Fire Case Relief

Fire Relief

Size relief for pool fire exposure with defensible wetted area, heat input, and capacity calculations aligned to API 521/520.

Launch Calculator Design checks

Exposure height

25 ft zone

Wetted area limited to 25 ft above grade per API 521.

Heat input

Q = C·A^0.82

C depends on drainage/insulation credit.

Accumulation

21% over MAWP

Fire case relieving pressure per API 520.

Contents

Use this when you need to:

  • Screen PSV capacity for pool fire exposure.
  • Document wetted area/heat input assumptions.
  • Compare insulation or water spray credits.

1. Fire Case Principles

Fire exposure can cause rapid pressure rise in vessels containing liquids that vaporize when heated. Relief devices must handle the vapor generation rate to prevent vessel rupture.

Fire Case Scenario

Heat source

Pool fire

Assume spill-fed fire around vessel; flame height ~25–30 ft.

Exposure time

Until inventory gone

No credit for firefighting unless fully justified.

Relief driver

Vapor generation

Boil-off from wetted area drives relief load; liquid-only cases are rare.

Spacing

25 ft zone

Only area ≤25 ft above grade is considered fire-exposed.

Fire case heat input concept showing vessel, pool fire, wetted area, and relief valve.
Fire case heat input concept: pool fire, 25 ft exposure zone, wetted surface, and relief valve location.

Governing Standards

Standard Scope
API 521 Pressure-relieving and depressuring systems (fire case methodology)
API 520 Part I Relief device sizing equations
NFPA 30 Flammable liquids storage
29 CFR 1910.106 OSHA flammable liquid requirements

2. Wetted Area Calculation

Wetted area is the vessel surface in contact with liquid that is also within the fire exposure zone (typically 25 ft above grade).

Horizontal Vessel

Wetted area (horizontal cylinder): A_w = L × [2r × arccos((r-h)/r) - (r-h)×√(2rh-h²)/r × 2] Simplified for h < D/2: A_w ≈ L × D × θ/360 × π Where: A_w = Wetted area (ft²) L = Vessel length (tan-to-tan) (ft) D = Vessel diameter (ft) r = Radius (ft) h = Liquid depth (ft) θ = Central angle subtended by liquid surface

Vertical Vessel

Wetted area (vertical cylinder): If liquid level ≤ 25 ft: A_w = π × D × h_liquid + π × D²/4 If liquid level > 25 ft: A_w = π × D × 25 + π × D²/4 Where: h_liquid = Liquid height (ft), capped at 25 ft Bottom head area included (π × D²/4)

Sphere

Wetted area (sphere): A_w = π × D × h Where h = height of liquid from bottom, capped at 25 ft For half-full sphere: A_w = π × D × D/2 = π × D²/2
25-ft rule: Only surface area within 25 ft of grade is considered exposed to fire. Area above 25 ft is excluded from wetted area calculation per API 521.

3. Heat Input Equations

API 521 provides equations for heat absorption based on wetted area and drainage/firefighting provisions.

Heat Input Equations

API 521 Heat Input (Pool Fire): For A > 200 ft² (large vessels): Q = C × F × A^0.82 For A ≤ 200 ft² (small vessels): Q = C × F × A Heat flux constant C: C = 21,000 BTU/hr·ft^1.82 — Adequate drainage & firefighting C = 34,500 BTU/hr·ft^1.82 — Inadequate drainage Where: Q = Heat absorption rate (BTU/hr) F = Environment factor (see table below) A = Wetted area (ft²)
Adequate drainage criteria (API 521 §5.15.2.2.1): Drainage slope ≥1% away from vessel, drainage capacity to remove spilled liquid, and prompt firefighting response available. If any criterion is not met, use C = 34,500.

Environmental Factor (F)

Condition F Factor Notes
Bare vessel (no insulation) 1.0 Default assumption
Water deluge (≥0.25 gpm/ft²) 0.5 Reliable water supply required
Depressuring + drainage 0.3 Auto-blowdown to safe pressure
Approved fireproof insulation 0.3 Must withstand 1660°F for 2 hrs
Insulation (conductance 4 BTU/hr·ft²·°F) 0.3 Minimum credit for insulation
Insulation (conductance 2 BTU/hr·ft²·°F) 0.15 Better insulation performance
Insulation (conductance 1 BTU/hr·ft²·°F) 0.075 High-performance insulation
Earth-covered storage 0.03 Underground or mounded tanks

Reference: API 521 Table 5 — Environment factors for fire exposure calculations.

⚠ Insulation requirements: To claim F < 1.0, insulation must be fireproof (calcium silicate, mineral wool with stainless steel jacket). Standard weatherproofing does not qualify.

01

Set exposure assumptions. Define drainage/spacing and insulation to pick the correct C and F factors.

02

Compute Q. Use the API 521 equation with wetted area capped at 25 ft.

03

Document credit. If claiming F < 1.0 or water spray, capture justification in the relief summary.

4. Relief Load Calculation

The relief load equals the vapor generation rate from heat input divided by latent heat of vaporization.

Vapor generation rate: W = Q / λ Where: W = Relief rate (lb/hr) Q = Heat input (BTU/hr) λ = Latent heat of vaporization at relief conditions (BTU/lb)

Latent Heat Values

Fluid Condition λ (BTU/lb)
Water 100 psig (338°F) 881
Water 250 psig (406°F) 820
Propane 100 psig (saturation) 150
Propane 250 psig (saturation) 110
Butane 100 psig (saturation) 130
Pentane 50 psig (saturation) 140
Crude oil (light) Atmospheric 100–120
Important: Latent heat decreases as pressure increases toward the critical point. Always use λ at the relieving pressure (set pressure + accumulation), not normal operating conditions. Use process simulation for accurate values.

Example Calculation

Given: Horizontal propane vessel, 10 ft diameter × 40 ft long, 80% full, bare vessel, adequate drainage

Step 1: Wetted area

80% full → θ ≈ 253° of circumference wetted A_w = 40 × π × 10 × (253/360) + 2 × π × 5² × 0.8 A_w = 883 + 126 = 1,009 ft²

Step 2: Heat input

Q = 21,000 × 1.0 × (1,009)^0.82 Q = 21,000 × 270 = 5,670,000 BTU/hr

Step 3: Relief load

λ = 130 BTU/lb (propane at relief pressure) W = 5,670,000 / 130 = 43,600 lb/hr

5. Design Considerations

Relief Device Sizing

Use API 520 gas sizing equation with fire case relief load:

A = W / (C × K_d × P₁ × K_b × √(M/TZ)) Where: A = Required orifice area (in²) W = Fire relief load (lb/hr) C = Gas constant (depends on k ratio) K_d = Discharge coefficient (0.975 typical) P₁ = Relief pressure (psia) K_b = Backpressure correction M = Molecular weight T = Temperature (°R) Z = Compressibility factor

Relief Pressure

Parameter Fire Case Allowance
Set pressure ≤ MAWP
Accumulation (fire only) 21% above MAWP
Relieving pressure 1.21 × MAWP
Fire case relief system diagram with vessel, PSV, flare header, and containment.
Fire case relief system: PSV on vessel nozzle, discharge to flare header, fireproofing/containment indicated.

💡 Design Margin Assurance

Relieving pressure of 121% MAWP is permitted for fire cases per API 520 Part I, Table 6. Vessel integrity is assured since ASME Section VIII requires hydrostatic testing to 150% MAWP (1.5 × design pressure), providing adequate margin above fire-case relieving conditions.

References:
• API 520 Part I, 10th Ed., Table 6 – Pressure Limits for Pressure-Relief Devices
• ASME BPVC Section VIII, Div. 1, UG-99 – Hydrostatic Testing Requirements

Alternative Protection Methods

  • Depressuring: Automatic blowdown to reduce pressure below failure threshold (API 521 Section 5.15)
  • Water spray: Deluge system reduces heat input (requires reliable water supply)
  • Fireproofing: Concrete or intumescent coating extends survival time
  • Remote location: Adequate spacing reduces fire exposure probability

References

  • API 521 – Pressure-Relieving and Depressuring Systems, 7th Edition
  • API 520 Part I – Sizing, Selection, and Installation of PRDs
  • API 2000 – Venting Atmospheric and Low-Pressure Storage Tanks
  • NFPA 30 – Flammable and Combustible Liquids Code

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