Safety Systems

Pressure Relief Valve Sizing

Size pressure relief valves per API 520/521 for gas, liquid, and two-phase service. Select standard orifices per API 526 and meet ASME VIII overpressure limits.

Launch Calculator Sizing Equations

Overpressure

10% / 21%

Non-fire vs. fire case accumulation limits

Set Pressure

≤ MAWP

First valve at or below MAWP

Orifices

D – T

0.110 to 26.0 in² per API 526

Contents

1. Overview & Terminology

Pressure relief valves (PRVs) are the last line of defense against overpressure. They open automatically at set pressure and discharge enough flow to keep vessel pressure within code limits. Sizing follows API 520 Part I; relief scenarios are defined in API 521.

PRV pressure relationships: MAWP, set, overpressure, accumulation, reseat.
PRV pressure relationships: MAWP, set, overpressure, accumulation, reseat.

Key Terms

Term Definition
MAWP Maximum Allowable Working Pressure – vessel design pressure limit
Set Pressure (Pset) Gauge pressure at which PRV starts to open (≤ MAWP for single valve)
Overpressure Pressure rise above Pset during relief: 10% normal, 21% fire case
Relieving Pressure (P₁) Sizing basis: P₁ = Pset × (1 + overpressure%) + Patm
Blowdown Pressure drop required for valve to reseat (typically 7–10% of Pset)
Backpressure Pressure at PRV outlet (superimposed + built-up during flow)

Accumulation Limits (ASME VIII)

Scenario Single Valve Multiple Valves
Non-fire (operating upset) 110% MAWP 116% MAWP
Fire exposure 121% MAWP 121% MAWP

PRV Types

Three PRV types comparison: conventional, balanced bellows, pilot-operated.
Three PRV types comparison: conventional, balanced bellows, pilot-operated.
Type Max Backpressure Best For
Conventional ≤10% Pset Atmospheric discharge, low-cost applications
Balanced Bellows ≤50% Pset Variable backpressure, corrosive service
Pilot Operated ≤90% Pset High backpressure, large orifices, tight shutoff
Valve Selection Rule: Choose valve type based on expected backpressure. Conventional valves are simplest but capacity drops sharply above 10% backpressure. Use balanced bellows or pilot-operated for closed discharge systems.

2. Sizing Equations

Gas/Vapor Service (API 520 Eq. 3a)

For critical (choked) flow—typical when backpressure ratio P₂/P₁ is below the critical ratio:

Required Orifice Area: A = (W / (C × Kd × P₁ × Kb × Kc)) × √(T × Z / M) Where: A = Required area (in²) W = Mass flow rate (lb/hr) C = Gas constant from k (see below) Kd = Discharge coefficient = 0.975 (vapor) P₁ = Relieving pressure, absolute (psia) Kb = Backpressure correction (1.0 if ≤10% for conventional) Kc = Combination factor (0.9 with rupture disk, else 1.0) T = Temperature (°R = °F + 460) Z = Compressibility factor M = Molecular weight

C Factor (Function of k = Cp/Cv)

C = 520 × √[k × (2/(k+1))(k+1)/(k-1)]
k C Typical Gas
1.15340Heavy hydrocarbons
1.26–1.30356–361Natural gas, methane
1.40373Air, N₂, diatomic gases
1.66398Monatomic (He, Ar)

Critical Pressure Ratio

Flow is critical (choked) when:

P₂/P₁ ≤ (2/(k+1))k/(k-1) Typical values: k = 1.28 (natural gas): Critical ratio = 0.549 k = 1.40 (air): Critical ratio = 0.528

Liquid Service (API 520 Eq. 3.1)

Required Orifice Area: A = Q / (38 × Kd × Kw × Kv × Kc) × √(G / ΔP) Where: A = Required area (in²) Q = Flow rate (gpm) Kd = Discharge coefficient = 0.65 (liquid) Kw = Backpressure correction (balanced bellows only) Kv = Viscosity correction (1.0 if Re > 10,000) Kc = Combination factor G = Specific gravity (water = 1.0) ΔP = P₁ - P₂ (psi)

⚠ Liquid Kd differs from vapor: Use Kd = 0.65 for liquid, not 0.975. Using the wrong coefficient undersizes the valve by ~50%.

Two-Phase Flow

Two-phase sizing is complex. API 520 Annex C provides the omega method, but for critical applications use vendor software or the conservative approach: size for all-vapor OR all-liquid, whichever requires the larger orifice.

Sizing Example: Gas PRV

Given: 50,000 lb/hr natural gas, Pset = 300 psig, 10% overpressure, T = 150°F, M = 18, k = 1.26, Z = 0.90

P₁ = (300 + 14.7) × 1.10 = 346 psia
C = 356, Kd = 0.975, Kb = 1.0, Kc = 1.0
A = (50,000 / (356 × 0.975 × 346)) × √(610 × 0.90 / 18)
A = 0.416 × 5.52 = 2.30 in²
→ Select Orifice L (2.853 in²)

3. Correction Factors

Discharge Coefficient (Kd)

Service Kd
Gas/Vapor (critical flow)0.975
Liquid0.65
Two-phase (typical)0.85
With rupture disk (uncertified combo)Reduce by 10%

Backpressure Correction (Kb / Kw)

Backpressure correction curves for PRV sizing factors.
Backpressure correction curves for PRV sizing factors.
Valve Type Backpressure Limit Kb Notes
Conventional ≤10% Pset Kb = 1.0 up to 10%; drops rapidly above
Balanced Bellows ≤50% Pset Kb = 0.90–1.0 per manufacturer curve
Pilot Operated ≤90% Pset Kb ≈ 1.0 across range

Combination Factor (Kc)

Configuration Kc
PRV only (no rupture disk)1.0
Rupture disk upstream (uncertified)0.9
Certified combination (tested)Use tested value
Installation Derating: A 10% installation factor (1/0.9) is commonly applied to the calculated area to account for inlet piping losses, tolerance variations, and other real-world conditions not captured by ideal equations.

Viscosity Correction (Kv) – Liquid Only

For viscous liquids (Re < 10,000), Kv reduces capacity. Calculate Reynolds number:

Re = (2800 × Q × √G) / (μ × √A) Where: Q = gpm, G = specific gravity, μ = viscosity (cP), A = orifice area (in²) Re > 10,000 → Kv = 1.0 Re < 10,000 → Kv from API 520 Fig. 31 (iterative)

API 526 Standard Orifices

Orifice Area (in²) Inlet × Outlet
D0.1101" × 2"
E0.1961" × 2"
F0.3071½" × 2½"
G0.5031½" × 3"
H0.7852" × 3"
J1.2873" × 4"
K1.8383" × 4"
L2.8534" × 6"
M3.604" × 6"
N4.344" × 6"
P6.386" × 8"
Q11.056" × 8"
R16.08" × 10"
T26.08" × 10"
Always round up: Select the next standard orifice LARGER than calculated area. Never interpolate or undersize.

4. Relief Scenarios

API 521 identifies overpressure scenarios. Evaluate all applicable cases; the governing case (largest required orifice) determines final PRV size.

Common Scenarios

Scenario Cause Sizing Basis
Blocked Outlet Downstream valve closed Max inlet flow (pump curve, control valve Cv)
Fire Exposure External fire heats vessel Vapor from heat input (API 521 Eq. 5)
Tube Rupture Exchanger tube fails High-P side flow into low-P side
Control Valve Failure CV fails open Max flow at upstream pressure
Thermal Expansion Blocked-in liquid heated Volume expansion rate (small PRV)

Fire Case Sizing (API 521)

Fire case wetted area diagram for vessel exposure.
Fire case wetted area diagram for vessel exposure.
Heat Input (Adequate Drainage): Q = 21,000 × F × A0.82 (BTU/hr) Heat Input (Inadequate Drainage): Q = 34,500 × F × A0.82 (BTU/hr) Where: F = Environment factor (see table) A = Wetted surface area (ft²) up to 25 ft above grade Relief Rate: W = Q / λ (lb/hr) Where λ = latent heat of vaporization (BTU/lb)

Environment Factor (F)

Condition F
Bare vessel (no protection)1.0
Approved water spray0.5
Insulation (1")0.3
Insulation (2")0.15
Insulation (3")0.075
Insulation (4")0.05
Fireproofing (concrete)0.03

Fire Case Example

Given: Horizontal propane vessel 10 ft × 30 ft, 50% full, bare (F=1.0), MAWP = 250 psig

Wetted area: A = π × 10 × 30 × 0.5 = 471 ft²
Heat input: Q = 21,000 × 1.0 × 4710.82 = 2.67 MMBTU/hr
Propane λ ≈ 130 BTU/lb at relief conditions
Relief rate: W = 2,670,000 / 130 = 20,540 lb/hr
P₁ = (250 + 14.7) × 1.21 = 320 psia (21% fire overpressure)
→ Size using gas equation with propane properties

⚠ Confined fires: If vessel is confined by walls or embankments ≥ vessel height, use exponent 1.0 instead of 0.82 per recent API 521 guidance.

5. Installation

Inlet Piping (API 520 Part II)

PRV installation schematic with inlet, outlet, and isolation valves.
PRV installation schematic with inlet, outlet, and isolation valves.
Requirement Limit
Inlet pressure drop≤3% of set pressure at rated flow
Inlet pipe size≥ PRV inlet size, as short as possible
Block valvesProhibited unless car-sealed-open (CSO)
ElbowsAvoid close to inlet; 3–5 diameters straight run if possible

Outlet Piping

Valve Type Max Backpressure
Conventional10% Pset
Balanced Bellows30–50% Pset
Pilot OperatedUp to 90% Pset

Outlet Design Rules

  • Support independently – never hang outlet pipe from PRV body
  • Drain low points – prevent liquid accumulation
  • Slope to drain – no liquid pockets in vapor service
  • Anchor for reaction force – F = ṁ × V at discharge

Common Errors to Avoid

  • ✗ Inlet piping smaller than PRV inlet
  • ✗ Inlet ΔP exceeds 3% of set pressure
  • ✗ Block valve without CSO and supervision
  • ✗ Conventional valve with >10% backpressure
  • ✗ Outlet pipe supported on PRV body
  • ✗ Liquid traps in outlet piping
  • ✗ Sizing for only one scenario (fire may govern)
  • ✗ Interpolating between orifice sizes

Testing (API 527)

  • Set pressure test: Verify opening at Pset ±3% (or ±3 psi, whichever greater)
  • Seat tightness: No visible leakage at 90% Pset per API 527
  • Blowdown test: Verify reseat at 90–93% of set pressure
  • Periodic recertification: Every 2–5 years per plant procedures

Key Design Considerations

  • Critical vs. Subcritical Flow: Most gas PRV sizing assumes critical (choked) flow. Flow is critical when P₂/P₁ ≤ critical ratio (~0.55 for natural gas). Below this ratio, mass flow is independent of downstream pressure.
  • Subcritical Flow: When backpressure ratio exceeds the critical ratio, use manufacturer's subcritical flow curves or API 520 Annex B methods.
  • Multiple Valves: When a single valve exceeds Size T (26 in²), use multiple smaller valves in parallel. Stagger set pressures by 5% to prevent simultaneous opening.

References

  • API 520 Part I – Sizing and Selection (9th Ed., 2014)
  • API 520 Part II – Installation (6th Ed., 2015)
  • API 521 – Pressure-relieving and Depressuring Systems (6th Ed., 2014)
  • API 526 – Flanged Steel PRVs (7th Ed., 2017)
  • API 527 – Seat Tightness
  • ASME BPVC Section VIII, Div. 1 (UG-125 to UG-136)

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