- Pressure relief valves are the last line of defence against vessel overpressure — sizing them correctly to API 520 is not optional engineering; an undersized relief valve in a fire case or blocked outlet scenario can lead to catastrophic failure with fatal consequences.
- Relief valve design selection — conventional, balanced bellows, or pilot-operated — depends on back-pressure characteristics and service conditions — the wrong design in a high back-pressure system will either fail to open at the set pressure or chatter destructively, both of which defeat the entire purpose of having the valve.
- API 521 relief system design and API 520 sizing must be treated as a system — the relief valve set pressure, the relieving capacity, the back-pressure in the flare header, and the vessel design pressure are all interdependent, and changing any one parameter requires re-evaluation of the others.
I have a great deal of respect for pressure relief valves. Not in an abstract sense — I mean I genuinely appreciate them as engineering devices, because every properly sized and functional PRV represents a specific engineering decision that protects lives and equipment. Every improperly specified one is a latent hazard waiting for the right overpressure scenario. This guide covers the design and sizing fundamentals properly.
Relief Valve Operating Principle
A spring-loaded pressure relief valve (PRV) uses a disc held on a seat by a calibrated spring. When process pressure exceeds the spring force (the set pressure), the disc lifts, flow passes through the valve, and the excess pressure is relieved to the flare header, atmosphere, or a collection system. When pressure falls below the set pressure (minus blowdown), the spring reseats the disc.
The set pressure is defined as the gauge pressure at which the valve begins to open. The relieving pressure is the pressure at which the valve achieves full rated capacity — for a conventional PRV, this is set pressure plus 10% overpressure (for ASME Section VIII applications). The blowdown is the pressure reduction below set pressure required to reseat the disc, typically 7–10% of set pressure.
Three Main PRV Designs
Conventional Spring-Loaded PRV
The conventional design has the valve spring chamber vented to the valve outlet (discharge side). This means back-pressure in the discharge system adds directly to the spring force — increasing the effective set pressure. For every 1 bar of back-pressure, the effective set pressure increases by 1 bar. This is acceptable when back-pressure is constant and known (it can be accounted for in spring calibration), but if back-pressure varies (as in most complex flare header systems), set pressure variation is unacceptable for safety.
Conventional PRVs are appropriate when total back-pressure (built-up plus superimposed) does not exceed 10% of set pressure.
Balanced Bellows PRV
The balanced bellows design uses a flexible metal bellows attached to the disc, with the bellows space vented to atmosphere (or a separate reference). This cancels the effect of back-pressure on the spring force — the effective set pressure remains constant regardless of back-pressure. The trade-off: the bellows must be maintained and can fatigue-crack, creating a maintenance item. Also requires venting the bonnet to a safe location (not safe to vent to atmosphere in H₂S service).
Balanced bellows PRVs are appropriate when back-pressure varies between 10–40% of set pressure.
Pilot-Operated PRV
A pilot-operated PRV (POPRV) uses a small pilot valve controlled by process pressure to operate a main valve through a pneumatic or hydraulic signal. The main valve piston or diaphragm is held closed by process pressure acting on a large area — when the pilot opens, the piston pressure is reduced and process pressure acting upward on a smaller seat area opens the main valve.
POPRVs offer: very tight seat sealing (process pressure helps seat the main valve, unlike spring-loaded designs where spring force must do all the work), the ability to handle very high back-pressure (up to 100% of set pressure for some designs), very low blowdown (the valve can reseat very close to set pressure), and large capacity in a compact body. They are the preferred choice for: high-pressure systems where tight seating is critical for gas conservation, systems with high or variable back-pressure, and large-capacity applications where spring-loaded designs would be physically impractical.
Relief Valve Sizing: The API 520 Framework
API Recommended Practice 520 Part I covers sizing and selection of PRVs. The sizing methodology determines the required orifice area (A) to pass the required relieving flow at the allowable relieving conditions.
Step 1: Establish the Design Basis
The design basis for a PRV comes from the API 521 hazard analysis — identifying all credible overpressure scenarios for the protected vessel. Common scenarios include: blocked outlet (flow in, no flow out), fire case (external fire heating vessel contents), cooling water failure (in condensing systems), control valve failure (stuck open allowing higher-pressure fluid in), reflux failure (in distillation columns), and utility failures (power failure causing compressor trip).
Each scenario generates a different required relieving rate and relieving conditions. The PRV must be sized for the worst credible case — typically either the blocked outlet case (maximum flow) or the fire case (for vessels containing flashing liquid).
Step 2: Gas/Vapour Sizing
For gas or vapour relieving service, the API 520 orifice area equation is:
A = W / (C × K × P1 × Kb × √(M / T × Z))
Where: W = required relieving capacity (kg/h or lb/h); C = coefficient based on specific heat ratio γ (tabulated in API 520 Table 2); K = effective coefficient of discharge (typically 0.975 for standard PRVs, then derated by 0.9 for sizing = 0.878); P1 = relieving pressure in kPaa or psia (set pressure × 1.1 + atmospheric); Kb = capacity correction factor for back-pressure (for balanced/pilot PRVs); M = molecular weight; T = relieving temperature in K or °R; Z = compressibility factor.
Step 3: Liquid Sizing
For liquid relieving service (thermal relief, blocked outlet with liquid-filled vessel): A = Q / (K × Kw × Kv × √(ΔP / G)) where Q is volumetric flow in US gal/min, ΔP is differential pressure (relieving pressure minus back-pressure), and G is specific gravity. Kw corrects for back-pressure effect on liquid capacity; Kv corrects for viscosity when viscosity is high enough to affect flow regime.
Step 4: Two-Phase Relieving
Where a vessel contains liquid with a boiling liquid (flashing) or the relief flow is two-phase, standard gas or liquid sizing equations are not applicable. API 520 Appendix D covers two-phase sizing using the omega (ω) method. Two-phase relief is significantly more complex and typically requires specialist calculation software.
Fire Case Sizing
For vessels with flammable contents that could be exposed to external fire, the fire case is usually a critical sizing scenario. The heat input from the fire vaporises liquid in the vessel, generating vapour that must be relieved. API 521 defines the fire heat input based on wetted surface area and whether the vessel has adequate drainage and fire fighting provision (which reduces the assumed heat input).
The relieving temperature for the fire case is the equilibrium boiling temperature at the relieving pressure — which for multi-component mixtures requires a process simulation (flash calculation) rather than a simple steam table lookup. Getting this wrong produces incorrect molecular weight and incorrect vapour generation rate, both of which affect the calculated orifice area.
Set Pressure Determination
The PRV set pressure must not exceed the Maximum Allowable Working Pressure (MAWP) of the vessel. For a single PRV, set pressure = MAWP. For supplemental PRVs (where the primary PRV cannot handle all scenarios alone), set pressure may be up to 105% of MAWP. For fire case supplemental PRVs, up to 110% of MAWP.
In practice, many engineers set the PRV somewhat below the MAWP (e.g., 95% of MAWP) to create operating margin, ensuring the PRV doesn’t lift during normal pressure transients. However, setting too far below MAWP wastes available capacity and may create sizing problems.
Common PRV Problems
- Chattering — valve opens and immediately reseats, cycling rapidly; caused by oversized valve (actual flow much less than rated capacity), insufficient system volume to maintain pressure during opening, or set pressure too close to operating pressure (insufficient margin). Fix: size correctly, maintain ≥10% margin between operating pressure and set pressure.
- Leakage/weeping — valve leaks at operating pressure below set pressure; caused by damaged or dirty seats, corrosion, erosion from previous lifting events, or set pressure too close to operating pressure. Fix: inspect and recondition seats, increase operating margin.
- Failure to lift — valve doesn’t open at set pressure; spring set incorrectly, stem frozen in guide by corrosion, outlet back-pressure too high for conventional valve design. Fix: regular proof testing at defined intervals.
Standards and Compliance
- API 520 Part I — sizing and selection
- API 520 Part II — installation
- API 521 — pressure-relieving and depressuring systems
- API 526 — flanged steel PRVs (defines standard orifice sizes from D to T)
- API 527 — seat tightness of PRVs
- ASME Section I — boiler PRVs (stamped with V, UV, or NV code symbol)
- ASME Section VIII Div. 1, UG-125 to UG-136 — pressure vessel PRV requirements
- PED 2014/68/EU — European pressure equipment directive for CE-marked safety valves
Pressure relief is not an area for engineering approximation. The consequence of undersizing is catastrophic. Use the API 520 methodology, get a qualified process engineer to define the relieving scenario, and verify the selected orifice size with the manufacturer’s certified capacity data before committing to the design.