Pressure relief valves (PRVs) are the last line of defense against overpressure in vessels, piping, and heat exchangers. They are designed to open at a set pressure, vent enough fluid to prevent the pressure from exceeding the equipment's maximum allowable working pressure (MAWP), and reseat when the pressure returns to normal. Sizing a relief valve means calculating the required orifice area to flow the maximum credible relief load at the allowed overpressure.
API 520 Part I (Sizing and Selection) is the industry standard for relief valve sizing in the petroleum, petrochemical, and chemical industries. It provides the equations for gas, steam, liquid, and two-phase relief scenarios. The calculated required area is then matched to the next larger standard orifice size designated by letter (D, E, F, G, H, J, K, etc.). This guide covers the sizing methodology, the orifice letter system, set pressure determination, and the backpressure effects that catch engineers off guard.
Set Pressure, MAWP, and Accumulation
The set pressure is the inlet pressure at which the relief valve begins to open. For a single relief device protecting a vessel, the set pressure cannot exceed the MAWP of the vessel. For supplemental (additional) relief devices, the set pressure can be up to 105% of MAWP. For fire case scenarios, the set pressure can be up to 110% of MAWP (ASME Section VIII).
Accumulation is how far the pressure is allowed to rise above the set pressure while the valve is relieving. ASME Section VIII allows 10% accumulation for a single valve at non-fire conditions, 16% for multiple valves, and 21% for fire case. This means the valve must flow the required relief load at the set pressure plus the allowed accumulation. The pressure at full flow (set pressure + accumulation) is the relieving pressure used in the sizing equation.
The operating pressure of the system must be below the set pressure by a sufficient margin to prevent the valve from weeping (leaking fluid past the seat during normal operation). API 520 recommends the operating pressure be no more than 90% of the set pressure for conventional spring-loaded valves. If the operating pressure is 250 psig, the minimum set pressure should be 250 / 0.90 = 278 psig. Round up to the next available spring range.
An important distinction: MAWP is a property of the vessel, stamped on the nameplate. Set pressure is a property of the relief valve, adjustable within the spring range. The vessel MAWP must be greater than or equal to the relief valve set pressure, and the set pressure must be greater than the maximum expected operating pressure. Getting these relationships wrong means the valve either opens during normal operation (set too low) or fails to protect the vessel (set too high).
API 520 Sizing for Gas and Vapor Service
The API 520 equation for required effective orifice area for gas or vapor service (critical flow) is: A = W / (C × K_d × P_1 × K_b × K_c) × √(T × Z / M), where A is the required area in square inches, W is the required mass flow rate in lb/hr, C is a coefficient depending on the ratio of specific heats (k), K_d is the discharge coefficient (0.975 for standard API valves), P_1 is the relieving pressure (absolute) in psia, K_b is the backpressure correction factor (1.0 for atmospheric discharge), K_c is the combination correction factor (1.0 for no rupture disc, 0.9 with a rupture disc upstream), T is the relieving temperature in degrees Rankine, Z is the compressibility factor, and M is the molecular weight of the gas.
The coefficient C depends on the ratio of specific heats (k = c_p/c_v) of the gas. For air (k = 1.4), C = 356. For methane (k = 1.31), C = 344. For hydrogen (k = 1.41), C = 357. C can be calculated from: C = 520 × √(k × (2/(k+1))^((k+1)/(k-1))).
Critical flow occurs when the downstream pressure is low enough that the gas reaches sonic velocity at the valve throat. The critical pressure ratio is: P_2/P_1 = (2/(k+1))^(k/(k-1)). For air, this is about 0.528. As long as the backpressure is below 52.8% of the relieving pressure, the flow is critical and independent of downstream conditions. If the backpressure exceeds this ratio, subcritical flow equations apply and the valve capacity is reduced.
For most atmospheric-discharge installations, critical flow is the governing case. The valve discharges to a vent stack at atmospheric pressure, and the relief pressure is well above 2× atmospheric. Subcritical flow becomes relevant when the valve discharges into a closed flare header or a pressurized system where the backpressure can build up significantly.
Standard Orifice Letter Designations
API 526 (Flanged Steel Pressure-Relief Valves) defines standard orifice sizes identified by letter. Once you calculate the required effective orifice area from the API 520 equation, you select the next larger standard orifice letter. The standard orifice sizes and their effective areas are:
- D: 0.110 sq in
- E: 0.196 sq in
- F: 0.307 sq in
- G: 0.503 sq in
- H: 0.785 sq in
- J: 1.287 sq in
- K: 1.838 sq in
- L: 2.853 sq in
- M: 3.600 sq in
- N: 4.340 sq in
- P: 6.380 sq in
- Q: 11.05 sq in
- R: 16.00 sq in
- T: 26.00 sq in
Each orifice letter corresponds to a specific inlet and outlet flange combination. For example, a "3K4" valve has a 3-inch inlet, K orifice, and 4-inch outlet. A "4L6" has a 4-inch inlet, L orifice, and 6-inch outlet. The inlet and outlet sizes are fixed by API 526 for each orifice letter to ensure proper flow capacity and structural integrity.
If your calculated required area falls between two orifice sizes, always select the next larger orifice. Selecting a smaller orifice means the valve cannot flow the required relief rate at the allowed overpressure, which is a code violation and a safety hazard. It is acceptable (and common) for the selected orifice to be significantly larger than the calculated requirement. An oversized orifice does not create problems as long as the valve is set and tested to the correct pressure.
Backpressure: The Variable That Changes Everything
Backpressure is the pressure at the outlet of the relief valve during relieving conditions. It has two components: superimposed backpressure (the pressure that exists at the outlet before the valve opens) and built-up backpressure (the additional pressure created by the flow through the discharge piping while the valve is relieving). The total backpressure is the sum of both.
Backpressure affects relief valves in two ways: it reduces the flow capacity, and it changes the effective set pressure. For conventional (spring-loaded) relief valves, superimposed backpressure acts on the disc area and adds to the spring force, raising the effective set pressure. If a conventional valve is set to open at 100 psig and the superimposed backpressure is 20 psig, the valve effectively opens at 120 psig. This can exceed the vessel MAWP and is a direct safety hazard.
Balanced bellows relief valves solve the superimposed backpressure problem. The bellows isolates the back side of the disc from the outlet pressure, so superimposed backpressure does not affect the set pressure. However, built-up backpressure still reduces the flow capacity through the valve. The K_b correction factor in the API 520 equation accounts for this reduction. At 30% backpressure ratio (P_backpressure / P_set), a balanced bellows valve loses about 5% of its flow capacity. At 50%, it loses about 20%.
Pilot-operated relief valves are the most backpressure-tolerant design. The main valve disc is held open by a pilot that senses inlet pressure only. The outlet backpressure has minimal effect on both the set pressure and the flow capacity, up to about 50% to 60% of set pressure. Pilot-operated valves are the preferred choice for variable-backpressure installations such as valves discharging into common flare headers where the backpressure changes depending on how many other valves are open simultaneously.
Installation and Testing Requirements
Relief valve installation details directly affect performance. The inlet piping between the vessel and the valve must be short and of a diameter equal to or larger than the valve inlet. API 520 recommends the total inlet pressure loss at full relieving flow not exceed 3% of the set pressure. Excessive inlet loss causes the valve to chatter (rapid cycling between open and closed) as the pressure drop through the inlet piping causes the inlet pressure at the valve to fall below the reseat pressure, closing the valve, which eliminates the pressure drop, allowing pressure to rebuild and reopen the valve. This cycle can repeat at several hertz, destroying the valve seat and internals.
The outlet piping must be sized to limit backpressure within the valve's design limits. For conventional valves, total backpressure should not exceed 10% of set pressure. For balanced bellows, 30% to 50% depending on the manufacturer. Discharge piping must be supported independently; the weight of the piping should not be carried by the valve body. A drip leg or drain at the bottom of a vertical discharge pipe prevents liquid accumulation that could freeze and block the outlet.
Testing requirements:
- Shop test (bench test): Every new or reconditioned valve must be set-pressure tested on a bench before installation. API 527 specifies the allowable seat leakage rate. The test verifies the valve opens within the tolerance of the nameplate set pressure (typically ±2% for ASME Section VIII valves above 70 psig).
- In-service testing interval: ASME and API 510 require periodic inspection and testing. Typical intervals are 5 years for non-corrosive clean services, 3 years for moderately corrosive services, and 1 year for severely corrosive or fouling services. Some jurisdictions require more frequent testing.
- In-situ pop testing: For valves that cannot be removed for bench testing without a shutdown, in-situ test equipment can apply a known force to the valve spindle to verify the set pressure without removing the valve from service. This test is less accurate than a bench test but provides verification between shutdowns.
Documentation for every relief valve must include: the protected equipment tag number and MAWP, the valve manufacturer, model, orifice letter, and serial number, the set pressure, the relieving scenario and required capacity, the test date and results, and the next scheduled test date. This information is tracked in the facility's pressure relief device register, which is an essential compliance document for OSHA PSM and EPA RMP programs.