Process Safety · Lesson 8 of 9 · 16 min read

Emergency relief and vent-sizing fundamentals

Relief scenarios, illustrative vapour, liquid and fire-case screening calculations, and why runaway relief is two-phase.

Educational overview. The principles here are general and simplified, and the figures and rules of thumb are typical values, not limits for your plant. Decisions need process-specific data, the applicable codes and standards, and a qualified assessment.

First: what is the relief for?

A relief device (safety valve or rupture disc) protects the vessel by letting material out before the pressure exceeds what the vessel can take. Sizing starts with the scenario, not the formula. (New to the devices themselves? See how a safety valve and a rupture disc work.) Typical scenarios for a batch reactor:

Blocked outlet / overfilling with a pump or gas supply still running
External fire heating the contents (pool fire under the vessel)
Utility failure: control valve fails open, steam to the jacket, nitrogen regulator fails
Thermal expansion of liquid trapped between closed valves
Runaway reaction: vapour and gas from the reaction and decomposition
Gas evolution from the normal reaction (e.g. HCl, CO₂) exceeding the vent capacity

Size for the worst credible scenario; the relevant codes are API 520 (sizing), API 521 (scenarios, depressuring) and API 526 (valve sizes). Relief must discharge to a safe place: a catch tank, scrubber or flare, never into the work area.

Vapour and gas relief

A = W / (C · K_d · P₁ · K_b · K_c) · √(T·Z / M) [A mm², W kg/h, P₁ kPa abs, T K]
C = 0.03948 · √( k · (2/(k+1))^{(k+1)/(k−1)} )P₁ = set pressure + overpressure (10 % normally, 21 % for fire) + atmospheric. K_d ≈ 0.975 for preliminary valve sizing; K_b corrects for backpressure; K_c = 0.9 if a rupture disc sits under the valve. k = c_p/c_v of the vapour (≈ 1.4 for N₂/air, 1.3 for steam, 1.1–1.2 for organic vapours).

🧮 Vapour / gas relief area (API 520, critical flow)

Example values: 1,200 kg/h of methanol vapour, valve set at 3 barg.

Educational screening tool Results are illustrative and depend on the stated assumptions. They are not a substitute for a qualified process-safety assessment, the applicable design code, vendor data, laboratory testing or engineering review. Illustrative preliminary calculation: not a final relief-device design.

Relief rate W (kg/h) Set pressure (barg) Overpressure (%) Relieving temperature (°C) Molecular weight M k = c_p/c_v Compressibility Z K_d K_b K_c (disc under valve: 0.9)

Fire case

A pool fire under a vessel boils the liquid inside. API 521 estimates the heat input from the wetted area A_w (the part of the vessel wall in contact with liquid, up to 7.6 m above grade):

Q = 43,200 · F · A_w^0.82 W (prompt fire-fighting and good drainage)
Q = 70,900 · F · A_w^0.82 W (otherwise)
W = Q / λ (λ = latent heat of vaporisation)F is the environment factor: 1.0 for a bare vessel, lower for fire-proof insulation (e.g. 0.3 for 25 mm, 0.15 for 50 mm, 0.075 for 100 mm of approved insulation). Fire-case relief uses 21 % overpressure.

🧮 Fire-case relief load

Vessel diameter D (m) Liquid height in shell (m) Environment factor F Latent heat λ (kJ/kg) Fire-fighting

Liquid relief

A = 11.78 · Q / (K_d · K_w · K_v) · √( G / (P₁ − P₂) ) [A mm², Q L/min, P kPa g]K_d = 0.65 for a certified liquid valve (preliminary), G = specific gravity, P₁ = set pressure + overpressure, P₂ = backpressure.

🧮 Liquid relief area

Flow (m³/h) Specific gravity G Set pressure (barg) Overpressure (%) Backpressure (barg)

Runaway reactions need two-phase relief

When a runaway boils the batch, the vapour bubbles swell the liquid and the vent discharges a foaming two-phase mixture, not clean vapour. Two-phase flow carries far less energy per unit area, so a vent sized with the vapour formula can be several times too small. Runaway relief is sized with the DIERS methods (e.g. Leung’s method) from adiabatic test data: the self-heating rate (dT/dt) at the set pressure, and whether the system is “tempered” (vapour), “gassy” or hybrid. That is specialist work, done from ARC / VSP2-type data.

T2 Laboratories (2007):

the reactor’s rupture disc was far too small for a runaway. The reactor burst and the explosion killed four people. See the case study.

✍️ Check yourself: Why is a vent sized with the vapour formula often too small for a runaway reaction?

Level swell turns the discharge into a two-phase flow. Two-phase venting needs much larger areas. Use DIERS methods with adiabatic calorimetry data.

✍️ Check yourself: Fire case, bare vessel, no prompt fire-fighting, wetted area 15 m². The heat input is about…

Q = 70,900 × 1 × 15^0.82 ≈ 70,900 × 9.2 ≈ 650 kW. Divide by the latent heat to get the vapour rate.

Key takeaways

Start from the scenario: blocked outlet, fire, utility failure, thermal expansion, runaway, gas evolution.
Vapour: A ∝ W·√(TZ/M)/(C·K_d·P₁). Fire: Q = 43,200 or 70,900·F·A_w^0.82 W. Liquid: A ∝ Q·√(G/ΔP).
Runaway relief is two-phase: use DIERS methods and adiabatic test data. Never the vapour formula alone.
Discharge to a safe place: catch tank, scrubber, flare.