Fire Dynamics I

1
Fire Dynamics I

• Lecture 2
• Physical Chemistry
• Chemical Reactions
• Jim Mehaffey
• 82.575 or CVG7300

2

• Physical Chemistry Chemical Reactions
• Outline
• Flaming combustion
• Ideal gas law
• Vapour pressure of liquids
• Chemical reactions
• Chemical equations

3

• Flaming Combustion
• Premixed Flames
• Fuel mixed with air (O2) before burning
• Examples Industrial burners dust suspensions
• Provide insight into ignition flame processes
• Diffusion Flames
• Fuel and air (O2) initially separated but burn in
  region where they mix
• Examples Gas jets // Combustible liquid or
  solids

4

• Diffusion Flames
• The Fire Triangle
• HEAT
• FUEL
  OXYGEN

5

• Diffusion Flames
• The Fire Tetrahedron
• HEAT
• REACTIONS
• FUEL
  OXYGEN

6

• Diffusion Flames

7

• Rate of Burning (Mass Loss Rate)
• Eqn (2-1)

8

• Rating of Burning (Heat Release Rate)
• Eqn (2-2)

9

• Heat Release Rate
• Eqn (2-3)
• governs fire dynamics and depends on
• material properties (LV and HC)
• flame properties (? and )
• heat transfer ( )

10

• Combustion of Liquids
• Flaming combustion occurs in gas phase
• Volatile generated by evaporation
• Molecular composition of volatile same as liquid
• Heat of vaporization Heptane LV 0.55
  kJ / g Octane LV 0.60 kJ /
  g Styrene LV 0.64 kJ / g MMA LV
  0.52 kJ / g

11

• Combustion of Solid
• Combustible solids polymers (macro-molecules)
• Thermoplastics melt before they burn (no char)
  (polyethylene, polystyrene, PMMA)
• Thermosets char as they burn (most do not melt)
  (polyurethane, wood)
• Flaming combustion occurs in gas phase

12

• Combustion of Solids
• Flaming combustion occurs in gas phase
• Volatile created by thermal decomposition
• Molecular composition of volatile is simpler than
  that of solid
• Heat of gasification Polyethylene LV
  2.30 kJ / g Polystyrene LV 1.76 kJ /
  g PMMA LV 1.62 kJ / g Wood LV 1.80
  kJ / g

13
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14

• Physical Chemistry Ideal Gas Law
• Gas generated or heated by fire can be assumed
  to obey the ideal gas law
• P V n R T Eqn (2-4)
• P pressure (atm)
• V volume (m3)
• n number of moles (mol)
• R 8.20575 x 10-5 m3 atm mol-1 K-1
• T temperature (K)

15

• Alternative Units
• P V n R T Eqn (2-4)
• P pressure (N m-2 Pa)
• V volume (m3)
• n number of moles (mol)
• R 8.31431 J mol-1 K-1
• T temperature (K)
• 1 atm 101,325 Pa 101.325 kPa

16

• Mole
• Mole amount of a substance containing as many
  atoms or molecules as 12 g of Carbon-12
• Mole 6.02 x 1023 atoms or molecules (Avagadro
  number)
• Molecular weight
• Mass of 1 mole of substance (g mol-1)

17

• Ideal Gas Law
• P V n R T Eqn (2-4)
• Incorporates
• Boyless Law PV constant at constant T
• Gay-Lussacs Law V/T constant at constant P
• Avogadros hypothesis equal Vs of different
  gases at the same T P contain the same
  number of molecules (moles)

18

• Volume Occupied by One Mole if
• P 1 atm n 1 mol T 293.17 K (20C)
• Substituting into the ideal gas law yields
• V 0.0241 m3
• 24.1 litres
• ? 5 gal (imp)
• At atmospheric pressure and 20C this volume is
  occupied by 28 g of N2, 32 g of O2 or 44 g of CO2

19

• Molecular Weight of Air
• One mole of dry air is composed of
• 0.7809 mol of N2
• 0.2095 mol of O2
• 0.0093 mol of Ar
• 0.0003 mol of CO2
• MW(air) 0.7809 x 28 0.2095 x 32
• 0.0093 x 39.9 0.0003 x 44
• MW(air) 28.95 (g mol-1)

20

• Atomic Weights of Selected Elements

21

• Density of Air
• P 1 atm and T 293.17 K (20C)
• ? M / V
• n MW / V
• P MW / R T Eqn (2-5)
• 1203 g m-3
• 1.203 kg m-3

22

• Ideal Gas Mixtures
• Partial Pressure Pi
• P n R T / V
• (? ni) R T / V
• ? Pi Eqn (2-6)
• Mole fraction (species i)
• ni / n
• Number (volume) concentration (species i)
• Vi ni / n x 106 ppm Eqn (2-7)

23

• Proportion of O2 in Air
• Mole fraction of O2 in air
• Number (volume) concentration of O2 in air
• Mass fraction of O2 in air
• Density of O2 in air (20C)

24

• Variations in ?, T and P
• Wide range of temperatures in gas associated with
  fire (flame, smoke, heated gas, ambient)
• Large differences in densities between hot gas
  ambient (induce buoyant flows)
• Pressure differences draw air into base of fire
  cause exchange of gas through vents in bldgs
• For fires burning in atmosphere, pressure
  differentials are small (15 Pa ? 1.5 x 10-4 atm)
• First approximation Ignore pressure
  differentials

25

• Variations in ? T
• ? P MW / R T Eqn (2-5)
• For fires burning in atmosphere, P ? 1 atm
• Assume MW ? 28.95. Fire gases are mainly N2
• ? T P MW / R constant
• ?1 T1 ?2 T2 Eqn (2-8)
• Temperature differences between adjacent masses
  of gas induce density differences
• Density differences between adjacent masses of
  gas induce buoyant flows

26

• Physical Chemistry Vapour Pressure of Liquids
• In the open, liquids evaporate forming vapours
• In a closed vessel, at equilibrium vapour
  pressure no net evaporation occurs
• Flammability of vapour-air mixture depends on
  partial pressure of vapour
• Correlation for closed vessels
• log10 p0 F 0.2185 E / T Eqn (2-9)
• p0 equilibrium vapour pressure (mm Hg) (760 mm
  Hg 1 atm)
• E and F constants (see next slide)
• T temperature (K)

27

• Equilibrium Vapour Pressure of Liquids

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29

• Liquid Fuel Mixtures
• Hydrocarbon mixtures approximate ideal
  solutions for which Raoults law applies
• pA xA Eqn (2-10)
• pA partial pressure of A above liquid
  mixture
• equilibrium vapour pressure of pure A
• xA mole fraction of A in the liquid mixture
• xA nA / (nA nB )

30

• Chemical Reactions
• HC heat of combustion when fuel at T 25C P
  1 atm is completely oxidized
• Complete (stoichiometric) combustion of propane
• C3H8 5 O2 ? 3 CO2 4 H2O Eqn (2-11)
• Gross heat of combustion (liquid water produced)
• HC 2220 kJ / mol
• Net heat of combustion (water vapour produced)
• HC 2044 kJ / mol (appropriate for fire)
• Difference is latent heat of evaporation of water
  (44 kJ / mol H2O)

31

• Net Heat of Combustion of C3H8
• Can be expressed per unit mole as
• HC 2044 kJ / mol
• 1 mole of propane has mass 44 g, so can write
• HC 2044 kJ mol-1 / (44 g mol-1) 46.45
  kJ / g
• Since combustion of 1 mole of C3H8 consumes 5
  moles of O2 or 5 x 32 g 160 g of O2
• 2044 kJ / (160 g of O2) 12.78 kJ
  / g of O2
• Since the mass fraction of O2 in air is 0.232
• HC,air 12.78 kJ/g(O2) x 0.232 g(O2)/g(air)
  2.96 kJ/g(air)

32

• Net Heat of Combustion of Fuels at 25C
• Net heat of combustion of combustibles is
  measured in an oxygen bomb calorimeter.
• Combustion initiated in a pure O2 atmosphere
  with a surplus of O2
• Results in complete combustion

33

• Net Heat of Combustion of Fuels at 25C

34

• Heat of Combustion / g(O2)
• Heat of combustion / g(O2) is almost constant
• For most organic liquids and gases
• 12.72 ? 3 kJ / g(O2)
• For most polymers
• 13.02 ? 4 kJ / g(O2)
• O2 consumption calorimetry used to calculate heat
  release rate in many fire tests.
• For ventilation-controlled fires, heat release
  rate estimated from supply rate of fresh air and
• 3 kJ / g(air)

35

• Incomplete Combustion
• Values on slide 33 are for complete combustion in
  oxygen bomb calorimeter. Fuel burns in pure O2
  and CO2 H2O are generated.
• Real fires burn in air which causes incomplete
  combustion (CO soot are also generated)
• Reduction in combustion efficiency means net heat
  of combustion is not released
• Example, combustion of octane
• heat of combustion in O2 44.77 kJ / g
• heat of combustion in air 41.0 kJ / g

36

• Stoichiometric Air Requirements
• 1 mol (air) 0.21 mol (O2) 0.79 mol (N2)
• 0.21 1 mol (O2) 3.76 mol (N2)
• Empirical formula for PMMA is C5H8O2n
• Complete (stoichiometric) combustion of PMMA
• C5H8O2 6 O2 6 x 3.76 N2 ? 5 CO2 4 H2O
  22.56 N2
• 1 mol (PMMA monomer) requires 28.56 mol air
• MW(PMMA monomer) 100 MW(air) 28.95
• Therefore 1 g (PMMA) requires 8.27 g (air)

37

• Stoichiometric Air Requirements
• Equation for complete combustion of fuel in air
• 1 g fuel r g air ? (1 r) g products
  Eqn (2-12)
• r stoichiometric air requirement
• r 8.27 for PMMA

38

• References
• D. Drysdale, An Introduction to Fire
  Dynamics,Wiley, 1999, Chap 1
• A. Tewardson, Generation of Heat and Chemical
  Compounds in Fires" Section 3 / Chapter 4, SFPE
  Handbook, 2nd Ed. (1995)