Fire Science and Combustion

Transcription

1 1 Fire Science and Combustion As a process, fire can take many forms, all of which involve chemical reactions between combustible species and oxygen from the air. Properly harnessed, it provides great benefit as a source of power and heat to meet our industrial and domestic needs, but, unchecked, it can cause untold material damage and human suffering. In the United Kingdom alone, direct losses probably exceed 2 billion (2010 prices), while over 400 people die each year in fires. According to the UK Fire Statistics (Department for Communities and Local Government, 2009), there were 443 fatalities in 2007, continuing a downward trend from over 1000 in In real terms, the direct fire losses may not have increased significantly over the past two decades, but this holding action has been bought by a substantial increase in other associated costs, namely improving the technical capability of the Fire Service and the adoption of more sophisticated fire protection systems. 1 Further major advances in combating unwanted fire are unlikely to be achieved simply by continued application of the traditional methods. What is required is a more fundamental approach that can be applied at the design stage rather than tacitly relying on fire incidents to draw attention to inherent fire hazards. Such an approach requires a detailed understanding of fire behaviour from an engineering standpoint. For this reason, it may be said that a study of fire dynamics is as essential to the fire protection engineer as the study of chemistry is to the chemical engineer. It will be emphasized at various places within this text that although fire is a manifestation of a chemical reaction, the mode of burning may depend more on the physical state and distribution of the fuel, and its environment, than on its chemical nature. Two simple examples may be quoted: a log of wood is difficult to ignite, but thin sticks can be ignited easily and will burn fiercely if piled together; a layer of coal dust will burn relatively slowly, but may cause an explosion if dispersed and ignited as a dust cloud. While these are perhaps extreme examples, they illustrate the complexity of fire behaviour in that their understanding requires knowledge not only of chemistry but also of many subjects normally associated with the engineering disciplines (heat transfer, fluid dynamics, etc.). Indeed, the term fire dynamics has been chosen to describe the subject of fire COPYRIGHTED MATERIAL 1 The total cost associated with fire in England and Wales in 2004 was estimated to be 7.03 billion. This figure includes costs of fire protection, the Fire and Rescue Service (including response), property damage and lost business, as well as the economic costs associated with deaths and injuries and the prosecution of arsonists (Office of the Deputy Prime Minister, 2006). An Introduction to Fire Dynamics, Third Edition. Dougal Drysdale John Wiley & Sons, Ltd. Published 2011 by John Wiley & Sons, Ltd.

2 2 An Introduction to Fire Dynamics behaviour as it implies inputs from these disciplines. However, it also incorporates parts of those subjects which are normally associated with the terms fire chemistry and fire science. Some of these are reviewed in the present chapter, although detailed coverage is impossible. It is assumed that the reader has some knowledge of elementary chemistry and physics, including thermodynamics: references to relevant texts and papers are given as appropriate. 1.1 Fuels and the Combustion Process Most fires involve combustible solids, although in many sectors of industry, liquid and gaseous fuels are also to be found. Fires involving gases, liquids and solids will be discussed in order that a comprehensive picture of the phenomenon can be drawn. The term fuel will be used quite freely to describe that which is burning, whatever the state of matter, or whether it is a conventional fuel such as LPG or an item of furniture within a room. With the exception of hydrogen gas, to which reference is made in Chapter 3, all fuels that are mentioned in this text are carbon-based. Unusual fire problems that may be encountered in the chemical and nuclear industries are not discussed, although the fire dynamics will be similar if not identical. General information on problems of this type may be gleaned from the National Fire Protection Handbook (NFPA, 2008) and other sources (e.g., Meidl, 1970; Stull, 1977; Mannan, 2005) The Nature of Fuels The range of fuels with which we are concerned is very wide, from the simplest gaseous hydrocarbons (Table 1.1) to solids of high molecular weight and great chemical complexity, some of which occur naturally, such as cellulose, and others that are man-made (e.g., polyethylene and polyurethane) (Table 1.2). All will burn under appropriate conditions, reacting with oxygen from the air, generating combustion products and releasing heat. Thus, a stream or jet of a gaseous hydrocarbon can be ignited in air to give a flame, which is seen as the visible portion of the volume within which the oxidation process is occurring. Flame is a gas phase phenomenon and, clearly, flaming combustion of liquid and solid fuels must involve their conversion to gaseous form. For burning liquids, this process is normally simple evaporative boiling at the surface, 2 but for almost all solids, chemical decomposition or pyrolysis is necessary to yield products of sufficiently low molecular weight that can volatilize from the surface and enter the flame. As this requires much more energy than simple evaporation, the surface temperature of a burning solid tends to be high (typically 400 C) (Table 1.2). Exceptions to this rule are those solids which sublime on heating, i.e., pass directly from the solid to the vapour phase without chemical decomposition. There is one relevant example, hexamethylenetetramine (also known as methenamine), which in pill form is used as the ignition source in ASTM D (American Society for Testing and Materials, 2006). It sublimes at about 263 C (Budavari, 1996). The composition of the volatiles released from the surface of a burning solid tends to be extremely complex. This can be understood when the chemical nature of the solid is 2 Liquids with very high boiling points ( 250 C) may undergo some chemical decomposition (e.g., cooking oil).

3 Fire Science and Combustion 3 Table 1.1 Properties of gaseous and liquid fuels a Common name b Formula Melting Boiling Density Molecular point ( C) point ( C) (liq) (kg/m 3 ) weight Hydrogen H Carbon monoxide CO Methane CH Ethane C 2 H Propane C 3 H n-butane n-c 4 H n-pentane n-c 5 H n-hexane n-c 6 H n-heptane n-c 7 H n-octane n-c 8 H iso-octane c iso-c 8 H n-nonane n-c 9 H n-decane n-c 10 H Ethylene (ethene) C 2 H (384) 28 Propylene (propene) C 3 H Acetylene (ethyne) C 2 H Methanol CH 3 OH Ethanol C 2 H 5 OH Acetone (CH 3 ) 2 CO Benzene C 6 H a Data from Lide (1993/94). b It should be noted that IUPAC (International Union of Pure and Applied Chemistry) has defined a standard chemical nomenclature which is not used rigorously in this text. Common names are used, although the IUPAC nomenclature will be given where appropriate. See, for example, iso-octane and ethylene in this table. c 2,2,4-Trimethyl pentane. considered. All those of significance are polymeric materials of high molecular weight, whose individual molecules consist of long chains of repeated units which in turn are derived from simple molecules known as monomers (Billmeyer, 1971; Open University, 1973; Hall, 1981; Friedman 1989; Stevens, 1999). Of the two basic types of polymer (addition and condensation), the addition polymer is the simpler in that it is formed by direct addition of monomer units to the end of a growing polymer chain. This may be illustrated by the sequence of reactions: R + CH 2 = CH 2 R CH 2 CH 2 R CH 2 CH 2 + CH 2 = CH 2 R CH 2 CH 2 CH 2 CH 2 (1.R1a) (1.R1b) etc., where R is a free radical or atom, and CH 2 =CH 2 is the monomer, ethylene. This process is known as polymerization and in this case will give polyethylene, which has the idealized structure: R ( CH 2 CH }{{} 2 ) nr monomer unit

4 4 An Introduction to Fire Dynamics Table 1.2 Properties of some solid fuels a Density Heat Thermal Heat of Melting (kg/m 3 ) capacity conductivity combustion point (kj/kg K) (W/m K) (kj/g) ( C) Natural polymers Cellulose V b 1.3 V 16.1 chars Thermoplastic polymers Polyethylene Low density High density Polypropylene Isotactic Syndiotactic Polymethylmethacrylate Polystyrene Polyoxymethylene Polyvinylchloride Polyacrylonitrile Nylon Thermosetting polymers Polyurethane foams V 1.4 V 24.4 Phenolic foams V V 17.9 chars Polyisocyanurate foams V V 24.4 chars a From Brandrup and Immergut (1975) and Hall (1981). Heats of combustion refer to CO 2 and H 2 O as products. b V = variable. in which the monomer unit has the same complement and arrangement (although not the same chemical bonding) of atoms as the parent monomer, CH 2 =CH 2 : n is the number of repeated units in the chain and is known as the degree of polymerization, which may be anything from a few hundred to several tens of thousands (Billmeyer, 1971). This type of polymerization relies on the reactivity of the carbon carbon double bond. In contrast, the process of polymerization which leads to the formation of a condensation polymer involves the loss of a small molecular species (normally H 2 O) whenever two monomer units link together. (This is known as a condensation reaction.) Normally, two distinct monomeric species are involved, as in the production of Nylon 66 from hexamethylene diamine and adipic acid. 3 The first stage in the reaction would be: NH 2 (CH 2 ) 6 NH 2 hexamethylene diamine +HO CO (CH 2 ) 4 CO OH adipic acid NH 2 (CH 2 ) 6 NH CO (CH 2 ) 4 CO OH + H 2 O (1.R2) 3 The IUPAC systematic names of these two compounds are: diaminohexane and butane-1,4-dicarboxylic acid, respectively.

5 Fire Science and Combustion 5 The formula of Nylon 66 may be written in the format used above for polyethylene, namely: H ( NH (CH 2 ) 6 NH CO (CH 2 ) 4 CO ) n OH It should be noted that cellulose, the most widespread of the natural polymers occurring in all higher plants (Section 5.2.2), is a condensation polymer of the monosaccharide d-glucose (C 6 H 12 O 6 ). The formulae for both monomer and polymer are shown in Figure An essential feature of any monomer is that it must contain two reactive groups, or centres, to enable it to combine with adjacent units to form a linear chain (Figure 1.1(a)). The length of the chain (i.e., the value of n in the above formulae) will depend on conditions existing during the polymerization process: these will be selected to produce a polymer of the desired properties. Properties may also be modified by introducing branching into the polymer backbone. This may be achieved by modifying the conditions in a way that will induce branching to occur spontaneously (Figure 1.1(b)) or by introducing a small amount of a monomer which has three reactive groups (unit B in Figure 1.1(c)). This can have the effect of producing a cross-linked structure whose physical (and chemical) properties will be very different from an equivalent unbranched, or only slightly branched, structure (Stevens, 1999). As an example, consider the expanded polyurethanes. In most flexible foams the degree of cross-linking is very low, but by increasing it substantially (e.g., by increasing the proportion of trifunctional monomer, B in Figure 1.1(c)), a polyurethane suitable for rigid foams may be produced. With respect to flammability, the yield of volatiles from the thermal decomposition of a polymer is much less for highly cross-linked structures since much of the material forms an involatile carbonaceous char, thus effectively reducing the potential supply of gaseous fuel to a flame. An example of this can be found in the phenolic resins, which on heating to a temperature in excess of 500 C may yield up to 60% char (Madorsky, 1964). The structure of a typical phenolic resin is shown in Figure 1.2. A natural polymer that exhibits a high degree of cross-linking is lignin, the cement that binds the cellulose structures together in higher plants, thus imparting greater strength and rigidity to the cell walls. Synthetic polymers may be classified into two main groups, namely thermoplastics and thermosetting resins (Table 1.2). A third group the elastomers may be distinguished on the basis of their rubber-like properties (Billmeyer, 1971; Hall, 1981; Stevens, 1999), Figure 1.1 Basic structure of polymers: (a) straight chain (e.g., polymethylene, with A=CH 2 ); (b) branched chain, with random branch points (e.g., polyethylene, with A=CH 2 CH 2,seetext); (c) branched chain, involving trifunctional centres (e.g., polyurethane foams in which the straight chains ( A A, etc.) correspond to a co-polymer of tolylene di-isocyanate and a polymer diol and B is a trihydric alcohol)

6 6 An Introduction to Fire Dynamics Figure 1.2 Typical cross-linked structure to be found in phenol formaldehyde resins but will not be considered further here. From the point of view of fire behaviour, the main difference between thermoplastics and thermosetting polymers is that the latter are cross-linked structures that will not melt when heated. Instead, at a sufficiently high temperature, many decompose to give volatiles directly from the solid, leaving behind a carbonaceous residue (cf. the phenolic resins, Figure 1.2), although with polyurethanes, the initial product of decomposition is a liquid. On the other hand, the thermoplastics will soften and melt when heated, which will modify their behaviour under fire conditions. Fire spread may be enhanced by falling droplets or the spread of a burning pool of molten polymer (Section 9.2.4). This is also observed with flexible polyurethane foams, although in this case the liquid melt is a product of the decomposition process Thermal Decomposition and Stability of Polymers The production of gaseous fuel (volatiles) from combustible solids almost invariably involves thermal decomposition, or pyrolysis, of polymer molecules at the elevated temperatures which exist at the surface (Kashiwagi, 1994; Hirschler and Morgan, 2008). Whether or not this is preceded by melting depends on the nature of the material (Figure 1.3 and Table 1.3). In general, the volatiles comprise a complex mixture of pyrolysis products, ranging from simple molecules such as hydrogen and ethylene, to species of relatively high molecular weight which are volatile only at the temperatures existing at the surface where they are formed, when their thermal energy can overcome the cohesive forces at the surface of the condensed fuel. In flaming combustion most of these will be consumed in the flame, but under other conditions (e.g., pyrolysis without combustion following exposure to an external source of heat or, for some materials,

7 Fire Science and Combustion 7 Figure 1.3 Different modes in which fuel vapour is generated from a solid (Table 1.3) Table 1.3 Formation of volatiles from combustible solids (Figure 1.3). It should be noted that pyrolysis is often enhanced by the presence of oxygen (Cullis and Hirschler, 1981; Kashiwagi and Ohlemiller, 1982) Designation Mechanism Examples (Figure 1.3) a Sublimation Methenamine (see text) b Melting and evaporation without Low molecular weight paraffin chemical change waxes, although the mechanism c d e Melting, then decomposition (pyrolysis) followed by evaporation of low molecular weight products Decomposition to produce molten products, a which decompose (pyrolyse) further to yield volatile species Decomposition (pyrolysis) to give volatile species directly and (commonly) a solid residue (char) likely to involve (b) and (c) Thermoplastics; high molecular weight waxes, etc. Polyurethanes Cellulose; most thermosetting resins (not standard polyurethanes) a The initial decomposition may also produce species which can volatilize directly. smouldering combustion (Section 8.2)), the high boiling liquid products and tars will condense to form an aerosol smoke as they mix with cool air. At high temperatures, a small number of addition polymers (e.g., polymethylmethacrylate, known by the acronym PMMA) will undergo a reverse of the polymerization process (Equations (1.R1a) and (1.R1b)), known as unzipping or end-chain scission, to give high yields of monomer in the decomposition products (Table 1.4). 4 This behaviour is a 4 It may be noted at this point that there is no exact equivalent to the unzipping process in the pyrolysis of condensation polymers (compare Equations (1.R1) and (1.R2)).

8 8 An Introduction to Fire Dynamics Table 1.4 Yield of monomer in the pyrolysis of some organic polymers in a vacuum (% total volatiles) (from Madorsky, 1964) Polymer Temperature Monomer (%) range ( C) Polymethylene a Polyethylene Polypropylene Polymethylacrylate Polyethylene oxide Polystyrene Polymethylmethacrylate Polytetrafluoroethylene Poly α-methyl styrene Polyoxymethylene Below a An unbranched polyethylene. direct result of the chemical structure of the monomer units, which favours the unzipping process: with PMMA this is to the exclusion of any other decomposition mechanism (Madorsky, 1964). It should be contrasted with the pyrolysis of, for example, polyethylene, in which the monomer structure allows the chains to break at random points along their length, causing the average chain length (defined by n, the degree of polymerization) and hence the molecular weight to decrease very rapidly. This leads to the formation of smaller molecules that allow the polymer to soften and melt, producing a mobile liquid at the temperature of decomposition. On the other hand, by unzipping, the average molecular weight (determined by n) of the PMMA molecules decreases very slowly and the polymer does not melt and flow (although, given time, it will soften). It is for this reason that PMMA is the polymer most commonly used in experimental work (e.g., see Figure 5.10). In addition to end-chain scission and random-chain scission, which are described above, two other decomposition mechanisms may be identified, namely chain stripping and cross-linking (Wall, 1972; Cullis and Hirschler, 1981; Hirschler and Morgan, 2008). Chain stripping is a process in which the polymer backbone remains intact but molecular species are lost as they break away from the main chain. One relevant example is the thermal decomposition of polyvinyl chloride (PVC), which begins to lose molecular HCl (hydrogen chloride) at about 250 C, leaving behind a char-like residue: R ( CH 2 CHCl ) n R polyvinylchloride R ( CH = CH ) n R + nhcl residue (1.R3) Although the residue will burn at high temperatures (giving much smoke), hydrogen chloride is a very effective combustion inhibitor and its early release will tend to extinguish a developing flame. For this reason, it is said that PVC has a very low flammability, or potential to burn. This is certainly true for rigid PVC, but the flexible grades commonly used for electrical insulation, for example, contain additives (specifically, plasticizers) which make them more flammable. However, even the rigid grades will burn if the ambient conditions are right (Section 5.2.1).

9 Fire Science and Combustion 9 Polymers which undergo cross-linking during pyrolysis tend to char on heating. While this should reduce the amount of fuel available for flaming combustion, the effect on flammability is seldom significant for thermoplastics (cf. polyacrylonitrile, Table 1.2). However, as has already been noted, charring polymers like the phenolic resins do have desirable fire properties. These are highly cross-linked in their normal state (Figure 1.2), and it is likely that further cross-linking occurs during pyrolysis. In subsequent chapters, it will be shown that some of the fire behaviour of combustible materials can be interpreted in terms of the properties of the volatiles, specifically their composition, reactivity and rate of formation. Thermal stability can be quantified by determining how the rate of decomposition varies with temperature. These results may be expressed in a number of ways, the most common arising from the assumption that the pyrolysis proceeds according to a simple kinetic scheme such that: ṁ = dm = k m (1.1) dt where m represents the mass (or more correctly, the concentration) of the polymer. While this is a gross simplification, it does permit k, the rate coefficient, to be determined although this is of little direct value per se. However, it allows the temperature dependence of the process to be expressed in a standard form, using the Arrhenius expression for the rate coefficient, i.e. k = A exp( E A /RT ) (1.2) where E A is the activation energy (J/mol), R is the universal gas constant (8.314 J/K.mol) and T is the temperature (K). The constant A is known as the pre-exponential factor and in this case will have units of s 1. Much research has been carried out on the thermal decomposition of polymers (Madorsky, 1964; National Bureau of Standards, 1972; Cullis and Hirschler, 1981; Hirschler and Morgan, 2008), but in view of the chemical complexity involved, combined with problems of interpreting data from a variety of sources and experimental techniques, it is not possible to use such information directly in the present context. Some activation energies which were derived from early studies (Madorsky, 1964) are frequently quoted (e.g., Williams, 1974b, 1982) and are included here only for completeness (Table 1.5). However, without a knowledge of A (the pre-exponential factor), these do not permit relative rates of decomposition to be assessed. Of more immediate value is the summary presented by Madorsky (1964), in which he collates data on relative thermal stabilities of a range of organic polymers, expressed as the temperature at which 50% of a small sample of polymer will decompose in 30 minutes (i.e., the temperature at which the half-life is 1800 s). (This tacitly assumes firstorder kinetics, as implied in Equation (1.1).) A selection of these data is presented in Table 1.6. They allowed Madorsky (1964) to make some general comments on polymer stability, which are summarized in Table 1.7. It is possible to make limited comparison of the information contained in these tables with data presented in Chapter 5 (Table 5.11) on the heats of polymer gasification (Tewarson and Pion, 1976). However, it must be borne in mind that the data in Table 1.6 refer to pure polymers while those in Table 5.11 were obtained with commercial samples, many of which contain additives that will modify their behaviour.

10 10 An Introduction to Fire Dynamics Table 1.5 Activation energies for thermal decomposition of some organic polymers in vacuum (from Madorsky, 1964) Polymer Molecular Temperature Activation weight range ( C) energy (kj/mole) Phenolic resin Polymethylmethacrylate Polymethylacrylate Cellulose triacetate Polyethylene oxide Cellulose Polystyrene Poly α-methyl styrene Polypropylene Polyethylene Polymethylene High With modern analytical equipment, it is possible to obtain much more detailed information about the decomposition of polymeric materials and their additives. Thermogravimetric analysis (TGA) can be used to investigate the rate of mass loss for a small sample as a function of temperature, while differential scanning calorimetry (DSC) provides information on the amount of energy exchanged during the decomposition process, also as a function of temperature (see Cullis and Hirschler, 1981). By coupling a mass spectrometer to TGA equipment it is possible to identify the decomposition products as they are formed. This technique is particularly useful in examining the way in which a flame retardant influences the decomposition mechanism. While at first sight the composition of the volatiles might seem of secondary importance to their ability simply to burn as a gaseous mixture, such a view does not permit detailed understanding of fire behaviour. The reactivity of the constituents will influence how easily flame may be stabilized at the surface of a combustible solid (Section 6.3.2), while their nature will determine how much soot will be produced in the flame. The latter controls the amount of heat radiated from the flame to the surroundings and the burning surface (Sections 2.4.3, and 5.2.1), and also influences the quantity of smoke that will be released from the fire (Section ). Thus, volatiles containing aromatic species such as benzene (e.g., from the carbonaceous residue which is formed during chainstripping of PVC, Reaction (1.R3)), or styrene (from polystyrene), give sooty flames of high emissivity (Section 2.4.3), while in contrast polyoxymethylene burns with a nonluminous flame, simply because the volatiles consist entirely of formaldehyde (CH 2 O) (Madorsky, 1964), which does not produce soot (Section ). It will be shown later how these factors influence the rates of burning of liquids and solids (Sections 5.1 and 5.2). In some cases the toxicity of the combustion products is affected by the nature of the volatiles (cf. hydrochloric acid gas from PVC, hydrogen cyanide from wool and polyurethane, etc.), but the principal toxic species (carbon monoxide) is produced in all fires involving carbon-based fuels, and its yield is strongly dependent on the condition of burning and availability of air (see Section ).

11 Fire Science and Combustion 11 Table 1.6 Relative thermal stability of organic polymers based on the temperature at which the half-life T h = 30 min (from Madorsky, 1964) Polymer Polymer unit T h ( C) Polyoxymethylene CH 2 O <200 Polymethylmethacrylate A (MW = ) Poly α-methyl styrene Polyisoprene CH 2 C(CH 3 ) 283 CO.OCH 3 CH 2 C(CH 3 ) 287 C 6 H 5 CH 2 C CH CH 2 CH Polymethylmethacrylate B (MW = ) as A 327 Polymethylacrylate CH 2 CH 328 CO.OCH 3 Polyethylene oxide CH 2 CH 2 O 345 Polyisobutylene CH 2 C(CH 3 ) Polystyrene (polyvinyl benzene) CH 2 CH 364 Polypropylene CH 2 CH 387 CH 3 Polydivinyl benzene CH 2 CH 399 CH 2 HC Polyethylene a CH 2 CH Polymethylene a CH 2 CH Polybenzyl CH Polytetrafluoroethylene CF 2 CF a Polyethylene and polymethylene differ only in that polymethylene is a straight chain with no branching at all (as in Figure 1.1(a)). It requires very special processing. Polyethylene normally has a small degree of branching, which occurs randomly during the polymerization process.

12 12 An Introduction to Fire Dynamics Table 1.7 Factors affecting the thermal stability of polymers (from Madorsky, 1964) a Factor Effect on Examples thermal stability (with values of T h, C) Chain branching b Weakens Polymethylene (415) Polyethylene (406) Polypropylene (387) Polyisobutylene (348) Double bonds in polymer backbone Weakens Polypropylene (387) Polyisoprene (323) Aromatic ring in polymer backbone Strengthens Polybenzyl (430) Polystyrene (364) High molecular weight c Strengthens PMMA B (327) PMMA A (283) Cross-linking Strengthens Polydivinyl benzene (399) Polystyrene (364) Oxygen in the polymer backbone Weakens Polymethylene (415) Polyethylene oxide (345) Polyoxymethylene (<200) a While these are general observations, there are exceptions. For example, with some polyamides (nylons), stability decreases with increasing molecular weight (Madorsky, 1964). b Branching refers to the replacement of hydrogen atoms linked directly to the polymer backbone by any group, e.g., CH 3 (as in polypropylene) or C 6 H 5 (as in polystyrene). See Figure 1.1. c Molecular weights of PMMA A and PMMA B are and , respectively. Kashiwagi and Omori (1988) found significant differences in the time to ignition of two samples of PMMA of different molecular weights (Chapter 6). 1.2 The Physical Chemistry of Combustion in Fires There are two distinct regimes in which gaseous fuels may burn, namely: (i) in which the fuel is intimately mixed with oxygen (or air) before burning, and (ii) in which the fuel and oxygen (or air) are initially separate but burn in the region where they mix. These give rise to premixed and diffusion flames, respectively: it is the latter that are encountered in the burning of gas jets and of combustible liquids and solids (Chapter 5). Nevertheless, an understanding of premixed burning is necessary for subsequent discussion of flammability limits and explosions (Chapter 3) and ignition phenomena (Chapter 6), and for providing a clearer insight into the elementary processes within the flame (Section 3.2). In a diffusion flame, the rate of burning is equated with the rate of supply of gaseous fuel which, for gas jet flames (Section 4.1), is independent of the combustion processes. A different situation holds for combustible liquids and solids, for which the rate of supply of volatiles from the fuel surface is directly linked to the rate of heat transfer from the flame to the fuel (Figure 1.4). The rate of burning (ṁ ) can be expressed quite generally as: ṁ = Q F Q L g/m 2 s (1.3) L v where Q F is the heat flux supplied by the flame (kw/m2 ) and Q L represents the losses expressed as a heat flux through the fuel surface (kw/m 2 ). L v is the heat required to

13 Fire Science and Combustion 13 Figure 1.4 Schematic representation of a burning surface, showing the heat and mass transfer processes. ṁ, mass flux from the surface; Q F, heat flux from the flame to the surface; Q L, heat losses (expressed as a flux from the surface) produce the volatiles (kj/g) which, for a liquid, is simply the latent heat of evaporation (Table 5.9). The heat flux Q F must in turn be related to the rate of energy release within the flame and the mechanisms of heat transfer involved (see Sections and 5.2.1). It will be shown later that the rate at which energy is released in a fire ( Q c ) is the most important single factor that characterizes its behaviour (Babrauskas and Peacock, 1992). It is given by an expression of the form: Q c = χ ṁ A f H c kw (1.4) where A f is the fuel surface area (m 2 ), H c (kj/g) is the heat of combustion of the volatiles and χ is a factor (<1.0) included to account for incomplete combustion (Tewarson, 1982) (Table 5.13). It is now possible to determine the rate of heat release experimentally using the method of oxygen consumption calorimetry (Section 1.2.3), but Equation (1.4) can still be of value when there is limited information available (see Chapter 5).

14 14 An Introduction to Fire Dynamics Closer examination of Equations (1.3) and (1.4) reveals that there are many contributory factors which together determine Q c including properties relating not only to the material itself (L v and H c ), but also to the combustion processes within the flame (which in turn determine Q F and χ). Equation (1.3) emphasizes the importance of the heat transfer terms Q F and Q L in determining the rate of supply of fuel vapours to the flame. Indeed, a detailed understanding of heat transfer is a prerequisite to any study of fire phenomena. Consequently, this subject is discussed at some length in Chapter 2, to which frequent reference is made throughout the book. The remainder of this chapter is devoted to a review of those aspects of physical chemistry that are relevant to the understanding of fire behaviour The Ideal Gas Law The release of heat in a fire causes substantial changes in the temperature of the surroundings (Section 10.3) as a result of heat transfer from flames and products of combustion which are formed at high temperatures. Most of the products are gaseous and their behaviour can be interpreted using the ideal gas law: PV = nrt (1.5) where V is the volume occupied by n moles of gas at a pressure P and temperature T (K). (In the SI system, the mole is the amount of a substance which contains as many elementary particles (i.e., atoms or molecules) as kg of carbon-12.) In practical terms, the mass of one mole of a substance is the molecular weight expressed in grams. Atomic weights, which may be used to calculate molecular weights, are given in Table 1.8. R is known as the ideal (or universal) gas constant whose value will depend on the units Table 1.8 elements Atomic weights of selected Symbol Atomic Atomic number weight Aluminium Al Antimony Sb Argon Ar Boron B Bromine Br Carbon C Chlorine Cl Fluorine F Helium He Hydrogen H Nitrogen N Oxygen O Phosphorus P Sulphur S

15 Fire Science and Combustion 15 Table 1.9 Values of the ideal gas constant R Units of Units of Units of R Value pressure volume N/m 2 m 3 J/K mol a atm cm 3 cm 3 atm/k mol atm L l atm/k mol atm m 3 m 3 atm/k mol a This is the value applicable to the SI system. However, in view of the variety of ways in which pressure is expressed in the literature, old and new, it is recommended here that the last value ( ) is used, with pressure and volume in atmospheres and m 3, respectively. Table 1.10 pressure Units Standard atmospheric Value Atmospheres 1 Bars Inches of mercury (0 C) Inches of water (4 C) kn/m 2 (kpa) mm Hg (torr) of P and V (Table 1.9). For simplicity, when the ideal gas law is used, pressure should be expressed in atmospheres as data available in the literature (particularly on the vapour pressures of liquids) are presented in a variety of units, including kn/m 2 (or kpa), mm of mercury (mmhg) and bars, all easily converted to atmospheres. Atmospheric pressure expressed in these and other units is given in Table Equation (1.5) incorporates the laws of Boyle (PV = constant at constant temperature) and Gay-Lussac (V/T = constantatconstant pressure),and Avogadro s hypothesis, which states that equal volumes of different gases at the same temperature and pressure contain the same number of molecules (or atoms, in the case of an atomic gas such as helium). Setting P = 1atm,T = K (0 C) and n = 1mole, V = m 3 (1.6) This is the volume that will be occupied by 28 g N 2,32gO 2 or 44 g CO 2 at atmospheric pressure and 0 C, assuming that these gases behave ideally. This is not so, but the assumption is good at elevated temperatures. Deviation from ideality increases as the temperature is reduced towards the liquefaction point. Although this clearly applies to a vapour that is in equilibrium with its liquid, Equation (1.5) can be used in a number of ways to interpret and illustrate the fire properties of liquid fuels (Section 6.2).

16 16 An Introduction to Fire Dynamics Table 1.11 atmosphere a Normal composition of the dry Constituent gas b Mole fraction (%) Nitrogen (N 2 ) Oxygen (O 2 ) Argon (Ar) 0.93 Carbon dioxide (CO 2 ) 0.03 a From Weast (1974/75). It is convenient for many purposes to assume that air consists only of oxygen (21%) and nitrogen (79%). The molar ratio N 2 /O 2 is then 79/21 = b Minor constituents include neon ( %), helium ( %), krypton ( %) and hydrogen ( %). The density, or concentration, of a gas may be calculated: for example, taking the composition of normal air as given in Table 1.11, it can be shown that one mole corresponds to M w = kg, so that its density at 0 C (273 K) will be: ρ = nm w V = PM w RT = kg/m3 (1.7) (see Table 11.7). The composition of a mixture of gases may also be expressed in terms of partial pressures (P i ) of the components, i, sothat: P = i P i (1.8) where P is the total pressure. As the volume fraction of oxygen in normal air is , its partial pressure will be atm. This can be converted into a mass concentration as before: thus at 273 K PM w RT = 273R = kg O 2 /m 3 (1.9) which gives the mass fraction of oxygen in air (Y O2 ) as / = 0.232, a quantity that is referred to later (e.g., Equation (5.24)). The effect of increasing the temperature of a volume of gas can be seen by referring to Equation (1.5): if the volume is kept constant then the pressure will rise in direct proportion to the temperature increase (see Section 1.2.5), while if the pressure is held constant, the gas will expand (V increases) and its density will fall. Density (ρ) varies with temperature (at constant pressure) according to Equation (1.7), i.e. ρ = PM w R 1 T (1.10)

17 Fire Science and Combustion 17 As PM w /R is constant, the product ρt will be constant. Consequently, we can write ρ 0 ρ = T T 0 (1.11) ρ 0 T where the subscripts 0 and refer to initial (or ambient) and final conditions, respectively. As T = P M w /R ρ, this can be rearranged to give ρ = β T (1.12) ρ where β = Rρ 0 /P M w = K 1, at the reference state of 1 atmosphere and 0 C. β is the reciprocal of 273 K and is known as the coefficient of thermal expansion. It was first derived for gases by Gay-Lussac in If there is any density difference between adjacent masses of air, or indeed any other fluid, relative movement will occur. As the magnitude of this difference determines the buoyant force, the dimensionless group which appears in problems relating to natural convection (the Grashof number, see Section 2.3), can be expressed in terms of either ρ/ρ or β T (Table 2.4). In most fire problems, it may be assumed that atmospheric pressure is constant, but it decreases with height (altitude) according to the relationship: dp dy = ρg (1.12a) where y is height (m), ρ is the density of the fluid (in this case, air) (kg/m 3 )andg is the acceleration due to gravity (9.81 m/s 2 ). Using Equation (1.10), and assuming constant temperature, this may be integrated to give: p = p o exp[ g(ρ o /p o )y] (1.12b) Substituting g = 9.81 m/s 2, ρ o = 1.2 kg/m 3 (20 C, see Table 11.6) and p o = Pa (the value for the standard atmosphere ), this becomes: p = p o exp[ y] (1.12c) Thus it is easy to show that at Denver, Colorado, which is 1 mile (1609 m) above sea level, atmospheric pressure is 83.8 kpa (or 631 mm Hg). The significance of this will be discussedinsection6.2. For small values of y for example, corresponding to the vertical dimension of a building the difference in pressure between the ground and the upper floors will be very small. If we assume as a first approximation that the density of the air (ρ) within the building is constant, Equation (1.12a) can be integrated to give: p h = p o ρgh (1.12d) where h is the height of the building (m). The decrease in pressure with height can be ignored for most purposes (for h = 50 m, p o p h = 0.6 kpa,lessthan1%).however, if the temperatures inside and outside the building differ by a few degrees, the resulting differences in air density will give rise to pressure differentials across the building

18 18 An Introduction to Fire Dynamics envelope. This is the cause of the stack effect that will be discussed in Chapter 11 (Section ). The same physics applies to a fully developed compartment fire when large temperature differences exist across the compartment boundaries (see Chapter 10). Strong buoyant flows, driven by differences in density between the hot gases and the ambient atmosphere, are responsible for drawing air into the base of the fire and for the expulsion of flame and hot gases from confined locations (Section 10.2) Vapour Pressure of Liquids When exposed to the open atmosphere, any liquid which is stable under normal ambient conditions of temperature and pressure (e.g., water, n-hexane) will evaporate as molecules escape from the surface to form vapour. (Unstable liquids, such as LPG, will be discussed briefly in Chapter 5.) If the system is closed (cf. Figure 6.8(a)), a state of kinetic equilibrium will be achieved when the partial pressure of the vapour above the surface reaches a level at which there is no further net evaporative loss. For a pure liquid, this is the saturated vapour pressure, a property which varies with temperature according to the Clapeyron Clausius equation: d(lnp o ) dt = L v RT 2 (1.13) where p o is the equilibrium vapour pressure and L v is the latent heat of evaporation (Moore, 1972; Atkins and de Paula, 2006). An integrated form of this is commonly used, for example: log 10 p o = ( E/T ) + F (1.14) where E and F are constants, T is in Kelvin and p is in mm Hg. Values of these for some liquid fuels are given in Table 1.12 (Weast, 1974/5). The equation may be used to calculate the vapour pressure above the surface of a pure liquid fuel to assess the flammability of the vapour/air mixture (Sections 3.1 and 6.2). The same procedure may be employed for liquid fuel mixtures if the vapour pressures of the components can be calculated. For ideal solutions to which hydrocarbon mixtures approximate, Raoult s law can be used. This states that for a mixture of two liquids, A and B: p A = x A p o A and p B = x B p o B (1.15) where p A and p B are the partial vapour pressures of A and B above the liquid mixture, pa o and po B are the equilibrium vapour pressures of pure A and B (given by Equation (1.14)), and x A and x B are the respective mole fractions, i.e. x A = n A n A + n B and x B = n B n A + n B (1.16) where n A and n B are the molar concentrations of A and B in the mixture. (These are obtained by dividing the mass concentrations (C A and C B ) by the molecular weights M w (A) and M w (B).) In fact, very few liquid mixtures behave ideally and substantial deviations will be found, particularly if the molecules of A or B are partially associated

19 Fire Science and Combustion 19 Table 1.12 Vapour pressures of organic compounds (Weast, 1974/75) Compound Formula E F Temperature range ( C) n-pentane n-c 5 H to 191 n-hexane n-c 6 H to 209 Cyclohexane c-c 6 H to 257 n-octane n-c 8 H to 281 iso-octane (2,2,4-Trimethyl pentane) to 99 n-decane n-c 10 H to 173 n-dodecane n-c 12 H to 346 Methanol CH 3 OH to 224 Ethanol C 2 H 5 OH to 242 n-propanol n-c 3 H 7 OH to 250 Acetone (CH 3 ) 2 CO to 214 Methyl ethyl ketone CH 3 CO.CH 2 CH to 80 Benzene C 6 H to 290 Toluene C 6 H 5 CH to 31 Styrene C 6 H 5 CH=CH to 145 Vapour pressures are calculated using the following equation: log 10 p o = ( E/T ) + F, where p is the pressure in mm Hg (torr) (Table 1.10), T is the temperature (Kelvin) and E is the molar heat of vaporization. (Note that the temperature range in the table is given in C.) in the pure state (e.g., water, methanol) or if A and B are of different polarity (Moore, 1972; Atkins and de Paula, 2006). Partial pressures must then be calculated using the activities of A and B in the solution, thus: where: p A = α A p o A and p B = α B p o B (1.17) α A = γ A x A and α B = γ B x B α and γ being known as the activity and the activity coefficient, respectively. For an ideal solution, γ = 1. Values for specific mixtures are available in the literature (e.g., Perry and Green, 2007) and have been used to predict the flashpoints of mixtures of flammable and non-flammable liquids from data on flammability limits (Thorne, 1976) (see Section 6.2) Combustion and Energy Release All combustion reactions take place with the release of energy. This may be quantified by defining the heat of combustion ( H c ) as the total amount of heat released when unit quantity of a fuel (at 25 C and at atmospheric pressure) is oxidized completely. For a hydrocarbon such as propane (C 3 H 8 ), the products would comprise only carbon dioxide and water, as indicated in the stoichiometric equation: C 3 H 8 + 5O 2 3CO 2 + 4H 2 O (1.R4)

20 20 An Introduction to Fire Dynamics in which the fuel and the oxygen are in exactly equivalent or stoichiometric proportions. The reaction is exothermic (i.e., heat is produced) and the value of H c will depend on whether the water in the products is in the form of liquid or vapour. The difference will be the latent heat of evaporation of water (44 kj/mol at 25 C). Thus for propane, the two values are: H c (C 3 H 8 ) = 2220 kj/mol (the gross heat of combustion) H c (C 3 H 8 ) = 2044 kj/mol (the net heat of combustion) where the products are liquid water and water vapour, respectively. In flames and fires, the water remains as vapour and consequently it is more appropriate to use the latter value. The heat of combustion of propane can be expressed as either 2044 kj/mol or (2044/44) = kj/g of propane (Table 1.13), where 44 is the gram molecular weight of C 3 H 8. By convention, these are expressed as negative values, indicating that the reaction is exothermic (i.e., energy is released). If the reaction is allowed to proceed at constant pressure, the energy is the result of a change in enthalpy ( H ) of the system as defined by Reaction (1.R4). However, heats of combustion are normally determined at constant volume in a bomb calorimeter, in which a known mass of fuel is burnt completely in an atmosphere of pure oxygen (Moore, 1972; Atkins and de Paula, 2006; Janssens, 2008). Assuming that there is no heat loss (the system is adiabatic), the quantity of heat released is calculated from the temperature rise of the calorimeter and its contents, whose thermal capacities are accurately known. The use of pure oxygen ensures complete combustion and the result gives the heat released at constant volume, i.e., the change in the internal energy ( U) of the system defined by Reaction (1.R4). The difference between the enthalpy change ( H ) and the internal energy change ( U) exists because at constant pressure some of the chemical energy is effectively lost as work done (P V) in the expansion process. Thus, H can be calculated from: H = U + P V (1.18) remembering that for exothermic reactions both H and U are negative. The work done may be estimated using the ideal gas law, i.e. PV = nrt (1.5) where n is the number of moles of gas involved. If there is a change in n, as in Reaction (1.R4), then: P V = nrt (1.19) where n = 7 6 =+1andT = 298 K. It can be seen that in this case the correction is small ( 2.5 kj/mol) and may be neglected in the present context, although it is significant given the accuracy with which heats of combustion can now be measured. Bomb calorimetry provides the means by which heats of formation of many compounds may be determined. Heat of formation ( H f ) is defined as the enthalpy change when a compound is formed in its standard state (1 bar and 298 K) from its constituent elements, also in their standard states. That for carbon dioxide is the heat of the reaction C(graphite) + O 2 (gas) CO 2 (gas) (1.R5)

21 Fire Science and Combustion 21 Table 1.13 Heats of combustion a of selected fuels at 25 C (298 K) H c H c H c,air H c,ox (kj/mol) (kj/g) (kj/g(air)) (kj/g(o 2 )) Carbon monoxide CO Methane CH Ethane C 2 H Ethene C 2 H Ethyne C 2 H Propane C 3 H n-butane n-c 4 H n-pentane n-c 5 H n-octane n-c 8 H c-hexane c-c 6 H Benzene C 6 H Methanol CH 3 OH Ethanol C 2 H 5 OH Acetone (CH 3 ) 2 CO d-glucose C 6 H 12 O Cellulose Polyethylene Polypropylene Polystyrene Polyvinylchloride Polymethylmethacrylate Polyacrylonitrile Polyoxymethylene Polyethyleneterephthalate Polycarbonate Nylon 6, a The initial states of the fuels correspond to their natural states at normal temperature and pressure (298 C and 1 bar). All products are taken to be in their gaseous state thus these are the net heats of combustion. All these reactions are exothermic, i.e., the heats of combustion are negative. For clarity, the negative signs appear in the titles of each column. where H 298 f (CO 2 ) = 393.5kJ/mol. The negative sign indicates that the product (CO 2 ) is a more stable chemical configuration than the reactant elements in their standard states, which are assigned heats of formation of zero. If the heats of formation of the reactants and products of any chemical reaction are known, the total enthalpy change can be calculated. Thus for propane oxidation (Reaction (1.R4)): H c (C 3 H 8 ) = 3 H f (CO 2 ) + 4 H f (H 2 O) H f (C 3 H 8 ) H f (O 2 ) (1.20) in which H f (O 2 ) = 0 (by definition). This incorporates Hess law of constant heat summation, which states that the change in enthalpy depends only on the initial and final states of the system and is independent of the intermediate steps. In fact, H c (C 3 H 8 ) is

22 22 An Introduction to Fire Dynamics Table 1.14 Standard heats of formation of some common gases Compound Formula H 298 f (kj/mol) Water (vapour) H 2 O Carbon monoxide CO Carbon dioxide CO Methane CH Propane C 3 H Ethene C 2 H Propene C 3 H Ethyne C 2 H easily determined by combustion bomb calorimetry, as are H f (CO 2 ) and H f (H 2 O), and Equation (1.20) would be used to calculate H f (C 3 H 8 ), which is the heat of the reaction 3C(graphite) + 4H 2 (gas) C 3 H 8 (gas) (1.R6) Values of the heats of formation of some common gaseous species are given in Table Those species for which the values are positive (e.g., ethene and ethyne) are less stable than the parent elements and are known as endothermic compounds. Under appropriate conditions they can be made to decompose with the release of energy. Ethyne (acetylene), which has a large positive heat of formation, can decompose with explosive violence. Values of heat of combustion for a range of gases, liquids and solids are given in Table 1.13: these all refer to normal atmospheric pressure (101.3kPa) and an ambient temperature of 298 K (25 C) and to complete combustion. It should be noted that the values quoted for H c are the net heats of combustion, i.e., water as a product is in the vapour state. They differ from the gross heats of combustion by the amount of energy corresponding to the latent heat of evaporation of the water (2.44 kj/g (44 kj/mol) at 25 C). Furthermore, it is not uncommon in fires for the combustion process to be incomplete, i.e., χ in Equation (1.4) is less than unity. The actual heat released could be estimated by using Hess law of constant heat summation if the composition of the combustion products was known. The oxidation of propane could be written as a two-stage process, involving the reactions: C 3 H O 2 3CO+ 4H 2 O (1.R7) and CO O 2 CO 2 (1.R8) Reaction (1.R4) can be obtained by adding together (1.R7) and three times (1.R8). Then by Hess law H R4 = H R7 + 3 H R8 (1.21)