Flare Stack Height — Engineering Fundamentals
API 521 radiation limits, Brzustowski flame geometry, Pasquill-Gifford dispersion of incomplete combustion products.
1. Two design criteria
Flare stack height is set by whichever of two criteria is more restrictive: thermal radiation at ground-level receivers (workers, fence line, equipment) and dispersion of incomplete-combustion products (CO, SOₓ if sour flare). Both must pass at the design flare load — typically peak emergency depressurization or PSV relief.
2. Radiation limits (API 521 §5.4)
| Receiver | Max heat flux (Btu/hr·ft²) | kW/m² |
|---|---|---|
| Worker, unprotected (≤ 1 min exposure) | 500 | 1.58 |
| Worker with PPE (≤ 30 s) | 1500 | 4.7 |
| Fence line / property boundary | 1500 | 4.7 |
| Equipment / structural steel | 2500 | 7.9 |
Heat flux from a point-source flame (modeled at flame center):
τ = atmospheric transmissivity (0.85 clear day, 0.6 hazy), F = radiant heat fraction (0.15 lean H₂, 0.30 sooty hydrocarbon), Q = total heat release ṁ · ΔH_c, R = slant distance from flame center to receiver.
3. Flame length + tilt
Brzustowski (1976) correlation for momentum-dominated jet flame:
Flame center is taken at half the flame length above the stack tip. Wind tilts the flame from vertical:
With v_jet ~ 500 ft/s (half-Mach typical), 10 mph wind tilts the flame ~1.7° — small for high-velocity flares. For low-velocity ground flares, wind can tilt the flame 30°+ and dominate the geometry.
4. Dispersion check
If combustion is < 100% complete, CO is emitted from the flame tip and disperses to ground level. A simplified Pasquill-Gifford Gaussian plume (neutral Class D, σ_y, σ_z fits) estimates ground-level CO concentration at the receiver. OSHA 8-hr TWA limit = 50 ppm.
For sour flares (H₂S in flare gas), the equivalent SO₂ + H₂S dispersion check often dominates and may force a taller stack than radiation alone.
5. References
- API Std 521 §5.4 — Pressure-Relieving and Depressuring Systems (radiation tables).
- API Std 537 §7 — Flare Details.
- Brzustowski, T.A. (1976). "Flaring in the energy industry." Prog. Energy Combust. Sci. 2, 129–141.
- Pasquill, F. & Gifford, F.A. (1961, 1976). Atmospheric dispersion classes.