1. Thermal Radiation Limits
API RP 521 Table 8 specifies maximum thermal radiation for personnel and equipment.
API RP 521 Table 8 Summary
| Exposure Type | Btu/hr-ft² | kW/m² | Duration | Application |
|---|---|---|---|---|
| Continuous | 500 | 1.58 | 8 hours | Manned areas (includes solar) |
| Emergency | 1,500 | 4.73 | 2-3 min | Shutdown actions, valve ops |
| Escape | 2,000 | 6.31 | ~30 sec | Evacuation routes only |
| Equipment | 3,000 | 9.46 | - | Cable trays (with fireproofing) |
| Steel | 4,000 | 12.6 | - | Uninsulated structures |
Design practice: Use 1,500 Btu/hr-ft² for grade-level equipment access. Reserve 500 Btu/hr-ft² for permanently manned areas (control rooms).
2. Point Source Model
Treats flame as a point radiating uniformly in all directions. Conservative for preliminary design.
Radiation Intensity:
I = (F × Q × τ) / (4π × R²)
Safe Distance:
R = √[(F × Q × τ) / (4π × I_limit)]
Where:
I = Radiation intensity [Btu/hr-ft²]
F = Radiation fraction (see table)
Q = Heat release [Btu/hr] = ṁ × LHV
τ = Atmospheric transmissivity (0.7–1.0)
R = Distance from flame center [ft]
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F-Factor (Radiation Fraction)
| Fuel Type | F-Factor | Range |
|---|---|---|
| Hydrogen | 0.15 | 0.10–0.18 |
| Natural Gas (lean) | 0.20 | 0.18–0.23 |
| Natural Gas (rich) | 0.25 | 0.23–0.28 |
| Propane, Butane | 0.30 | 0.28–0.32 |
| Crude Oil, Diesel | 0.35 | 0.33–0.40 |
Atmospheric Transmissivity (τ)
| Conditions | τ |
|---|---|
| Arid / Desert | 0.95–1.0 |
| Temperate | 0.85–0.90 |
| Humid / Coastal | 0.70–0.80 |
Example Calculation
Given: Q = 100 MMBtu/hr, F = 0.25, τ = 0.85
I_limit = 1,500 Btu/hr-ft² (emergency)
R = √[(0.25 × 100×10⁶ × 0.85) / (4π × 1,500)]
= √[21.25×10⁶ / 18,850]
= √1,127,320
= 1,062 ft from flame center
If flame center is 226 ft above grade:
D = √(R² - H²) = √(1062² - 226²) = 1,038 ft horizontal
3. Flame Geometry
Flame length determines radiation source location. Longer flames require taller stacks.
Brzustowski (subsonic):
L/D = 5.3 × Fr^0.4 × [(ρ_a - ρ_g)/ρ_a]^0.2
Kalghatgi (sonic):
L/D = 18 × Ma^0.4 × (ρ_g/ρ_a)^0.2
Where:
L = Flame length, D = Tip diameter
Fr = U²/(g×D), Froude number
Ma = Mach number at exit
Typical Flame Lengths
| Tip Dia. | Velocity | L/D | Flame Length |
|---|---|---|---|
| 12 in | 50 ft/s (subsonic) | 15–25 | 15–25 ft |
| 12 in | 1,100 ft/s (sonic) | 40–60 | 40–60 ft |
| 24 in | 50 ft/s (subsonic) | 15–25 | 30–50 ft |
| 24 in | 1,100 ft/s (sonic) | 40–60 | 80–120 ft |
4. Flare Selection
Assisted flares reduce radiation by improving combustion. Steam/air assist can reduce F-factor by 40-55%.
F-Factor by Flare Type
| Flare Type | Multiplier | Effective F | Radiation Reduction |
|---|---|---|---|
| Single Point (reference) | 1.00 | 0.25 | - |
| Sonic Flare | 0.75 | 0.19 | 25% |
| Multipoint Ground | 0.70 | 0.18 | 30% |
| Air Assisted | 0.60 | 0.15 | 40% |
| Steam Assisted | 0.55 | 0.14 | 45% |
Technology Comparison
| Factor | Single Point | Steam Assist | Air Assist |
|---|---|---|---|
| Capital cost | Lowest | Moderate | Highest |
| Operating cost | None | High (steam) | Moderate (power) |
| Smoke suppression | Poor | Excellent | Good |
| Reliability | Excellent | Good (steam req'd) | Good (power req'd) |
| Best for | Emergency only | High capacity | Remote sites |
Common Design Errors
- Using 500 Btu/hr-ft² for equipment: That's for continuous human exposure. Use 1,500 for grade-level design.
- τ = 1.0 everywhere: Humidity reduces transmissivity. Use 0.7-0.85 for humid climates.
- Ignoring wind tilt: 20 mph wind tilts flame ~45°. Check worst-case wind direction.
- Flame center at grade: Use actual flame center height (H_stack + L/2), not stack base.
References
- API RP 521, 6th Edition – Table 8 Radiation Limits
- Brzustowski & Sommer (1973) – Radiant Heating from Flares
- Shell DEP 80.45.10.10 – Flare System Design
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