Pressure Relief Valves —
Sizing, Selection and
Code Requirements

A pressure relief valve is the last line of defence between a pressurised system and a catastrophic overpressure failure. Every other protective layer — high pressure alarms, shutdown systems, operator response — can fail or be disabled. The relief valve is required to function correctly even if everything else has gone wrong, in the worst credible scenario, at the worst credible time. This is why its sizing and selection are not detail decisions made late in a project — they are fundamental safety engineering decisions that must be made correctly before the system is put into service.

This article covers the purpose of pressure relief devices, the overpressure scenarios that govern sizing, the API 520 and ASME VIII requirements, the sizing calculations for the principal fluid phases, back pressure effects and valve type selection, rupture discs, and installation requirements. It is written for mechanical and process engineers who need to specify and size relief systems, not for specialists in pressure safety valve repair or certification.

The Purpose — and the Legal Basis

Every pressure vessel designed to ASME VIII, EN 13445, or BS PD 5500 must be protected against overpressure by a pressure-relieving device unless the system cannot be overpressurised by any credible means — a definition that applies to very few real systems. ASME VIII Paragraphs UG-125 through UG-136 specify the requirements for overpressure protection. The Pressure Equipment Directive (PED) and the Pressure Systems Safety Regulations 2000 (PSSR) both require that pressure systems are protected against overpressure as part of their Written Scheme of Examination and safe operating limit documentation.

The relief valve is not just good engineering practice — it is a legal requirement for pressure-containing systems, and its absence, incorrect sizing, or defeated function makes the operator liable for any resulting incident.

Pressure Terminology — Getting the Definitions Right

Confusion between pressure terms is the most common source of errors in relief valve specifications. The definitions are precise and must be used correctly:

• Maximum Allowable Working Pressure (MAWP) — the maximum gauge pressure at the designated coincident temperature for which the vessel is designed. Set by the vessel designer, stamped on the nameplate. The relief valve must be set at or below the MAWP.
• Set pressure — the gauge pressure at which the relief valve begins to open (for spring-loaded valves, the pressure at which the disc lifts). Must be ≤ MAWP. For a single relief device on a non-fire case, set pressure = MAWP is the usual practice.
• Accumulation — the pressure increase above MAWP during relieving, expressed as a percentage of MAWP. The allowable accumulation defines the maximum relieving pressure. ASME VIII permits 10% accumulation for a single relief valve on non-fire cases (so maximum relieving pressure = 1.1 × MAWP) and 21% for fire cases (1.21 × MAWP). For multiple valves, the first valve is set at MAWP and additional valves may be set up to 5% above MAWP, with total accumulation still limited to 10% (non-fire) or 16% (multiple valves, fire case).
• Relieving pressure — the actual inlet pressure at which the valve relieves during the sizing case. For a single valve, relieving pressure = set pressure × (1 + accumulation/100). This is the pressure used in the sizing equation.
• Overpressure — the pressure increase above the set pressure at the time the valve is relieving. Overpressure = accumulation when the set pressure equals the MAWP.
• Back pressure — the pressure at the valve outlet. Superimposed back pressure exists before the valve opens (from pressure in the discharge header). Built-up back pressure develops during relieving (from flow through the discharge piping). Back pressure reduces the effective pressure differential across the valve and must be accounted for in sizing.

Overpressure Scenarios — Identifying the Governing Case

The relief valve must be sized for the worst credible overpressure scenario — the case that demands the largest relieving capacity. API 521 provides the systematic framework for identifying and evaluating overpressure scenarios. The principal scenarios encountered in process plant:

Blocked outlet (blocked discharge)

The most common governing case. A downstream valve is closed or a pump discharge is blocked, and the source continues to supply pressure to the protected equipment. The relief valve must pass all the flow the source can deliver at relieving pressure. For a centrifugal pump discharging into a blocked vessel, the relieving flow equals the pump's shut-off head flow rate — typically close to the rated flow but at a higher head.

Control valve failure open

A control valve on a high-pressure inlet fails to its open position, admitting full source pressure and maximum flow to the downstream system. The relieving flow is the maximum flow through a fully open control valve at the upstream pressure, minus any flow continuing downstream.

Heat input — external fire

An external fire surrounds the vessel and vaporises the liquid contents. The relieving flow is calculated from the wetted surface area of the vessel and the latent heat of vaporisation of the liquid. API 521 provides heat input equations for fire cases based on vessel surface area and whether adequate drainage and fire-fighting are available. Fire cases typically produce large relieving flows and govern the relief valve size for liquid-filled vessels.

Cooling water failure

Loss of cooling water to a heat exchanger or condenser causes the process side to heat up, increasing pressure. The relieving flow is the additional vapour generated from loss of cooling at the operating heat duty.

Thermal expansion (liquid-full systems)

A liquid-full piping section blocked in at both ends — between two isolation valves, for example — will overpressurise if subjected to heat input (solar radiation, steam tracing, process fluid on one side of a heat exchanger). Liquid thermal expansion cases require relatively small relief area but very specific valve sizing — small orifice sizes for liquid cases that many designers underestimate.

Tube rupture

Failure of a heat exchanger tube can expose the low-pressure shell side to the high-pressure tube-side pressure. The relieving flow is the maximum leakage through a single failed tube (two-phase or liquid, depending on the process) and may require a separate relief device on the shell side if the design pressure ratio exceeds approximately 1.5:1.

Sizing — Vapour and Gas Service

The API 520 Part 1 sizing equation for vapour and gas service (critical flow — the normal case where the pressure ratio across the valve is sufficient to produce sonic flow at the throat):

A = W / (C × K_d × P₁ × K_b × K_c) × √(TZ/M)
A = required effective discharge area (mm² or in²)
W = required relieving mass flow (kg/h or lb/h)
C = coefficient from ratio of specific heats k (from API 520 Table)
K_d = effective coefficient of discharge (0.975 for vapour, from valve manufacturer, or use 0.865 conservatively)
P₁ = relieving pressure = set pressure × 1.10 (non-fire) or × 1.21 (fire) in kPa absolute or psia
K_b = back pressure correction factor (1.0 for conventional valves with ≤10% back pressure; from manufacturer curves for balanced bellows)
K_c = combination correction factor (1.0 if no rupture disc upstream; 0.9 if rupture disc fitted)
T = relieving temperature (K or °R)
Z = compressibility factor (1.0 for ideal gas; calculate for real gas or high-pressure service)
M = molecular weight of gas

The required area A is compared against the standard API 526 orifice letter designations (D, E, F, G, H, J, K, L, M, N, P, Q, R, T) and the next larger standard orifice selected. The orifice letter also determines the valve body size and the flanged connections. API 526 standardises the inlet and outlet flange sizes for each orifice letter — a 1.5" × 2" valve body (1.5" inlet, 2" outlet) carries orifice letters up to F; larger orifices require larger bodies.

Sizing — Liquid Service

Liquid sizing uses a different equation because the flow is incompressible. The API 520 liquid sizing equation:

A = Q / (K_d × K_w × K_c × K_v) × √(SG / (P₁ - P₂))
Q = volumetric flow rate (US gpm or m³/h)
K_d = effective coefficient of discharge (0.65 for liquid service — lower than vapour)
K_w = back pressure correction factor for balanced bellows valves (1.0 for conventional valves)
K_c = combination correction factor (1.0 without rupture disc; 0.9 with)
K_v = viscosity correction factor (1.0 for most liquids; <1.0 for viscous fluids — requires iteration)
SG = specific gravity of liquid relative to water at flowing conditions
P₁ = relieving pressure (set pressure × 1.10 for non-fire), gauge
P₂ = total back pressure at relieving conditions, gauge

Note the Kd of 0.65 for liquid service versus 0.975 for vapour — liquids produce much less relieving capacity per unit area than vapours. A valve sized for a liquid thermal expansion case will have a small orifice (often D or E) even for reasonably large systems, because the required flow is low — but the sizing must still be done correctly.

Sizing — Steam Service

Steam has its own API 520 sizing equation that accounts for the thermodynamic properties of steam and the superheat correction:

A = W / (51.45 × K_d × K_n × K_sh × K_b × K_c × P₁)
K_n = Napier steam correction factor (applies above 1,500 psia; normally 1.0)
K_sh = superheat correction factor (1.0 for saturated steam; <1.0 for superheated — from API 520 Table 9)
All other terms as per vapour equation

Valve Types — Conventional, Balanced Bellows and Pilot-Operated

Conventional spring-loaded PRV

The most common type. A spring holds the disc closed against the inlet pressure. When inlet pressure equals the set pressure, the net upward force on the disc overcomes the spring force and the valve opens. The opening force is the inlet pressure acting on the disc area minus the outlet (back pressure) force on the disc area — which means that back pressure directly reduces the effective set pressure and opening force.

Conventional valves are suitable where superimposed back pressure is less than approximately 10% of set pressure. Above this, the back pressure compensation required and the set pressure instability make conventional valves unreliable. If a conventional valve is opened and reclosed at back pressures above 10% of set, it may chatter or fail to reseat properly.

Balanced bellows PRV

A flexible metal bellows attached to the valve disc assembly compensates for back pressure effects by exposing the back of the disc to atmospheric pressure rather than to the discharge pressure. The set pressure and opening behaviour are therefore independent of superimposed back pressure up to approximately 30–50% of set pressure (depending on manufacturer). Built-up back pressure is still limited — typically to 30–40% of set pressure — before it affects valve performance.

Balanced bellows valves are used where back pressure is significant (long or elevated discharge headers, multiple valves discharging to a common manifold) and where the increased back pressure correction of a conventional valve would require impractical oversizing. The bellows is a wearing component — it must be inspected and replaced at intervals, and the valve cannot be used where the process fluid would attack the bellows material.

Pilot-operated PRV

The main valve disc is held closed by process pressure acting on the top of a larger piston area (the dome). A small pilot valve senses inlet pressure and, at set pressure, vents the dome, allowing the inlet pressure to lift the main disc. Because the main disc is held closed by process pressure proportional to inlet pressure, pilot-operated valves maintain near-zero leakage at up to 98% of set pressure — significantly better than spring-loaded valves, which typically begin to show leakage above 90% of set.

Pilot-operated valves are used where the operating pressure must be maintained close to the set pressure, where process fluid is valuable or toxic and leakage must be minimised, and where the back pressure may be higher than balanced bellows valves can handle. Limitations: the pilot valve is sensitive to dirty or particulate-laden fluids; they require clean, dry process fluid; and the pilot circuit must be protected from freezing in outdoor or cold service.

Rupture Discs

A rupture disc (bursting disc) is a non-reclosing pressure relief device — a thin metal disc that bursts irreversibly at a specified differential pressure. It provides instantaneous full-bore relief but cannot reseat, requiring the system to be shut down and the disc replaced after activation.

Rupture discs are used:

• As the sole relief device where zero leakage is required (toxic or valuable fluids, sterile processes), and the process can tolerate a full shutdown on activation
• In combination with a PRV — the disc upstream of the valve provides a hermetic seal against process fluid leakage through the valve seat, protecting the valve from corrosion or fouling. ASME VIII requires a tell-tale gauge between the disc and valve to detect disc failure before the combination assembly loses its relief function.
• As a secondary relief device providing rapid large-area relief in severe fire or runaway reaction cases where the response speed of a PRV would be insufficient

When a rupture disc is installed upstream of a relief valve, the Kc combination correction factor of 0.9 is applied to the valve sizing (reducing the effective discharge area by 10%) unless the combination has been flow-tested and a certified Kc determined. The space between the disc and valve must be vented, and the vent monitored — a failed disc with the vent blocked converts the arrangement to a conventional PRV with the disc providing no function, removing all burst protection.

Back Pressure and Discharge Header Design

The discharge piping from a relief valve — from the valve outlet to the disposal point (flare, scrubber, atmosphere) — creates back pressure that affects valve performance and must be calculated as part of the relief system design. The two components:

• Superimposed back pressure — pressure in the discharge header before the valve opens. Arises from other valves discharging simultaneously, from a pressure-controlled flare header, or from elevation. Fixed for a given system state.
• Built-up back pressure — the additional back pressure created by the flow from the valve itself passing through the discharge piping. Calculated from the pipe friction and fitting losses at the relieving flow rate. Allowable built-up back pressure limits: 10% of set pressure for conventional valves, 30–40% for balanced bellows (manufacturer-specific).

Discharge piping must be designed to limit back pressure within the allowable limits for the valve type selected. Short, generously sized discharge headers with minimum bends and restrictions are the design objective. Long, small-bore runs from relief valves to remote flare stacks are a common source of excessive back pressure that is only discovered late in the project when the piping is already designed.

Installation Requirements — API 520 Part 2

API 520 Part 2 covers installation requirements. The critical points:

• Inlet pressure drop — the pressure drop in the piping between the protected equipment and the PRV inlet must not exceed 3% of the valve's set pressure at the relieving flow rate. Excessive inlet pressure drop causes the valve to chatter — it opens, the inlet pressure drops below the reseating pressure, the valve closes, inlet pressure builds back up, the valve opens again, repeatedly. Chattering damages the valve seat and disc rapidly. The 3% rule is strict — inlet piping to relief valves should be as short and direct as possible, full bore, with no reducers unless the inlet nozzle on the protected vessel is smaller than the valve inlet.
• Valve orientation — spring-loaded PRVs must be installed vertically with the spindle in the upright position unless the manufacturer confirms other orientations are acceptable. Off-vertical installation changes the spring preload and can affect set pressure.
• Isolation valves — relief valves on pressure vessels must not be isolated from the protected vessel in normal service. Where isolation valves are provided for maintenance purposes, they must be car-sealed open, locked open, or a management of change procedure must ensure the valve is never isolated without an alternative relief device in service.
• Drain connections — the valve body and discharge piping must be self-draining to prevent accumulation of liquid that could slug or freeze. Drain pockets in the discharge piping between the valve outlet and the flare header are a common installation error.

Testing and Certification

Relief valves must be tested before installation to confirm set pressure and capacity. New valves are tested and certified by the manufacturer. In-service valves must be retested at intervals specified in the Written Scheme of Examination under PSSR — typically every 2–5 years depending on service severity, fluid corrosiveness, and operating history.

Test records must be maintained showing the valve tag, set pressure, test date, condition found (did it lift at set pressure, was the seat undamaged on reseating), and any corrective action. A relief valve with no test history or overdue for test is a compliance failure under PSSR regardless of whether it appears to be working.

The Relief Valve Datasheet

Every relief valve must be specified on a datasheet that captures the complete sizing basis. The minimum content of a relief valve datasheet:

• Tag number and service description
• Protected equipment tag and MAWP
• Governing relief scenario (blocked outlet, fire case, etc.)
• Relieving fluid, phase, molecular weight or specific gravity, viscosity
• Relieving temperature and pressure
• Required relieving flow (mass or volumetric)
• Calculated required orifice area
• Selected API 526 orifice letter and effective area
• Set pressure
• Inlet and outlet flange size and rating
• Valve body and trim material
• Back pressure — superimposed and built-up
• Valve type (conventional, balanced bellows, pilot-operated)
• Discharge location (atmosphere, flare, closed system)

Summary

Pressure relief valve design is a three-step process: identify all credible overpressure scenarios and determine the governing case, size the relief device for the governing case using the appropriate API 520 equation, and select the valve type that handles the back pressure conditions of the installation. The sizing equations are not complex, but the inputs must be correct — relieving pressure at the right accumulation, relieving temperature, real fluid properties, and correct back pressure — and the governing scenario must be correctly identified. A relief valve sized for the wrong scenario, or sized correctly but with the wrong back pressure assumed, provides only the appearance of protection.