Explosion venting - Revision history

Jan: Remove links to pages that do not exist; retain displayed text (wiki-wide link audit).

2026-11-02T21:32:48Z

Remove links to pages that do not exist; retain displayed text (wiki-wide link audit).

← Older revision		Revision as of 22:32, 2 November 2026
Line 119:		Line 119:
	Lithium-ion batteries raise the same issue in a different way. Van der Graaf and co-workers note that the cells of an electric vehicle battery release gas as soon as they go into thermal runaway.<ref name="VdG-27">Van der Graaf et al. (2021/2023), p. 27.</ref> If this gas is not ignited at once, an explosive mixture can build up in a confined, enclosed or poorly ventilated space.<ref name="VdG-27" /> A fire gas explosion can follow if the mixture reaches its lower explosion limit and is ignited.<ref name="VdG-27" />		Lithium-ion batteries raise the same issue in a different way. Van der Graaf and co-workers note that the cells of an electric vehicle battery release gas as soon as they go into thermal runaway.<ref name="VdG-27">Van der Graaf et al. (2021/2023), p. 27.</ref> If this gas is not ignited at once, an explosive mixture can build up in a confined, enclosed or poorly ventilated space.<ref name="VdG-27" /> A fire gas explosion can follow if the mixture reaches its lower explosion limit and is ignited.<ref name="VdG-27" />

	Fires in electric vehicles can also involve repeated minor explosions.<ref name="VdG-29">Van der Graaf et al. (2021/2023), p. 29.</ref> Any enclosure that holds batteries, from a battery room to a [[battery energy storage system]], can therefore contain a flammable atmosphere when the batteries are overcharged or damaged.<ref name="IS-16-5" /><ref name="VdG-27" /> Vent guidelines, however, rest on tests with near worst-case mixtures, and most do not account for an enclosure that is only partly filled with fuel.<ref name="Z-415" /><ref name="Z-416" />		Fires in electric vehicles can also involve repeated minor explosions.<ref name="VdG-29">Van der Graaf et al. (2021/2023), p. 29.</ref> Any enclosure that holds batteries, from a battery room to a battery energy storage system, can therefore contain a flammable atmosphere when the batteries are overcharged or damaged.<ref name="IS-16-5" /><ref name="VdG-27" /> Vent guidelines, however, rest on tests with near worst-case mixtures, and most do not account for an enclosure that is only partly filled with fuel.<ref name="Z-415" /><ref name="Z-416" />

	== Limitations ==		== Limitations ==

Jan: Add 4 watermarked SVG illustrations from the Expert visual plan

2026-11-02T16:48:14Z

Add 4 watermarked SVG illustrations from the Expert visual plan

← Older revision		Revision as of 17:48, 2 November 2026
Line 1:		Line 1:
	'''Explosion venting''' is the discharge of combustion gases from an enclosure during a [[deflagration]], so that the pressure stays below the level at which the enclosure would be damaged.<ref name="Z-414">Zalosh (2002), p. 3-414.</ref> The enclosure can be a room, a building or a piece of process equipment, and the fuel can be a gas, a dust, a mist or a hybrid mixture of dust and gas.<ref name="Z-414" /> The vent opening is usually covered at first by blow-off panels, rupture discs or other engineered vent devices, which open once the explosion has started.<ref name="Z-414" /> The most effective vents open early, are as large as possible and let the combustion gases escape without restriction.<ref name="Z-414" />		'''Explosion venting''' is the discharge of combustion gases from an enclosure during a [[deflagration]], so that the pressure stays below the level at which the enclosure would be damaged.<ref name="Z-414">Zalosh (2002), p. 3-414.</ref> The enclosure can be a room, a building or a piece of process equipment, and the fuel can be a gas, a dust, a mist or a hybrid mixture of dust and gas.<ref name="Z-414" /> The vent opening is usually covered at first by blow-off panels, rupture discs or other engineered vent devices, which open once the explosion has started.<ref name="Z-414" /> The most effective vents open early, are as large as possible and let the combustion gases escape without restriction.<ref name="Z-414" />
			[[File:fse-explosion-venting-v1.svg\|thumb\|upright=1.5\|alt=Cross-section of a room with a burning gas cloud inside and a blow-off panel in one wall through which flame and gas leave.\|Principle of explosion venting: a panel in the enclosure wall opens at the release pressure Pstat and lets combustion gases out, so that the pressure stays below the reduced pressure Pred that the enclosure can withstand. Based on Zalosh (2002), pp. 3-414 to 3-416.]]

	The vent area needed depends on the size and strength of the enclosure and on how fast the pressure rises, which for dusts is expressed by the [[deflagration index]].<ref name="Z-414" /><ref name="Z-417">Zalosh (2002), p. 3-417.</ref> Design guidance treats weak enclosures, such as buildings, with an equation based on their internal surface area, and strong process equipment with equations based on their volume.<ref name="Z-415">Zalosh (2002), p. 3-415.</ref><ref name="Z-416">Zalosh (2002), p. 3-416.</ref> Unlike explosion suppression, which is costly to install and to reset, venting discharges flame and unburned material and sends a blast wave into the surroundings.<ref name="Z-417" /><ref name="Z-419">Zalosh (2002), p. 3-419.</ref> It cannot protect against a detonation, because the peak pressure arrives with the shock front before any vent can open.<ref name="Z-414" />		The vent area needed depends on the size and strength of the enclosure and on how fast the pressure rises, which for dusts is expressed by the [[deflagration index]].<ref name="Z-414" /><ref name="Z-417">Zalosh (2002), p. 3-417.</ref> Design guidance treats weak enclosures, such as buildings, with an equation based on their internal surface area, and strong process equipment with equations based on their volume.<ref name="Z-415">Zalosh (2002), p. 3-415.</ref><ref name="Z-416">Zalosh (2002), p. 3-416.</ref> Unlike explosion suppression, which is costly to install and to reset, venting discharges flame and unburned material and sends a blast wave into the surroundings.<ref name="Z-417" /><ref name="Z-419">Zalosh (2002), p. 3-419.</ref> It cannot protect against a detonation, because the peak pressure arrives with the shock front before any vent can open.<ref name="Z-414" />
Line 7:		Line 8:

	Typical failure pressures of building elements, collected by Harris, show the size of the gap. Glass windows fail at 2 to 7 kPa, room doors at 2 to 3 kPa, light partition walls at 2 to 5 kPa and unrestrained brick walls at 7 to 15 kPa.<ref name="IS-15-13">Iqbal and Salley (2004), p. 15-13.</ref> Even 200 g of butane, mixed with part of the air in a 48 m³ room and ignited, can raise the pressure by about 0.46 bar, more than the strength of rooms in industrial facilities.<ref name="Z-410" /> Normal process openings let some gas escape, but they are usually far too small to prevent destructive pressures.<ref name="IS-15-3" />		Typical failure pressures of building elements, collected by Harris, show the size of the gap. Glass windows fail at 2 to 7 kPa, room doors at 2 to 3 kPa, light partition walls at 2 to 5 kPa and unrestrained brick walls at 7 to 15 kPa.<ref name="IS-15-13">Iqbal and Salley (2004), p. 15-13.</ref> Even 200 g of butane, mixed with part of the air in a 48 m³ room and ignited, can raise the pressure by about 0.46 bar, more than the strength of rooms in industrial facilities.<ref name="Z-410" /> Normal process openings let some gas escape, but they are usually far too small to prevent destructive pressures.<ref name="IS-15-3" />
			[[File:fse-explosion-venting-v2.svg\|thumb\|upright=1.5\|alt=Bar chart on a logarithmic pressure axis comparing failure pressures of windows, doors and walls with the far higher pressure of an unvented explosion.\|Failure pressures of building elements compared with the final pressure of an unvented gas or dust deflagration in a closed vessel. Based on Iqbal and Salley (2004), p. 15-13, and Zalosh (2002), p. 3-407.]]

	Explosion protection can interrupt the chain of events at three points. It can prevent the flammable mixture, remove the ignition sources, or limit the pressure rise by venting or suppression.<ref name="Z-402">Zalosh (2002), p. 3-402.</ref> For flammable liquid operations, an American loss-prevention guideline summarised in NUREG-1805, FM Data Sheet 7-32 (1993), accordingly asks for at least one of four measures. Equipment with an explosion potential should be vented, built to withstand the explosion pressure, inerted or fitted with suppression.<ref name="IS-B-27">Iqbal and Salley (2004), p. B-27.</ref> Venting accepts that the explosion occurs and limits its pressure to a reduced value, P<sub>red</sub>, that the enclosure can withstand.<ref name="Z-415" /><ref name="Z-416" />		Explosion protection can interrupt the chain of events at three points. It can prevent the flammable mixture, remove the ignition sources, or limit the pressure rise by venting or suppression.<ref name="Z-402">Zalosh (2002), p. 3-402.</ref> For flammable liquid operations, an American loss-prevention guideline summarised in NUREG-1805, FM Data Sheet 7-32 (1993), accordingly asks for at least one of four measures. Equipment with an explosion potential should be vented, built to withstand the explosion pressure, inerted or fitted with suppression.<ref name="IS-B-27">Iqbal and Salley (2004), p. B-27.</ref> Venting accepts that the explosion occurs and limits its pressure to a reduced value, P<sub>red</sub>, that the enclosure can withstand.<ref name="Z-415" /><ref name="Z-416" />
Line 12:		Line 14:
	== Course of a vented explosion ==		== Course of a vented explosion ==
	A vented explosion passes through several phases, which NUREG-1805 shows in a diagram after Harris.<ref name="IS-15-5">Iqbal and Salley (2004), p. 15-5.</ref> First the flame expands inside the closed enclosure and the pressure rises as in an unvented explosion. When the pressure reaches the release pressure of the vent, the vent cover is removed, and shortly afterwards venting is established.<ref name="IS-15-5" /> Later the flame reaches its maximum area and burnt gas flows out through the vent.<ref name="IS-15-5" />		A vented explosion passes through several phases, which NUREG-1805 shows in a diagram after Harris.<ref name="IS-15-5">Iqbal and Salley (2004), p. 15-5.</ref> First the flame expands inside the closed enclosure and the pressure rises as in an unvented explosion. When the pressure reaches the release pressure of the vent, the vent cover is removed, and shortly afterwards venting is established.<ref name="IS-15-5" /> Later the flame reaches its maximum area and burnt gas flows out through the vent.<ref name="IS-15-5" />
			[[File:fse-explosion-venting-v3.svg\|thumb\|upright=1.5\|alt=Four small sketches of a room during a vented explosion above a pressure curve with a first peak at vent opening and a higher second peak.\|Phases of an explosion in a vented building: confined explosion, removal of the vent cover, established venting and maximum flame area. The first pressure peak occurs when the vent opens, the second when turbulence and the largest flame area drive the burning rate. Based on Iqbal and Salley (2004), p. 15-5.]]

	The pressure history shows a first peak when the vent opens and a second peak later in the event.<ref name="IS-15-5" /> NUREG-1805 explains that the release of gases through a vent, even a door or a window, can create turbulence that produces this second peak and increases the overpressure.<ref name="IS-15-5" /> In the example diagram the second peak is the higher of the two.<ref name="IS-15-5" /> Cooper and co-workers identified four types of pressure peak in a near-cubic vessel with a low-pressure vent, and depending on the conditions any one of them can be the maximum.<ref name="Z-415" />		The pressure history shows a first peak when the vent opens and a second peak later in the event.<ref name="IS-15-5" /> NUREG-1805 explains that the release of gases through a vent, even a door or a window, can create turbulence that produces this second peak and increases the overpressure.<ref name="IS-15-5" /> In the example diagram the second peak is the higher of the two.<ref name="IS-15-5" /> Cooper and co-workers identified four types of pressure peak in a near-cubic vessel with a low-pressure vent, and depending on the conditions any one of them can be the maximum.<ref name="Z-415" />
Line 102:		Line 105:

	The square root makes the result sensitive to the strength of the room. If the room could withstand only 0.6 psig, with the same release pressure, the vent area would rise to 0.17 × 80/√0.6, or about 17.6 m², more than the whole roof. If the fuel were methane, with C = 0.14 psig<sup>1/2</sup>, the area at 1.0 psig would be 11.2 m².<ref name="Z-416" /> These calculations use the recommended constants; with the most likely constant for propane, one third of 0.17, the area would be only about 4.6 m². That difference shows how much conservatism the enveloping constants contain.<ref name="Z-416" />		The square root makes the result sensitive to the strength of the room. If the room could withstand only 0.6 psig, with the same release pressure, the vent area would rise to 0.17 × 80/√0.6, or about 17.6 m², more than the whole roof. If the fuel were methane, with C = 0.14 psig<sup>1/2</sup>, the area at 1.0 psig would be 11.2 m².<ref name="Z-416" /> These calculations use the recommended constants; with the most likely constant for propane, one third of 0.17, the area would be only about 4.6 m². That difference shows how much conservatism the enveloping constants contain.<ref name="Z-416" />
			[[File:fse-explosion-venting-v4.svg\|thumb\|upright=1.5\|alt=Three falling curves of vent area against reduced pressure for ammonia, methane and propane-like gases, with lines for the wall and roof areas.\|Vent area for a 4 m × 4 m × 3 m room from the Swift-Epstein equation, for three fuel constants, against the pressure the room can withstand. Horizontal lines show the area of one wall and of the roof. Based on Zalosh (2002), p. 3-416.]]

	Strong process equipment needs far less vent area relative to its volume. For a 400 m³ electrostatic precipitator handling bituminous coal dust, with P<sub>red</sub> = 1.2 bar and P<sub>stat</sub> = 0.4 bar, the dust equation gives 1.96 m².<ref name="Z-416" /><ref name="Z-417" /> Zalosh adds that this area does not include the effect of the weight, or inertia, of heavy vent panels, which needs extra vent area.<ref name="Z-417" />		Strong process equipment needs far less vent area relative to its volume. For a 400 m³ electrostatic precipitator handling bituminous coal dust, with P<sub>red</sub> = 1.2 bar and P<sub>stat</sub> = 0.4 bar, the dust equation gives 1.96 m².<ref name="Z-416" /><ref name="Z-417" /> Zalosh adds that this area does not include the effect of the weight, or inertia, of heavy vent panels, which needs extra vent area.<ref name="Z-417" />

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

2026-11-01T23:31:30Z

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

← Older revision		Revision as of 00:31, 2 November 2026
Line 64:		Line 64:
	<math display="block">A_\mathrm{v} = 8.535 \times 10^{-5} \left( 1 + 1.75 P_\mathrm{stat} \right) K_\mathrm{St} V^{0.75} \sqrt{\frac{1 - \Pi}{\Pi}}, \qquad \Pi = \frac{P_\mathrm{red}}{P_\mathrm{max}}</math>		<math display="block">A_\mathrm{v} = 8.535 \times 10^{-5} \left( 1 + 1.75 P_\mathrm{stat} \right) K_\mathrm{St} V^{0.75} \sqrt{\frac{1 - \Pi}{\Pi}}, \qquad \Pi = \frac{P_\mathrm{red}}{P_\mathrm{max}}</math>

	For enclosures with a length-to-diameter ratio above 2, both equations need an additional vent area.<ref name="Z-416" /> The two equations differ in their sensitivity to reactivity: the gas equation contains the logarithm of K<sub>G</sub>, while the dust equation is linear in K<sub>St</sub>.<ref name="Z-416" /> Going from propane to hydrogen multiplies K<sub>G</sub> by 5.5, but raises the first term of the gas equation by a factor of only about 1.5.<ref name="Z-407" /><ref name="Z-416" />		For enclosures with a length-to-diameter ratio above 2, both equations need an additional vent area.<ref name="Z-416" /> The two equations differ in their sensitivity to reactivity: the gas equation contains the logarithm of K<sub>G</sub>, while the dust equation is linear in K<sub>St</sub>.<ref name="Z-416" /> A calculation made for this article, not printed in the source, illustrates the difference. Going from propane to hydrogen multiplies K<sub>G</sub> by 5.5, but raises the first term of the gas equation by a factor of only about 1.5.<ref name="Z-407" /><ref name="Z-416" />

	{\| class="wikitable"		{\| class="wikitable"

Mark: New FSE wiki article: Explosion venting (written by Claude Opus 5.5)

2026-11-01T22:16:11Z

New FSE wiki article: Explosion venting (written by Claude Opus 5.5)

New page

'''Explosion venting''' is the discharge of combustion gases from an enclosure during a [[deflagration]], so that the pressure stays below the level at which the enclosure would be damaged.<ref name="Z-414">Zalosh (2002), p. 3-414.</ref> The enclosure can be a room, a building or a piece of process equipment, and the fuel can be a gas, a dust, a mist or a hybrid mixture of dust and gas.<ref name="Z-414" /> The vent opening is usually covered at first by blow-off panels, rupture discs or other engineered vent devices, which open once the explosion has started.<ref name="Z-414" /> The most effective vents open early, are as large as possible and let the combustion gases escape without restriction.<ref name="Z-414" />

The vent area needed depends on the size and strength of the enclosure and on how fast the pressure rises, which for dusts is expressed by the [[deflagration index]].<ref name="Z-414" /><ref name="Z-417">Zalosh (2002), p. 3-417.</ref> Design guidance treats weak enclosures, such as buildings, with an equation based on their internal surface area, and strong process equipment with equations based on their volume.<ref name="Z-415">Zalosh (2002), p. 3-415.</ref><ref name="Z-416">Zalosh (2002), p. 3-416.</ref> Unlike explosion suppression, which is costly to install and to reset, venting discharges flame and unburned material and sends a blast wave into the surroundings.<ref name="Z-417" /><ref name="Z-419">Zalosh (2002), p. 3-419.</ref> It cannot protect against a detonation, because the peak pressure arrives with the shock front before any vent can open.<ref name="Z-414" />

== Purpose and principle ==
NUREG-1805 defines an [[explosion]] as a sudden and violent release of high-pressure gases into the environment.<ref name="IS-15-1">Iqbal and Salley (2004), p. 15-1.</ref> When a flammable mixture ignites inside a closed enclosure, the hot combustion products cannot expand freely and the pressure rises. The maximum pressure is reached after a time that depends on the enclosure size and the fuel, and that can extend to a few hundred milliseconds.<ref name="IS-15-3">Iqbal and Salley (2004), p. 15-3.</ref> In a closed vessel, the final pressure of the gas and dust deflagrations tabulated in the SFPE Handbook lies between 5.4 and 11.2 bar g.<ref name="Z-407">Zalosh (2002), p. 3-407.</ref> Ordinary rooms and buildings fail at a small fraction of that pressure.<ref name="Z-410">Zalosh (2002), p. 3-410.</ref>

Typical failure pressures of building elements, collected by Harris, show the size of the gap. Glass windows fail at 2 to 7 kPa, room doors at 2 to 3 kPa, light partition walls at 2 to 5 kPa and unrestrained brick walls at 7 to 15 kPa.<ref name="IS-15-13">Iqbal and Salley (2004), p. 15-13.</ref> Even 200 g of butane, mixed with part of the air in a 48 m³ room and ignited, can raise the pressure by about 0.46 bar, more than the strength of rooms in industrial facilities.<ref name="Z-410" /> Normal process openings let some gas escape, but they are usually far too small to prevent destructive pressures.<ref name="IS-15-3" />

Explosion protection can interrupt the chain of events at three points. It can prevent the flammable mixture, remove the ignition sources, or limit the pressure rise by venting or suppression.<ref name="Z-402">Zalosh (2002), p. 3-402.</ref> For flammable liquid operations, an American loss-prevention guideline summarised in NUREG-1805, FM Data Sheet 7-32 (1993), accordingly asks for at least one of four measures. Equipment with an explosion potential should be vented, built to withstand the explosion pressure, inerted or fitted with suppression.<ref name="IS-B-27">Iqbal and Salley (2004), p. B-27.</ref> Venting accepts that the explosion occurs and limits its pressure to a reduced value, Pred, that the enclosure can withstand.<ref name="Z-415" /><ref name="Z-416" />

== Course of a vented explosion ==
A vented explosion passes through several phases, which NUREG-1805 shows in a diagram after Harris.<ref name="IS-15-5">Iqbal and Salley (2004), p. 15-5.</ref> First the flame expands inside the closed enclosure and the pressure rises as in an unvented explosion. When the pressure reaches the release pressure of the vent, the vent cover is removed, and shortly afterwards venting is established.<ref name="IS-15-5" /> Later the flame reaches its maximum area and burnt gas flows out through the vent.<ref name="IS-15-5" />

The pressure history shows a first peak when the vent opens and a second peak later in the event.<ref name="IS-15-5" /> NUREG-1805 explains that the release of gases through a vent, even a door or a window, can create turbulence that produces this second peak and increases the overpressure.<ref name="IS-15-5" /> In the example diagram the second peak is the higher of the two.<ref name="IS-15-5" /> Cooper and co-workers identified four types of pressure peak in a near-cubic vessel with a low-pressure vent, and depending on the conditions any one of them can be the maximum.<ref name="Z-415" />

These multiple peaks come from flame instabilities that also complicate testing. In vented gas explosions they depend on the ignition location, the wall lining of the enclosure and the presence of equipment inside it.<ref name="Z-414" /> In dust tests, the strength of the igniter, the uniformity of the dust cloud and the delay between dispersion and ignition matter as well.<ref name="Z-414" /> A vent design must therefore cover the highest of several possible peaks, not only the pressure at the moment the vent opens.<ref name="Z-415" />

== Factors that set the vent area ==
The rate of pressure rise in an unvented enclosure is proportional to the effective burning velocity and to the flame surface area, and it falls as the enclosure becomes larger.<ref name="Z-414" /> The rate at which a vent relieves the pressure is proportional to the vent area and to the gas velocity through the vent.<ref name="Z-414" /> That velocity depends on the pressure in the enclosure and on whether burned or unburned gas is flowing out.<ref name="Z-414" /> The vent is large enough when the outflow keeps the pressure below Pred despite the continuing production of hot gas.<ref name="Z-414" />

Theoretical models of vented explosions exist, either as two-fluid models or as computational fluid dynamics models.<ref name="Z-414" /> Computational models were too complex and computationally demanding for routine design when the handbook was written, and design rests mainly on large-scale tests.<ref name="Z-414" /> The most influential series was carried out by Bartknecht and co-workers at the Ciba-Geigy test centre in Basel, Switzerland.<ref name="Z-415" /> They used vessels of 2.4 to 250 m³ with a pressure rating of 10 bar, mostly with dusts, strong igniters and worst-case concentrations.<ref name="Z-415" /> Their data were correlated in successive versions of the German VDI guideline for dust explosion venting.<ref name="Z-415" />

The tests show which factors matter. They include the reactivity of the mixture, turbulence from the initial state and from the interaction of the flame with obstacles, the volume and shape of the vessel, and the vent itself.<ref name="Z-414" /> For the vent, the area, the release pressure and the inertia of the vent panel all count.<ref name="Z-414" /> Recent correlations use dimensionless groups that make interpolation and extrapolation easier.<ref name="Z-415" /> The pressure parameter π compares the reduced pressure with the maximum pressure of the unvented explosion, and the dust vent parameter Γ combines the vent area with the volume and the deflagration index:<ref name="Z-415" />

<math display="block">\pi = \frac{\Delta P_\mathrm{red}}{\Delta P_\mathrm{max}}, \qquad \Gamma = \frac{a_\mathrm{CD} A_\mathrm{v} P_0}{V^{2/3} K_\mathrm{St}}</math>

The product of the vent discharge coefficient and the speed of sound, aCD, is taken as 230 m/s, and the initial pressure P0 as 1 bar absolute.<ref name="Z-415" /> For gases, Swift and Epstein based their vent parameter on the burning velocity and the internal surface area of the enclosure. Bradley and Mitcheson based theirs on the vent area, the volume, the burning velocity and the expansion of the burned gas.<ref name="Z-415" />

== Design equations ==
The guidance in NFPA 68, the American guide for venting of deflagrations, distinguishes low-strength from high-strength enclosures.<ref name="Z-415" /> The boundary lies at a damage threshold of 1.5 psig, or 0.1 bar.<ref name="Z-415" /> The split reflects the test data: the high-strength guidelines grew out of European test programmes without low-pressure tests, while many American programmes used large, low-strength structures.<ref name="Z-415" />

For low-strength enclosures, such as rooms and buildings, the guidance follows the Swift–Epstein correlation.<ref name="Z-415" /> In that correlation the internal surface area of the enclosure stands for the largest flame area, reached when the enclosure is completely filled with flame.<ref name="Z-415" /> The vent area is therefore proportional to the internal surface area:<ref name="Z-416" />

<math display="block">A_\mathrm{v} = \frac{C \, A_\mathrm{s}}{\sqrt{P_\mathrm{red}}}</math>

The equation applies for Pred between 0.35 and 1.5 psig and for a difference of more than 0.35 psi between Pred and the vent release pressure Pstat.<ref name="Z-416" /> The enclosure must also be compact, with a length-to-diameter ratio below 3.<ref name="Z-416" /> The constant C depends on the fuel, as the following table shows.

{| class="wikitable"
|+ Constant C in the Swift–Epstein vent equation<ref name="Z-416" />
! Fuel !! C (psig1/2) !! C (bar1/2)
|-
| Anhydrous ammonia || 0.05 || 0.013
|-
| Methane || 0.14 || 0.037
|-
| Gases with a burning velocity below 60 cm/s || 0.17 || 0.045
|-
| Dusts with KSt below 200 bar·m/s || 0.10 || 0.026
|-
| Dusts with KSt from 200 to 300 bar·m/s || 0.12 || 0.030
|-
| Dusts with KSt above 300 bar·m/s || 0.20 || 0.051
|}

The constants are the highest values inferred from test data in 18 references cited in NFPA 68.<ref name="Z-416" /> These tests covered enclosures of 0.18 to 82.3 m³ with both quiescent and turbulent mixtures.<ref name="Z-416" /> Most results correspond to much lower values; for propane the most likely value is about one third of the recommended 0.17.<ref name="Z-416" /> For gases that are not listed and lack test data, Zalosh suggests scaling the propane value by the ratio of the burning velocities. With extreme turbulence, as in a hammer mill, even the recommended constant can underestimate the pressure.<ref name="Z-416" />

High-strength enclosures, such as the process equipment in the worked example below, are covered by guidance that grew out of the European test programmes described above.<ref name="Z-415" /> For compact high-strength enclosures, with a length-to-diameter ratio of at most 2, NFPA 68 gives an equation for gases.<ref name="Z-416" /> It uses the gas deflagration index KG, the closed-vessel measure of how fast a gas explosion develops:<ref name="Z-416" /><ref name="Z-409">Zalosh (2002), p. 3-409.</ref>

<math display="block">A_\mathrm{v} = \left[ \left( 0.127 \log_{10} K_\mathrm{G} - 0.0567 \right) P_\mathrm{red}^{-0.582} + 0.175 \, P_\mathrm{red}^{-0.572} \left( P_\mathrm{stat} - 0.1 \right) \right] V^{2/3}</math>

It applies for Pstat up to 0.5 bar and Pred up to 2 bar.<ref name="Z-416" /> For a [[dust explosion]] in a compact high-strength enclosure, the 1998 edition of NFPA 68 used the equation of the German guideline VDI 3673. The handbook gives the following equation, which had been proposed for the 2002 edition, with V in m³ and Av in m²:<ref name="Z-416" />

<math display="block">A_\mathrm{v} = 8.535 \times 10^{-5} \left( 1 + 1.75 P_\mathrm{stat} \right) K_\mathrm{St} V^{0.75} \sqrt{\frac{1 - \Pi}{\Pi}}, \qquad \Pi = \frac{P_\mathrm{red}}{P_\mathrm{max}}</math>

For enclosures with a length-to-diameter ratio above 2, both equations need an additional vent area.<ref name="Z-416" /> The two equations differ in their sensitivity to reactivity: the gas equation contains the logarithm of KG, while the dust equation is linear in KSt.<ref name="Z-416" /> Going from propane to hydrogen multiplies KG by 5.5, but raises the first term of the gas equation by a factor of only about 1.5.<ref name="Z-407" /><ref name="Z-416" />

{| class="wikitable"
! Symbol !! Description !! Unit
|-
| <math>A_\mathrm{v}</math> || vent area || m²
|-
| <math>A_\mathrm{s}</math> || internal surface area of the enclosure || m²
|-
| <math>C</math> || fuel constant of the Swift–Epstein equation || psig1/2 or bar1/2
|-
| <math>V</math> || enclosure volume || m³
|-
| <math>P_\mathrm{red}</math> || reduced pressure: highest pressure the vented enclosure may reach || psig or bar g
|-
| <math>P_\mathrm{stat}</math> || pressure at which the vent opens || psig or bar g
|-
| <math>P_\mathrm{max}</math> || maximum pressure of the unvented explosion || bar g
|-
| <math>P_0</math> || initial pressure, 1 bar absolute || bar
|-
| <math>\pi</math>, <math>\Pi</math> || pressure ratio of reduced to unvented explosion pressure || none
|-
| <math>\Gamma</math> || dimensionless vent parameter for dusts || none
|-
| <math>a_\mathrm{CD}</math> || vent discharge coefficient times speed of sound, 230 m/s || m/s
|-
| <math>K_\mathrm{G}</math>, <math>K_\mathrm{St}</math> || deflagration index of a gas or of a dust || bar·m/s
|}

== Worked example: venting a room ==
Zalosh considers a room of 4 m × 4 m × 3 m with a damage threshold of 1.0 psig and vents that open at 0.2 psig.<ref name="Z-416" /> The worst case is a butane–air mixture that is initially at rest.<ref name="Z-416" /> Butane has a burning velocity similar to that of propane, so C = 0.17 psig1/2.<ref name="Z-416" /> The internal surface area is 2 × (4 × 4 + 4 × 3 + 4 × 3) = 80 m², and the low-strength equation gives:<ref name="Z-416" />

<math display="block">A_\mathrm{v} = \frac{0.17 \times 80}{\sqrt{1.0}} = 13.6\ \mathrm{m^2}</math>

The conditions of the equation are met. Pred lies between 0.35 and 1.5 psig, the difference with the release pressure is 0.8 psi, and the room is compact.<ref name="Z-416" /> The required area is larger than one 4 m × 3 m wall, which has 12 m², and close to the 16 m² of the roof. The equation is used here as in the handbook, with C in psig1/2 and Pred in psig, so the area comes out in the unit of As.<ref name="Z-416" />

The square root makes the result sensitive to the strength of the room. If the room could withstand only 0.6 psig, with the same release pressure, the vent area would rise to 0.17 × 80/√0.6, or about 17.6 m², more than the whole roof. If the fuel were methane, with C = 0.14 psig1/2, the area at 1.0 psig would be 11.2 m².<ref name="Z-416" /> These calculations use the recommended constants; with the most likely constant for propane, one third of 0.17, the area would be only about 4.6 m². That difference shows how much conservatism the enveloping constants contain.<ref name="Z-416" />

Strong process equipment needs far less vent area relative to its volume. For a 400 m³ electrostatic precipitator handling bituminous coal dust, with Pred = 1.2 bar and Pstat = 0.4 bar, the dust equation gives 1.96 m².<ref name="Z-416" /><ref name="Z-417" /> Zalosh adds that this area does not include the effect of the weight, or inertia, of heavy vent panels, which needs extra vent area.<ref name="Z-417" />

== Discharge, blast and siting ==
A vent relieves the enclosure by moving part of the explosion outside it. Flame and unburned fuel leave through the opening.<ref name="Z-417" /> Explosion suppression involves no such discharge, which is why it is often easier to use on indoor equipment and on equipment that contains toxic materials.<ref name="Z-417" /> Vents in the exterior walls and roofs of buildings must open at a pressure slightly above the highest expected wind load, typically 0.96 to 1.44 kPa.<ref name="Z-414" />

A vented explosion also sends a blast wave into the surroundings. Its analysis is more complicated than for a bursting vessel, because combustion outside the vent adds energy to the blast.<ref name="Z-419" /> Correlations for blast waves from vented explosions are contained in NFPA 68, and Forcier and Zalosh described more recent developments that include two-dimensional effects.<ref name="Z-419" /> The damage thresholds collected in NUREG-1805 give a sense of scale. Typical glass failure occurs at 0.15 psig, about 1 kPa, and houses become uninhabitable through partial demolition at 1.0 psig, about 7 kPa.<ref name="IS-15-7">Iqbal and Salley (2004), p. 15-7.</ref><ref name="IS-15-8">Iqbal and Salley (2004), p. 15-8.</ref>

== Battery rooms and energy storage ==
Battery rooms are a documented source of explosions in buildings. Vented lead-acid batteries release a stoichiometric mixture of hydrogen and oxygen when they are overcharged, and faults such as a poorly maintained cell terminal can ignite it.<ref name="IS-16-5">Iqbal and Salley (2004), p. 16-5.</ref> In nuclear power plants, battery room ventilation therefore typically keeps hydrogen below 2 % of the room volume, with about 10 air changes per hour.<ref name="IS-16-6">Iqbal and Salley (2004), p. 16-6.</ref> Outside the nuclear industry, hydrogen explosions have been reported in battery charging areas from submarine battery rooms to uninterruptible power supply rooms.<ref name="IS-16-6" /> In March 2001 a hydrogen explosion in the battery room of a large computer data centre in Sacramento, California, blew a hole of more than 400 ft², about 37 m², in the roof.<ref name="IS-16-6" /> It also collapsed walls and ceilings throughout the data centre and damaged a large part of the 50,000 ft² building.<ref name="IS-16-6" />

Lithium-ion batteries raise the same issue in a different way. Van der Graaf and co-workers note that the cells of an electric vehicle battery release gas as soon as they go into thermal runaway.<ref name="VdG-27">Van der Graaf et al. (2021/2023), p. 27.</ref> If this gas is not ignited at once, an explosive mixture can build up in a confined, enclosed or poorly ventilated space.<ref name="VdG-27" /> A fire gas explosion can follow if the mixture reaches its lower explosion limit and is ignited.<ref name="VdG-27" />

Fires in electric vehicles can also involve repeated minor explosions.<ref name="VdG-29">Van der Graaf et al. (2021/2023), p. 29.</ref> Any enclosure that holds batteries, from a battery room to a [[battery energy storage system]], can therefore contain a flammable atmosphere when the batteries are overcharged or damaged.<ref name="IS-16-5" /><ref name="VdG-27" /> Vent guidelines, however, rest on tests with near worst-case mixtures, and most do not account for an enclosure that is only partly filled with fuel.<ref name="Z-415" /><ref name="Z-416" />

== Limitations ==
Vent guidelines are only as good as the tests behind them. They do not account for the turbulence and obstructions of a particular application, so a designer either assumes conditions comparable to the tests or accepts an ill-defined degree of conservatism.<ref name="Z-416" /> Gas data were often enveloped rather than correlated, and the recommended constants lie well above most measurements.<ref name="Z-415" /><ref name="Z-416" /> Research by Tamanini was providing a basis for overcoming these limitations when the handbook was written.<ref name="Z-416" />

The equations in this article are those described in the 2002 SFPE Handbook. They come from the 1998 edition of NFPA 68, the German guideline VDI 3673 of 1995, and an equation then proposed for the 2002 edition of NFPA 68.<ref name="Z-416" /><ref name="Z-421">Zalosh (2002), p. 3-421.</ref> They show the structure of vent design rather than the current text of any standard. General building fire engineering guidance does not fill the gap. The Australian version of Part 0 of the International Fire Engineering Guidelines (2005 edition) excludes hazards outside the range normally encountered in buildings, such as the handling of explosive materials.<ref>National Research Council of Canada et al. (2005), Part 0 – Australia, p. 0.1-3.</ref> The United States version adds that hazardous materials are not specifically addressed by the guidelines.<ref>National Research Council of Canada et al. (2005), Part 0 – United States, p. 0.1-4.</ref>

Finally, venting addresses deflagrations only. The sudden, spatially non-uniform pressure rise of a detonation or quasi-detonation rules out both venting and suppression.<ref name="Z-411">Zalosh (2002), p. 3-411.</ref> Where a detonation is possible, the hazard has to be controlled in other ways, for example by preventing the flammable mixture.<ref name="Z-402" /><ref name="Z-411" />

== See also ==
* [[Detonation]]
* [[Deflagration-to-detonation transition]]
* [[Inerting]]
* [[Hydrogen safety]]
* [[TNT equivalence]]

== Notes ==
<references />

== References ==
* 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.
* National Research Council of Canada, International Code Council, Department of Building and Housing, & Australian Building Codes Board. (2005). ''International fire engineering guidelines'' (2005 ed.). Australian Building Codes Board.
* Van der Graaf, J., Hessels, T., & Rosmuller, N. (2023). ''Fire safety of indoor car parks accommodating electrically powered vehicles''. Nederlands Instituut Publieke Veiligheid. (Original work published 2021)
* Zalosh, R. (2002). Explosion protection. 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. 3-402–3-421). National Fire Protection Association; Society of Fire Protection Engineers.

[[Category:Explosions & Industrial Fires]]