Burning rate

The burning rate of a fire is the rate at which its fuel is consumed. It is usually expressed as the mass of fuel lost per second (kg/s), or per second and square metre of burning surface (kg/(m²·s)). It is also known as the mass loss rate and is measured by weighing the fuel as it burns. Multiplied by the heat of combustion, the burning rate gives the heat release rate, the quantity that describes how large a fire is.

The term is used loosely. In the SFPE Handbook, Babrauskas notes that "burning rate" may mean either the heat release rate or the mass loss rate. He recommends reserving it for qualitative descriptions and using the more precise terms in calculations. Some fire models even specify a "burning rate" in kW/m².

The burning rate depends on the fuel and its form, on the heat flux that reaches the fuel surface and on the supply of air. Typical values for large pools of hydrocarbon liquids are about 0.02 to 0.1 kg/(m²·s). Engineers use the burning rate to estimate the heat release rate of a fire and how long a given amount of fuel can burn.

Definitions and related quantities

NUREG-1805 is a set of fire dynamics tools for nuclear power plants in the United States. Its glossary defines the mass loss rate as the mass of fuel turned into vapour, but not necessarily burned, per unit time. The burning rate per unit area of fuel surface is called the mass burning flux. The difference between evaporated and burned fuel matters in a fire with too little air. In such a fire, part of the fuel vapour leaves the room unburned.

For liquid pools, the burning rate is also expressed as a regression rate. This is the speed at which the liquid surface descends as the fuel burns, often given in mm/min. The regression rate equals the mass burning rate per unit area divided by the density of the liquid. For confined pools larger than 1 m in diameter, experiments by Blinov and Khudiakov found a regression rate of roughly 4 mm/min for all the fuels they tested.

The burning rate links three quantities that are used throughout fire safety engineering. The heat release rate is the energy released per second. Introduction to Fire Safety Engineering gives about 2.5 MW for an average sofa and a peak of about 8.5 MW for a car. The heat of combustion is the energy per kilogram of fuel, for example 42 MJ/kg for diesel oil and 18 MJ/kg for beech wood. The burning rate connects the two: it tells how many kilograms of fuel are consumed each second.

Why fuels burn at a certain rate

A solid or liquid does not burn directly. It must first be turned into gas, by evaporation for most liquids or by pyrolysis for solids such as wood and plastics. Pyrolysis is the decomposition of a material by heating into smaller molecules, which form flammable pyrolysis gases. The fire heats the fuel, and the gases released by the fuel in turn feed the fire. When this exchange stays in balance, the fire sustains itself.

The burning rate is therefore governed by how much heat reaches the fuel surface and how much energy the fuel needs to turn into gas. Tewarson describes the mass loss rate as the net heat flux into the surface divided by the heat of gasification. The net heat flux is the sum of the radiative and convective heat flux from the flame and any external heat flux, minus the heat that the hot surface radiates away. The heat of gasification is the energy needed to turn a unit mass of the fuel into vapour.

Heat balance at a burning surface: the net heat flux divided by the heat of gasification gives the mass loss rate. Based on Tewarson (2002), p. 3-98.

A worked example in the SFPE Handbook shows the size of the effect. A material with a heat of gasification of 1.8 kJ/g receives a combined flame and external heat flux of 70 kW/m² and loses 10 kW/m² by re-radiation. Its mass loss rate is then (70 − 10)/1.8, or about 33 g/(m²·s). Over a burning area of 2 m², this gives about 67 g/s. If the incoming heat flux rises, for example because hot smoke radiates down on the fuel, the burning rate rises with it.

The form of the fuel matters as well. The burning rate depends both on the chemistry of the fuel, such as cellulosic or petroleum-based, and on its form. An important form factor is the ratio of the surface area available to burn to the total mass of the material. For wood cribs, which are regular stacks of sticks, the burning rate is governed by one of three limits. These are the free burning of the stick surfaces when the sticks are widely spaced, the flow of air through a tightly packed crib, or the oxygen supply of the room.

Pool fires

A liquid pool is possibly the simplest arrangement of fuel, and pool fires have been studied extensively for decades. NUREG-1805 defines a pool fire as a fire on a horizontal, upward-facing fuel surface. This is usually a liquid, but flat slabs of plastics such as PMMA that decompose like liquids also qualify. The burning rate per unit area depends on the pool diameter. Small pools are heated mainly by convection and by conduction from the walls of the pan, large pools mainly by radiation from their own flames.

Babrauskas distinguishes four burning modes by diameter. Pools below 0.05 m burn in a convective laminar mode and pools of 0.05 to 0.2 m in a convective turbulent mode. Between 0.2 and 1.0 m, burning is radiative but the flames are optically thin. Above 1.0 m, the flames are optically thick, and the burning rate per unit area approaches a constant maximum. Pools smaller than about 0.2 m rarely pose a significant hazard, so most fire hazard calculations concern the radiative regime.

Burning rate per unit area of four liquid fuels as a function of pool diameter, with the burning regimes. Based on Babrauskas (2002b), pp. 3-25 to 3-26.

The following relation is the usual way to turn a tabulated burning rate into a heat release rate. It assumes that the heat of combustion stays roughly constant while the fuel burns. For large pools, the heat release rate follows from the burning rate per unit area, the effective heat of combustion and the area of the pool: $$\dot{Q}={\dot{m}}^{″}\cdot \mathrm{\Delta }{H}_{c,\mathrm{e}\mathrm{f}\mathrm{f}}\cdot A_f$$

Symbol	Description	Unit
$\dot{Q}$	heat release rate of the fire	kW
${\dot{m}}^{″}$	burning rate (mass loss rate) per unit area of a large pool	kg/(m²·s)
$\mathrm{\Delta }{H}_{c,\mathrm{e}\mathrm{f}\mathrm{f}}$	effective heat of combustion of the fuel	kJ/kg
$A_f$	horizontal burning area of the fuel	m²

The relation holds for free-burning pools in the open, in still air, in a pan or tank without a high lip. It assumes that the pool is at least several millimetres deep. For pools of a few metres or less, the burning rate per unit area is lower than the large-pool value. NUREG-1805 and the SFPE Handbook therefore multiply by a correction factor that depends on the diameter and on an empirical constant for each fuel. The effective heat of combustion is slightly lower than the value from an oxygen bomb calorimeter, but for most liquids the difference is small.

As a worked example, consider a petrol (gasoline) spill that forms a pool of 3 m diameter in a diked area. The SFPE Handbook gives a large-pool burning rate of 0.055 kg/(m²·s), a heat of combustion of 43.7 MJ/kg and a density of 740 kg/m³ for gasoline. The pool area is 7.07 m², so the heat release rate is 0.055 × 43,700 × 7.07, or about 17 MW. With the empirical constant of 2.1 m⁻¹ for gasoline, the diameter correction changes this result by less than 1% for a pool of this size. The fire is about twice as large as the peak of a burning car.

The same data give the duration of the fire. The regression rate is 0.055/740 m/s, or about 4.5 mm/min. If 100 litres of petrol spread over the 3 m pool, the layer is about 14 mm deep, and the pool burns out in roughly 3 minutes. NUREG-1805 notes the general rule behind this result. For a given amount of fuel, a spill with a large surface burns with a high heat release rate for a short time, while a small spill burns longer at a lower rate.

Tabulated burning rates vary considerably between fuels. Heptane burns at 0.101 kg/(m²·s), kerosene at 0.039 kg/(m²·s) and PMMA at 0.020 kg/(m²·s). Alcohols show little flame radiation and burn slowly. For methanol and ethanol, Babrauskas recommends 0.015 kg/(m²·s) for pools below 0.6 m and 0.029 kg/(m²·s) for pools above 3.0 m.

Large-pool burning rates per unit area of common fuels. Based on Babrauskas (2002b), p. 3-26.

Spills differ from deep pools. A thin layer of liquid on a smooth floor, less than 1 mm deep, burns with a much lower heat release rate per unit area. On smooth surfaces, measured values were only about one-fifth of those for deep pools. Tests with unconfined jet fuel spills on concrete confirmed this. For diameters above about 1 m, their burning rates were about one-fifth of the maximum rates of confined pools, because the thin fuel layer loses much heat to the concrete.

Burning rate in a compartment

Free-burning data apply to fires that are not influenced by the room around them, like a fire outdoors on a calm day. Inside a room, two effects change the burning rate. Hot smoke and heated walls and ceiling radiate back to the fuel surface and increase the burning rate. At the same time, small openings may limit the oxygen supply and reduce the heat release rate. Babrauskas suggests that free-burning pool data become unreliable once the fire would raise the room temperature by more than about 100 °C. Above that, radiative feedback becomes important and no simple formula is available.

In a fuel-controlled fire, enough oxygen is available, and the fire is governed by the rate at which the fuel releases pyrolysis gases. In a ventilation-controlled fire, the supply of oxygen through the openings limits the burning. A fully developed fire in a room is usually ventilation-controlled. The heat release rate in the room is then limited by the available air. For most fuels, about 3000 kJ of heat is released for each kilogram of air consumed.

Fuel-controlled fire (left) and ventilation-controlled fire (right): in the second case the air flow through the opening limits the burning. Based on Van Rossum (2027), §4.8, and Walton and Thomas (2002), pp. 3-173 to 3-174.

For ventilation-controlled room fires, the SFPE Handbook gives an empirical rule from early wood fire tests by Kawagoe. Wood in rooms with small windows burned at about 0.09 kg/s for each unit of the ventilation factor, the opening area times the square root of the opening height. For a door of 0.8 m by 2.0 m, the ventilation factor is 1.6 × √2.0, or about 2.26 m^5/2. The rule then gives a burning rate of about 0.20 kg/s. With an effective heat of combustion of 10.75 MJ/kg for wood in fully developed fires, this corresponds to about 2.2 MW.

A practical consequence is that more fuel does not always mean a faster fire. In an example in the SFPE Handbook, doubling the fire load of a room does not double the burning rate, because the window area restricts the ventilation. The extra fuel then mainly lengthens the fire, since the total heat released still grows with the fire load. Some of the unburned pyrolysis gases may also leave the room and burn outside it.

Uses and limits

The burning rate is mainly used to turn measured or tabulated fuel data into a heat release rate for design and hazard analysis. NUREG-1805 uses it to estimate the heat release rate of pool fires from oil leaks, transformer spills and transient liquids in nuclear power plants. It also uses it to estimate how long a given amount of fuel can burn. In fire models, the burning rate can either be prescribed or be calculated from the heat flux that reaches the fuel. In the computer simulations of the World Trade Center fires, NIST prescribed a burning rate of 450 kW/m² for the furnishings in the workstations. For damaged furnishings, the value was lowered to 300 kW/m².

The simple relation between burning rate and heat release rate has limits. It assumes a constant heat of combustion, which is not always true. For a 17 mm thick sample of western red cedar, the effective heat of combustion rose from about 12 MJ/kg early in the test to about 30 MJ/kg during the charring stage. The same mass loss rate can therefore correspond to very different heat release rates. When the effective heat of combustion is not constant, experimenters therefore normally measure the heat release rate directly instead of converting a mass loss rate.

The ventilation rule also has limits. It was derived mainly from experiments in rooms the size of single offices or rooms in houses. In experiments with long and wide compartments, the fires moved towards the openings, stayed there while local fuel lasted and then travelled through the floor. In such spaces the simple dependence on the ventilation factor does not predict the burning rate well. Most data are also for wood, often in the form of cribs, and other fuels may pyrolyse at different rates.

See also

• Heat release rate per unit area
• Effective heat of combustion
• Boilover

References

• Babrauskas, V. (2002b). Heat release rates. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), SFPE handbook of fire protection engineering (3rd ed., pp. 3-1–3-37). National Fire Protection Association; Society of Fire Protection Engineers.
• Gottuk, D. T., & White, D. A. (2002). Liquid fuel fires. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), SFPE handbook of fire protection engineering (3rd ed., pp. 2-297–2-316). National Fire Protection Association; Society of Fire Protection Engineers.
• Iqbal, N., & Salley, M. H. (2004). Fire Dynamics Tools (FDTs): Quantitative fire hazard analysis methods for the U.S. Nuclear Regulatory Commission Fire Protection Inspection Program (NUREG-1805). U.S. Nuclear Regulatory Commission, Office of Nuclear Reactor Regulation.
• McGrattan, K. B., Bouldin, C., & Forney, G. P. (2005). Computer simulation of the fires in the World Trade Center towers (NIST NCSTAR 1-5F). National Institute of Standards and Technology.
• Tewarson, A. (2002). Generation of heat and chemical compounds in fires. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), SFPE handbook of fire protection engineering (3rd ed., pp. 3-82–3-161). National Fire Protection Association; Society of Fire Protection Engineers.
• Van Rossum, E. (2027). Introduction to Fire Safety Engineering. Fire Safety Academy.
• Walton, W. D., & Thomas, P. H. (2002). Estimating temperatures in compartment fires. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), SFPE handbook of fire protection engineering (3rd ed., pp. 3-171–3-188). National Fire Protection Association; Society of Fire Protection Engineers.