Reaction to Fire of Liquids

Stanislav I. Stoliarov

Ecole thématique du CNRS sur la Science des Incendies et ses Applications Porticcio, 30/05 – 04/06 2015

Fire Protection Engineering

Piloted Ignition of Gasesg Ignitability of fuel/oxidizer gaseous mixtures is frequently characterized by lower and upper flammability limits (LFL and UFL).

These limits are usually expressed as the minimum and maximum volumetric fraction (or concentration) of fuel in air capable of propagating self‐sustained flame.

The underling physics of these limits is associated with a competition between energy and active species (radicals) production in combustion reactions and energy and active species loss due to diffusion and radiation.

The limits are typically measured experimentally using the Bureau of Mines Flammability A tApparatus.

Piloted Ignition of GasesgBureau of Mines Flammability Apparatus

Glass Tube filled withGlass Tube filled withmixture to be tested

(UFL)

150 cm

5 cm5 cm(LFL)

Piloted Ignition of Gasesg*

* SFPE Fire Protection Engineering Handbook

Flammability Limits and Stoichiometryy yFor most simple hydrocarbons:

11

nV

nV

stoicstoic21

21LFL

FuelAir

Fuel

FuelAir

Fuel

nnn

VVV

stoicstoic

22UFL

FuelAir

Fuel

FuelAir

Fuel

nnn

VVV

LFL of mixtures (Le Chatelier’s) rule: Each gaseous fuel contribution to flammabilityLFL of mixtures (Le Chatelier’s) rule: Each gaseous fuel contribution to flammabilityis equal to the faction of its LFL.

1

total

i

VV

In other words, the LFL of mixture is reached when: 1LFL

i i

In other words, the LFL of mixture is reached when:

;LFL

i i

itotal

VV

ii

iii total

imix V

VVVV 1

LFL

1LFL

i i

Fuelsi i VLFL

LFL

Ignition of Liquidsg q

Vapor‐Air Mixture Application of igniter 

Premixedflame

Liquid Increase in liquid surfacetemperature

Increase in fuel vaporconcentration(controlled by thermodynamics)

Does the concentrationDoes the concentrationreach LFL?

No

No ignition

Yes

No ignitionFlash point

Ignition of Liquidsg q

Vapor‐Air Mixture Flash point

Premixedflame

Liquid

Does the liquid produce enough gaseous fuel during the time between flashes to create UFL mixture in the

b it f th i f th fl hi

No

space above it of the size of the flame quenchingdistance?

Yes

No ignitionPotential transition to sustained diffusion flame ‐ fire point

States of Pure Substance

Second Law of ThermodynamicsySpontaneous process:

A function of state that defines randomness of a system is called entropy (S)A function of state that defines randomness of a system is called entropy (S).

,ln NS where N is the number microstates comprising the system.

dQdS S d L f Th d i t t th tTQdS Second Law of Thermodynamics states that:

PdVdUdQ According to the First Law of Thermodynamics:

PdVdUTdS

0 TdSPdVdU

Gibbs Free Energy

If pressure and temperature are constant: 0 dGTSPVUd

Enthalpy (function of state)

Clausius‐Clapeyron Equationp y qTSPVUG

SdTTdSVdPPdVdUdG SdTTdSVdPPdVdUdG

SdTTdSVdPPdVPdVTdSdG

PdVdUTdS For reversible process: PdVTdSdU

SdTTdSVdPPdVPdVTdSdG

SdTVdPdG

Vapor

In equilibrium:dn

dGdn

dGdndn

dGdndn

dG VLVL 0)(

molar quantities

dPdP

Liquid dTSdPVdTSdPV VVLL

molar quantities

VVLL SdTdPVS

dTdPV

Clausius‐Clapeyron Equationp y qVVLL S

dTdPVS

dTdPV

Vapor

Liquid

Vapor VLVL SS

dTdPVV

LV SSdP

TQS

TdQdS

orFor reversible process:

LV

LV

VVdT

TT

LV VVTQ

dTdP

heat of vaporization, hfg

LV

PRTT

hTVh

dTdPVV

VLV

fgfg

PdT

RTh

PdP

2fg

Clausius‐Clapeyron Equationp y q

VapordT

RTh

PdP

2fg

boiling point

Air

Liquid

Vapor

bb

2fg

T

T

P

P

dTRTh

PdP

boiling point

TTRh

PP 11lnlnb

fgb

TTR

hPP 11ln

b

fg

b

partial vapor pressure

TTRh

PP 11exp

b

fg

batmospheric pressure(101,325 Pa)

partial vapor pressure

Vtotal

V

VV

l(101,325 Pa) Key Result

Application to Ignition of Liquidspp g q

TTRh

V11exp

b

fgVapor

Air

b

Lb

fg 11expLFLTTR

hLiquid

Vapor

flash point

Cleveland Open Cup Tester (ASTM D92)is used to measure:

flash point, TL

temperature of onset of sustainedburning (fire point)burning (fire point)

Application to Ignition of Liquidspp g qa

Lb

fg 11expLFLTTR

h

112861000350MWHexane (g mol-1)

021.0

112861000350

2511

3421

314.82.86100035.0expLFLHexane

closed cup TL

hfg from NIST chemistry webbook

017.0247

1342

1314.8

2.86100035.0expLFLHexane

open cup TL

aData from Fundamentals of Fire Phenomena, page 138.014.0

2471

3421

314.831730expLFLHexane

Application to Ignition of Mixturespp g

Application of Raoult's law (the ratio is molar fraction in liquid mixture)

total

i

VV

LFL

i

i

jj

i

h

PP

nn

b

11

i

i

i

jj

i

h

TTRh

nn

b

fg

11

11exp

1 indicates ignitioni iLFL

iii TTR

h

Lb

fg 11exp

iii TTR

h

Lb

fg 11exp (Le Chatelier’s rule)

Burning RateBurning rate – the rate of mass loss or heat release per unit surface area ofcondensed‐phase fuel.

qin T

Steady‐State Burning of Solid or Liquid:Tqin

Tp yp

Ti tt y

x kg of gaseous fuel isgenerated per unit surface area during t

ttt

Tp yp

Ti

T

y

constmFt

xf

Tiy

For steady‐state to exist, x kg of fuel must be heated from Ti to Tp and vaporized during t:

fgxhTTxc ips tqin

qx

- hfg may represent heat of decomposition or vaporization;- Tp may represent pyrolysis temperature or boiling point. 

fghTTcq

tx

ips

in

p y p py y p g p

Burning RateBurning rate – the rate of mass loss or heat release per unit surface area ofcondensed‐phase fuel.

qin T

Steady‐State Burning of Solid or Liquid:Tqin

Tp yp

Ti tt y

x kg of gaseous fuel isgenerated per unit surface area during t

ttt

Tp yp

Ti

T

y Tiy

fghTTcqmF

ips

inf

fghdTc

qmFpT

s

inf

If cs is a function of T:

= L ‐ heat of gasificationiT

L heat of gasification

Pool Fire Analysis LB

chqg

in 1lnConvection from flame only:

441'1ln kD TTeLBhq Convection and radiation from flame:

Spalding B number

Mean beam length

11ln psflamesg

in TTeLBc

q Convection and radiation from flame:

TTcXYsH

Bpgroxid

c

1

'where

Fraction of combustion energy that is radiated out

qF in)( t d

LsB 'where

TTeBh psflame

kDs

441'1l

Mass of oxidizer consumed per unit mass of fuel

LqmF in

f )(steady LL

Bc

psflames

g

'1ln

*

*Figure from Quintiere, Fundamentals of Fire …

Case Study*

Questions need to be answered:

*From Quintiere, Fundamentals of Fire …

Case StudyLqmF in)(steadyevap

fghL

)( airsurfin TThq

Lewis number

2222evap

ClCHair

ClCHsurf YYKmF 1LeIf 2222

evapClCH

airClCH

surfair

YYchmF

ll ClCHh

ClCH hMWh 11f

Lewis number

2222 ClCHair

ClCHsurf YY 22

evapClCH

surfair

YchmF

surfair

ClCH

air TTRh

MWMW

ch 11exp

b

fg22

fg )(11exp22TThhMWh airsurfClCH

C20 o fTfgb

exphTTRMWc surfairair

C20 surfT

2/100spillsevap 05.022 HAYAmF ClCH bldg

22 VYdtd

airClCH Mass conservation for CH2Cl2: dt

22cancans0

spillsevap ClCHVNdtAmF 02.022

max ClCHY

Result: LFL is not reached