Oxygen consumption principle - Revision history

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	The '''oxygen consumption principle''' states that the burning of organic fuels releases a nearly constant amount of heat per unit mass of oxygen consumed, about 13.1 kJ per gram of oxygen.<ref name="JA-45">Janssens (2002), p. 3-45.</ref> Thornton found this regularity in 1917 for organic liquids and gases. Huggett later showed that it also holds for organic solids, with an average value that is accurate within ±5 % with very few exceptions.<ref name="TH">Thornton (1917) and Huggett (1980), as cited in Janssens (2002), p. 3-45.</ref> The [[heat release rate]] of a fire can therefore be determined by measuring how much oxygen the fire removes from the air, without knowing exactly what is burning.<ref name="JA-45" />		The '''oxygen consumption principle''' states that the burning of organic fuels releases a nearly constant amount of heat per unit mass of oxygen consumed, about 13.1 kJ per gram of oxygen.<ref name="JA-45">Janssens (2002), p. 3-45.</ref> Thornton found this regularity in 1917 for organic liquids and gases. Huggett later showed that it also holds for organic solids, with an average value that is accurate within ±5 % with very few exceptions.<ref name="TH">Thornton (1917) and Huggett (1980), as cited in Janssens (2002), p. 3-45.</ref> The [[heat release rate]] of a fire can therefore be determined by measuring how much oxygen the fire removes from the air, without knowing exactly what is burning.<ref name="JA-45" />

	This idea is the basis of oxygen consumption calorimetry. The method is regarded as the most accurate and practical technique for measuring heat release rates in fire experiments, at bench scale and at large scale.<ref name="JA-46">Janssens (2002), p. 3-46.</ref> The [[cone calorimeter]], the [[room corner test]] and the [[Single Burning Item test]] all rely on it.<ref name="BA-64">Babrauskas (2002a), p. 3-64.</ref><ref name="JA-58">Janssens (2002), p. 3-58.</ref><ref name="BB-32">Babrauskas (2002b), p. 3-32.</ref> The heat release rate is the single most important parameter characterising a fire, and in many fire experiments it is measured by oxygen consumption calorimetry.<ref name="HM-31">Hamins and McGrattan (2007), p. 3-1.</ref><ref name="HM-32">Hamins and McGrattan (2007), p. 3-2.</ref>		This idea is the basis of oxygen consumption calorimetry. The method is regarded as the most accurate and practical technique for measuring heat release rates in fire experiments, at bench scale and at large scale.<ref name="JA-46">Janssens (2002), p. 3-46.</ref> The [[cone calorimeter]], the [[room corner test]] and the Single Burning Item test all rely on it.<ref name="BA-64">Babrauskas (2002a), p. 3-64.</ref><ref name="JA-58">Janssens (2002), p. 3-58.</ref><ref name="BB-32">Babrauskas (2002b), p. 3-32.</ref> The heat release rate is the single most important parameter characterising a fire, and in many fire experiments it is measured by oxygen consumption calorimetry.<ref name="HM-31">Hamins and McGrattan (2007), p. 3-1.</ref><ref name="HM-32">Hamins and McGrattan (2007), p. 3-2.</ref>

	== Principle ==		== Principle ==

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	The constancy can be checked with [[stoichiometry]], which gives the amounts of substances consumed and formed in a reaction. One mole of methane, about 16 g, burns completely with two moles of oxygen, about 64 g.<ref name="VR-3.3">Van Rossum (2027), §3.3.</ref> With a heat of combustion of 800 kJ/mol, methane therefore releases 800/64 = 12.5 kJ per gram of oxygen.<ref name="DR-93" /> Propane releases 2,044 kJ/mol and needs five moles, or 160 g, of oxygen, which gives 12.8 kJ/g. Both values lie within 5 % of the average of 13.1 kJ/g.<ref name="DR-93" />		The constancy can be checked with [[stoichiometry]], which gives the amounts of substances consumed and formed in a reaction. One mole of methane, about 16 g, burns completely with two moles of oxygen, about 64 g.<ref name="VR-3.3">Van Rossum (2027), §3.3.</ref> With a heat of combustion of 800 kJ/mol, methane therefore releases 800/64 = 12.5 kJ per gram of oxygen.<ref name="DR-93" /> Propane releases 2,044 kJ/mol and needs five moles, or 160 g, of oxygen, which gives 12.8 kJ/g. Both values lie within 5 % of the average of 13.1 kJ/g.<ref name="DR-93" />
			[[File:fse-oxygen-consumption-principle-v1.svg\|thumb\|upright=1.5\|alt=Two bar charts for nine fuels: heat per gram of fuel ranges from 10 to 50 kJ, heat per gram of oxygen stays near 13 kJ except for CO.\|Heat of combustion per gram of fuel (left) and per gram of oxygen consumed (right), with the average of 13.1 kJ/g. Based on Drysdale (2002), p. 1-93.]]

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	== Measuring the heat release rate ==		== Measuring the heat release rate ==
	The basic requirement is that all combustion products are collected and removed through an exhaust duct. Far enough downstream for the gases to be well mixed, both the flow rate and the composition of the gases are measured. The inflow of air does not have to be measured, as long as the flow in the exhaust duct is known.<ref name="JA-46" /> Applying Thornton's rule to such a system gives a simple oxygen balance:<ref name="JA-46" />		The basic requirement is that all combustion products are collected and removed through an exhaust duct. Far enough downstream for the gases to be well mixed, both the flow rate and the composition of the gases are measured. The inflow of air does not have to be measured, as long as the flow in the exhaust duct is known.<ref name="JA-46" /> Applying Thornton's rule to such a system gives a simple oxygen balance:<ref name="JA-46" />
			[[File:fse-oxygen-consumption-principle-v2.svg\|thumb\|upright=1.5\|alt=Fire under a hood connected to an exhaust duct with a fan; flow and oxygen are measured in the duct.\|An oxygen consumption calorimeter: all products are collected in a hood; flow rate and oxygen concentration are measured in the exhaust duct. Based on Janssens (2002), p. 3-46.]]

	<math display="block">\dot{q} = E \left( \dot{m}_a \, Y^a_{\mathrm{O_2}} - \dot{m}_e \, Y^e_{\mathrm{O_2}} \right)</math>		<math display="block">\dot{q} = E \left( \dot{m}_a \, Y^a_{\mathrm{O_2}} - \dot{m}_e \, Y^e_{\mathrm{O_2}} \right)</math>
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	== Calorimeters based on the principle ==		== Calorimeters based on the principle ==
	The cone calorimeter is the preferred instrument for measuring the heat release rate at bench scale. A specimen of 100 mm by 100 mm, 6 to 50 mm thick, is exposed to a radiant heat flux of up to 110 kW/m² and ignited by an electric spark.<ref name="BA-63" /> The instrument has been designed to use only oxygen consumption as its measuring principle. Besides the heat release rate, it measures the effective heat of combustion, the mass loss rate, ignitability, smoke and toxic gases.<ref name="BA-63" /><ref name="BA-64" />		The cone calorimeter is the preferred instrument for measuring the heat release rate at bench scale. A specimen of 100 mm by 100 mm, 6 to 50 mm thick, is exposed to a radiant heat flux of up to 110 kW/m² and ignited by an electric spark.<ref name="BA-63" /> The instrument has been designed to use only oxygen consumption as its measuring principle. Besides the heat release rate, it measures the effective heat of combustion, the mass loss rate, ignitability, smoke and toxic gases.<ref name="BA-63" /><ref name="BA-64" />
			[[File:fse-oxygen-consumption-principle-v3.svg\|thumb\|upright=1.5\|alt=Cross-section of a cone calorimeter: specimen on a load cell under a conical heater, with hood, exhaust duct, gas sampling and blower above.\|Main parts of the cone calorimeter. Based on Babrauskas (2002a), pp. 3-63 and 3-64.]]

	The room corner test is a standardised large-scale test for wall and ceiling linings. Specimens line the walls and ceiling of a small room, and a gas burner in one rear corner ignites them. All combustion products leave through the doorway into a hood, where the gases are analysed.<ref name="JA-39">Janssens (2002), p. 3-39.</ref>		The room corner test is a standardised large-scale test for wall and ceiling linings. Specimens line the walls and ceiling of a small room, and a gas burner in one rear corner ignites them. All combustion products leave through the doorway into a hood, where the gases are analysed.<ref name="JA-39">Janssens (2002), p. 3-39.</ref>
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	Interlaboratory trials, known as round robins, show the random error separately. They quantify the repeatability within one laboratory and the reproducibility between laboratories. For the peak heat release rate, both limits are much wider for the larger apparatus than for the cone calorimeter.<ref name="BB-33">Babrauskas (2002b), p. 3-33.</ref>		Interlaboratory trials, known as round robins, show the random error separately. They quantify the repeatability within one laboratory and the reproducibility between laboratories. For the peak heat release rate, both limits are much wider for the larger apparatus than for the cone calorimeter.<ref name="BB-33">Babrauskas (2002b), p. 3-33.</ref>
			[[File:fse-oxygen-consumption-principle-v4.svg\|thumb\|upright=1.5\|alt=Bar chart of 95 % limits for peak heat release rate: cone 17 and 23 %, SBI 38 and 54 %, room calorimeter 65 and 79 %.\|Repeatability (r) and reproducibility (R) of the peak heat release rate in round robins, as 95 % confidence limits. Based on Babrauskas (2002b), p. 3-33.]]

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FSE wiki: corrections after independent fact-check (written by Claude Opus 5.5)

Mark: New FSE wiki article: Oxygen consumption principle (written by Claude Opus 5.5)

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New FSE wiki article: Oxygen consumption principle (written by Claude Opus 5.5)

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The '''oxygen consumption principle''' states that the burning of organic fuels releases a nearly constant amount of heat per unit mass of oxygen consumed, about 13.1 kJ per gram of oxygen.<ref name="JA-45">Janssens (2002), p. 3-45.</ref> Thornton found this regularity in 1917 for organic liquids and gases. Huggett later showed that it also holds for organic solids, with an average value that is accurate within ±5 % with very few exceptions.<ref name="TH">Thornton (1917) and Huggett (1980), as cited in Janssens (2002), p. 3-45.</ref> The [[heat release rate]] of a fire can therefore be determined by measuring how much oxygen the fire removes from the air, without knowing exactly what is burning.<ref name="JA-45" />

This idea is the basis of oxygen consumption calorimetry. The method is regarded as the most accurate and practical technique for measuring heat release rates in fire experiments, at bench scale and at large scale.<ref name="JA-46">Janssens (2002), p. 3-46.</ref> The [[cone calorimeter]], the [[room corner test]] and the [[Single Burning Item test]] all rely on it.<ref name="BA-64">Babrauskas (2002a), p. 3-64.</ref><ref name="JA-58">Janssens (2002), p. 3-58.</ref><ref name="BB-32">Babrauskas (2002b), p. 3-32.</ref> The heat release rate is the single most important parameter characterising a fire, and in many fire experiments it is measured by oxygen consumption calorimetry.<ref name="HM-31">Hamins and McGrattan (2007), p. 3-1.</ref><ref name="HM-32">Hamins and McGrattan (2007), p. 3-2.</ref>

== Principle ==
The [[heat of combustion]] of a fuel is the heat released when it burns completely. Expressed per gram of fuel, it differs strongly between materials, from about 16 kJ/g for cellulose to 50 kJ/g for methane. Expressed per gram of oxygen consumed, it is approximately constant for most fuels, with an average of 13.1 kJ/g. Per gram of air consumed, the average is about 3 kJ/g.<ref name="DR-93">Drysdale (2002), p. 1-93.</ref> Thornton's rule implies that it is enough to measure the oxygen consumed in a combustion system to determine the net heat released.<ref name="JA-45" />

Perhaps the first application of the principle in fire research was made by Parker on the ASTM E-84 tunnel test. The technique was then refined at the National Bureau of Standards, now the National Institute of Standards and Technology, in the late 1970s and early 1980s.<ref name="JA-46" /> Since then it has become routine in fire research and fire testing. It is used for small samples as well as for items of furniture and wall lining materials.<ref name="DR-96">Drysdale (2002), p. 1-96.</ref>

The constancy can be checked with [[stoichiometry]], which gives the amounts of substances consumed and formed in a reaction. One mole of methane, about 16 g, burns completely with two moles of oxygen, about 64 g.<ref name="VR-3.3">Van Rossum (2027), §3.3.</ref> With a heat of combustion of 800 kJ/mol, methane therefore releases 800/64 = 12.5 kJ per gram of oxygen.<ref name="DR-93" /> Propane releases 2,044 kJ/mol and needs five moles, or 160 g, of oxygen, which gives 12.8 kJ/g. Both values lie within 5 % of the average of 13.1 kJ/g.<ref name="DR-93" />

{| class="wikitable"
|+ Heat of combustion per gram of fuel and per gram of oxygen consumed, at 25 °C<ref name="DR-93" />
! Fuel !! kJ per g of fuel !! kJ per g of oxygen
|-
| Methane || 50.00 || 12.54
|-
| Propane || 46.45 || 12.80
|-
| Ethanol || 26.78 || 12.88
|-
| Cellulose || 16.09 || 13.59
|-
| Polyethylene || 43.28 || 12.65
|-
| Polystyrene || 39.85 || 12.97
|-
| Polymethylmethacrylate || 24.89 || 12.98
|-
| Polyoxymethylene || 15.46 || 14.50
|-
| Carbon monoxide || 10.10 || 17.69
|}

Other sources give slightly different averages. Tewarson found an average of 12.8 kJ/g with a spread of ±7 % for a large set of materials. He notes that this is close to the 13.4 kJ/g used in the heating and power industries and to Huggett's 13.1 kJ/g.<ref name="TE-104">Tewarson (2002), p. 3-104.</ref> For most testing, the standard value of 13.1 MJ per kilogram of oxygen is used. A small number of substances differ substantially from it, and if their composition is known, the value can be corrected.<ref name="BB-32" />

A related technique uses the carbon dioxide and carbon monoxide generated instead of the oxygen consumed. Tewarson reports average values of 13.3 kJ per gram of carbon dioxide generated, with a spread of ±11 %, and 11.1 kJ per gram of carbon monoxide, with a spread of ±18 %.<ref name="TE-103">Tewarson (2002), p. 3-103.</ref> Both spreads are wider than the ±7 % of the oxygen-based value.<ref name="TE-103" /><ref name="TE-104" />

== Measuring the heat release rate ==
The basic requirement is that all combustion products are collected and removed through an exhaust duct. Far enough downstream for the gases to be well mixed, both the flow rate and the composition of the gases are measured. The inflow of air does not have to be measured, as long as the flow in the exhaust duct is known.<ref name="JA-46" /> Applying Thornton's rule to such a system gives a simple oxygen balance:<ref name="JA-46" />

<math display="block">\dot{q} = E \left( \dot{m}_a \, Y^a_{\mathrm{O_2}} - \dot{m}_e \, Y^e_{\mathrm{O_2}} \right)</math>

Here <math>E</math> is about 13.1 kJ per gram of oxygen, and the mass fraction of oxygen in dry incoming air is 0.232.<ref name="JA-46" /> In practice the equation cannot be used directly, for three reasons. Oxygen analysers measure mole fractions rather than mass fractions. Water vapour is removed from the gas sample before it reaches the analyser, so the reading is on a dry basis. Flow measurements give the volume flow rather than the mass flow, and the combustion reactions change the volume of the gas slightly.<ref name="JA-46" /> For the common case in which only oxygen is measured, after water vapour and carbon dioxide have been removed from the sample, Janssens gives the working equations:<ref name="JA-47">Janssens (2002), p. 3-47.</ref>

<math display="block">\dot{q} = E \, \frac{\phi}{1 + \phi (\alpha - 1)} \, \dot{m}_e \, \frac{M_{\mathrm{O_2}}}{M_a} \left( 1 - X^a_{\mathrm{H_2O}} - X^a_{\mathrm{CO_2}} \right) X^{A,a}_{\mathrm{O_2}}</math>

<math display="block">\phi = \frac{X^{A,a}_{\mathrm{O_2}} - X^{A,e}_{\mathrm{O_2}}}{\left( 1 - X^{A,e}_{\mathrm{O_2}} \right) X^{A,a}_{\mathrm{O_2}}}</math>

{| class="wikitable"
|+ Symbols used in the oxygen consumption equations
! Symbol !! Description !! Unit
|-
| <math>\dot{q}</math> || heat release rate || kW
|-
| <math>E</math> || heat released per mass of oxygen consumed (about 13,100) || kJ/kg
|-
| <math>\dot{m}_a</math>, <math>\dot{m}_e</math> || mass flow rate of incoming air and of exhaust gas || kg/s
|-
| <math>Y^a_{\mathrm{O_2}}</math>, <math>Y^e_{\mathrm{O_2}}</math> || mass fraction of oxygen in the incoming air and in the exhaust gas || –
|-
| <math>\phi</math> || oxygen depletion factor || –
|-
| <math>\alpha</math> || volumetric expansion factor (recommended average 1.105) || –
|-
| <math>M_{\mathrm{O_2}}</math>, <math>M_a</math> || molar mass of oxygen (32) and of air (29)<ref name="VR-3.3" /> || g/mol
|-
| <math>X^a_{\mathrm{H_2O}}</math>, <math>X^a_{\mathrm{CO_2}}</math> || mole fraction of water vapour and of carbon dioxide in the incoming air || –
|-
| <math>X^{A,a}_{\mathrm{O_2}}</math>, <math>X^{A,e}_{\mathrm{O_2}}</math> || measured (dry) mole fraction of oxygen in the incoming air and in the exhaust gas || –
|}

The expansion factor depends on the fuel. It equals 1 for the complete combustion of carbon in dry air and 1.21 for pure hydrogen, and an average of 1.105 is recommended when the fuel is unknown. Air contains about 330 ppm of carbon dioxide and usually less than a few percent of water vapour.<ref name="JA-47" /> With these generic values, the equations are expected to be accurate within ±10 % if the combustion is complete. The error can be larger when much carbon monoxide or soot forms, or when the products include other species such as hydrogen chloride.<ref name="JA-47" />

Adding analysers for carbon dioxide, carbon monoxide and water vapour improves the accuracy. Burning carbon monoxide to carbon dioxide releases about 17.6 kJ per gram of oxygen, so a correction term accounts for carbon that leaves as carbon monoxide.<ref name="JA-47" /> Even under the worst conditions considered by Janssens, ignoring the carbon monoxide causes an error of less than 5 %.<ref name="JA-48">Janssens (2002), p. 3-48.</ref>

High-quality work requires a paramagnetic oxygen analyser. The standards for the cone calorimeter allow at most 50 ppm of noise and drift, and the best instruments reach 20 ppm.<ref name="BA-64" /><ref name="BA-65">Babrauskas (2002a), p. 3-65.</ref> Because a paramagnetic analyser responds to the partial pressure of oxygen, changes in atmospheric pressure must be compensated. Otherwise the calculated heat release rate can contain a significant error. Carbon dioxide in the sample causes an error of less than 0.3 % in the oxygen reading.<ref name="BA-65" />

== Worked example: a cone calorimeter test ==
The cone calorimeter draws air through its exhaust system at 24 L/s.<ref name="BA-69">Babrauskas (2002a), p. 3-69.</ref> At 20 °C, air has a density of about 1.2 kg/m³, so the exhaust mass flow is about 0.024 × 1.2 = 0.0288 kg/s.<ref name="VR-3.2">Van Rossum (2027), §3.2.</ref> Air contains 21 % oxygen by volume.<ref name="VR-4.2">Van Rossum (2027), §4.2.</ref> Suppose that, during a test, the dry oxygen reading in the exhaust falls from 21.0 % to 20.5 %. The depletion factor and the heat release rate then follow from the equations above. The calculation uses the expansion factor of 1.105, dry incoming air with 330 ppm of carbon dioxide and molar masses of 32 and 29 g/mol:<ref name="JA-47" />

<math display="block">\phi = \frac{0.210 - 0.205}{(1 - 0.205) \times 0.210} \approx 0.0300</math>

<math display="block">\dot{q} = 13{,}100 \times \frac{0.0300}{1 + 0.0300 \times 0.105} \times 0.0288 \times \frac{32}{29} \times (1 - 0.00033) \times 0.210 \approx 2.6\ \mathrm{kW}</math>

The specimen in a cone calorimeter measures 100 mm by 100 mm, or 0.01 m², so this corresponds to about 261 kW/m².<ref name="BA-63">Babrauskas (2002a), p. 3-63.</ref> The result lies well within the normal calibrated range of the instrument, 0 to 12 kW.<ref name="BA-63" /> The example also shows why the analyser must be so precise. A drop of 0.5 percentage points equals 5,000 ppm, so an analyser noise of 20 to 50 ppm corresponds to 0.4 to 1 % of the signal.<ref name="BA-65" />

== Calorimeters based on the principle ==
The cone calorimeter is the preferred instrument for measuring the heat release rate at bench scale. A specimen of 100 mm by 100 mm, 6 to 50 mm thick, is exposed to a radiant heat flux of up to 110 kW/m² and ignited by an electric spark.<ref name="BA-63" /> The instrument has been designed to use only oxygen consumption as its measuring principle. Besides the heat release rate, it measures the effective heat of combustion, the mass loss rate, ignitability, smoke and toxic gases.<ref name="BA-63" /><ref name="BA-64" />

The room corner test is a standardised large-scale test for wall and ceiling linings. Specimens line the walls and ceiling of a small room, and a gas burner in one rear corner ignites them. All combustion products leave through the doorway into a hood, where the gases are analysed.<ref name="JA-39">Janssens (2002), p. 3-39.</ref>

In the international version, ISO 9705 of 1992, the room is about 2.4 m wide, 3.7 m deep and 2.4 m high, with a single doorway of about 0.8 m by 2.0 m. A sand burner of 0.17 m by 0.17 m releases 100 kW for 10 minutes and then 300 kW for another 10 minutes.<ref name="JA-58" /> The American room test standard NFPA 286 uses a nearly identical room with a burner output of 40 kW for 5 minutes, followed by 160 kW for 10 minutes. In one series of room tests, a total heat release rate of 1 MW served as one of the criteria for [[flashover]].<ref name="JA-58" />

The Single Burning Item test is a European regulatory heat release test for building products. It uses two wall panels in a corner configuration, without a ceiling.<ref name="BB-32" /> Larger set-ups follow the same principle. Furniture calorimeters measure the heat release rate of chairs, sofas and mattresses placed on a load cell beneath a hood.<ref name="JA-57">Janssens (2002), p. 3-57.</ref> Industrial-size calorimeters reach into the megawatt range, and measurements from fires of a few kilowatts up to 100 MW have been reported.<ref name="JA-58" /> For comparison, an average living room sofa burns with a heat release rate of about 2.5 MW.<ref name="VR-4.5">Van Rossum (2027), §4.5.</ref>

== Accuracy and uncertainty ==
Uncertainty arises from both bias and random error. The fixed value of 13.1 MJ/kg is one source of bias, and calibration with a metered flow of pure gas reduces bias in general.<ref name="BB-32" /> NUREG-1824 summarises several uncertainty studies of oxygen consumption calorimetry. For the Single Burning Item test and the room corner test, the relative expanded uncertainty ranged from 0.07 to 0.14, and for the cone calorimeter from 0.10 to 0.12.<ref name="HM-32" /> The oxygen measurement and the exhaust mass flow were consistently identified as major sources of uncertainty, and the heat release factor also contributed. Larger oxygen deficits give smaller combined uncertainties.<ref name="HM-32" />

Interlaboratory trials, known as round robins, show the random error separately. They quantify the repeatability within one laboratory and the reproducibility between laboratories. For the peak heat release rate, both limits are much wider for the larger apparatus than for the cone calorimeter.<ref name="BB-33">Babrauskas (2002b), p. 3-33.</ref>

{| class="wikitable"
|+ 95 % confidence limits of the peak heat release rate from round robin tests (r = repeatability, R = reproducibility)<ref name="BB-33" />
! Apparatus !! Year of round robin !! r (%) !! R (%)
|-
| Cone calorimeter || 2000 || 17 || 23
|-
| Single Burning Item test || 1997 || 38 || 54
|-
| Room calorimeter || 1994 || 65 || 79
|}

== Use in fire safety engineering ==
The heat release rate is the primary variable that determines how much a material contributes to the hazard of a compartment fire.<ref name="JA-38">Janssens (2002), p. 3-38.</ref> It controls how strongly a fire heats its surroundings, and it is the most significant input uncertainty of fire models.<ref name="HM-31" /> The fire models evaluated in NUREG-1824 do not predict the heat release rate but take it as an input. In the experiments used for that evaluation, it was determined from the fuel mass loss rate or by oxygen consumption calorimetry.<ref name="HM-31" /><ref name="HM-32" /> Data from furniture calorimeters serve as input to compartment fire and smoke transport models.<ref name="JA-57" /> Bench-scale data can also be used with calculation methods to predict the behaviour of linings in the room corner test.<ref name="JA-39" />

The principle also appears inside fire models. CFAST takes the heat of combustion based on oxygen consumption as 13.1 MJ/kg, representative of typical hydrocarbon fuels, when it limits burning by the available oxygen.<ref name="PE-13">Peacock et al. (2026), p. 13.</ref> The Fire Dynamics Simulator uses about 13,100 kJ/kg for most fuels in its extinction model.<ref name="MG-62">McGrattan et al. (2026), p. 62.</ref>

Building regulations refer to test methods based on the principle. In Australia, the non-mandatory data sheets for the Fire Safety Verification Method of the Australian Building Codes Board (2020) define a reference design scenario closely aligned to ISO 9705.<ref name="AB-B2">Australian Building Codes Board (2020a), Data Sheet B2, p. 1.</ref> A corner fire burns at 100 kW for 10 minutes and then at 300 kW for 10 minutes, unless the wall and ceiling linings become involved.<ref name="AB-48">Australian Building Codes Board (2020a), Data Sheet B4, p. 48.</ref> The group number of the lining, determined in accordance with AS 5637, then sets the growth of the design fire.<ref name="AB-48" /> In New Zealand, Building Code clause C3.4 as reproduced in the 2013 commentary to C/VM2 specified internal surface linings by material group numbers determined under ISO 9705.<ref name="NZ-18">Ministry of Business, Innovation and Employment (2013), p. 18.</ref> The second edition of C/VM2 (2025) has removed its references to product test standards such as ISO 5660 and ISO 9705, which now appear in separate Building Product Specifications.<ref name="NZ-3">Ministry of Business, Innovation and Employment (2025b), p. 3.</ref>

== Limitations and misconceptions ==
The method only works if all combustion products reach the exhaust duct.<ref name="JA-46" /> The standard exhaust flow of the cone calorimeter, 24 L/s, is about twice the minimum flow at which no gases spill out of the hood.<ref name="BA-69" /> The constant of 13.1 kJ/g is an average. Fuels such as polyoxymethylene, at 14.50 kJ/g, and carbon monoxide, at 17.69 kJ/g, deviate considerably from it.<ref name="DR-93" />

Oxygen consumption gives the total heat release rate, not how that heat is divided between convection and radiation. The convective fraction depends on the design of the apparatus and on the size of the specimen, so it is not a material property. The cone calorimeter was therefore deliberately designed without a separate measurement of the convected heat.<ref name="BA-64" />

The measured heat release also differs from what a bomb calorimeter suggests. The effective heat of combustion is the ratio of the heat release rate to the mass loss rate. For most solid materials it is significantly lower than the heat of combustion measured in pure oxygen at high pressure in a bomb calorimeter. The effective value is the one to use in fire hazard assessment.<ref name="JA-39" /> A single test result is not an exact number either, given the reproducibility of 23 to 79 % between laboratories for the peak heat release rate.<ref name="BB-33" />

== See also ==
* [[Effective heat of combustion]]
* [[Equivalence ratio]]
* [[Adiabatic flame temperature]]
* [[Incomplete combustion]]

== Notes ==
<references />

== References ==
* Australian Building Codes Board. (2020a). ''Data sheets: Fire Safety Verification Method'' (Handbook annex, Print version 1.1).
* Babrauskas, V. (2002a). The cone calorimeter. 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. 3-63–3-81). National Fire Protection Association; Society of Fire Protection Engineers.
* 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.
* Drysdale, D. D. (2002). Thermochemistry. 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. 1-90–1-98). National Fire Protection Association; Society of Fire Protection Engineers.
* Hamins, A., & McGrattan, K. (2007). ''Verification and validation of selected fire models for nuclear power plant applications: Vol. 2. Experimental uncertainty'' (NUREG-1824; EPRI 1011999). U.S. Nuclear Regulatory Commission, Office of Nuclear Regulatory Research; Electric Power Research Institute.
* Janssens, M. (2002). Calorimetry. 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. 3-38–3-62). National Fire Protection Association; Society of Fire Protection Engineers.
* McGrattan, K., Hostikka, S., Floyd, J., McDermott, R., Vanella, M., Mueller, E., & Paul, C. (2026). ''Fire Dynamics Simulator technical reference guide: Vol. 1. Mathematical model'' (6th ed., NIST Special Publication 1018-1). National Institute of Standards and Technology. https://doi.org/10.6028/NIST.SP.1018
* Ministry of Business, Innovation and Employment. (2013). ''Commentary for Building Code clauses C1–C6 and Verification Method C/VM2''.
* Ministry of Business, Innovation and Employment. (2025b). ''Verification Method C/VM2: Framework for fire safety design'' (2nd ed.).
* Peacock, R. D., McGrattan, K. B., Forney, G. P., & Reneke, P. A. (2026). ''CFAST – Consolidated Fire and Smoke Transport: Vol. 1. Technical reference guide'' (Version 7, NIST Technical Note 1889v1). National Institute of Standards and Technology. https://doi.org/10.6028/NIST.TN.1889v1
* 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.

[[Category:Combustion]]

← Older revision		Revision as of 00:22, 2 November 2026
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	\| <math>\alpha</math> \|\| volumetric expansion factor (recommended average 1.105) \|\| –		\| <math>\alpha</math> \|\| volumetric expansion factor (recommended average 1.105) \|\| –
	\|-		\|-
	\| <math>M_{\mathrm{O_2}}</math>, <math>M_a</math> \|\| molar mass of oxygen (32) and of air (29)<ref name="VR-~~3.3~~" /> \|\| g/mol		\| <math>M_{\mathrm{O_2}}</math>, <math>M_a</math> \|\| molar mass of oxygen (32)<ref name="VR-3.3" /> and of dry air (29)<ref name="JA-47" /> \|\| g/mol
	\|-		\|-
	\| <math>X^a_{\mathrm{H_2O}}</math>, <math>X^a_{\mathrm{CO_2}}</math> \|\| mole fraction of water vapour and of carbon dioxide in the incoming air \|\| –		\| <math>X^a_{\mathrm{H_2O}}</math>, <math>X^a_{\mathrm{CO_2}}</math> \|\| mole fraction of water vapour and of carbon dioxide in the incoming air \|\| –
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	\|}		\|}

	The expansion factor depends on the fuel. It equals 1 for the complete combustion of carbon in dry air and 1.21 for pure hydrogen, and an average of 1.105 is recommended when the fuel is unknown. ~~Air~~ contains about 330 ppm of carbon dioxide and ~~usually~~ less than a few percent ~~of water vapour~~.<ref name="JA-47" /> With these generic values, the equations are expected to be accurate within ±10 % if the combustion is complete. The error can be larger when much carbon monoxide or soot forms, or when the products include other species such as hydrogen chloride.<ref name="JA-47" />		The expansion factor depends on the fuel. It equals 1 for the complete combustion of carbon in dry air and 1.21 for pure hydrogen, and an average of 1.105 is recommended when the fuel is unknown. Dry air contains about 330 ppm of carbon dioxide, and in a temperature-controlled laboratory the water vapour content is typically less than a few percent.<ref name="JA-47" /> With these generic values, the equations are expected to be accurate within ±10 % if the combustion is complete. The error can be larger when much carbon monoxide or soot forms, or when the products include other species such as hydrogen chloride.<ref name="JA-47" />

	Adding analysers for carbon dioxide, carbon monoxide and water vapour improves the accuracy. Burning carbon monoxide to carbon dioxide releases about 17.6 kJ per gram of oxygen, so a correction term accounts for carbon that leaves as carbon monoxide.<ref name="JA-47" /> Even under the worst conditions considered by Janssens, ignoring the carbon monoxide causes an error of less than 5 %.<ref name="JA-48">Janssens (2002), p. 3-48.</ref>		Adding analysers for carbon dioxide, carbon monoxide and water vapour improves the accuracy. Burning carbon monoxide to carbon dioxide releases about 17.6 kJ per gram of oxygen, so a correction term accounts for carbon that leaves as carbon monoxide.<ref name="JA-47" /> Even under the worst conditions considered by Janssens, ignoring the carbon monoxide causes an error of less than 5 %.<ref name="JA-48">Janssens (2002), p. 3-48.</ref>
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	== Worked example: a cone calorimeter test ==		== Worked example: a cone calorimeter test ==
	The cone calorimeter draws air through its exhaust system at 24 L/s.<ref name="BA-69">Babrauskas (2002a), p. 3-69.</ref> At 20 °C, air has a density of about 1.2 kg/m³, so the exhaust mass flow is about 0.024 × 1.2 = 0.0288 kg/s.<ref name="VR-3.2">Van Rossum (2027), §3.2.</ref> Air contains 21 % oxygen by volume.<ref name="VR-4.2">Van Rossum (2027), §4.2.</ref> Suppose that, during a test, the dry oxygen reading in the exhaust falls from 21.0 % to 20.5 %. The depletion factor and the heat release rate then follow from the equations above. The calculation uses the expansion factor of 1.105, dry incoming air with 330 ppm of carbon dioxide and molar masses of 32 and 29 g/mol:<ref name="JA-47" />		The cone calorimeter draws air through its exhaust system at 24 L/s.<ref name="BA-69">Babrauskas (2002a), p. 3-69.</ref> At 20 °C, air has a density of about 1.2 kg/m³, so the exhaust mass flow is about 0.024 × 1.2 = 0.0288 kg/s.<ref name="VR-3.2">Van Rossum (2027), §3.2.</ref> Air contains 21 % oxygen by volume.<ref name="VR-4.2">Van Rossum (2027), §4.2.</ref> Suppose that, during a test, the dry oxygen reading in the exhaust falls from 21.0 % to 20.5 %. The depletion factor and the heat release rate then follow from the equations above. The calculation uses the expansion factor of 1.105, dry incoming air with 330 ppm of carbon dioxide and molar masses of 32 and 29 g/mol:<ref name="JA-47" /><ref name="VR-3.3" />

	<math display="block">\phi = \frac{0.210 - 0.205}{(1 - 0.205) \times 0.210} \approx 0.0300</math>		<math display="block">\phi = \frac{0.210 - 0.205}{(1 - 0.205) \times 0.210} \approx 0.0300</math>
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	The principle also appears inside fire models. CFAST takes the heat of combustion based on oxygen consumption as 13.1 MJ/kg, representative of typical hydrocarbon fuels, when it limits burning by the available oxygen.<ref name="PE-13">Peacock et al. (2026), p. 13.</ref> The Fire Dynamics Simulator uses about 13,100 kJ/kg for most fuels in its extinction model.<ref name="MG-62">McGrattan et al. (2026), p. 62.</ref>		The principle also appears inside fire models. CFAST takes the heat of combustion based on oxygen consumption as 13.1 MJ/kg, representative of typical hydrocarbon fuels, when it limits burning by the available oxygen.<ref name="PE-13">Peacock et al. (2026), p. 13.</ref> The Fire Dynamics Simulator uses about 13,100 kJ/kg for most fuels in its extinction model.<ref name="MG-62">McGrattan et al. (2026), p. 62.</ref>

	Building regulations refer to test methods based on the principle. In Australia, the non-mandatory data sheets for the Fire Safety Verification Method of the Australian Building Codes Board (~~2020~~) define a reference design scenario closely aligned to ISO 9705.<ref name="AB-B2">Australian Building Codes Board (2020a), Data Sheet B2, p. 1.</ref> A corner fire burns at 100 kW for 10 minutes and then at 300 kW for 10 minutes, unless the wall and ceiling linings become involved.<ref name="AB-48">Australian Building Codes Board (2020a), Data Sheet B4, p. 48.</ref> The group number of the lining, determined in accordance with AS 5637, then sets the growth of the design fire.<ref name="AB-48" /> In New Zealand, Building Code clause C3.4 as reproduced in the 2013 commentary to C/VM2 specified internal surface linings by material group numbers determined under ISO 9705.<ref name="NZ-18">Ministry of Business, Innovation and Employment (2013), p. 18.</ref> The second edition of C/VM2 (2025) has removed its references to product test standards such as ISO 5660 and ISO 9705, which now appear in separate Building Product Specifications.<ref name="NZ-3">Ministry of Business, Innovation and Employment (2025b), p. 3.</ref>		Building regulations refer to test methods based on the principle. In Australia, the non-mandatory data sheets for the Fire Safety Verification Method of the Australian Building Codes Board (2020a) define a reference design scenario closely aligned to ISO 9705.<ref name="AB-B2">Australian Building Codes Board (2020a), Data Sheet B2, p. 1.</ref><ref name="AB-48" /> A corner fire burns at 100 kW for 10 minutes and then at 300 kW for 10 minutes, unless the wall and ceiling linings become involved.<ref name="AB-48">Australian Building Codes Board (2020a), Data Sheet B4, p. 48.</ref> The group number of the lining, determined in accordance with AS 5637, then sets the growth of the design fire.<ref name="AB-48" /> In New Zealand, Building Code clause C3.4 as reproduced in the 2013 commentary to C/VM2 specified internal surface linings by material group numbers determined under ISO 9705.<ref name="NZ-18">Ministry of Business, Innovation and Employment (2013), p. 18.</ref> The second edition of C/VM2 (2025) has removed its references to product test standards such as ISO 5660 and ISO 9705, which now appear in separate Building Product Specifications.<ref name="NZ-3">Ministry of Business, Innovation and Employment (2025b), p. 3.</ref>

	== Limitations and misconceptions ==		== Limitations and misconceptions ==