Chapter 3 Fire accidents

Chapter 3

Fire accidents 1 INTRODUCTION

Of the various accidents that can occur in the process industry, fire is, generally speaking, the type whose effects are felt over the shortest distances: toxic gas clouds and explosions usually cover much larger areas. However, the effects of a fire can be severe as the thermal flux may affect other equipment (domino effect), thus giving rise to other events (explosions, releases) that can dramatically increase the scale of the accident. In fact, in many major accidents occurring in process plants or in the transportation of hazardous materials, fire is an initial stage, followed by a release or an explosion. Thus, different combinations may be observed: fire+ larger fire, fire +explosion, fire +gas cloud, fire + BLEVE/fireball. Diverse historical analyses have demonstrated that fires are the most frequent type of accident, followed by explosions and gas clouds. Darbra et al. [ 1] found that, for accidents occurring in sea ports, 51% corresponded to the general case of "loss of containment", 29% were fires, 17% were explosions and 3% were gas clouds. If only accidents leading to fire, explosions or gas clouds are considered, these values become 59.5% for fire, 34.5% for explosions and 6% for gas clouds. Another survey [2] obtained similar results for accidents occurring during the transport of hazardous substances by road and rail: 65% were fires, 24% explosions and II% gas clouds. Both for establishing safety distances and for estimating the cooling flow rates required to protect equipment affected by thermal radiation, the usefulness of being able to foresee the effects of a fire as a function of distance is evident. The mathematical modelling of a fire allows predictions to be made regarding the possible damage to people and equipment, and the establishment of the necessary safety measures to reduce or prevent this damage. In this chapter, the main features of common fuels and of the various types of fire are analyzed and the most common mathematical models are described. 2 COMBUSTION

Combustion is a chemical reaction in which a fuel reacts with an oxidant, yielding various products and releasing energy. Combustion always takes place in the gas phase: liquid fuels become vaporized due to the heat from the flames and then react with the oxygen in the air; solids are decomposed due to the high temperature and the gases released react with the oxidizer, usually oxygen from the air. The flames are these reacting gases at high temperature. Combustion products are released as smoke, which also contains unbumt fuel; in accidental

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fires combustion is usually fairly bad, due to the poor mixing of fuel gas or vapour with oxygen, and large amounts of black smoke are generated. Chemical chain reaction

Oxigen

Fuel

Ignition source (heat)

Heat

Fig. 3-1. The fire triangle. For combustion to proceed, the three sides must be connected. A chemical chain reaction is also required: the fire triangle evolves towards the fire tetrahedron. For combustion to occur, three elements are required: fuel, an oxidant and a source of ignition. These three elements can be represented by the fire triangle (Fig. 3-1 ): if one side is missing, combustion is impossible; if the three sides are connected, combustion is possible. Strictly speaking, another element is also required: the occurrence of a chemical chain reaction. Without this chemical reaction -for example, because of the presence of a Halon extinguisher- fire is not possible. Thus, the fire triangle evolves towards a fire tetrahedron. However, in practice some additional conditions must be fulfilled for combustion to take place: the oxidizer and the fuel must be present in sufficient quantities, the fuel must be ready to ignite (for example, its temperature must be above a minimum value) and the source of ignition must have a minimum intensity. 2.1 Combustion reaction and combustion heat In a fire, thermal energy is released because a fuel is burnt. Combustion is an exothermal chemical reaction in which a substance combines with an oxidant, commonly oxygen from the air. The fuel may be solid, but most fires in the process industry involve liquid or gas fuels. Some of the energy released is used to sustain the reaction. Thus: (3-1) 2 1 where m is the combustion rate (kg m- s- ) QF is the heat flux from the flames into the fuel (kW m- 2) QL is the heat lost from the fuel surface (kW m- 2) and qv is the heat required to produce the gas (the heat needed to increase its temperature 1 to boiling point plus the latent heat of evaporation in the case of a liquid) (kJ kg- ). The heat released from the combustion, &lc, will have two different values depending on whether the water formed with the reaction products is considered to be in the liquid or

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vapour state. The difference will be the vaporization heat of water (44 kJ mor 1 or 2444 kJ kg- 1 at 25 °C). For example, for methane,

M( = -888 kJ mor 1 (-5.55·104 kJ kg- 1) 1

4

!'::J!c = -800 kJ mor ( -5·1 0 kJ

1 kg. )

if water is considered to be a liquid

if water is considered to be a vapour.

As in a fire the water leaves the system in the smoke as a vapour, commonly the iJHc value is used and is called the net combustion heat rate. The gases undergoing the diverse chemical reactions associated with combustion are extremely hot and therefore luminous: this luminous zone is the flame. From a practical point of view, we should consider two types of combustion: one associated with premixed flames and the other one associated with diffusion flames.

2.2 Premixed flames and diffusion flames Premixed flames exist when the vapour or gas fuel and the oxidant have been well mixed before burning as, for example, in a Bunsen burner. The premixed flame is short, very hot, has a blue colour and gives off a relatively small amount of very hot gas: combustion is good. This is the type of combustion which occurs in burners and other combustion tools. If the air inlet of the burner is closed, then the fuel exiting from the burner nozzle will undergo fairly poor mixing with air, mainly by entrainment and diffusion. The flame will now be long, undulating, yellow, very luminous and sooty: this is a diffusion flame. Its temperature is significantly lower than that of the premixed flame, larger amounts of black smoke are produced, some unburnt fuel is lost and the overall efficiency of the combustion is lower. Diffusion flames are typical of most accidental fires.

3 TYPES OF FIRE The fires that can occur in industrial installations or in the transportation of hazardous substances can be classified according to the state of the fuel involved and the conditions in which ignition takes place. A simplified diagram indicating the diverse types of fire that can occur as a consequence of the loss of containment of a flammable material can be seen in Fig. 3-1. Although the combustion of solid materials may also cause large fires, the most common fuels in industrial accidents are usually liquids and gases. Therefore, the accident starts with the loss of containment of a flammable fluid. If it is a liquid, the release can create a pool on the ground -covering a limited area if a dike is present- or on water; the outcome is similar in the case of a tank that has lost its roof due to an explosion. In all of these cases, the ignition will start a pool fire (a tank fire may be considered to be a particular case of a pool fire). If the liquid is flowing, which is not common, the ensuing running liquid fire will have different features and can sometimes be very difficult to extinguish. If the liquid undergoes flash vaporization due to a sudden depressurization, a fireball will probably be created. When the material released is a gas or a vapour, if ignition takes place immediately there will be a jet fire. If ignition is not immediate, a cloud containing a flammable mixture may build up under

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certain meteorological conditions; the ignition of this cloud will cause a flash fire. A flash fire can also occur if a pool is not ignited, due to the vaporization of the fuel. Pool and tank fires are the most frequent types of fire, followed by jet fires, flash fires and fireballs. While pool fires and jet fires may bum for long periods, a fireball will usually last less than one minute (often only a few seconds) and a flash fire is a very short phenomenon, lasting only a few tens of seconds.

Fig. 3-2. Types of fire that may occur in an industrial installation. 3.1 Pool fires Pool fires occurring in industrial accidents are characterized by turbulent diffusion flames on a horizontal pool of fuel that is vaporized. The liquid receives heat from the flames by convection and radiation and may lose or gain heat by conduction towards/from the solid or liquid substrate under the liquid layer. Once the fire has reached the steady state, there is a feedback mechanism that controls the feeding of fuel vapour to the flames. The amount of heat transferred between the fuel and the underlying interface will depend on the fuel and the substrate conditions. If the substrate is cool water and the fuel is a liquid that is initially at ambient temperature, heat losses can be substantial and the fuel vaporization can decrease to such an extent that the flame cannot be maintained. By contrast, if the fuel is cryogenic, heat will be transferred from the substrate to the fuel -at least in the first period- and combustion can be improved. The burning rate is a function of the pool diameter. Blinov and Khudiakov [3, 4] carried out an experimental study of the behaviour of pool fires with different fuels and diameters. They observed the same behaviour for all fuels. The highest burning rates corresponded to the smaller pool diameters, in the laminar regime. Burning rates then decreased as the diameter increased, reaching a minimum at approximately D = 0.1 m (Re ~ 20). Over the range 0.1 m < D < 1 m (20 < Re < 200) burning velocity increased with pool diameter. For larger diameters (D > 1 m, Re > 200) the flames were fully turbulent and the burning velocity was essentially constant and did not depend on the diameter. This correlation between the burning rate and the pool diameter can be explained in terms of the relative contribution of the various mechanisms to the heat transfer from the flame to the liquid fuel [5].

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In large pool fires -more than 1 min diameter-large amounts of soot are produced due to poor combustion. This soot gives the flames their yellow colour; it then cools and gives off black smoke which absorbs radiation from the flame. This phenomenon, known as smoke blockage, has a strong effect on the overall thermal radiation emitted from the fire. Pool fires on the ground occur when a fuel release creates a pool in a dike or on the ground. The release can be instantaneous, for example due to the collapse of a tank, or continuous or semi-continuous, for example due to leakage through a hole. If there is no dike, the diameter of the pool will depend on the type of release, the combustion rate and the ground slope. In an instantaneous release, the liquid will spread out until it reaches a barrier or until all of the fuel has been burnt. In a continuous release, the size of the pool will increase until the burning rate is equal to the release flow rate, thus reaching an equilibrium diameter. The fuel (usually a hydrocarbon) can bum over a layer of water, usually created by the intervention of firemen. If the fire bums for a certain time, the water may boil, giving rise to the phenomenon known as thin-layer boilover. In large tank fires, the existence of a layer of water can lead to boilover, which is a dangerous phenomenon. Pool fires can also take place on the sea surface. In this case, the heat transfer from the fuel to the water can be significant and a situation can be reached in which the flame cannot be maintained. Furthermore, if ignition is delayed the diameter of the pool will increase and its thickness may reach a minimum value below which ignition is no longer possible. 3.2 Jet fires Jet fires are turbulent diffusion flames caused by the combustion of a flammable gas or vapour released at a certain velocity though a hole, a flange, etc. The release is not always accidental: flares are widely used in process plants to safely dispose of flammable gases. Jet fires entrain large amounts of air into the flame, due to the turbulence of the flow. Typically, the volume of entrained air can be up to five times that required for stoichiometric combustion [6]. Due to the efficiency of the mixing and the better combustion rate, temperatures in jet fire flames are often higher than those reached in natural diffusion flames in a pool fire. As a consequence, jet fires can cause serious damage to equipment, through both thermal radiation and flame impingement. 3.3 Flash fires If a flammable gas or vapour is released in certain meteorological conditions --calm or low wind speed- a cloud will be formed. This can also be caused by the release of a pressurized liquid undergoing a flash vaporization or by evaporation from a pool. This is the case of liquefied natural gas or liquefied propane: if a pool is formed, it will undergo intense vaporization. The release may be instantaneous or continuous. The flammable cloud will disperse, increasing in size, and will move according to wind direction. If it meets a source of ignition -an electrical device, a flame, an electrostatic spark- the mass between the flammability limits will bum very quickly, as the flames are propagated through the cloud. The flame propagation velocity for LPG-air mixtures has been reported to be in the range of 5-l 0 m s· 1 [7] and to increase with wind speed. The duration of the phenomenon is very short -a few tens of seconds. The area covered by the flammable mixture will be subjected to a very strong heat flux, while outside this area the effects of the thermal radiation will be greatly reduced and in practice are often considered to be negligible. If the mass of fuel in the cloud is large, a significant blast can also occur; in this case, the accident is considered to be an explosion rather than a flash fire.

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3.4 Fireballs If a tank containing a pressurized liquid is heated, the pressure inside the tank will increase. If the walls are not able to withstand the high stress, they will eventually collapse. Upon failure, due to the instantaneous depressurization, a sudden flash of a fraction of the liquid will take place and a biphasic liquid/vapour mixture will then be released. If the substance is a fuel, as is often the case in the process industry (for example, propane), this mixture will probably ignite, creating a fireball, initially at ground level. Subsequently, the whole turbulent mass will increase in volume and will rise, producing a wake. The thermal radiation can be very strong. Due to the difficulty in foreseeing the moment at which the fireball may occur (it can happen at any moment from the beginning of the emergency, without warning) fireballs have killed many people, most of them firemen. The mechanical aspects of explosions usually associated to fireballs are described in detail in Chapter 5. 4 FLAMMABILITY

Not all of the substances are equally hazardous in terms of causing fire accidents. It is well known that with some flammable liquids, for example acetone or gasoline, it is relatively easy for an accident to occur when the substance is handled without the required care, while with others, for example diesel oil, the likelihood of such a problem is reduced -although a risk still exists. This depends on the different properties of the substance, the most important of which (for practical purposes) are its flammability limits, its flash point temperature and its autoignition temperature. 4.1 Flammability limits Mixtures of a flammable gas or vapour with air are flammable only if the concentration of the vapour ranges between two values called the lower flammability limit (LFL) and the upper flammability limit (UFL). If the concentration is lower than the LFL, there is not enough fuel for combustion to occur; if the concentration is higher than the UFL, the mixture is too rich and there is not enough oxygen. The flammability limits can be obtained experimentally, using standard methods, with devices that determine whether the flame propagates through a given mixture of fuel/air. According to the experimental procedure followed, rather different values can be obtained; this explains the data scattering that is sometimes found in the literature. The flammability limits are commonly expressed as the volume percentage of fuel at 25 °C. For example, the limits for propane are 2.1% and 9.5%. The range covered by these limits is important from the point of view of the fire hazards associated with a given substance. For example, hydrogen is a very dangerous gas: its flammability limits are 4% and 75%. This means that the probability of a flammable atmosphere in the event of a hydrogen release is very high. For gasoline, the LFL is approximately 1.4%: if there is a release or if gasoline is being handled, a flammable gasoline/air mixture will quickly appear nearby. From the point of view of safety, the LFL is probably the most important limit, as it is related to the formation of a flammable atmosphere; the UFL can be significant when flammable substances are handled in closed volumes (rooms or tanks). Flammability limits for several common substances can be seen in Table 3-1. A more complete list has been included in the annexes. The best study published in this field is probably that by Zabetakis [8], which gives a set of values obtained experimentally with the apparatus developed at the US Bureau of Mines.

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Table 3-1. Flammability limits, flash point temperature and autoignition . pressure substances m mr at atmosplhenc UFL, % volume LFL, % volume Substance 2.6 12.8 Acetone 2.5 Acetylene 80.0 1.2 11.0 Aniline 15.0 28.0 Ammonia 1.4 8.0 Benzene 8.4 n-Butane 1.8 I 6.0 Crude oil 8.3 1.3 Cyclohexane 15.0 Methane 5.3 34.0 2.8 Ethylene 12.4 Ethane 3.0 19.0 3.5 Ethanol n-Hexane 1.2 6.9 4.0 74.2 Hydrogen 6.0 Kerosene 0.7 Motor gasoline 1.4 7.6 15.0 Methane 5.3 Octane 1.0 6.7 n-Pentane 1.3 7.6 2.1 9.5 Propane 2 11.7 Propylene 7.0 Toluene 1.3

temperature for several common Tr,

oc

-17.8 -17.8 14.4 ---

-11 -60 -18 -17 -222.5 ---

-135 12.8 -26 --49 -46 -222.4 13.3 -40 -104.4 ---

4.4

°C 700 305 615 630 562 405 230-250 260 632 450 515 558 234 400 229 280 632 458 287 493 443 536

Tautoivw

4.1.1 Estimation offlammability limits Several methods have been proposed for calculating the values of flammability limits. All of these give only approximate results, so experimental determination is always more accurate and reliable. A very simple procedure [9], proposed essentially for hydrocarbons, gives the values of the limits as a function of the stoichiometric concentration Cst:

LFL = 0.55 c,,

(3-2)

UFL =3.5c,,

(3-3)

Cst is the stoichiometric concentration of fuel in air, expressed as volume percentage (fuel in fuel plus air), that allows complete combustion, consuming all the oxygen available. This method was improved by Hilado and Li [10], who proposed the following expressions: LFL=aC 51

(3-4)

UFL=bcs,

(3-5)

where a and b are constants that depend on the chemical structure of the substance. Their values have been included in Table 3-2.

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Table 3-2 Values of constants a and bin ~qs. (3-4) and_D-5) DO Substance a b Linear saturated hydrocarbons 0.555 3.10 3.34 Cycloalkanes 0.567 Alkenes 3.41 0.475 3.16 Aromatic hydrocarbons 0.531 Alcohols-glycols 3.12 0.476 Ethers-oxides 0.537 7.03 10.19 Epoxides 0.537 2.88 Esters 0.552 Other compounds C, H, 0 3.09 0.537 Monochlorinated compounds 0.609 2.61 0.716 2.61 Dichlorinated compounds 1.147 Brominated compounds 1.50 Amines 0.692 3.58 Compounds containing S 3.95 0.577

Example 3-1 Estimation of the flammability limits for ethanol using both methods. Solution The combustion reaction is:

Therefore, the stoichiometric concentration is: c,,=

molesfuel ·100= 1 ·100=6.54% moles fuel+ moles air + . 100 1 3 21 Applying Eqs. (3-2) and (3-3), LFL = 0.55 · 6.54 = 3.60% volume UFL = 3.5 · 6.54 = 22.89% volume.

Using the values from Table 3-2 for alcohols, LFL=0.476·6.54=3.ll% volume UFL = 3.12 · 6.54 = 20.40% volume.

Comparing these results with the values in Table 3-1, it can be seen that Eq. (3-2) gives a fairly accurate prediction for the value of the LFL, while for the UFL Eq. (3-5) seems to be more accurate.

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4.1.2 Flammability limits ofgas mixtures If the fuel is a mixture of different components, the flammability limits can be estimated -again with a certain margin of error, which can be significant in some cases- as a function of their respective concentrations, using the empirical expressions proposed by Le Chatelier [ 11]:

LFL nuxt .

=

n

l

I_S_ i=I

(3-6)

LFLi 1

UFLmixt =-n---

L_S_ i=l

(3-7)

UFLi

where LFL; is the value of the LFL for component i (%volume) c; is the concentration(% vol.) of component ion a fuel basis (li:; = 100) and n is the number of combustible components in the mixture. Example 3-2 Estimation of the flammability limits of a mixture containing acetone (3% by volume), benzene (2%) and ethanol (7%) in air. Solution The concentrations of the three components on a fuel basis are:

c

%vol i

=~------------------------------~---

/

(% vol acetone+% vol benzene+% vol ethanol )mixture

Therefore: 0.25 Cbenzene = 0.17 Cethanol = 0.58 Taking into account the values of the LFL and UFL for the three components (Table 3-1 ), the flammability limits of the mixture are: Cacetone =

LFLmixt = 0. 25 O.l 7 0. 58 =2.70% volume --+--+-3 1.4 3.5 1

UFLmixt = 0. 25 0.1 7 0. 58 = 14.1% volume --+--+-13 8 19 The mixture is flammable, as 3% + 2% + 7% = 12%.

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4.1.3 Flammability limits as a function ofpressure Although most situations involving fuel/air flammable mixtures usually occur at what is essentially atmospheric pressure, storage or transportation are sometimes carried out under different conditions, and this can cause variations in the flammability limits. Flammability limits depend on pressure. Below atmospheric pressure, as pressure decreases (at constant temperature) the values of the two limits converge and the gap between them is narrowed until a certain pressure is reached at which they have the same value; at lower pressures, the flame cannot propagate through the mixture. This is due [12] to the fact that the concentration of gas is too low to sustain combustion. A method for predicting flammability limits at reduced pressures has been proposed by Amaldos eta!. [13]. However, if pressure is reduced in a tank containing a fuel at constant temperature, the increase in partial pressure of the fuel vapour can change the atmosphere above the liquid surface from a non-flammable condition to a concentration in the flammable range. This situation can occur in the fuel tanks of aircraft following take-off [5], when the aircraft climbs above a certain altitude. As the pressure rises above atmospheric pressure, flammability limits become greater. In fact, the LFL decreases only very slightly as pressure increases, but the UFL increases substantially. The variation of the UFL as pressure increases can be estimated using the following empirical expression [8]:

(3-8) where Pi is the absolute pressure (N m- 2) and UFL is the upper flammability limit at atmospheric pressure (% volume).

4.1.4 Flammability limits as a function of temperature Flammability limits also change with temperature: as temperature increases, the range of concentrations between the two limits widens. Of the various correlations that can be found in the literature to determine this variation, the most well known are probably the following [14]: LFLr = LFL 298

-

3 ;

6

(r- 298)

(3-9)

(T- 298)

(3-1 0)

c

UFLr

3

= UFL 298 - ;

6 c

where Tis the temperature (K) and &!cis the net heat of combustion (kJ mole- 1). Another empirical expression has been proposed [ 15] for estimating the LFL at a temperature T as a function of the same parameter at another temperature T1:

LFL T

= LFL7j (1 -

T- T; ) 873- T,I

(3-11)

where the temperatures are expressed in K.

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Example 3-3

Estimation of the LFL of octane at 100 °C. Solution

The LFL of octane at 25 oc is (Table 3-1) 1.0% volume. Therefore, LFL100

= 1.0 ( 1- 373-298) = 0.870Yo volume. 873-298

4.1.5 Inerting and flammability diagrams

In some industrial operations, flammable mixtures of a flammable gas and air can be generated. A typical example is the extraction of a liquid fuel from a vessel. As the liquid level descends, air must enter the vessel to avoid the creation of a vacuum, which could cause the tank walls to collapse and impede liquid flow. If air is allowed to enter, it will mix with the vapour already existing in the volume above the liquid surface, creating a mixture that will probably reach a concentration within the flammable range. To avoid this occurrence, it is a common practice to introduce an inert gas (nitrogen, carbon dioxide) to reduce the concentration of oxygen, thus preventing the generation of a flammable atmosphere. In the latter case, a more complex gas system will exist - for example hydrocarbon, oxygen and nitrogen - and the flammable conditions, which must be determined experimentally, must be represented in a two-dimensional diagram. An interesting practical example is that of filling or emptying a tank, a relatively dangerous operation: an historical analysis [ 16] has shown that 8% of all accidents occurring in process plants and during the transportation of hazardous materials are associated with these operations. A major source of accidents when filling a tank with a flammable liquid or emptying a tank that contains a flammable liquid is the fact that when air is present in the tank or enters during the operation, a flammable mixture can build up in the vapour space above the liquid. There are a number of possible ignition sources, the most frequent being sparks created by the electrostatic charge built up between the flowing fluid and the equipment. To avoid this dangerous situation, appropriate procedures can be applied by using an inert gas. These procedures may be better explained with the help of an x vs. y diagram, where x

y

=

inert volume ·l 00 flammable volume

=

flammable volume+ inert volume ·l 00 total volume(flammable+inert+air)

When an empty tank has to be filled with a flammable liquid, the tank is often initially full of air; therefore, before starting the operation x = 0 andy= 0 (see Fig. 3-3-a). In this case, as the liquid is introduced, its vapour will diffuse into the headspace, and its concentration in the air-vapour mixture will increase with time. At a certain point, this concentration will reach the LFL; from that point on, and for a certain period, a flammable mixture will exist inside the tank, with the associated risk of explosion.

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To avoid this risk, an inert gas must be introduced at the beginning of the operation. Thus, x = oo andy will progressively increase. When y reaches a certain value higher than any other within the flammable region (value A in Fig. 3-3-a) the flammable liquid may be introduced. The value of x will now gradually decrease, but will always remain outside the flammability range. y

y

100r--------------------+,

B

X

(a)

X

(b)

Fig. 3-3. a) Filling a tank with a flammable liquid using an inert gas. b) Emptying a tank which contains a flammable liquid using an inert gas. The opposite case is emptying a tank that contains a flammable liquid. In this case, an increasing gas headspace is built up as the liquid level descends. To avoid reduced pressure in the volume (which could impede liquid flow), gas must be allowed to enter the tank. If this gas is an oxidant (for example, air) a mixture within the flammability limits may occur, with the consequent risk of explosion. One way to remove this risk is again to use an inert gas. If the tank is being emptied, the headspace will initially be full of fuel vapour (it will contain neither air nor inert gas). Therefore, initially x = 0% andy= 100% (Fig. 3-3-b). If inert gas is added, y will remain constant (100%) and x will progressively increase until it reaches point B. As of this moment, air can be introduced while the liquid flows without any risk of creating a flammable mixture: the concentration in the head space will always be outside the flammability region.

4.2 Flash point temperature The flash point is the lowest temperature at which a flammable liquid gives off enough vapour to form a mixture with air that is flammable if an ignition source is present. It gives an idea of the ease with which a liquid can be ignited: gasoline (TJ "" -42 °C) is practically always ready to ignite; by contrast, diesel oil (Tr "" 66 oq is fairly difficult to ignite under standard room conditions. Substances with higher flash points are less flammable or hazardous than those with lower flash points. Thus, the flash point is an essential parameter in establishing how hazardous a substance is in terms of fire risk. The flash point temperature is obtained experimentally. Two procedures are used: opencup and closed-cup. Closed-cup methods give lower values. The flash point measured may also change according to the apparatus used. This may create some confusion and an amount

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of scattering in the published data. The flash point temperature for various substances is shown in Table 3-1. A more extensive survey can be found in the annexes. It is well known that there is a close relationship between the boiling point of a liquid and its flash point, and many correlations (commonly parabolic and hyperbolic equations) have been published, although most of them show large deviations when their predictions are compared to experimental data. Satyanarayana and Rao [17] proposed a new expression, which seems to be much more accurate, by correlating the data (closed-cup flash point temperature) for 1200 organic compounds with a high degree of accuracy (average absolute error less than 1%) with the following expression:

c b ( To

J2 e

_.!!__ To

(3-12)

where T0 is the boiling temperature of the substance (K) at atmospheric pressure, and a, band care constants (K) (see Table 3-3). Table 3-3 Constants in Eq.J3-12) [17] Chemical group a Hydrocarbons 225.1 Alcohols 230.8 Amines 222.4 Acids 323.2 Ethers 275.9 Sulphur 238.0 Esters 260.8 260.5 Ketones Halogens 262.1 Aldehydes 264.5 Phosphorus 201.7 Nitrogens 185.7 Petroleum fractions 237.9

b 537.6 390.5 416.6 600.1 700.0 577.9 449.2 296.0 414.0 293.0 416.1 432.0 334.4

c 2217 1780 1900 2970 2879 2297 2217 1908 2154 1970 1666 1645 1807

4.3 Autoignition temperature The autoignition temperature, also called spontaneous ignition, is the temperature at which a substance is ignited in the absence of any ignition source. It has also been defined as the lowest temperature at which a substance undergoes self-heating at a sufficient rate to cause its ignition. This second definition establishes a delay prior to ignition; this is again the explanation for a certain amount of scattering often found in the experimental data. The values of the autoignition temperature for several substances have been included in Table 3-1; more data can be found in the annexes. The theoretical estimation of this parameter can be performed by taking into account the chemical structure of the substance through a rather complicated methodology [15]. Nevertheless, the most reliable values will always be those obtained experimentally under the same conditions (pressure, fuel concentration, oxygen concentration) that would exist in a real situation.

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5 ESTIMATION OF THERMAL RADIATION FROM FIRES The ability to predict the effects of a fire is highly useful, both from the point of view of applying preventive measures and for emergency management. If, for example, the thermal radiation intensity that will affect a tank is known, it is possible to design a deluge system to protect the tank and to avoid the domino effect. In order to establish safety distances, it is also necessary to know the effects of the different kinds of accidents; if a foam monitor is installed in a location that, in the event of a fire, will be subjected to a strong heat flux, firemen will not be able to use it. Therefore, mathematical modelling is required to predict the thermal radiation that will reach a given target located at a certain distance from the flames. A number of mathematical models have been proposed by several authors. Some of them are too simple to provide reliable information, whilst others are too sophisticated and require data that in most cases is unknown. Here, one of the most well known and commonly used models, the solid flame model, has been selected. A description of the point source model is also included because of its applicability in some situations.

5.1 Point source model The point source model assumes that the fire can be represented by a point that irradiates thermal energy in all directions (Figure 3-4). The point source is usually located in the geometrical centre of the fire. The radiated energy is a fraction of the total energy released by the combustion. It is generally assumed that this energy is radiated in all directions. Therefore, the thermal radiation intensity reaching a given target, which is assumed to be proportional to the inverse square of the distance from the source, is given by

l=_g_

(3-13)

4tr ~~

where I is the thermal radiation intensity (kW m· 2) Qr is the heat released as thermal radiation per unit time (kW) and lp is the distance between the point source and the target (m). For jet fires and pool fires, Qr is a function of the burning rate m' (kg s· 1), the heat of combustion L1Hc and the radiative fraction or radiant heat fraction 'lrad, i.e. the fraction of the combustion energy that is transferred as thermal radiation: (3-14) The radiant fraction is a significant parameter that affects the whole fire, which in tum depends on several factors: the type of fuel, the flame temperature, the type of flame, the amount of smoke formed during combustion, etc. Values ranging between 0.1 and 0.4 have been obtained experimentally for hydrocarbons. It is rather difficult to estimate the value theoretically, and this is in fact one of the limitations of the point source model. The following expression has been proposed for pool fires with a diameter D (m) [18]: 'lrad

= 0.35

(3-15)

e-005D

74

Fig. 3-4. The point source model. The point source model is so simple that it does not take into account the absorption of the thermal radiation by the atmosphere or the position of the surface that receives the radiation: it is assumed that this surface faces toward the radiation source so that it receives the maximum thermal flux [19]. Eq. (3-14) can be modified to include these two factors, giving the expression: I= '7radm'11Hcrcosrp 4Jrl~

(3-16)

where rp is the angle between the plane perpendicular to the receiving surface and the line joining the source point and the target ( and r is the atmospheric transmissivity (-). The point source model overestimates the intensity of the thermal radiation near the fire, due to the fact that it does not take into account the flame geometry. It should not therefore be used, for example, to establish separation distances between adjacent equipment. However, it predicts with reasonable accuracy the radiation intensity in the far field, at distances greater than 5 pool diameters from the centre of the fire; thus, it is sometimes used to perform conservative calculations of danger to personnel. 0

)

5.1.1 Atmospheric transmissivity The atmospheric transmissivity accounts for the absorption of the thermal radiation by the atmosphere, essentially by carbon dioxide and water vapour. This attenuates the radiation that finally reaches the target surface. The atmospheric transmissivity depends on the distance between the flames and the target. While the carbon dioxide content in the atmosphere is essentially constant, the water vapour content depends on the temperature and the atmospheric humidity. It can be estimated from the following equations: (3-17-a)

75

(3-17-b) (3-17-c) where P w is the partial pressure of water in the atmosphere (N m- 2) and d is the distance between the surface of the flame and the target. Pw can be estimated by the following expression:

p =P HR w wa 100

(3-18)

is the saturated water vapour pressure at the atmospheric temperature (N m- 2) and HR is the relative humidity of the atmosphere(%). Pwa can be obtained from the prevailing temperature of the atmosphere [19]:

where

P wa

lnP = 23.18986wa

3816 2 .4

(3-19)

(T -46.13)

where P wa is expressed in N m- 2 and Tin K. Example 3-4. There is a pool fire of diesel oil with a diameter of 6 m and an average flame height of 11.5 m. Calculate the thermal radiation that reaches the vertical surface of a tank, at a height of 1.6 m above the ground; the tank wall is at a distance of 15 m from the diesel oil pool perimeter (Fig. 3-4). &ic diesel= 41900 kJ kg- 1. Ambient temperature is 16 °C. Atmospheric relative humidity is 79%. m = 0.05 kg m- 2 s- 1. Solution The distance between the point source and the target is:

y

11.5

2

IP = ( - --1.6) +(15+3) =18.5 m 2 and the distance between the surface of the flames and the target is: 18 cos a = - - = 0.97 18.5

___!2__ = --.!2_

d =

cosa

=

15.5 m

0.97

Estimation of the atmospheric transmissivity: lnP wa

=23.18986-

3816 2 .4 =7.486 (289.16-46.13)

76

Pwa = 1783 N m- 2 P

= w

1783~ = 1408 N m- 2 100

Pw d = 1408 ·15.5 = 21824; therefore, by applying Eq. (3-17-b): r=2.02(1408·15.5t Tfrad

= 0.35e-

0056

009

= 0.82

=0.26

The overall burning rate is: 62

m = 0.05Jr- = 1.414 kg s- 1 4

Therefore

I= 0.26·1.414·41900·0.82·0.97 = _ kWm-2 28 4Jrl8.5 2 (The experimental thermal radiation intensity for this situation, measured with a radiometer, was 2.3 kW m- 2 [20]).

5.2

Solid flame model

This is the most common model used to estimate the thermal radiation from fires. It is more accurate than the point source model, even at short distances from the flame. The solid flame model assumes that the fire is a still, grey body encompassing the entire visible volume of the flames, which emits thermal radiation from its surface (Figure 3-5). The irradiance of the smoke (non visible flame) plume above the fire is partly taken into account. In fact, most models use the maximum length of the flame rather than the average one, and this includes some of the smoke volume above the flame. The shape of the flames will depend on the features of the fire. In the case of a pool fire, the pool shape will be essential: if the pool is circular, the fire will approximate to a cylinder; if there is any wind, the cylinder will be tilted. If a rectangular dike retains the liquid fuel, the fire will be assumed to be parallelepipedic. In more general cases, it is assumed that the body radiates energy uniformly from its whole surface. The thermal radiation intensity reaching a given target is

I=rFE

(3-20)

where r is the atmospheric transmissivity (-) F is the view factor (-) and 2 E is the average emissive power of the flames (kW m- ).

77

In the following paragraphs the estimation of the view factor and the emissive power is discussed; the atmospheric transmissivity has already been discussed in Section 5.1.1. a)

b)

a

Fig. 3-5. The solid flame model. 5.2.1 View factor The view factor, a parameter which appears in practically all thermal radiation calculations, is the ratio between the amount of thermal radiation emitted by a flame and the amount of thermal radiation received by an object not in contact with the flame. This ratio depends on the shape and size of the fire, the distance between the flame and the receiving element and the relative position of the flame and target surfaces. It can be represented by a general equation: (3-21)

where

78

Table 3-4 Vertical view factor (Fv) for a cylindrical fire l/(D/2) 1.10 1.20 1.30 1.40 1.50 2.00 3.00 4.00 5.00 10.00 20.00 50.00

0.1 0.330 0.196 0.130 0.096 0.071 0.028 0.009 0.005 0.003 0.000 0.000 0.000

0.2 0.415 0.308 0.227 0.173 0.135 0.056 0.019 0.010 0.006 0.001 0.000 0.000

0.5 0.449 0.397 0.344 0.296 0.253 0.126 0.047 0.024 0.015 0.003 0.000 0.000

1.0 0.453 0.413 0.376 0.342 0.312 0.194 0.086 0.047 0.029 0.006 0.001 0.000

H/(D/2) 2.0 3.0 0.454 0.454 0.416 0.416 0.384 0.383 0.354 0.356 0.329 0.330 0.236 0.245 0.132 0.150 0.100 0.080 0.053 0.069 0.013 0.019 0.003 0.004 0.000 0.000

5.0 0.454 0.416 0.384 0.356 0.333 0.248 0.161 0.115 0.086 0.029 0.007 0.001

6.0 0.454 0.416 0.384 0.357 0.333 0.249 0.163 0.119 0.091 0.032 0.009 0.001

10.0 0.454 0.416 0.384 0.357 0.333 0.249 0.165 0.123 0.097 0.042 0.014 0.002

20.0 0.454 0.416 0.384 0.357 0.333 0.249 0.166 0.124 0.099 0.048 0.020 0.004

5.0 0.362 0.312 0.277 0.250 0.228 0.158 0.091 0.057 0.037 0.007 0.001 0.000

6.0 0.362 0.312 0.277 0.251 0.229 0.160 0.095 0.062 0.043 0.009 0.001 0.000

10.0 0.363 0.313 0.278 0.252 0.231 0.164 0.103 0.073 0.054 0.017 0.003 0.000

20.0 0.363 0.313 0.279 0.253 0.232 0.166 0.106 0.078 0.061 0.026 0.003 0.000

0.25 0.0606 0.0604 0.0598 0.0581 0.0494 0.0431 0.0331 0.0184 0.0149 0.0076 0.0038 0.0015

0.2 0.0490 0.0489 0.0483 0.0470 0.0400 0.0349 0.0268 0.0149 0.0121 0.0062 0.0031 0.0012

0.1 0.0249 0.0248 0.0245 0.0239 0.0203 0.0178 0.0137 0.0076 0.0062 0.0031 0.0016 0.0006

0.05 0.0125 0.0124 0.0123 0.0120 0.0102 0.0089 0.0069 0.0038 0.0031 0.0016 0.0008 0.0003

Table 3-5 Horizontal view factor (Fh) for a cylindrical fire //(D/2) 1.10 1.20 1.30 1.40 1.50 2.00 3.00 4.00 5.00 10.00 20.00 50.00

0.1 0.132 0.044 0.020 0.011 0.005 0.001 0.000 0.000 0.000 0.000 0.000 0.000

0.2 0.242 0.120 0.065 O.o38 0.024 0.005 0.000 0.000 0.000 0.000 0.000 0.000

0.5 0.332 0.243 0.178 0.130 0.097 0.027 0.005 0.001 0.000 0.000 0.000 0.000

1.0 0.354 0.291 0.242 0.203 0.170 0.073 0.019 0.007 0.003 0.000 0.000 0.000

H/(D/2) 2.0 3.0 0.362 0.360 0.307 0.310 0.268 0.274 0.246 0.238 0.222 0.212 0.126 0.145 0.050 0.071 0.022 0.038 0.011 0.021 0.001 0.003 0.000 0.000 0.000 0.000

Table 3-6 Vertical view factor (Fv) for a parallelepipedic fire Hlx 10 5 3 2 I 0.75 0.50 0.25 0.20 0.10 0.05 0.02

10 0.2480 0.2447 0.2369 0.2234 0.1767 0.1499 0.1118 0.0606 0.0490 0.0249 0.0124 0.0050

5 0.2447 0.2421 0.2350 0.2221 0.1760 0.1494 0.1114 0.0604 0.0489 0.0248 0.0123 0.0050

3 0.2369 0.2350 0.2292 0.2176 0.1734 0.1475 0.1101 0.0598 0.0483 0.0245 0.0122 0.0049

2 0.2234 0.2221 0.2176 0.2078 0.1674 0.1427 0.1068 0.0581 0.0470 0.0239 0.0120 0.0048

I 0.1767 0.1750 0.1734 0.1674 0.1385 0.1193 0.0902 0.0494 0.0400 0.0203 0.0102 0.0041

wlx 0.75 0.5 0.1499 0.1118 0.1491 0.1114 0.1478 0.1101 0.1427 0.1068 0.1193 0.0902 0.1032 0.0784 0.0784 0.0599 0.0431 0.0331 0.0349 0.0268 0.0178 0.0137 0.0089 0.0069 0.0036 0.0027

0.02 0.0050 0.0050 0.0049 0.0048 0.0041 0.0036 0.0027 0.0015 0.0012 0.0006 0.0003 0.0001

The value of the maximum view factor, corresponding to a surface located perpendicularly to the direction of the radiation, can be calculated using the following expressiOn: (3-22)

79

This is a simplified expression, which can not be used if the flames are inclined crosswind with respect to the target. Table 3-7 Horizontal view factor (Fh) for a parallelepipedic fire Hlw xlw 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.2 1.5 2.0 3.0 4.0 5.0

0.1 0.0732 0.0263 0.0127 0.0073 0.0047 0.0032 0.0023 0.0017 0.0013 0.0010 0.0007 0.0004 0.0002 0.0001 0.0000 0.0000

0.2 0.1380 0.0728 0.0414 0.0257 0.0171 0.0120 0.0087 0.0065 0.0050 0.0040 0.0026 0.0015 0.0007 0.0002 0.0001 0.0000

0.3 0.1705 0.1105 0.0720 0.0485 0.0339 0.0245 0.0182 0.0139 0.0108 0.0086 0.0056 0.0032 0.0015 0.0005 0.0002 0.0001

0.5 0.1998 0.1549 0.1182 0.0899 0.0687 0.0530 0.0414 0.0327 0.0261 0.0211 0.0142 0.0084 0.0041 0.0013 0.0006 0.0003

0.7 0.2126 0.1774 0.1459 0.1190 0.0966 0.0784 0.0638 0.0522 0.0429 0.0355 0.0249 0.0152 0.0076 0.0026 0.0011 0.0006

1.0 0.2217 0.1944 0.1687 0.1452 0.1243 0.1059 0.0903 0.0767 0.0653 0.0557 0.0409 0.0265 0.0139 0.0050 0.0023 0.0012

1.5 0.2279 0.2063 0.1855 0.1660 0.1478 0.1312 0.1162 0.1028 0.0908 0.0803 0.0629 0.0440 0.0253 0.0100 0.0047 0.0026

2.0 0.2305 0.2113 0.1928 0.1752 0.1588 0.1436 0.1296 0.1169 0.1054 0.0951 0.0774 0.0572 0.0355 0.0154 0.0077 0.0043

5.2.2 Emissive power The emissive power is the radiant heat emitted per unit surface of the flame and per unit time (kW m- 2); it represents the radiative characteristics of the fire. In fact, the thermal radiation emitted from the flame is really generated by the whole volume of the fire (from the hot fuel gas, the combustion products, the soot particles) and not only on its surface. Thus, the emissive power is a useful two-dimensional simplification of a complex, three-dimensional complex heat transfer problem. Two types of emissive power can be distinguished: a) point emissive power, associated with the value measured over a small area of the flame; b) average emissive power, corresponding to the emissive power of the whole flame surface. Emissive power can be expressed as a function of emissivity and flame temperature:

(3-23) where uis the Stefan-Boltzmann constant (W m- 2 K-4 ) & is the emissivity (-) Tjz is the radiation temperature of the flame (K) and Ta is the ambient temperature (K). However, it is very difficult to calculate both Tfl (significantly lower than the adiabatic flame temperature) and c: as the temperature is not uniform over the flame and varies with time, and the emissivity depends on the substances present in the flame. Therefore, empirical procedures are commonly applied to estimate the value of E for the different types of fire; alternatively, experimental values from similar fires are assumed. The emissive power changes with the position in the fire, with higher values near the bottom and decreasing values as the height increases. Fig. 3-6 shows two typical mean emissive power contour plots [20, 23] produced by a 3 m gasoline pool fire (left) and a 6 m diesel pool fire (right). The vertical and horizontal dimensions were converted to a dimensionless form by dividing their values by the pool diameter (D). A high-radiance zone

80

appears near the base, approximately between HID = 0.1 and HID = 0.6; the values of E for this zone varied from 80-100 kW m· 2 for pools of 1.5 min diameter to 120-160 kW m- 2 for pools with larger diameters. Significantly lower values of E can be observed in the top part of the fire, where luminous flame has been almost completely substituted by black smoke. Gasolme

D=3m

kW/m2 140

2.414 2.165

1.839 1.647

120

1.916 100

1.668 0

12C

1.456

1419

1264 0

80 ~

~

1.170

10C

1.073 0.881

80

0.921

0.690

0.672

0.498

40 0.423 20

x/D

Fig. 3-6. Two mean E contour plots. Left: 3 m gasoline pool fire. Right: 6 m diesel pool fire. Taken from [23], by permission.

Although an average value of E is often assumed for the entire fire surface, there are in fact two zones commonly found for many fuels: a luminous zone and a non-luminous zone, both of which have different values of emissive power. Fig. 3-7 shows the luminous and nonluminous parts of a fire (diesel oil, 6 m diameter), obtained by superimposing the IR and visible images [20, 23]. luminous part

Fig. 3-7. Luminous and non-luminous parts of a pool fire of diesel oil (6 m diameter). Taken from [23], by permission.

81

The contribution of the two parts changes according to the type of fire and the properties of the fuel. An average value of the emissive power for the whole fire can be estimated by taking the two contributions into account: (3-24) where x 1um is the fraction of the fire surface covered by the luminous flame and E 1um and Esoot are the values of E for the luminous and non-luminous zones of the fire, respectively (kW m- 2). For gasoline and diesel oil pool fires, the experimental data obtained for a circular pool with a diameter of 1.5 m s D s 6 m [23] indicate that Esoot is independent of the diameter and 2 of the type of fuel: Esoot = 40 kW m- . However, the average value of E1um ranged between 80 2 2 kW m- and 120 kW m- , as it is a function of the diameter and the type of fuel. E 1um increased with the pool diameter up to 5 m; thus, for D < 5 m: £/umgasoline £/umdiesel

=

= 53.64D0.4?4 28.03D

(3-25)

0 877 -

while forD~ 5 m E1um= 115 kW m- 2 . X!um is constant forD< 5 m (Xlum gasoline= 0.45, X!um diesel oil= 0.30) while forD> 5 m it decreases. There are not enough data to establish the exact decrease and the minimum value of x1um; some authors state that beyond D > 20 m X!um = 0. 0.5 0.4 0.3 E

X:;!

0.2 0.1 0.0

---- EIurn

NE ~ 6 w

100 90 80 70 60 50

···-·· E

40 30 2

3

4

5

6

7 8 9 10

20

30

Diameter (m)

Fig. 3-8. Evolution ofx1um, Etum and E as a function of pool diameter for gasoline. Taken from [23], by permission.

Consequently, the emissive power of fires involving gasoline, diesel oil and similar fuels can be estimated as follows:

82

E = xlumElum

+ (1- xlum )Esoot forD< 20m

(3-26)

E"" Esoot forD~ 20m

There is experimental evidence that E increases with pool diameter, which is essentially due to the increase of Etum (while the ratio between the surfaces of luminous and nonluminous flame remains constant); once it reaches a maximum value, E then starts to decrease as a result of the decrease in the luminous flame surface. The variation of Xtum and E for gasoline is plotted in Figure 3-8. Finally, the following expression was also suggested for estimating the value of E: E

= l7rad mMfc

(3-27)

A

where A is the area of the solid flame from which radiation is released (m2). The suggested conservative value for lJrad is 0.35. 6 FLAME SIZE Knowledge of the size and shape of the flames is required to estimate the effects of the fire - i.e. the radiation that will reach a given target - using the solid flame model. It is also required, when considering short distances, in order to discern whether there will be any flame impingement on nearby equipment. This can be comparatively difficult to predict for a number of reasons. First of all, the exact shape of the flames is not known, as it is always fairly irregular; the shape is usually compared to a given geometric body (a cylinder, a parallelepiped, a sphere). Secondly, the size of the flames varies with time due to the turbulence of the phenomenon, particularly for large fires. This is why average and maximum values have been defined.

1.0

0.8

>(.) c: 0.6

~

E

Q5 0.4

c

0.2

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4

LID Fig. 3-9. Intermittency corresponding to a 3m gasoline pool fire [20].

83

A helpful concept in defining these values is the intermittence criterion, developed by Zukoski et a!. [24]. The intermittency i (L) is defined as the fraction of time during which the length of the flame is at least greater than L; this concept is represented in Fig. 3-9 for a gasoline pool fire. Thus, the average length of a flame is defined as the length at which the intermittency reaches a value of0.5. The maximum flame length is commonly defined as the length at which the intermittency is 0.05. The size of the flames depends on the burning rate, which, in tum, depends on several factors (type of fuel, type of fire, etc.). Empirical or semiempirical equations are commonly used to estimate these values. In the followings paragraphs a selection of these equations is presented for pool fires and jet fires.

6.1 Pool fire size 6.1.1 Pool diameter When a liquid is spilled and a pool is formed, there are two possibilities: a pool on the ground or a pool on the water surface. The following paragraphs briefly discuss the difference between the two. Pools on ground If there is a dike or a barrier that contains the liquid spill, the pool diameter is fixed. If the dike is right-angled, the equivalent diameter must be used:

D=

4

surface area of the pool

(3-28)

J[

The size of a pool caused by a liquid spill on the ground depends on the duration and flow rate of the spill. Thus, liquid spills can be divided into two categories: Instantaneous spills Continuous spills If the spill is instantaneous, the pool will grow until it finds a physical barrier (for example, a dike) or until it is burnt if there is a pool fire. In the case of a continuous spill, the pool will grow until it finds a physical barrier or until the vaporization velocity or the burning rate equals the spill flow rate. Although many spills will in fact be semi-continuous (i.e. a certain amount of liquid is spilled during a given time), it is useful to have a criterion for distinguishing between instantaneous and continuous spills. The following has been proposed [25]: (spill

Y

(3-29)

tc,=vm I

where

is a dimensionless critical time (-) is the duration of the spill ( s) y is the fuel burning rate (m s- 1), and V1 is the total volume of the spilled liquid (m\ fer

fspill

84

According to this criterion, spills are instantaneous if tcr < 2 · 1o- 3. Otherwise, they are considered continuous. For an instantaneous spill, without any containing barriers, the pool diameter can be expressed as a function of time by the following expression [21, 31]:

(3-30)

where Dmax is the maximum diameter (m) that the pool can reach:

3 )1/8

7~ g

(3-31)

Dmax =2 (

and tmax is the time (s) required to reach this maximum diameter: 1/4

(3-32)

!max =0.6743 ( ; ; 2 )

However, a pool with the maximum diameter Dmax exists only for a short time. Using it to calculate the thermal radiation from a pool fire would lead to an overestimation of fire hazards [7]. Therefore, in practice it is better to use an average pool diameter value expressed as: (3-33) In the case of a continuous release without any physical barriers, the equilibrium diameter for a burning pool (for a situation in which the release rate equals the burning rate) and the time required to reach it can be estimated with the following expressions [21]: 1/2

D =2l ( Jr Y ) eq

feq

D =0.564 ( eq gyDeq

(3-34)

t

(3-35)

3

where Deq is the equilibrium diameter (m) 3 1 Vt is the leak rate (m s' ), and teq is the time required to reach Deq (s).

Pools on water In the case of a spill on water (usually seawater), if there is immediate ignition, the equations proposed for spills on smooth ground can be applied by replacing g with an "effective" value g' defined as follows [6]:

85

J

-g ' =g ( 1 -p,

(3-36)

Pwater

3

where Pt is the density of the spilled liquid (kg m- ), and 3 Pwater is the density of water (or seawater) (kg m- ). If, in the case of a continuous spill, there is delayed ignition and the pool diameter has become larger than the equilibrium diameter, the equilibrium diameter will soon be reached after ignition and this value will be maintained while the spill flow rate is constant. If the diameter has reached such a value that the thickness of the spilled layer has become very small (approximately 1.25 mm), ignition will not be possible even though an ignition source exists. If the spill is instantaneous and the ignition is delayed, the diameter will evolve as a function of time, passing through the following phases [26]. In phase 1, gravitational and inertial forces prevail:

(3-37)

3 is the density of water (kg m- ) 3 Pt is the density of the spilled liquid (kg m- ) V1 is the volume of liquid fuel released instantaneously (m\ and tis the time elapsed from the start of the release (s). In phase 2, viscous forces prevail:

where

Pw

2 3/2

D =196 [(Pw-Pt ) gV, t 1/2 • 2 vw p,

]l/

6

(3-38)

2 1 where Vw is the seawater viscosity (m s- ). Finally, in phase 3, the surface tension is the dominant spreading mechanism:

D3 =3.2

where

2 3Jl/4 f; t ( Pw Vw

(3-39)

fr is the interface tension (N m- 1) (ranging between 0.005 and 0.02 N m- 1).

6.1.2 Burning rate The burning rate is usually estimated using the following expression:

m = moo (1- e -kD)

(3-40)

2 1 where moo is the burning velocity for an infinite diameter pool (kg m- s- ) and k is a constant 1 (m- ). Various authors have proposed values for moo and k (Table 3-8). For large scale fires, m

86

Table 3-8 Expressions for the estimation ofbuming velocity Diesel oil k ,m-1 Authors moo 'kg m- 2 s- 1 Babrauskas [27] Rew et al. [28] Munoz et al. [23]

0.034 0.054 0.054

2.80 1.30 0.88

Gasoline moo 'kg m- 2 s- 1 0.055 0.067 0.082

k,m-1

2.10 !.50 1.31

An alternative way for estimating the burning rate is to apply the expression proposed by Burgess [29]:

(3-41) is the net combustion heat (kJ kg- 1) L1hv is the vaporization heat of the fuel at its boiling temperature (kJ kg- 1) and To is the boiling temperature at atmospheric pressure (K). The burning rate of a pool fire can also be expressed in m s- 1• Obviously, the relationship between this burning rate and the mass burning rate is:

where

&fc

m p,

y=-

(3-42)

6.1.3 Height and length of the flames The height of the visible flame is a function of pool diameter and burning velocity. Of the various expressions that have been proposed for the estimation of this value, the most commonly used is the one developed by Thomas [30]: 0.61

H -42

D-

m [

(3-43)

Pafii5 ]

This expression gives the average flame height (or length, if the flame is tilted). The maximum length can be estimated as a function of the average value as follows [22]:

(!:__) D

=

1.

52(!:__) D

max

(3-44) average

6.1.4 Influence of wind Wind can have an influence on flame length. A recent study [31] found that the influence of wind on burning velocity is almost negligible at Uw < 2 m s- 1• At higher velocities, the following equation is [30] is often used: 0.67

H

-=55 D

m [

Pa~gD ]

,-o21

(3-45)

u

87

u* being a dimensionless wind velocity: u*=

uw

113

;(ifu*
(g;aD J

where Uw is the wind velocity (m s- 1). Wind can also tilt the flames and significantly move their bottom part (Fig. 3-1 0), thus causing the flames to spill over the edge of the pool and elongating the flame base. This can be highly significant if there is equipment nearby, as the level of thermal radiation will mcrease. Wind

~

Wind

~

Fig. 3-10. Flame tilt and drag in pool and tank fires. Taken from [32], by permission.

If there are short separation distances between equipment, for example adjacent tanks, the flames may engulf part of this equipment. If there is flame impingement, the thermal flux can increase dramatically, leading to the structural failure of the equipment. Therefore, both flame tilt and drag must be evaluated in the presence of wind. The flame tilt can be estimated using the following expression [25, 32]: cos a= 1

for u* :s; 1

cos a= 1/ -J;i

for u* > 1

and the flame drag can be estimated for any fuel [32, 33] by means of:

88

!2_=1.5 ~ '

D

(

2 )0.069

(3-47)

gD

Example 3-5 Imagine the instantaneous rupture of a tank containing 3500 m3 of gasoline. The tank is located in a dike with a diameter of 60 m. There is a slow wind (uw = 1.5 m s· 1). a) Estimate the maximum thermal radiation on the wall of a tank located 25 m from the dike wall. b) If for a short period the wind speed increases to 6 m s· 1, will a set of valves located 14 m downwind of the dike wall be engulfed by the fire? Gasoline liquid density= 870 kg m· 3 . Ambient temperature = 18 °C. Relative humidity = 70%. Air density= 1.2 kg m· 3.

Solution a) Calculation of the maximum pool diameter (Eq. (3-31)), using the approximate value for the burning rate of0.082 kg m·2 s· 1 (Table 3-8):

3

D max

= 2 3500 ·9.81-870 ( 0.0822

2)1/8 =

576 m_

As this value is higher than the dike diameter, the diameter of the pool will be 60 m. The approximate burning rate can now be verified for this pool diameter (Eq. (3-40)):

Estimation of flame height (Eq. 3-43)):

H = 60 · 42[

0 082 · ] 1.2-h.81· 60

0 61 .

= 70 m

The influence of the wind can be ruled out (u* = 0.44). Emissive power: as D >20m, E ""Esoot ""40 kW m· 2 • Calculation of atmospheric transmissivity: from Eq. (3-19), Pwa = 2027 N m· 2 , therefore,

By applying Eq. (3-17 -b): T

= 2.02 (1419 · 25t

009

= 0.79

The view factor can be obtained from Table 3-4; H/(D/2) = 2.3, l/(D/2) = 1.8; interpolating, Fv = 0.265. For a horizontal surface, from Table 3-5, Fh = 0.165. Therefore,

89

By applying the solid flame model,

I= 0.79·0.312·40 = 9.8 kW m· 2 b) With a wind speed of 6 m s· 1, the flame drag will be significant; it can be estimated using Eq. (3-47):

D' = 60 ·1.5

6 2 )0.069 = 75.5 m ( 9.81·60

D' -D = 15.5 m >14m, the valves will be engulfed by the fire.

6.2 Size of a jet fire Jet or flare fires are characterized by highly turbulent diffusion flames. They can occur due to the accidental release of a fuel gas -for example, through a broken pipe or a flange, or from a relief valve- or in process or emergency flaring. Accidental jet fires have occurred in many parts of process plants or in transportation accidents and often impinge on equipment; in this case, large heat fluxes occur due to the high convective heat transfer caused by the relatively good combustion and the high flow velocities. A number of BLEVEs or similar explosions have been caused by jet fires. Flares also release large amounts of radiant energy, although they are located in high stacks to assure safe operation. In both cases, the prediction of the jet fire size and of the thermal flux as a function of distance is required in order to determine the effects of a jet fire and to establish safety distances. 6.2.1 Jetjlow In an accidental release, the sonic velocity (velocity of sound in the gas in exit gas conditions) is reached if the following relationship is fulfilled:

(3-48) where Po is the atmospheric pressure (N m· 2 ) and 2 Peont is the pressure inside the container or the pipe (N m· ). The sonic velocity is the maximum possible velocity in an accidental release. It is also called choked velocity. Once the speed of sound has been reached, further increases in Peont will not produce any further increase in the gas exit velocity. However, as the density of gas increases with pressure, the mass flow rate will increase linearly with pressure. For most gases, the sonic velocity is reached if the pressure at the source is greater than 1.7-1.9 bar. This is usually the situation in accidental releases. The following expressions concerning the gas jet are of interest. The speed of sound in a given gas at a temperature Tis:

90

(3-49)

where Us is expressed in m s- 1 and R is the ideal gas constant (8.314 kJ kmor 1 K- 1). The temperature of the gas in the expanded jet downstream at the orifice outlet is:

(3-50)

where Po is the atmospheric pressure (N m- 2) 2 Pcant is the initial pressure of the gas in the container or pipe (N m- ) and Tcant is the temperature in the container or pipe (K). The effective orifice diameter, ds, is the diameter of an imaginary orifice that would release air with a density Pa at the same flow rate at which gas is being emitted. It can be calculated with the following expression:

ds

=

(3-51-a)

where m' is the mass flow rate of gas (kg s- 1) and u1 is the velocity in the expanded jet at the gas outlet (m s- 1). ds can also be calculated as follows:

d =d s

[P; orv;:

(3-52-a)

where Pair is the density of ambient air (kg m- 3) and Pi is the density of the gas in the expanded jet. For unchoked flow, PJ = p~ (27311}); for choked flow, the jet expands to atmospheric pressure downstream of the exit hole. Then: 1

(3-52-b)

ds =dJ¥ 1 Pa

where dj is the diameter of the expanded jet

d j-

(3-53)

where Pi is the density of the gas in the expanded jet (kg m- 3). u1 can be calculated as follows:

91

(3-54)

(3-55) MJ =

where A1j is the Mach number for choked flow of an expanding jet (-) Po is the atmospheric pressure (N m- 2) and Par is the static pressure at the orifice exit plane (N m- 2):

(3-56)

6.2.2 Shape and size ofthejetjire There are various sets of equations proposed by different authors for predicting the shape and size of a jet fire, with significant scattering in the results. Two classical treatments, for calm situations and the presence of wind, respectively, have been selected here. In a calm wind situation, the length of the flames in a jet fire can be estimated in a simple way using the expression proposed by Hawthorne et al. [34]:

[

C +(1-c )Ma .i_=_}_]_ ~ st M st T v est-val a,, cant ( dar

l/2

l

(3-57)

J

where L is the length of the visible flame, from the lift-off distance to the tip (m) Cst-vai is the mole fraction of fuel in the stoichiometric fuel-air mixture (-) Tad is the adiabatic flame temperature (K) Ma is the molecular weight of air (kg kmole- 1) and as1 is the ratio of the number of moles of reactants to moles of product for a stoichiometric fuel-air mixture (-). Eq. (3.57) can be simplified for hydrocarbon gases to [6] [34]:

(3-58)

The lift-off distances can be estimated using the following expression [35]: (3-59)

where

is the diameter of the orifice (m), and Uavis the average jet velocity (m s- 1) (uav :::::0.4 u1).

dar

92

Finally, the diameter of the jet fire can be estimated as a function of its length using the following expression: L D 1 =0.29x[ In~

]1;z

(3-60)

where xis the axial distance from the orifice (m), and sis the lift-off distance (m). Example 3-6 A cylindrical tank containing butane has been heated to 51 oc. Gas is vented upwards from a release device (outlet internal diameter: 0.025 m) located on the top of the tank, 4 m above ground (Fig. 3-11 ). There is no wind. Estimate the maximum thermal radiation on the wall of a tank located at a horizontal distance of 9 m from the jet axis, at a height of 4.5 m above the ground. !Jlfc = 45700 kJ kg- 1• y = 1.11. Constants in the Antoine equation for butane: A= 4.35576, B = 1175.58, C = -2.071. Ambient temperature= 18 oc. Relative humidity= 50%.

Fig. 3-1 I. Jet fire in a calm situation.

Solution The combustion reaction is:

c
=

13 1 =0.0313 1+-2 0.21

93

Estimation of the length of the flame using Eq. (3-58): 15 29 L = 0.025-- - ( 0.0313 58 )

112

= 8.4 m

Estimation of the lift-off distance using Eq. (3-59): s

=

6.4

1£

0.025 u j

4·0.4 u 1

= 0.3

m

Pressure inside the vessel: log P = 4.35576-

1175 58 · ; P = 5 bar. 324- 2.071

Calculation of the mass flow rate of fuel using Eq. (2-19):

m

0.025 2

=1£--

4

58 2 ):~~=: 1·5 ·10 5 1.09( - = 0.71 kg s- 1 1.09+1 324·8.314·10 3

For butane jet fires, Brzustowski [35] obtained lJrad = 0.3 (radiant heat fraction). Recent tests have given lower values; lJrad = 0.1 will be taken here. If the jet fire is assumed to be a cylinder, from Eq. (3-60) an average diameter D "" 1 m is obtained. Estimation of the average emissive power using Eq. (3-27):

E= 0.1·0.71-45,700 =ll 5 kWm_ 2

e

Jr·1·8.4+2;r4 Estimation ofthe view factor from Table (3-4): Fv= 0.0238. For a relative humidity of 50% and l = 9 m, r = 0.88. Therefore, the thermal radiation intensity (Eq. (3-20)) is:

I= 0.0238 ·115 · 0.89 = 2.4 kW m- 2

6.2.3 Influence of wind

The wind can have a significant influence on the jet fire. The model proposed by Chamberlain [36, 37], relatively complex, describing the jet flames by the frustrum of a cone (Fig. 3-12) has been selected here. First of all, the auxiliary parameter Y must be calculated by iteration: 113

o.o24 [

gu;s

Y 513 + o.2 Y 213 )

-

cc = o

(3-59)

94

For parafins, 213 = (2.85/cst-mass) where Cst-mass is the stoichiometric mass fraction of fuel(-). In still air, the length of the flame measured from the centre of the exit orifice to the tip of the flame can be calculated with the following expression:

Cc

(3-60) where Lbo is expressed in m.

s

Fig. 3-12. Influence of wind on a jet fire [36, 39].

Under the influence of wind: (3-61)

where f:1v is the angle between the hole axis and the wind vector CO). The lift-off distance is: s = Lb sin ((0.185

2

e(-. 0R,.)

+ 0.015)a)

(3-62-a)

sma where Rw is the ratio of wind speed to jet velocity: Rw = uwfuj. In still air,

(3-62-b) The length of the flames (length offrustrum) is:

95

(3-63) If Rw :s; 0.05, the tilt angle can be calculated as follows:

a=(Bjv -9o)(1-e-256 R" )+8000~

(3-64-a)

RzLbo

and if Rw > 0.05,

a= (ejv _ 90 )(I- e-256 R,. )+ (134 + 1726 (~w- 0.026t

2 )

(3-64-b)

RzLbo where Rhbo is the Richardson number based on Lbo,

and cos Bjv =cos n cos Bj

n is the angle between the wind direction and the normal perpendicular to the pipe in the horizontal plane; ej is the angle between the hole axis and the horizontal in the vertical plane. Finally, the width of frustrum (base and tip, respectively)can be calculated with the following expressions: (3-65)

(3-66) where Rids is the Richardson number based on the source diameter and C' is a function of Rw:

c' =1000e-IOOR,.

+0.8

The diameter of the jet fire can be estimated as a function of its length using Eq. (3-58). The surface of the flames (A) can also be approximated by considering a cylinder with an average width:

96

(3-67)

The value of E can be estimated using Eq. (3-27), with [36] 'lrad

=

0.2le -0.00323u, + 0.11

(3-68)

For relatively large distances, for example in the case of flares, the point source model can be applied. Example 3-7 Based on Example 3-6, with a wind speed of 6 m s· 1• Determine the size and shape of the jet fire. Estimate the radiation (point source model) on a target located at ground level at 15 m downwind. Solution Calculation of the diverse jet parameters: 109

)109-l = 2.93 bar

2 For= 5 ( - 1.09+ 1

r~

09-lJ

101\1:09

Temperature of the expanded jet: T1 = 324 ( S)

= 284 K

273 -3 p 1 =2.6-=2.5 kgm 284 l 09-l

2 93 (1.09+ 1)( · 1.01) MJ = (1.09-1)

ll:09- 2

U

1

=1.76

= 1.76

m s_ 1 1.09 · 8314 · 284 = 370 58.1

Diameter of the expanded (supersonic) jet: d 1 =

d = 0 0245 s

{2.6 = 0 045 m fu

Calculation of Y by trial and error:

97

7r

4 0 71 · · = 0.0313 m 370.2.5

csf-mass =

58 1 · 29 = 0.0607 13 58.1+-2 0.21

113 ys 13 + 0.2 Y 213 0 _024 ( 9 81· 0 2045 ) 370

_

(

~ )213 = O

0.0607

y =265 L 60 = 265 · 0.045 = 11.9 m L 6 = 11.9 (0.51 e- 04

6

+ 0.49) (1- 6.07 · 10-3 (90- 90))= 6.38 m ]13

9.81 RiLbo =11.9 ( 0.045 2 . 370 2 )

Rw =

6

370

a= 8000

=3.91

= 0.0162 0162 °·3.91 = 33°

Lift-off distance: s=56.38

sin ((0.185

\~

e(- 2000162)

+ 0.015)33)

sin 33

=1m

Flame length: L=J6.38 2 -1 2 ·sin 2 33-1·cos33=5.5 m Width offrustum base and tip:

Rid = 0.045 s

9 (

·~

1/3

1

0.045 370 2

)

= 0.0148

c' = 1000 e-1oo oo14s + 0.8 = 228.4

98

w2

= 6.38 (0.18 e-IS.00 162 + 0.31)(1 - 0.47 e-25 ' 00162)= 2.1 m

Taking into account the flames tilt and size, the distance from the centre of the flames to the target is 15.4 m. From Eqs. (3-17-b) and (3-19), r =0.84. Therefore, the intensity of thermal radiation at the target is: l= 0.1·0.71·45700·0.84 =0. 91 kWm-2 4Jr15.4 2

6.3 Flash fire In a flash fire two completely different situations must be considered in terms of the thermal flux: the targets that are engulfed by the fire and those that are beyond the area covered by the flames. For natural gas, heat fluxes of 160-300 kW m· 2 were measured within the fire contour [40], while outside it -although relatively near the contour- the heat flux was approximately 5 kW m- 2. For natural gas and propane, the average flame speed measured 1 1 was in the range of 12 m s· , although transient values of up to 30m s· were detected. For 2 these substances, an average surface emissive power of 173 kW m- was recorded. The size and position of a flammable cloud (i.e. the volume of the cloud that is within the flammability limits) can be predicted for a given case by applying atmospheric dispersion models. However, from the point of view of the mathematical modelling of fire features, flash fires are practically unknown. The only method for estimating the size of the flames in a flash fire was proposed by Raj and Emmons [40], who gave the following semiempirical expression for the visible flame height:

y~]

113

H=20h[£(Pf-a gh Pa) (1-w)

(3-70)

where his the cloud height (m) Sis the flame speed (m s- 1) PJ-a is the density of the fuel-air mixture (kg m· 3) Pa is the density of air (kg m- 3) r is the stoichiometric air-fuel mass ratio(-), and

tP- tPst

c

w = 0 for¢ ~

tPst

d.

d.

w= a'(1-¢s,)tOr'f'>'f'st

(3-71)

where a' is the constant pressure expansion ratio for stoichiometric combustion (typically 8 for hydrocarbons) ¢is the fuel volume ratio in the fuel-air mixture and tPst is the stoichiometric fuel volume ratio.

99

Predicting the thermal radiation from a flash fire requires a series of simplified assumptions to be made: the composition of the cloud is fixed and homogeneous, and the surface of the flame is similar to a vertical plane moving through the stationary cloud. Overall, the prediction will be only a rough approximation. However, as stated before, the consequences of a flash fire are very serious inside the flame contour, while outside it they are far less severe and often negligible. 7 BOILOVER Fires in large fuel storage tanks are relatively frequent. These large fires are comparatively difficult to extinguish, requiring large amounts of water/foam, and often last several hours. In this case, a particular phenomenon can occur during the fire, which increases the size of the flames and the area covered by the thermal radiation and thus increasing potential serious consequences of the event. This phenomenon is known as a boilover. A boilover can occur essentially in tanks containing mixtures of different hydrocarbons with a wide range of boiling temperatures, for example with crude oil. A typical scenario would consist in an initial explosion blowing out the tank roof, followed by a fire. During the fire, in the top boiling fuel layer the most volatile compounds are preferentially vaporized. There is in fact a distillation process, and this layer is progressively enriched in the heaviest (higher boiling point) components: its temperature also increases progressively. As the fire bums, the thickness of this layer -rich in high boiling temperature components- increases and progresses in depth. The expansion of the hot zone is caused by convective motions induced by vapour bubble formation during the vaporization of the lighter fuel components [41]. The speed at which the thickness of the layer increases is greater than the speed at which the surface of the fuel descends. Thus, a heat wave propagates towards the bottom of the tank. If the tank contains a water layer that is denser than the fuel, or an oilwater emulsion layer suspended in the fuel, at a certain point the heat wave (at a temperature higher than the boiling temperature of water) will reach this aqueous layer. This will cause the initial vaporization of some of the water. The turbulence of the phenomenon will cause both layers to mix, causing the extensive vaporization of water. The practically instantaneous generation of a large amount of steam -with a specific volume 1600 times that of liquid water- will cause a violent eruption, ejecting ignited fuel out of the tank and dramatically increasing the size of the flames (Fig. 3-13). The boiling temperature of the water layer will be higher than 100 oc due to the hydrostatic pressure. For a high tank, this temperature may reach 120 oc. In a boilover, the upper fuel layer may reach temperatures of up to 430 K. The speed at 1 1 which the heat wave progresses usually ranges between 0.3 m h- and 1 m h- , although in 1 some cases it has reached values of 1.2 m h- . The presence of water inside a fuel tank may be explained in several ways: a) it may enter with the fuel; b) it may be rain water, which enters through holes in the roof; c) it may be due to atmospheric humidity, as a result of the tank breathing and condensing the humidity inside; and d) it may be water used by firemen to extinguish the fire. There are also two special cases associated with this situation, known as frat hover and slopover. Frothover occurs when the vaporization of water is smoother and the steam bubbles cause the tank to overflow due to the continuous frothing of burning fuel. Slopover can occur when water is applied to the burning surface of the fuel and sinks into the hot oil. The vaporization of the water causes the ignited fuel to overflow.

100

Fig. 3-13. Boilover in a fuel tank. In special circumstances, a boilover could also occur without the presence of water, although this is fairly infrequent. In this case, the density of the upper hot layer increases with the distillation process. The temperature of the lower fuel layers increases slowly due to heat conduction, while at the same time its density decreases. The upper layer has a high content of components with high boiling points, while the lower layer is still rich in volatile components. At a certain point, this situation -the existence of a dense, very hot layer above another with a lower density- can lead to the turbulent mixing of the two layers, resulting in the instantaneous vaporization of the volatile liquid and the occurrence ofboilover. The phenomenon described in the previous paragraphs corresponds to the so-called hot zone boilover. A somewhat different phenomenon is the thin layer boilover, which occurs when a thin layer of fuel bums over a layer of water. This can happen when there is a spillage of fuel on the ground. If the fuel is ignited, after a short time (about one minute) the water starts to boil and the bubbles eject fuel upwards, significantly increasing the size of the flames. This phenomenon is characterized by a strong crackling sound. An important aspect when dealing with boilover is the ability to predict the moment at which it will occur. The highest value (tboilover) can be estimated from a simple heat balance of

101

the mass of fuel contained in the tank: the fuel is heated by the fire from its surface until all of the fuel has reached the heat wave temperature:

p, cphHc(Thw -TJ

t

= -----,"----,-----;; boitover

(3-72)

QJ _ m (t-.h v + C p (TOav _ Ta ))

3 where PI is the density of fuel at Ta (kg m- ) cp is the specific heat offuel at Ta (kJ kg- 1 K- 1) hHc is the initial height of fuel in the tank before the fire starts (m) m is the burning rate (kg m- 2 s- 1) !Jhv is the vaporization heat at Toav(kJ kg- 1) Ta is the ambient temperature (K) Thw is the temperature of the heat wave when the boilover occurs (K) Toav is the average boiling temperature of the fuel (K), and 2 Q1is the thermal flow entering the fuel from its surface ( ~ 60 kW m- ). Thw can be estimated from the distillation curve of the fuel by an iterative procedure. However, Eq. (3-72) assumes that the layer of water is at the bottom of the tank, and does not take into account the possibility of a layer of water-hydrocarbon emulsion in a higher position, which would shorten the time needed for boil over to occur. In the case of a tank fire, the progression of the heat wave can be followed if vertical bands of intumescent paint have been applied to the tank wall. Another possibility is to throw water against the tank wall and observe its behaviour (i.e. whether it boils or not). Recently, the use of thermographic (IR) cameras has been proposed. However, although both procedures may indicate the progression of the heat wave, the possible presence of water at a certain height inside the tank again creates uncertainty about the moment at which the boilover may occur. From Eq. (3-72), a theoretical expression for the speed at which the heat wave progresses can be obtained:

(3-73)

7.1 Tendency of hydrocarbons to boilover For a hot zone boilover to occur, the following conditions are required: the presence of water inside the tank; the existence of a mixture of components with a wide range of boiling temperatures; a fuel with a relatively high viscosity. The conditions for a boilover were quantified by Michaelis et al. [42] as follows. The average boiling temperature of the fuel ( Toav) must be higher than that of water at the pressure at the water-fuel interface. Toav can be determined using the following expression: (3-74) The pressure at the water-fuel interface is: ~nterface =Po+ hHC Pt g

(3-75)

For common fuel storage conditions, this criterion generally reduces to:

102

The range of boiling temperatures in the fuel must be sufficiently wide to generate the heat wave. LITo =Tomax- Tomin must be higher than 60 °C if Tomin is higher than the boiling temperature of water at the pressure at the water-fuel interface (a temperature of 393 K is assumed); if Tomin < 393 K, then (393- Tomax) should be greater than 60 oc [43]. Finally, these authors state that the kinematic viscosity of the fuel must be higher than that of kerosene at the boiling temperature of water at the water-fuel interface, VHc z 0.73 eSt. These three criteria were combined in an empirical parameter called the factor of propensity to boilover [42], which indicates the tendency of a hydrocarbon to generate a boilover during a fire:

2

113

PB0=[1- 393. )(!J.To) (VHc ) T 60 0.73

(3-76)

0 .,

According to this criterion, hydrocarbons with a value of PBO boilover. However, this expression should be applied with caution.

z

0.6 could generate a

7.2 Boilover effects The effects of the boilover are essentially the generation of a fireball, which is the most serious effect, and, to a minor extent, the ejection of ignited fuel around the tank. If a fireball is created, the value of E for liquid hydrocarbons can be assumed to be approximately 150 kW m· 2 • The heat radiation over a given target can be calculated using the solid flame model (see the next section in this chapter). For the threshold values of 1000 (kW·m· 2 1\ for 1% lethality and 600 (kW·m-2 ) 413 s for irreversible consequences (serious burns), applying the conservative assumption that the entire contents of the tank at the moment of the boilover participate in the fireball, INERIS [44] proposed the following expression for calculating the distances corresponding to lethality and irreversible consequences:

t

d lethality

k lethality woAs

(3-77-a) (3-77-b)

dirreversible == kirreversible W OAS

where W is the mass of fuel in the tank at the beginning of the fire. The exponent 0.45 is in fact an average value and the other constants depend on the type of fuel (Table 3-9). Table 3-9 Values of constants in Eqs. (3-68) and (3-69) r44 Fuel ktethalitv kirreversible Fuel oil N. 2 0.420 0.573 Kerosene 0.387 0.525 Domestic fuel 0.317 0.439 Diesel oil 0.319 0.439 Crude oil 0.267 0.363

103

8 FIREBALL When a BLEVE explosion involves a flammable substance, it is usually followed by a fireball, which releases intense thermal radiation. Fireballs can also occur during boilover. The thermal energy is released rapidly, which is a function of the mass in the tank. The phenomenon is characterized from the beginning by strong radiation, eliminating the possibility of escape for individuals nearby (who will also have suffered the effects of the blast). To estimate the radiation received by a surface located at a given distance, the solid flame model can be applied (Eq. (3-20). It is necessary, therefore, to know the value of the emissive power (E), the view factor (F), the atmospheric transmissivity rand the distance between the flame and the target. To know this distance, it is necessary to estimate the diameter of the fireball as well as the height at which its centre is located. The shape of the fireball can vary according to the type of tank failure. Rapid failures produce approximately spherical fireballs, whilst slower BLEVEs tend to produce cylindrical fireballs with high lift-offs. However, to estimate their effects, a spherical shape is usually assumed. The parameters that must be evaluated to predict the effects of a fireball are the diameter, the duration and the height at which the fireball is located; this will allow the thermal radiation to be estimated at any given distance. In this section, a methodology is described with which to estimate these values. 8.1 Fireball geometry 8.1. I Ground diameter The zone on the ground that can be engulfed by flames during the initial development of the fireball can be approximated by the following expression [45]: D groundf/a< h

=

(3-78)

1·3 · D max

where Dmax is the maximum diameter achieved by the fireball (see Eq. (3-83)). 8.1.2 Fireball duration and diameter Various authors have proposed correlations for the prediction of the diameter and duration of a fireball generated by a given mass M of fuel [40]. Most of them have the following general expression:

(3-79) t =c ·Me

(3-80)

where a, b, c and e are empirical or semi-empirical constants. A comparative study of 16 of these expressions was made by Satyanarayana et a!. [46]. Although it is rather difficult to establish which is really the best equation, due to the lack of experimental data at large scale, taking into account this and other studies, the duration and diameter of the fireball can be estimated using the following expressions.

104

For the duration (time): (3-81)

t=0.9·M 025

where the units are kg (M) and s (t). According to a model proposed by Martinsen and Marx [47, 48], the fireball main features (D, H, E) change as a function of time. The fireball is considered to reach its maximum diameter during the first third of the fireball duration. Thus, while the fireball is growing the following equation applies: (3-82) (3-83) where Dmax is the maximum value achieved by D and ti is the time at any instant i. It is worth noting, however, that there is very little experimental data available to support this type of comparative analysis. Furthermore, these data -obtained from real accidents in the case of large fireballs- are not always accurate, as often the films are incomplete or of poor quality. In fact, the lack of accuracy is not only due to differences in the predictions arising from diverse correlations. Another factor influencing it is the estimation of the fraction of the overall mass of fuel that is really involved in the fireball. As happens in many cases of risk analysis, the inaccuracy arises from the definition of the problem itself. It should be taken into account that some fuel has been leaving the vessel through the safety valves from the moment at which they opened; the amount released will depend on the time elapsed between this moment and that of the explosion. Furthermore, more fuel is sucked into the wake of the propelled fragments. Consequently, it is essentially impossible to accurately establish the mass of fuel that will contribute to the fireball. If more accurate information is not available, 90% of the maximum capacity of the vessel should be used. The fact that in Eqs. (3-82) and (3-83) the mass of fuel is affected by an exponent equal to approximately 1/3 considerably reduces its influence on the value of D. Finally, the lack of accuracy is also due to the fire wake left by the fireball, the size of which can be significant [49]; this modifies the flame surface and, consequently, the radiation that will reach a given point. The correlations mentioned in the previous paragraphs nevertheless allow an estimation of the size of the fireball. It should be taken into account that, as its size and position change continuously, the thermal radiation is not constant. The available films of BLEVE accidents show that the fireball grows quickly to its maximum diameter, remaining at this diameter for a short time and then dissipating. Sometimes, calculation of the radiation received by a given target is performed by supposing that the fireball achieves its maximum size immediately after reaching a certain height. Some guidelines suggest calculating the hazard distances for the fireball located just over the ground (i. e., H =D) [50]. 8.1.3 Height reached by the centre of the fireball This height is a function of the specific volume and the latent heat of vaporization of the fuel; therefore, strictly speaking, it varies with the substance. This is not usually taken into account. Usually, the fireball rises at a constant rate from its lift-off position to three times

105

this height during the last two-thirds of its duration. The following equations [4 7] can be used to estimate this height: H = 0.5 D 3D t 2t

H=~

for 0 :S: t 1 :S: t/3

(3-84)

(3-85)

fortl3
where His the height at which the centre of the fireball is located (m). If an average value must be taken, the following expression can be used: (3-86)

H=0.75D

The values obtained with these expressions have been compared with those corresponding to four real cases (Table 3-10). The heights correspond to the top of the fireball (h = H+D/2). The diameter has been calculated with Eqs. (3-82) and (3-83). The height has been calculated with Eq. (3-85) and (3-86); with Eq. (3-85) a value oft;= 2t/3 has been taken: note that if t; = t/2 is assumed, the results are the same as those obtained with Eq. (3-86). Table 3-10 Predicting the height (top of the flame) of the fireball Accident Fuel M, kg H, m (observed) H, m [Eq. (3-86)] Crescent City Priolo Priolo Paese

Propane Ethylene Propylene Propane

35,000 80,000 50,000 800

230

237

225

312

250 95

267 67

H, m [Eq. (3-85)]

(at t; = 2t/3) 284 375 320 81

The results from both expressions are relatively good, taking into account the accuracy of the data; therefore, Eqs. (3-84) and (3-85) can be used if a variable height is assumed, and Eq. (3-86) can be used if a constant value is assumed.

8.2 Thermal features 8.2.1 Radiant heat fraction Once more, we do not know for certain what fraction of the energy released is emitted as thermal radiation. In fact, this is one of the most important uncertainties in the calculation of the thermal radiation from a fireball. The following correlation has been proposed [51] to estimate this value: 'lrad

=

0.00325. p032

(3-87)

where P is the pressure in the vessel just before the explosion, in N·m· 2 Typically, this pressure can be supposed to be the relief pressure (when calculated for fire). The value of 'lrad usually ranges between 0.2 and 0.4, its maximum value being limited to 0.4. From this radiation coefficient and the heat released from the fireball, the radiated energy can be

106

= 1/3 can be assumed according to some well known guidelines for offsite consequence analysis [52]. deduced. If Pis not known, a thumb rule value of

lJrad

Fig. 3-14. Position of fireball and target.

8.2.2 Emissive power An average value of the emissive power can be calculated as the radiant heat emitted divided by the surface ofthe fireball: (3-88) where tis the time corresponding to the duration of the fireball (s) M is the mass of the fuel (kg), and iJHc is the heat of combustion (lower value) of the fuel (kJ kg- 1). Experimental work shows that the emissive power varies with time, reaching a maximum very quickly at the end of the fireball expansion and then decreasing slowly until extinction. Again, the value of E can be calculated [47] separately for the fireball growth phase and for the last two thirds of the duration. For the growth phase, Emax, this expression can be used: (3-89) If Eq. (3-89) gives a value higher than 400 kW·m- 2 , then 400 kW·m-2 must be taken. During the last two-thirds of the duration of the fireball, E can be calculated using this expression:

(3-90) The average value of E ranges between 200 and 350 kW·m- 2 [53] and for an LPG fireball usually ranges between 250 and 400 kW·m- 2 .

107

8.2.3 View factor The maximum view factor is that corresponding to a sphere and a surface perpendicular to its radius. Due to the geometrical simplicity of this system, this factor can be calculated using a very simple equation:

(3-91)

where (D/2+d) is the distance between the surface receiving the radiation and the centre of the fireball (Fig. 3-14). For a given source, this is the situation corresponding to the maximum radiation intensity on the target. For other positions of the surface of the target, the value ofF must be corrected by using the angle formed between this surface and the surface perpendicular to the radius of the fireball. Fig. 3-14 clearly shows that a given radiation bunch falls over a surface whose area varies with its inclination, the minimum area (and maximum radiation flux) corresponding to a surface perpendicular to the radiation. Thus, Fverticat

=

Fhoriwntat

F max·

=F

cos a

max·

(3-92-a)

sin a

(3-92-b)

8.3 Constant or variable D, Hand E Fireball height, diameter and emissive power can thus be calculated using Eqs. (3-86), (385) and (3-88), assuming that they are constant with time, or, when it is assumed that they are not constant, using Eqs. (3-84), (3-85), (3-82), (3-83), (3-89) and (3-90) with different values for the growth phase and for the last two-thirds of the duration, respectively. Fig. 3-15 shows how these variables change as a function of time (variable D, Hand E model), for a given case ( 100,000 kg of propane; see Example 3-8). The trend of these three variables is quite different during the first five seconds and during the rest of the duration of the fireball. For accurate results, this alternative is probably better. For a rapid, estimative calculation, constant values of D, Hand E can be taken; in this way, more conservative results are obtained. Fig. 3-16 shows the variation in the thermal radiation reaching a vertical surface located at a certain distance as a function of time, for a given case (see Example 3-8). It can be observed that in the variable D model, Iv increases quickly with time, reaching a sharp maximum at ti = t/3, subsequently decreasing abruptly. In the constant D model, the thermal radiation intensity has a constant value. This different behaviour has some influence on the calculation of the dose received by a target located at a given distance,

dose= t · 1 413

(3-93)

If the dose is calculated using the two methods (see Fig. 3-17), more conservative values are obtained for the constant D model, although higher values of the thermal radiation intensity are calculated for he variable D model.

108

Emissive power

E

I

<;'

E 400 ~ .;,:: a3 300

400

·a; .r::.

300

~

Q)

0

....

~

Q)

Cl..

>

:E Ol

200

200

'ii)

E

.!!!

'0

=«<

(/)

.E

.0

w

100

4

2

10

8

6

12

14

~

u::

16

Time,s Fig. 3-15. Emissive power, fireball height and fireball diameter as a function of time, for a BLEVE of 100,000 kg of propane (see Example 3-8). Recently [54], it has been emphasized that a good estimation of D, Ep and r is very important for the calculation of thermal radiation from a fireball, whilst the influence of H is not so important. 9 EXAMPLE CASE

Example 3-8 3 A tank with a volume of 250 m , 80% filled with propane (stored as a pressurized liquid at room temperature), is heated by a fire to 55 oc (~ 19 bar) and bursts. The thermal radiation, as well as the consequences on people, must be estimated at a distance of 180m from the initial location of the tank. Data: Room temperature= 20°C; HR =50% (partial pressure of water vapour, 1155 Pa); y =1.14; He -1

-3

= 46,000 kJ·kg ; Tc = 369.8 K; Tboil. atm. pres.= 231.1 K; Piiquid, 20 oc = 500 kg·m , P!iquid, 55 oc =

. -3.

444 kg m 'Pvapour, 55 oc

=

.

-3,

37 kg m '

Cp liquid

=

.

3

,

-I.

-I

2.4 I 0 1 kg K .

Solution: First of all, the mass of propane involved is calculated: M = ~ · p 1 20oc = (0.8 ·250m

3

)·

3

500 kg m- = 100,000 kg

The thermal radiation will be calculated using the two models discussed previously.

Estimation of thermal radiation (D, Hand E constant) By using Eq. (3-83), the fireball diameter is estimated:

109

D = 5.8 · Mu 3 = 5.8 ·100000 113 =269m Its duration is estimated with Eq. (3-81 ): t=0.9·M 025 =0.9·100000° 25 =16s

and the height reached by the fireball is estimated by Eq. (3-86):

H = 0.75-D = 0.75·269 =202m The distance between the flame and the target, according to Fig. 3-14, can be calculated as follows:

The atmospheric transmissivity will be: '= 2.85. (1155 -136r0 12 = 0.68 The view factor is calculated with Eq. (3-91):

The fraction of heat radiated is: 1J rad = 0.00325 · (1.9 ·1 0 6 )

032

= 0.33

The emissive power is (Eq. (3-88)): E= 0.33·100,000-46,000 = 417 kwm· 2 ;r-269 2 ·16

A value of E = 400 kW m· 2 will be taken. The radiation intensity on a surface perpendicular to the radiation will be: I=

T ·F

· E P = 0.68 · 0.25 · 417 = 70.9 kW m .2

on a vertical surface, Iv =I ·cos a= 70.9 ·0.67 = 47.5 kW m· 2

and on a horizontal surface,

110

Ih =I· sin a= 70.9 · 0.75

= 53.2 kW m· 2

The dose received by a person exposed to a radiation intensity Iv for the entire duration of the fire ball is:

Estimation of thermal radiation (variable D, Hand E) Growth phase (first 5.3 s; see Fig. 3-15): The diameter increases up to Dmax = 269 m. H increases up to 135 m. The emissive power has a constant value of Emax = 400 kW·m- 2 (Eq. (3-90) gives a value of 527 kW·m- 2). Last two thirds (from ts.J to t16): The diameter is practically constant at Dmax = 269 m. The average height of the fireball centre, H, increases steadily. The emissive power decreases steadily. The thermal radiation received by a vertical surface located at 180 m varies as a function of time, as shown in Fig. 3-16: it increases up to a maximum value of approximately 82 kW m· 2 during the growth phase (first 5.3 s) and afterwards it decreases significantly during the second third and more smoothly during the last third. In this figure, the value corresponding to the constant D, Hand E model has also been plotted. 90.-------------------------------, 80 70

20

10

0

o

1

2

3

4

s s

7 a Time, s

Fig. 3-16. Variation of the thermal radiation intensity from a fireball as a function of the time, according to the two models, for a given case (see Example 3-8).

The dose received by a person exposed to this radiation can be calculated (Fig. 3-17) with the following expression:

Ill

f

dose= Iv,r

4 '3

· dt

The dose received by a person exposed to the thermal radiation intensity fv for the entire duration of the fireball is 2·10 7 s (W·m- 2) 413 • It can be observed that the values of the dose calculated by the two methods are similar, with a lightly higher dose obtained with the constant D, Hand E model. Consequences on people Thermal radiation: For a dose of 2.8·10 7 s (W m- 2) 413 (constant D, Hand E model), the probit function for lethality (unprotected people) is (see chapter 7, section 4):

Y = -36.38 + 2.56 In 2.8·1 07 = 7.52 This value implies (chapter 7, Table 7-1) 99.4% mortality. By applying the same expression, for a dose of 2·107 s (W m- 2) 413 (variable D, H and E model): Y = -36.38 + 2.56ln 2·10 7 = 6.65 This value implies 95% mortality. 3.---------------------------------~

2,5

" 0

M'

Variable D, H and E model

2

"~ "! E

~ ui

1,5

ai

"'0

0

Constant D, H and E model

0,5

0

2

4

8

6

10

12

14

16

Time.s

Fig. 3-17. Variation of the dose received by a person located at 180 m as a function of time, according to both models.

Taking into account the accuracy of the probit function, both values can be considered similar.

112

NOMENCLATURE 2

surface of the solid flame through which heat is radiated (m ) 2 Aor cross sectional area of the orifice (m ) a constant in Eq. (3-12) (K); constant in Eq. (3-79) (-) b constant in Eq. (3-12) (K); constant in Eq. (3-79) (-) c constant in Eq. (3-12) (K); constant in Eq. (3-80) (-) CD discharge coefficient (-) c; concentration of component i on a fuel basis (% volume) cp specific heat at constant pressure (kJ kg- 1 K- 1) mole fraction of fuel in the stoichiometric fuel-air mixture (-) Cst-vol Cst-mass stoichiometric mass fraction of fuel in Eq. (3-59) (-) Cv specific heat at constant volume (kJ kg- 1 K- 1) D pool or fireball diameter (m) D' pseudo pool diameter in the wind direction (m) Deq pool equilibrium diameter (m) Dgroundfinitial fireball diameter (m) D1 diameter of the jet fire (m) Dmax fireball maximum diameter (m); maximum pool diameter for an instantaneous spill on water (m) Dpoot pool diameter at timet (m) d distance between the surface of the flames and the target (m) di diameter of the expanded jet (m) dar orifice or outlet diameter (m) ds effective orifice diameter (m) E emissive power of the flames (kW m- 2) Etum value of E for the luminous zone of the flames (kW m-2) Esoot value of E for the non-luminous zone of the flames (kW m- 2) e constant in Eq. (3-80) (-) F view factor (-) Fh view factor, horizontal surface (-) fr interface tension (N m- 1) Fv view factor, vertical surface (-) g acceleration of gravity (m s- 2 ) H average height of the fire (m); height at which the fireball centre is located (m) HR relative humidity of the atmosphere(%) h height at which the fireball top is located (m); cloud height (m) hHc initial height of fuel in the tank before the fire starts (m) L1hv vaporization heat at boiling temperature (kJ kg- 1) L1Hc' combustion heat (kJ mole- 1 or kJ kg- 1) L1Hc net combustion heat (kJ mole- 1 or kJ kg- 1) I intensity of the thermal radiation reaching a given target (kW m- 2) L length of the visible flame (m) l distance between the centre of the cylindrical fire and the target (m) Lnv vertical distance between the gas outlet and the flame tip (m) lp distance between the point source and the target (m) M mass of substance (kg) m fuel mass burning rate per unit surface and per unit time (kg m- 2 s- 1) m mass flowrate in the jet (kg s- 1); mass burning rate per unit time (kg s- 1) A

113

moo Ma Mv p

P; Pinterf Pcont Po

Par Pw Pwa

QF QL Qr qv R Rids Rhbo

Rw r

Re

s s

T Ta Tad Tcont

TJ Tfl Thw

To iJTo Toav t;

Tj Tspill

Tv Uav Uj

Usound

Uw Uw* Uwave

2

1

burning velocity of an infinite diameter pool (kg m- s- ) 1 molecular weight of air (kg kmole- ) molecular weight of fuel (kg kmole- 1) 2 pressure in the vessel just before the explosion (N m- ) 2 pressure (N m- ) 2 pressure at the water-fuel interface (N m- ) 2 pressure inside the container or pipe (N m- ) 2 atmospheric pressure (N m- ) 2 static pressure at the orifice (N m- ) 2 partial pressure of water in the atmosphere (N m- ) 2 saturated water vapour pressure at the atmospheric temperature (N m- ) 2 heat flux from the flame (kW m- ) 2 heat lost from the fuel surface (kW m- ) heat released as thermal radiation (kW) 1 heat required to produce the gas or vapour (kJ kg- ) 1 1 ideal gas constant (8.314 kJ kmole- K- ) Richardson number based on ds (-) Richardson number based on Lho (-) ratio between wind velocity and jet velocity at gas outlet (-) mass-ratio in the stoichiometric air/fuel mixture (-) Reynolds number (-) flame speed (m s- 1) lift-off distance (m) temperature (K) fireball duration (s) ambient temperature (K) adiabatic flame temperature (K) temperature inside the container (K) flash point temperature (K) radiation temperature of the flame (K) temperature of the heat wave when boilover occurs (K) boiling temperature at atmospheric pressure (K) range of boiling temperatures in the fuel (K) average boiling temperature of the fuel (K) time at instant i (s) jet temperature at the gas outlet (K) duration of the spill (s) temperature of the fuel before it is released (K) 1 average jet velocity (m s- ) 1 velocity in the jet at the gas outlet (m s- ) 1 velocity of sound in a given gas (m s- ) wind speed (m s- 1) dimensionless wind speed (-) 1 velocity at which the heat wave progresses (m s- ) 1 3 flow rate ofliquid release (m s- ) volume of liquid spilled instantaneously (m3 ) 3 volume of liquid in the vessel (m\ total volume of spilled liquid (m ) 3 1 liquid leak rate (m s- )

114

w w X

X{um

y

a a'

Bj Bjv £

'lrad VHC

n PI Pa Pgo Pi-a {Jj

Pw a T

mass of fuel in the tank at the beginning of the fire (kg) width of the flame front (m) horizontal distance from the flames to the target (m) (Table 3-6); axial distance from the orifice in Eq. (3-60) (m); horizontal distance between the centre of the fireball and the target (m) fraction of fire surface covered by luminous flame (-) burning rate (m s- 1) tilt angle of a pool fire or a jet fire CO) constant pressure expansion ratio for stoichiometric combustion (-) angle between the axis of the orifice and the line joining the centre of the orifice and the tip of the flame (0 ) moles of reactant per mole of product in a stoichiometric fuel-air mixture(-) angle between the hole axis and the horizontal in the vertical plane CO) angle between the hole axis and the horizontal in the wind direction CO) emissivity (-) angle between the plane perpendicular to the receiving surface and the line joining the source point and the target CO) fuel volume ratio in the fuel-air mixture(-) stoichiometric fuel volume ratio (-) ratio of specific heats of the gas, C/Cv (-) radiant heat fraction (-) kinematic viscosity of the fuel (eSt) angle between the wind direction and the normal to the pipe in the horizontal plane CO) liquid fuel density (kg m-3) air density (kg m- 3) density of gas at standard conditions (kg m-3 ) density of the fuel-air mixture (kg m- 3) density of gas fuel in the outlet (kg m- 3) water density (kg m- 3) Stefan-Boltzmann constant (5.67·10-8 W m- 2 K-4) atmospheric transmissivity (-)

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117