Flare & Relief Systems — Fundamentals

1. Relief load scenarios

API STD 521 defines the upset cases that can over-pressure equipment: external fire, blocked outlet, control-valve failure, tube rupture, thermal (hydraulic) expansion, loss of cooling/reflux, power failure, and others. The governing relief load is the largest credible single case (with some double-jeopardy exclusions). The fire case uses API 521's wetted-area heat-input correlation:

with the constant set by whether adequate drainage and firefighting are present. The vapour generation rate from that heat input (Q ÷ latent heat) feeds the relief device and the flare network.

2. PRV orifice sizing

Pressure-relief-valve area is sized per API STD 520 Part I. For critical-flow gas/vapour service:

where W is the relief mass rate, C the gas coefficient (function of k = c_p/c_v), K_d the discharge coefficient (~0.975 effective), P₁ the relieving pressure (set + overpressure + atmospheric), K_b the backpressure correction, K_c the rupture-disk combination factor, T/Z/M the relieving temperature, compressibility and molar mass. The computed area is rounded up to the next standard API 526 lettered orifice (D, E, F … T). Liquid and two-phase service use the Part-I liquid and (Annex C) two-phase methods respectively.

3. Disposal header & backpressure

All relief devices discharge into a collection header to the flare. The header must be sized so that built-up backpressure stays within each PRV's tolerance — typically ≤ 10% of set for a conventional valve, higher for balanced-bellows or pilot-operated valves (via K_b). Header flow is compressible; sizing checks Mach number (often ≤ 0.5–0.7 in the header, near sonic only at the tip) and the cumulative backpressure from simultaneous relieving loads.

4. Flare knockout drum

A flare knockout (KO) drum removes entrained liquid so the flare does not rain burning droplets. It is sized in API 521 §5.4.2 to drop out droplets (commonly 300–600 µm design droplet) by gravity settling: the vapour velocity must stay below the droplet terminal settling velocity from the force balance

with the drag coefficient C_D from the droplet Reynolds number (Schiller–Naumann correlation). The drum is also sized for liquid surge holdup. (A common citation slip is to attribute KO-drum sizing to "§7.3" — the droplet-settling method lives in §5.4.2 of the 7th edition.)

5. The flare tip

The flare itself is covered by API STD 521 (radiation) and API STD 537 (flare equipment). Two limits govern the tip and stack height:

• Exit velocity — to avoid flame lift-off/blow-out, tip Mach number is checked per contingency and held to roughly ≤ 0.2 for continuous and up to ~0.5 for short emergency relief (sonic/staged tips excepted).
• Thermal radiation — stack height and sterile-radius are set so ground-level radiation at occupied locations meets API 521 limits (e.g. ~1.58 kW/m² / 500 BTU/hr·ft² at the property line; higher transient limits with escape time). The simple point-source model q = τ·F·η·Q/(4π·D²) (with F the fraction radiated) gives the screening flux.

6. References

• API STD 520 Part I (Sizing & Selection) & Part II (Installation) — pressure-relieving devices.
• API STD 521 7th Ed — Pressure-relieving and Depressuring Systems (relief scenarios, fire case, KO drum §5.4.2, flare radiation).
• API STD 526 — Flanged Steel Pressure-Relief Valves (orifice letter areas).
• API STD 537 — Flare Details for Petroleum, Petrochemical, and Natural Gas Industries.
• GPSA Engineering Data Book — relief & flare sections (supporting correlations).