Pool Fire

1. Introduction and Physical Phenomenon#

1.1 Pool Fire#

The Pool Fire model simulates the steady-state combustion of a flammable liquid that has spilled onto a flat surface and ignited. The model computes:

• Maximum pool diameter based on spill type
• Mass burning rate per unit area (burning rate)
• Flame geometry (height, wind-induced tilt angle)
• Thermal radiation intensity at any given distance
• Human effects (1st/2nd degree burns, fatalities) via Probit functions
• Domino effects on neighboring vessels using Cozzani correlations
• Expected fatalities by integrating thermal radiation with population density

1.2 Industrial Context#

1.3 Scope of This Model#

This model calculates:

1. Pool diameter and geometry based on source type (continuous, massive, circularDike, rectangularDike)
2. Burning rate using Burgess-Strasser, Mudan, or tabulated methods
3. Flame height via Thomas or Pritchard-Binding correlations
4. Surface Emissive Power (SEP) accounting for soot shielding in large hydrocarbon fires
5. Thermal radiation at any distance — Point Source or Solid Plume (tilted cylinder) model
6. Distance to a specified radiation threshold (inverse problem via Newton-Raphson)
7. Thermal dose and probit-based probability of 1st/2nd degree burns and fatalities
8. Domino effect time-to-failure for neighboring vessels (Cozzani correlations)
9. Population fatalities using concentric annular ring integration

2. Calculation Sequence#

flowchart TD
  A["Input Data<br/>(fuel, source type, weather)"] --> B["Chemical Properties<br/>YAWS: ΔHvap, cP, ρL at Tamb & Tb"]
  B --> C["Burning Rate<br/>ṁ'' = f(ΔHc, ΔHvap, cP, ρL)"]
  C --> D["Pool Diameter<br/>D = f(sourceType, Q or V)"]
  D --> E["Flame Geometry<br/>u*, H(Thomas|Pritchard), θ, SEP"]
  E --> F["For each distance x:<br/>F_view, τ_atm, q(x)"]
  F --> G["Forward problem<br/>q(x)"]
  F --> H["Inverse problem<br/>x(q_target) — Newton-Raphson"]
  G --> I["Thermal Dose<br/>D_dose = t_exp · (q×10³)^(4/3)"]
  H --> I
  I --> J["Probit Analysis<br/>(Burns 1°/2°, Fatalities TNO/CCPS, Domino)"]
  J --> K["Fatality Calculation<br/>(Concentric Rings + FatalityUtils)"]

  style A fill:#e1f5fe
  style K fill:#c8e6c9
  style F fill:#fff3e0

1. Chemical Properties — Retrieve fuel properties from YAWS database at $T_{amb}$: heat of vaporization $\Delta H_{vap}$, liquid heat capacity $c_P$, and liquid density $\rho_L$.

2. Burning Rate — Compute $\dot{m}''$ [kg/(m²·s)] using Burgess-Strasser, Mudan, or tabulated value (gasoline).

3. Pool Diameter — Determine maximum pool diameter $D$ based on source type: continuous spill, massive release, circular dike, or rectangular dike.

4. Flame Geometry — Compute dimensionless wind speed $u^*$, flame height $H$ (Thomas or Pritchard-Binding), tilt angle $\theta$, and Surface Emissive Power (SEP).

5. Thermal Radiation — Compute radiation $q(x)$ [kW/m²] at target distances using Point Source or Solid Plume (tilted cylinder) view factor model.

6. Probit Analysis — Convert thermal dose into probability of 1st/2nd degree burns, fatalities (TNO or CCPS), and domino effects (Cozzani).

7. Fatality Estimation — Integrate fatality probability over concentric annular rings to estimate total casualties.

3. Chemical Properties (YAWS Correlations)#

All fuel properties are retrieved from the YAWS chemical database evaluated at ambient temperature $T_{amb}$ (Kelvin).

4. Burning Rate — burningRate()#

The burning rate $\dot{m}''$ [kg/(m²·s)] is the mass of fuel consumed per unit area per unit time. It governs fire intensity and pool diameter.

5. Pool Diameter — poolDiameter()#

6. Time Calculations#

7. Dimensionless Wind Speed — ux()#

The physical minimum $u^* = 1.0$ corresponds to the no-wind condition. Dry air density uses ISA 1976 altitude correction:

Reference: ISA 1976. Code: PoolFire.js, lines 414–430.

8. Flame Height — alturaFlama()#

9. Surface Emissive Power (SEP) — SEP()#

The SEP [kW/m²] is the radiant power emitted per unit area of the flame surface.

10. Flame Tilt Angle — anguloFlama()#

Wind tilts the flame from the vertical. The angle $\theta$ [rad] is computed from the Froude and Reynolds numbers:

For $u_w \leq 0$, $\theta = 0$ (vertical flame). Kinematic viscosity $\nu$ [m²/s] is obtained from an empirical polynomial in $T_{amb}$ [K].

Code: PoolFire.js, lines 523–542.

11. View Factor — viewFactor(x)#

12. Atmospheric Transmissivity — ta(x)#

Atmospheric humidity attenuates thermal radiation. Transmissivity $\tau$ uses Wayne's correlation (cited in CCPS):

The partial pressure of water vapor $P_w$ [Pa]:

where $HR$ is relative humidity [%] and $T = T_{amb}$ [K]. Code: PoolFire.js, lines 620–638.

13. Thermal Radiation — qTermAtX(x)#

14. Distance to a Given Radiation Level — xTerm(q_target)#

Given a target radiation level $q_{target}$ [kW/m²], the distance $x$ [m] is found via Newton-Raphson. For the Point Source model:

Convergence tolerance: 0.01 m. Code: PoolFire.js, lines 681–737.

15. Thermal Dose — dose(x)#

The factor $10^3$ converts $q$ from kW/m² to W/m². Code: PoolFire.js, line 758.

16. Effects — Probit Functions#

Probit functions transform the thermal dose into damage probability via the standard normal distribution.

17. Time to Failure for Vessels (Domino Effect) — Cozzani Correlations#

18. Fatality Calculation — fatalidades()#

The method numerically integrates the probability of death over concentric annular rings:

For polygon receivers (zones with known population), FatalityUtils.js uses a 10 m grid to distribute the population within the polygon and excludes that area from the uniform density calculation.

Code: PoolFire.js, lines 818–860; delegated to FatalityUtils.js.

19. Model Limitations#

20. Bibliographic References#