Pool Fire Modeling

1. Pool Fire Physics

A pool fire occurs when a flammable liquid spill ignites, forming a turbulent diffusion flame above the liquid surface. Unlike premixed flames where fuel and oxidizer are mixed before combustion, pool fires draw air into the flame envelope through buoyancy-driven entrainment. The liquid fuel vaporizes from the pool surface, mixes with entrained air at the flame boundary, and burns in a luminous reaction zone that surrounds a fuel-rich core. Pool fires represent one of the most common fire scenarios in the petroleum and midstream industries, arising from tank overflows, pipeline ruptures, flange leaks, and vessel failures.

Pool Fire vs. Other Fire Types

Pool fires differ fundamentally from jet fires and BLEVE fireballs in their geometry, duration, and radiation characteristics. A jet fire is a momentum-driven flame from a pressurized release, producing an elongated, high-velocity flame with very high local heat fluxes but a relatively narrow hazard footprint. A BLEVE fireball is a transient event lasting only seconds, with an expanding spherical flame that radiates intensely but briefly. In contrast, a pool fire is a buoyancy-controlled, quasi-steady-state fire that can persist for hours as long as fuel supply is maintained. The steady-state nature makes pool fires particularly dangerous for structural steel exposure, where prolonged heat flux above 15-25 kW/m² can weaken supports and lead to structural collapse.

For consequence analysis in facility siting studies per API RP 752, pool fires often define the thermal radiation hazard zone for ground-level receptors because they persist long enough for thermal dose to accumulate. Jet fires may produce higher instantaneous fluxes but affect smaller areas, while BLEVEs produce the highest peak radiation but for durations measured in seconds rather than minutes or hours.

2. Burning Rate and Regression

The mass burning rate per unit area is the most fundamental parameter in pool fire modeling. It determines how quickly the fuel is consumed, controls the total heat release rate, and directly influences flame height. The burning rate depends on the fuel properties, pool diameter, ambient conditions, and wind speed. For pool diameters greater than approximately 1 meter, radiative heat feedback from the flame to the liquid surface dominates over conductive and convective heat transfer, and the burning rate approaches an asymptotic maximum value characteristic of each fuel.

Burning Rate Data for Common Fuels

The following table presents experimentally determined burning rate parameters from the SFPE Handbook and other standard references. The maximum burning rate (m"_infinity) is the asymptotic value for large-diameter pools where radiative heat feedback is fully developed. The k-beta product controls how quickly the burning rate approaches the asymptotic value as pool diameter increases. Fuels with large k-beta values reach their maximum burning rate at smaller pool diameters.

Diameter Effects on Burning Rate

For small pools with diameters below about 0.3 meters, convective heat transfer from the flame to the liquid surface is significant, and the burning rate may actually be higher than for moderate-size pools. As the diameter increases from 0.3 to 1.0 meters, the burning rate passes through a minimum as convective effects diminish but radiative feedback has not yet fully developed. Above 1 meter, radiative heat feedback dominates and the burning rate increases monotonically with diameter, approaching the asymptotic value at pool diameters of approximately 2-3 meters for fuels with high k-beta values (such as condensate and kerosene) and 5 meters or more for fuels with low k-beta values (such as gasoline and diesel). This diameter dependence is critical because it means that the same volume of spilled fuel will burn more intensely in a confined dike with a larger surface area, even though the pool depth is shallower.

3. Flame Height Correlations

Flame height is a critical parameter for thermal radiation modeling because it defines the geometry of the radiating surface. The most widely used correlation for pool fire flame height is the Thomas correlation (1963), which relates the flame height-to-diameter ratio to a dimensionless burning rate parameter. The Thomas correlation has been validated against a wide range of experimental data for hydrocarbon pool fires with diameters from 1 meter to over 50 meters.

Flame Tilt and Wind Effects

Wind has a profound effect on pool fire behavior. At wind speeds above approximately 2 m/s, the flame tilts downwind and the base drag effect causes the flame to extend beyond the pool boundary on the downwind side. This asymmetry significantly increases the thermal radiation hazard to receptors located downwind while reducing it upwind. The American Gas Association (AGA) tilt correlation, widely adopted in industry, predicts that at moderate wind speeds of 5-8 m/s, flame tilt angles reach 40-60 degrees from vertical for large pool fires. At these angles, the effective flame length increases and the flame approaches closer to ground-level receptors downwind, creating a much larger hazard footprint than the calm-wind case.

Wind also affects the burning rate itself. Moderate wind speeds can increase the burning rate by 20-40% through enhanced oxygen supply to the combustion zone and increased convective heat transfer to the fuel surface. However, very high wind speeds may partially blow out the flame or break it into intermittent flamelets, reducing the overall burning efficiency. For conservative consequence analysis, standard practice is to evaluate pool fire radiation at the maximum expected wind speed in the direction of vulnerable receptors.

Large-Diameter Pool Fires

Pool fires with diameters exceeding approximately 10 meters exhibit behavior that deviates from small-scale experiments. The flame breaks up into multiple intermittent flamelets separated by dark, soot-filled gaps rather than maintaining a continuous luminous surface. The mean flame height-to-diameter ratio decreases with increasing diameter, approaching values of 1.0-1.5 for very large pools above 30 meters in diameter. This breakup phenomenon reduces the time-averaged surface emissive power because the sooty regions between flamelets radiate at lower temperatures. The SFPE Handbook recommends reducing the surface emissive power for large-diameter pools to account for this mass fire effect, with recommended values dropping from 100-150 kW/m² for small pools to 20-40 kW/m² for pools exceeding 30 meters in diameter.

4. Thermal Radiation Modeling

Thermal radiation from a pool fire is modeled using the solid flame approach, which treats the visible flame as an opaque, solid body with a uniform surface emissive power (SEP). This method, developed and refined by Mudan and Croce and documented in the SFPE Handbook, is the standard approach used in facility siting and consequence analysis. The incident radiation flux at any receptor point is the product of three quantities: the surface emissive power, the geometric view factor, and the atmospheric transmissivity.

Surface Emissive Power by Fuel Type

The surface emissive power varies significantly among fuel types due to differences in flame luminosity, soot production, and combustion temperature. Clean-burning fuels like LNG and methanol produce relatively transparent flames with high effective emissive power because radiation from the hot combustion zone passes through the flame with minimal absorption. Sooty fuels like crude oil and heavy fuel oil produce dense black smoke that obscures the luminous flame zone, reducing the average emissive power but creating intermittent luminous spots (clear-air windows) where radiation briefly exceeds the average value.

5. View Factor and Atmospheric Transmissivity

The geometric view factor quantifies the fraction of radiation leaving the flame surface that reaches the receptor. It depends on the flame geometry (modeled as a tilted cylinder for pool fires), the flame dimensions (diameter and height), and the distance and orientation of the receptor relative to the flame. For pool fires, the solid flame is typically modeled as a right circular cylinder with a height equal to the mean flame height and a diameter equal to the pool diameter, tilted at an angle determined by the wind-tilt correlation.

Atmospheric Transmissivity

As thermal radiation travels through the atmosphere from the flame to the receptor, it is partially absorbed by water vapor and carbon dioxide molecules. The degree of absorption depends on the path length, the humidity, and the ambient temperature. The Wayne (1991) correlation, widely used in consequence modeling software, estimates transmissivity as a function of the product of path length and partial pressure of water vapor.

At short distances (under 50 meters) and low humidity (below 40% relative humidity), atmospheric transmissivity is typically 0.85-0.95, meaning only 5-15% of the radiation is absorbed en route. At longer distances of 200-500 meters or in humid tropical environments, transmissivity can drop to 0.4-0.6, providing significant natural attenuation of the thermal hazard. This effect is important in establishing safe distances: the atmosphere itself provides a margin of safety that increases with distance, and humid climates experience somewhat lower thermal radiation levels at the same distance compared to arid environments.

When to Use Solid Flame vs. Point Source

The point source model treats the entire flame as a single radiating point located at the center of the flame. This simplification is computationally convenient but significantly overestimates radiation at close distances (within 2-3 pool diameters) because it ignores the extended geometry of the flame. The solid flame model treats the flame as a cylinder with distributed emissive power and produces accurate results at all distances. Industry practice and regulatory guidance (API RP 752, CCPS) require the solid flame model for facility siting studies. The point source model remains useful for quick screening calculations and for receptors at distances greater than five pool diameters, where both models converge to similar predictions.

6. Fuel Properties and Dike Design Impact

The characteristics of a pool fire are strongly influenced by both the fuel properties and the geometry of the containment system. In midstream and pipeline operations, the most commonly encountered pool fire fuels are crude oil, condensate, natural gas liquids (NGL), refined products such as gasoline and diesel, and produced water containing dissolved hydrocarbons. Each fuel has distinct burning rate, heat of combustion, boiling point, and smoke production characteristics that must be properly modeled.

Dike Design and Pool Diameter

Dike design is one of the most effective engineering controls for managing pool fire consequences. By confining the spilled liquid to a defined area, the dike determines the pool diameter, which in turn controls the flame height, burning rate, and radiation intensity. The fundamental trade-off in dike design is between pool area and flame height: a larger dike area produces a wider, shorter flame with a higher total heat release rate but potentially lower SEP due to soot effects, while a smaller dike produces a narrower, taller flame with higher SEP but a smaller radiating area.

API 2610 and NFPA 30 provide requirements for dike sizing around storage tanks. The dike must contain the full volume of the largest tank plus freeboard for firewater and rainfall. For consequence analysis, the key parameter is the effective pool diameter, which for rectangular dikes is calculated as the hydraulic diameter: D_eff = 4 × A / P, where A is the diked area and P is the dike perimeter. Irregular dike shapes should be converted to equivalent circular diameters using D = (4A / π)^0.5 for radiation modeling.

Unconfined Spills

When a liquid hydrocarbon is released without containment, it spreads across the terrain until either the supply ceases or the spreading rate reaches equilibrium with the regression rate from burning. For continuous releases, the equilibrium pool diameter depends on the release rate and the mass burning rate. For instantaneous releases (such as a sudden tank failure), the pool spreads to a maximum diameter and then contracts as the fuel burns. On flat, impervious ground, an unconfined spill of crude oil can spread to very large diameters, potentially exceeding 100 meters for a large tank failure, creating an enormous fire with relatively low SEP but extremely high total heat output. On porous soil or gravel, absorption limits the pool extent and typically produces smaller, deeper pools with correspondingly smaller fire diameters.

7. Hazard Zones and Safe Separation Distances

Safe separation distances from pool fires are established using thermal radiation flux thresholds that correspond to specific injury and damage criteria. These thresholds are applied in facility siting studies per API RP 752 and quantitative risk assessments to determine minimum distances between potential fire sources and occupied buildings, property boundaries, equipment, and emergency response positions. Unlike BLEVE fireballs, which are transient events, pool fires are sustained hazards where the duration of exposure is a critical factor in injury assessment.

Practical Example: Crude Oil Dike Fire

Consider a crude oil tank with a 30-meter diameter dike. The effective pool diameter is approximately 30 meters. Using the burning rate for crude oil (m" = 0.045 kg/m²s for a 30-meter pool), the Thomas correlation gives a flame height of approximately 30-35 meters (H/D ratio of approximately 1.0-1.2). The surface emissive power at this diameter is approximately 30-40 kW/m² due to heavy soot obscuration. Applying the solid flame model with atmospheric transmissivity of 0.80 (moderate humidity), the 4.7 kW/m² contour (emergency response perimeter) occurs at approximately 100-120 meters from the pool edge, and the 1.6 kW/m² contour (property boundary limit) at approximately 180-220 meters. These distances form the basis for facility layout and emergency planning.

Wind Direction and Asymmetric Hazard Zones

Under windy conditions, the hazard zone becomes asymmetric around the pool. The downwind sector experiences significantly higher radiation due to flame tilt and base drag, while the upwind sector receives reduced radiation. For a 20-meter crude oil pool fire in a 5 m/s wind, the 4.7 kW/m² contour may extend 50% farther downwind compared to the calm-wind case and contract by 30% upwind. Conservative practice for facility siting is to evaluate the radiation contour for the prevailing wind direction blowing toward each receptor, ensuring adequate separation under the worst-case wind scenario.

Comparison with Jet Fire and BLEVE Hazard Zones

Pool fires, jet fires, and BLEVE fireballs produce different thermal radiation hazard footprints. A pool fire creates a broad, roughly circular (or wind-elongated) hazard zone centered on the pool at ground level. The hazard decreases gradually with distance due to the extended source geometry. A jet fire creates an elongated hazard zone aligned with the release direction, with very high radiation near the flame impingement zone but rapid decrease perpendicular to the flame axis. A BLEVE fireball creates a circular hazard zone centered on the vessel location, with the radiation decreasing rapidly with distance from the elevated fireball. For the same total fuel mass, a BLEVE generally produces higher peak radiation but for a much shorter duration than a pool fire. Consequence analysis for a complete QRA should model all three scenarios where applicable.

Key Takeaways

• Pool diameter controls everything: Burning rate, flame height, surface emissive power, and hazard zone extent all depend primarily on the effective pool diameter. Dike design is the most important engineering control for managing pool fire consequences.
• Soot reduces SEP for large fires: Pool fires larger than 10 meters in diameter produce significant soot that reduces the time-averaged surface emissive power to 20-40 kW/m², but intermittent clear-air windows can produce peak values 2-3 times higher.
• Use the solid flame model: The point source model overestimates radiation at close range. API RP 752 and CCPS guidelines require solid flame modeling with the tilted cylinder geometry for facility siting studies.
• Wind creates asymmetric hazards: Flame tilt under windy conditions significantly increases the downwind hazard zone. Always evaluate the worst-case wind direction toward each receptor location.
• Transmissivity matters at distance: Atmospheric absorption reduces incident radiation by 20-50% at typical facility boundary distances, providing some natural attenuation that increases with path length and humidity.
• Duration distinguishes pool fires: Unlike transient BLEVE fireballs, pool fires persist for minutes to hours, making structural exposure time a critical factor in fire protection design and personnel egress planning.