OpenSpecEngineering

Finds the heat a pool fire puts into a liquid-filled vessel and the vapor flow its relief valve must pass as the liquid boils off. It follows the wetted-area method of API 521 [1]. Process and safety engineers use it for the fire case when sizing a pressure relief valve.

Equations

Q = C·F·A_ws^0.82     W = Q/λ

Q is the heat absorbed, in W. A_ws is the wetted surface area, in m². F is the environment factor. C is 43,200 when the site has adequate drainage and firefighting, and 70,900 when it does not [1]. W is the vapor relief rate, in kg/s, and λ is the latent heat of the liquid, in J/kg.

Inputs

• The wetted area is the vessel surface in contact with liquid, up to 7.6 m (25 ft) above the grade or other surface where a pool fire could burn [1]. Use the normal high liquid level.
• F is 1.0 for a bare vessel. A lower value is allowed only for insulation that stays in place and works during a fire, and for earth-covered or buried vessels [1]. Don’t take credit for water spray.
• For water, choose Water and enter the relieving pressure: the set pressure plus the allowed overpressure, 21 % of set for the fire case [1]. The page takes λ at that pressure from the IAPWS-IF97 steam tables [2]. For any other liquid, enter λ at the relieving conditions.

Limits and common mistakes

• The method is for a vessel holding a boiling liquid. A vessel full of gas, or one with a liquid near its critical point, needs other methods in API 521 [1].
• Don’t mix up gauge and absolute pressure. The latent heat falls as pressure rises, so a wrong reference changes W.
• λ of a mixture changes as the light parts boil off. Use the value at the relieving conditions.
• The page gives the relief load, not the valve. Size the orifice for W at the relieving pressure and temperature.

Worked example

A bare deaerator storage tank holds hot water, with 45 m² of wetted shell. Its relief valve is set at 3.5 barg, so it relieves at 3.5 × 1.21 = 4.235 barg. The site has good drainage. What vapor rate must the valve pass in a fire?

1. Enter Wetted Surface Area 45 m² and Environment Factor 1.
2. Choose Drainage & Firefighting Adequate (C = 43 200).
3. Choose Relieving Fluid Latent Heat Water, boiling at the relieving pressure.
4. Enter Relieving Pressure 4.235 bar, choose Relieving Pressure Is Gauge, and press Solve. The Solution shows: Fire heat-input coefficient C: 43,200
   Relieving temperature (water saturation): 153.671 °C
   Latent heat λ used (water, IAPWS-IF97): 2,102.14 kJ/kg
   Absorbed heat Q: 979.756 kW
   Required vapour relief rate W: 0.466076 kg/s
   Required vapour relief rate W: 1,677.87 kg/h

Check by hand: 45^0.82 = 22.680, and 43,200 × 22.680 = 979,760 W. The relieving pressure is 5.248 bar absolute. Between 5.0 and 5.5 bar, steam tables give λ = 2,107.4 and 2,097.0 kJ/kg, so about 2,102 kJ/kg here. W = 979.8/2,102 = 0.466 kg/s.