three valves with one kept offline. Do not have the offline valve in service with the other valve(s) because then you risk chattering
• Boilers: They have special rules. Check ASME I or whatever the appropriate standard is for you.
• Revamp projects: Whenever a process is modified the relief valves have to be checked to make sure they can still be used. In big modifications, it becomes a large exercise to see what can be reused. (Sometimes the company will invest in fancy dynamic simulators and other tools, and find that the design margin in the original calculations was so high that the old relief valve can be reused. This is a big savings). Often in these cases the hard part of the exercise can be gathering the data: finding the original datasheets and calculations where available for valves and vessels, learning the layout, waiting for the records guy to get back to you, etc. The actual calculation may be easy
• Relief valves in equipment packages: Sometimes vendors 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 the equipment. This can save you time and heart ache
• Relief valve vendors: Are quite knowledgeable. Ask for their help and advice. Ask about things like balanced and pilot relief valves if you are worried about back pressure, chattering, etc.

Edit 2010-04-22: Minor rewrite for clarity, added note on offline valves/maintenance.

This closes the introduction. Return to Part 1 here or Part 2 here. More topics and advice may come in subsequent posts.

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Related posts:

1. Introduction to Pressure Relief Valve Design Part 1 – Types & Set Pressure
2. Introduction to Pressure Relief Valve Design Part 2 – Relief Scenarios and the Relief Rate
3. Piping and Instrumentation Diagram (P&ID) Designer Checklist
4. Fluid Controls Institute Articles on Piping Elements
5. Introduction to Process Hazard Safety Meetings: Part 1 Concepts and Worksheet