NRL Report 6617

Flammability Properties of Hydrocarbon Fuels

Part 3 - Flammability Properties of

Hydrocarbon Solutions in Air

November 21, 1967

NAVAL RESEARCH LABORATORY

c· c:~c~.~_: =.=~. '< :::; :,., ,; 5 ~ Washington, D.C.;~.c ::,.:;.,"'" ':::::.,"~; ;:-: ~, -~,-,,::_~,!,:,';

:~':::-~,""~~"'; :::'.;~;'.:':~ \,,! 2]'~'

This document has .been approved for pubJic release and sale; its distribution is unlimited.

PREVIOUS REPORTS IN THIS SERIES

"Par,o1':"InterrelationS· of Flammability Properties of n,Alkanes in Air," W. A.

Affens. NRLRepoit6270, May 25. 1965 t\li-~ r~; 1 '6~"Part. 2-The Importance of VoJatik Components at Low Concemration of the

.FJammabili'yof Liquid Fuels," W. A. Affens, NRL Report 6578,]uly 10, 1967

~-.·~·.1. ''..f~~....-. - .. l ._> '-

NRL Report 6617

Flammability Properties of Hydrocarbon Fuels

Part 3 - Fiarnmability Properties ofHydrocarhon Solutions in Air

W. A. AFFE:-;S

Fuels BranchChemistr), Division

November 21, 1967

NAVAL RESEARCH LABORATORYWashington, D.C.

1lJi.s document h~ been approved ror public release and sale: its distribution is unlimited.

CONTENTS

Abstract iiProbiem Status iiAuthorization ii

INTRODUCTION 1

PRINCIPLES INVOLVED 1

LIMITATIONS 2

CHOICE AND HANDLING OF LITERATURE DATA 2

FLAMMABILITY LIMITS OF VAPOfi-AiR MlXTURES 2

STOICHIOMETRIC CONCENTRATIONS OF VAPOR-AIRNITXTURBS 3

MOLAR HEAT OF CO.M!3USTION OF VAPOR-AIRNUXTURES 3

VAPOR MIXTURES CONTAINING TWO FUEL COMPONENTS 3

FLAMMABILITY lNDrX OF VAPOR-AIR MIXTURES 5

EFFECT OF TEMPERATURE ON FLAMMABILITY LIMITSOF VAPOR-AIR MIXTURES 6

VAPOR COMPOSITION ABOVE THE LIQUID SOLUTION 7

FLA~{MABlLiTY UMITS OF LIQUID SOLUTIONS 7

BINARY LIQUID SOLUTIONS 9

FLAMMABILITY INDEX OF LIQUID· SOLUTIONS 9

FLASH POINT 11

SUMMARY AND CONCLUSIONS -.5

REFERENCES 16

i

ABSTRACT

Previous work on the interrelations 01 the flammability propertieson ", -alkanes in air have been extended to both vapor and liquid fuel mix­tl'!Ies. Based on the application of Raoult's and Dalton's laws governingvapor pressure and composition above a solution of two or mere liquidhydrocarbons to Le Chatelier's rule governing the flammability limitsof vapor mixtures, equations have been derived which make it possibleto predict overall flammability properties of mixtures from the prop­erties and proportions of the individual components. The flammabilitypropi!rties which were studied include: lower and upper flammabilitylimits, heat of combustion, stoichiometric concentration, flash point,and flammability index (" explosivenessttl. The derived equations demon­strate, quantitatively, why '"aper pressure of individual constituentsplays a more important role than concentration on the overall flamma­bility properties of liquid hydrocarbon solutions, and that a very smallamount of a highly volatile contaminant in a relatively nonflammableiuel may make it flammable.

PROBLEM STATUS

This is an interim report; work is continuing on the problem.

AUTHORIZATION

NRL Problem C01-03Projects SR 001-06-02-0600 and RR 010-01-44-5850

ManusGript submitted July 18, 1967.

ii

FLAM..1VIABIUTY PROPERTIES OF HYDROCARBON FUELS

PART 3 - FLAMMABIUTY PROPERTlES OFHYDROCARBON SOLUTiONS IN AIR

INTRODUCTION

As a result of ccntamination, improper preparation, or other ::easons, less volatile,liquid combustibles may sometimes contain sClail quantities of highly volatile, flamma­ble components, which can signific•.ntly influence the overall flammability properties ofthe mixture. It would be useful to be able to predict these and related effects quantita­tively. Some physical properties of liquid sol1:.tions, such as density, are generally pro­portional to the properties and con.centrations of the individual components. Combustion,on the other hand, occurs in the vapor phase; hence, flammability is a function of vaporconcentration above the liquid. T.lerefore, it depends not only on the flammability prop­erties and concentrations (both varnr and lic.uidj, but also on the vapor pressures of theindividual components of the solution to a marked degree.

:r'~'om the standpoint of fire hazard in the storage a"d handling: of flammable liquidsand fuels, more knOWledge is needed concerning the t:lammability properties of mulli­component, liquid mixtures. Th,= main goal of this work was to obtain a better under­standing of the flammability properties of complex fuel mb:tur"s - particularly hydro­carbon fuds, such as gasoline, jet fuels, and diesel fuels. The flammability propertieswhich wili be discussed are lower and uppe~' flammability limits, heat of combustion,stoichiometric conc~ntration(oxidati,m), flash point, and flammability index (1,2).

PRINCIPLES INVOLVED

Le Chatelier's rule governing the flammability limits of vapor mixtures (3) and theuseful rearrangement 0: this formula by Coward, et al. (4), have be~n known for a longtime. These equations, which have been summarized by Coward and Jones (5) and, morerecently, by Zabetakis (6), have been fauna to be applicahk to hydrocarbol"' vapor mix­tures (5-7) for both lower as well as upper flammability li,nits (5,7,8).

For liquid solutions it is first necessary to determine the vapor composition abovethe liquid before application ,of Le Chatelier's rule. Since hydrocarbon solutions do notdeviate appreciably from Raoult's law (6,9), a combination of Raoult's and Dalton's lawsgovern vapor pressure and c:omposition above a solution of two or m0re liqUids. Thistreatment has been :..,plied to low!:r flammability limits of liquid solutions containingmethyl ethyl ketone and tetrahydrofuran by Z:ilietakis, et al. (10). Zabetakis (6j also re­ported its application to flammability limits of two-component liquid h~rdrocl'rbon mix­ture,;. Empirical formul: .;, making .Ise of certain of thes·? concepts for calculating HashPOint3 of complex mixtures and blends, we!" reported by l'hiele (11), Butler, et al. (12),and Mullins (13).

As a continuati.:>n of previous work at this Laooratory on the interrebtions of the.i1ammability prope-ties of the n-alkanE~s in air (1,2), it was decided to extend some oftbe df'-ived reb.:iono.hips to both vaJor and liquid hydrocarbon mixtures, ~) as to be ableto pNdict overall flamma.bility properties fror... the properties and proportions of theindividual components.

1

2

LIMITATIONS

w. A. AFFENS

The present discussion will be limited to liquid and vapor hydrocarbon fuels, exclud­ing droplets and mists, in air at atmospheric prE3sure. It will be assumed that vapor isin equilibrium with the liquid at a given temperature and that vapor-air mixtures areuniform throughout. Except where otherwise stated, flammability ~imits, related prop­erties, and vapor pressures are at 25 cc.

CHOICE AND HANDLING OF LITERATURE DATA

As a rule, a generalized apP'.'oach will be taken, and symbols, rather than specificdata, will be employed. Multk .Jmponent solutions will be considered, but to illustratesome of the relationships, birary mixture systems will be given with solutions of n­a.lkanes in n-undecane as ex~,mples. Specific flammability data, where given, have beencalculated from averaged literature data by means of the relationS'lips which were de­scribed previously (1,2). Vapor pressure data and relationships are from standardsources (14-16).

FLAMMABILITY LIMI'rS OF VAPOR-AIR MIXTURES

Le Chatelier's rule (3) for a flammable vapor-air mixture of two or more compo­nents is

(1)

where X' is the actual vapor concentration. and L the concentration at the lower flam­mability limit (both expressed in percent by volume). The subscript i refers to theproperty in question of a general component, and A, B, etc., to that property of the spe­cific components, A, B, etc., respectively. The equation, which is a simple additiverelationship, states that for a mixture of gases to be at the lower flammability limit, thesum of the ratios of the actual concentration to that at the lower flammability limit foreach constituent is equal to unity. By algebraic rearrangement, Coward, Carpenter, andPayman (4) derived a useful form of Le Chatelier's rule,

(2)

Where N' is the mole fraction of a given fuel component in the total fuel vapor on an"air-free" basis, and the subscript M refers to the overall property of the mixture.Equation 2 expresses the lower flammability limit of the flammable vapor or gas mix­ture as a function of the sum of the ratios of the proportion of each component to that ofits lower flammability limit.

Analogous f'xpressions (5,7,8) can be used for the upper flammability limit u:

(3)

and

(4)

NRL REPORT 6617

ST .)ICHIOMETRIC CONCENTRATIONS OFVAPOR-AIR MIXTURES

3

A similar expression for stoichioJ:letric concentration (assuming complete combus­tion to carbon dioxide and water) can be derived with the aid of previously derived rela­tionships (1);

(5)

MOLAR BEAT OF COMBUSTION OFVAPOR-Am MIXTURES

Le Chatelier's rule, which was developed from experin.ental considerations (3), canalso be derived from molar heat of corobustion (llH",) concepts. It ca.. be shown readilyfrom energy considerations of a gas mixture that

(6)

But as has been discussed previously (1,2), the molar heat of combustion is proportionalto the reciprocal of the lower flammability limit. It has also been found that for hydro­carbons in general the constants of proportionality lU"e approximately equal (17). Thus,IlL can be substituted in Eq. (6), which, on canceling out the constants, becomes Eq. (2).This equation is Le Chatelier's rule.

VAPOR MIXTURES CONTAINING TWOFUEL COMPONENTS

For fuel-air mixtures containing only two fuel components, Eqs. (1) and (2) become

X,i,fLA t XB/I""]3 = 1

and

l/LM = NAILA + NEiLs'

On rearrangement. Eq. (7) becomes

(7)

(8)

(9)

Thus, for a lower limit mixture a plot of xg as a function of Xi. is a straight line (Fig. 1).Similarly, Eq. (8) may be rearranged, and by substitution oi (1 - N.e) for :'Ii. (the sua:. of::.he mole fractions is unity), Eq. (8) becomes

(10)

Equation (10) is, likewise, linear. Thus, ':or a two-component fuel vapor-air mixture,for which the individual flammability limits axe known constants, Eqs. (9) and (10) be­come simple linear equations which are useful for calculating or plotting concentrationsof limit mixtures.

Analogous eq'lations may be derived fo::- the other flammability properties.

Examination of Eqs. (2), (4), (5), and (6) show that they are in the form

FLAMMABLE REGION

NONFLAMP.lA8l.E REGION

W. A. AFFENS

'I09 --LA'O.392~.

as

oL~06tlZa;:: 05

~ !z8 0 4-~

!,,~

::r--:::,:---I ~,~0.1 0,2 03 0'" 0:556" 07

n-UNOeCANE CONCENTRIoTION.);S' (CY.. vtvl

Fig. 1 - Theoretical lower flarr.mabilitylimits of binary Euel vapor componentsof n-octane and n-undecane in air

(11)

or for binary mixtures

(12)

where <I> represents a generalized symbol for the various fJ~mmabilityproperties IlL,l/U, lies, and 6Hm • The generalized equations analogous to Eqs. (9) and (10) are

(13)

and

(14)

Thus, since ¢A and <l>B are fixed flammability properties of the individual pure fuel com­ponents, both Eqs. (13) and (14) are straight line functions. The generalized flamma­bility property functions of the mixture <l>M CEq. (14)) vary between the two extremes ofthe two components <l>A and <l>B' as is shown in Fig. 2. The magnitude of the variationsdiffers, depending on the given properties. It would be useful to be able to compare thesesolution effects vs concentration for flammability properties of Wll1el;" dili:?rent magni­tudes (for example, lower compared to upper flammability limits. both vs concentration)

NRL REPORT 6617 5

,

~ 1.21:_-------------:::;

~--

>­....

j o8t ---~....::!·~IIC:;s~...~-----------1

5" O.4__~'____ t'·"MOt.. _

t I I I0:' 0"2 0"3 0.4 "0.5 06 G7 08 019 ,

II-CII H204 CONCENTRATION (MOLE FR:ACTluN.Ne) _ B

Fig. Z. - Theoretical flammability limits of binary fuc.lvapor mixtures of n-octane and n-=decane in air

or of different units (such as heat of combustion compared to lower flamm2.bility limits)or even against other physical properties. This comparison is possible by inventing adimensionless, normalizing function Z for this purpose, where

(15)

Z represents the fraction of change (for a given prop<'rty) of t..'l.e mixture from A, relativeto the total range between tte two components. Thus, if Nil = 0, z = 0, and if :>i = 1,Z = 1. By substitution of <l>M from Eq. (14), Eq. (15) becomes

Z = Ni. (16)

This relationship means that z, a colligative prop<lrty of the fuel vapor, is a function ofits concentration. The Z-fundion will be found to be more useful in the discussion onliquid solutions which will follow.

FLAMMABILITY INDEX OF VAPOR-AIR MIXTURES

Another useful ,:lammability property, which can be measured readily for a givenfuel vapor-air mixtu;:e, has been referred to by various terms: "percent explosiveness,""explosivity," or "percent of the lower explosive limit" (2,18). This property, which nasbeen discussed previously (2), is temperature-dependent, although it is usually expressedat 125 of" It is actually a me<.!.sure of potential flammability hazard rather than "~~­

plosiveness" as such. For this r·:U)on the term "flammability ii1dex" is suggested asmore descriptive of this pl"Operty and will be used here. Regardless of the name givento it, this property i::; an expresshm of the fraction, or ratio, of the actual concentrationof fuel vapor to that at its lower flammability Bmit. T:,e fractions may be expressed asa decimal or percentage of volum~concentrations, b-;t the former, which is based onunity rather than 100, is simple aile will be used as 2. basis of flammability units in L!],epresent discussion. If x~ is the volume concentra~iopof fuel vapor in equilibrium withthe liquid at a given ti:mperat\lre t, and li L, is tile lower flammability Unit (;; v/v),then the flammability index E t is defined as

E, = X~t1..t - (17)

6 W. A. AFFENS

Thus, if the fuel vapor concp.ntration in a given air-fuel mixture is equal to the concen­trations at the lower flammability limit (x~ ~ L t ), the flammability index is unity (E t ~ 1).If E, is equal to or greater than unity, the mixture is flammable, provided it is not solarge as to exc,=ed the uppe. flammability value. If E

tis less than unity, the mixture is

r,onflammable. l~ Chatelier's rule CEq. (1)) is, tl11arefore, a sum of ratios which are'lctually flammability indices. Thus, Eq. (1) becomes

(18)

TherefGre, the flammability index of a mixture is equal to the sum of the indices of thecomponents.

From Eq. (18) it can be shown that lower-limit air miAi:n-es, if mixed in any propor­ti,'ns, will give rise to mixtures which are also at their lower limits (5).

EFFECT OF TEMPERATURE ON FLAM;\'lABILITYLIMITS OF VAPOR-AIR MIXTURES

Flammability limits of hydrocarbons do not vary signiiicantly wit:1 moderate changesin temperature (5), but over a wide temperature range a correction fo;:" this variationmust be made. Flammability limits of a hydrocarbon vapor-air mixture decrease ap­prOXimately linearly with increasing temperature (1,2,5,6). The equation given byZabetakis (6) will be used and can be put in the form

LtlL ~ 1.02 - O.000721t , (19)

where L and Lt are the lower flammability limits at 25 °c and t "C, respectively. It willb(' convenient to write Eq. (19) in the form

where

QL,

Q ~ 1.02 - O.000721t .

(20)

(21)

The F1t!estion of the flammability limits of a multicomponent vapcr-air limit mixtureis treatNI h:J 'l.;)phr;;'~icr: of the ~emperaturecQrrection factor· (Eq. (20)) to the rearrangedLe Chateher's ':ormula (Eq. (2)). At any tempcrat:.lre t, Eq. (2) becomes

Substituting the value of L t from Eq. (20) for each L t in Eq. (22) and rearranging,

(23)

By substituting 1~ from Eq. (2) for the right side of Eq. (23),

which on rearranging becomes

~t~: Q.

(24)

(25)

NRL REPORT 6617

Substituting the value of Q from Eq. (21), Eq. (25) becomes

~t'~ = 1.02 - 0.::lOOi2lt

7

(26)

Equation (26) is similar to Eq. (19); therefore, the flammability limits of a mixturevary with temperature in the same way as a single componed fuel-air mixture.

The same relationships which have been demonstrated for lower flammahility limitsalso apply to upper limits (5,7,8).

VAPOR COMPOSITION ABOVE THE LIQUID SOLUTION

Since hydrocarbon solutions obey Raoult's law (6,9), the vapor composition above asolution of hydrocarbol's may be de.termined by a combination of Dalton's and Raoult'slaws, i.e.,

(27)

'.vhere Ni has been previously defined tEq. (2», Pi is the vapor pressure (atmospheres)of the pure liq~id component i, Ni is its liquid concentrati':ln (:?:~ll; ~r~ction), and thesummation term (denominator) is equal to the total vapor pressure.

The conyentional textbook example (Fig. 3) of this ideal solution relationship lor atVlo-compcnent liquid solution usually plots the partial and total vapor pressures againstconcentration for two liquids of relatively similar vapor pressure. The top line (totalpressure) is almost horizontal, forming what is approximately a rectangle wi.th relativelyequivalent diagonals representing the partial pressures of the individual solvents. In thecase of binary liquid mixtures of two components of more widely different vapor pres­sures, the general shape of the graph is highly distorted from that of the textbook case,as is shown in Fig. 4 for <l solution of n-octane and n -undeca.\,.e. The graph demon­strates that the total vapor pl"eSSUre of a liquid solution of volatUe and relatively non­volatile components is approximately eqUivalent to the partia.1 pressure of the morevolatile constituents. This relationsJ,ip has an importallt bearing on vapor compositionand the flammability properties of liquid solutions.

FLAMMABILITY LIMITS OF LIQUID SOLUTIONS

By substitution of t.'le right side of Eq. (27) for N{, Eq. (2) becomes the equivalentequations for liquid solutions:

(28)

or for a binary solution

(29)

This equation is plotted in Fig. 5 for three separate solutions of n-hexane, n-octane, andn-decane, each in n-undecane at 25°C. The curves in Fig. 5 also demonstrate t.~e rela­tively large L'lfluence of the more volatile constituent. Analogous equations apply to up­per flammability limits, stoichiOmetric concentrations, and molar heats of combustion.

8 W. A. AFFENS

280,--------------------------.........,

200

'":I:

f~ 160wor::0<0OJ.,g: 120a:o"";;

PARTIAL VAPOR PRESSURE OF A [PA')

PARTIAL VAPOR PRESSURE OF B (PB~-""

ao

40

Fig. 3 - Vapor pressure vs concentrationof ideal binary liquid solution

PARTIAL VAFOR PRESSURE

OF, n-UN,DECANE (ps')

°0~-::O:':.I~"'O!'O.2c='=;O!=.~;==:O:.=.4;===:O;;:.5~::;O~.6;=::;O;:;.7~:;Q.~6;==O::r.9;:':~,n -UIllECANE CONCENTRATION, NS (MOLE FRACTION OF TOTAL FUEL)~

.... n - OCTANE OONCENTRATlON, NA (.IAOLE FRACTION OF TOTAL FUEL)

14' 0.9 o.a 0,7 ~6 o~ 04 03 02 0;' ~

- '-PA=13.92mm Hg !~12

]'0wa:::0:;;6wa:0-

I}

Fig. 4 - Vapor pressure vs concentrationof binary liquid solutions of n-octane andn-undecane at 2S·C

?'RL REPORT 6617

__ n- en Hzrh2 CONCE:NTF?ATION, NA (MOLE FR"CTlQN OF" TOTAL f='uEU

;-/=309==0:ie==o~.7==0l:.6=j05=:0J:~=~CI3=~0[2=lO.'-' ----'j0/2",

~ 1,/..~ 1,0

!::1" n'B

~ G~=IO~

H IO,50--:0L.I_..J0.L?-O:-'3:'---O:':.~'---:O":"--='C.-:C-6---'0"'7:'---:0"=.e--=0'="9---"

n-uNoEcANE COW;e:NiRAT1QN. NB {~~OI..E FR,ClCTION OF iOTt..L FUEL)-

Fig. 5 - Theoretical lcwer flammabilitylimit>. of binary liquid solutions of n­alkanes and n-undecane in air

BINARY liQUID SOLUTIONS

The generalized functior, ~ (analogous to Eq. (14) for vapor mixtures) for a liquidsolution is

9

and for a binary solution

¢M ~ (NAPA<I>A + NBPB~)t1'lAPA + NBPE) .

Substituting the right side of Eq. (31) for <l>M in Eq. (15) and rearranging,

(30)

(31)

(32)

After expressing the reciprocal of Z as a function of the reciprocal of NB ane! substituting(1 - NB ) for NA> Eq. (32) becomes

(33)

Thus, 1/2 is a linear function of 1/1'."B (at constant temperature) with slope PA/Pe and in­tercept (PB- PA)/PBo Theoretical plots of ;:: vs NB and lIZ vs lINe are given in Figs. 6and 7, respectively, for binary liquid solutions of n-alkanes in n-unde~ane. In addition,a reciprocal type plot for some limited experimental data of Zabetakis, Cooper, andFurno (10) is given in Fig. 8. The graphs of both Figs. 7 and 8 are linear.

FLAMMABILITY INDEX OF LIQUID SOLUTIONS

The equilibrium vapor concentration in percent by volume x; of a particular compo­nent of a liquid solution in the vapor space above the liquid is

Xi " 100 Ni Pi . (34)

10 w. A. AFFENS

Fig. 6 - Theoretical Z valuesof binary liquid solutions of n­alkanes in n-undecane

15,,,--------,--------------,------------,

I.

,'7

I

8--5 7 9 II 13 IS

n-CIl Ht4 CONCENTRATICN (MOLE FRt.':TION. Ne f'

n=12

Fig. 7 - Reciprocal Z values vs reciprocal concentrationsof binary liquid solutions of n-alkanes in air

where p. is in atmospheres. By substitution of the value of Xi from Eq. (34), Eq. (17)(at temp~rature t) becomes

Similarly, substituting the value of Eit from Eq: (35) in Eq. (18),

But the flammabi.lty index of the vapors above a pure liquid component E~ t is

(35)

(36)

(37)

NRL REPORT 6b17 11

7lI

38~I

341

:lliZ

2r18

1.4

1I 148-

2.2 2.6 3 3.4 ;'6 C,2TOLU!.NE CONt:EN'TRATtOr(' {MOL£: FRACTION, Nsf'

4.6_0

Fig. 8 - Reciprocal Z values vs reciprocal concentrationsof binary liquid solutions of THF and MEK in toluene fromexperimental data of Zabetakis, Cooper, and Furno (10)

Substituting E~. for its eq,uivalent 011 the right side of Eq. (36),

For a binary solution

which on substituting (1 - NB) for NA becomes

EM. = E~. - (E~t - ~.) Na .

(38)

(39)

(40)

Equation (40) is linear, as is shown in Fig. 9, which is a plot of the flammability indices(at 125 of, or 51.7°C) of several binary solutions of n -alkanes in n-undecane vs the con­centration of n-undecane. The temperature is that of a standard test methc·<J (18). Bothvapor pressure and flammability limits were calculated at 125 OF to obtam the flamm:;;,­bili.ty indices. The horizontal line at F"M equal to unity delineates flammable from non­flammable solutions, and the n-alkane concentrations (NA ) needed to make n-undecaneflammable at 125 OF are indicated. A plot of NA vs carbon number is indicated in Fig. 10.The two figures demonstrate that at higher vapor pressure, increasingly small concen­trations of volatile components are required to make the relatively nonvolatile n -u..:decaneflammable.

FLASH POINT

The concepts and meanings of flash point have been discussed previously (1). Forthese purposes we will accept the previous definition of flash point as that temperature

14~

12r-

:? 10~

12 W. A. AFFENS

+- n-ALKANE CClIlCENTRATlON, r>:A(MOLE FRACTION

I 0.9 OS 07 OS OS 0.4 0.3

1.6

"::! 1.4

xU.J

~ l2

SLO :f--",W=,G',,-i'b><:~,,:-A_S_LE= -"'~:-"'-'-'-- "'lo;_-T~~as NONFU.~·1MASLE

io.s- REGIOII.<l

~05-

04[ _o 0.1 0.2 0:;' ·---::"0.-='"4-,,!,0.S,,--"'0.S,.....-,0""'.7,---,0""'.S,......,0"".9--'1

"-UNDECANE CONCENTRATION, NS(MOL.E :=RACTION fY' TOTAL FUEL.)"

Fig. 9 - Flammability indices (explosive­ness) of b.nary liquid solutions of n-alkanesand n-undecane in air at lZS'F (S1.7·C)

-Ir 0.16:xl -0.06~ 0.02z

If"'" J2L ·, I'

% w ~ ~ ~ ~ M ~ M ~ In - ALKANE CONCENTRATION, NA (MOLE FRACTION OF TOTAL FUEL J--+

Fig. 10 - Flanunable concentratiuns vscarbon number of binary liquid solutionsof n-alkanes and n-undecane in air at125· F (51. 7'C)

at which the vapor pressure of the fuel giv..s an equilibrium concentration which is theconcentration at the lower fJ.z..r:amability limit. There are actually two flash point tem­peratures (1,2,6), i.e., a lower flash point t L and an upper flash pobt t u ' The abovedefinition defines t L ; the upper flash point t u may be defined in a similar manner, byupper flammability limit. These values are sometimes referred to as "lower and upperflammability limit temperatures." These concepts may be expressed graphically (1,2,6)as the intersections of the vapor pressure and the two flammability limit curves, bothplotted against temperatu::-e.

For solutions of two or more flammable liquids the problem of defining these con­-::epts is more comple,;::. For solutions the lower flash point temper2.ture is that temper­ature at which the vapor pressure of each of the flammable, volatile components is such

NRL REPORT 6617 13

that the composition of the vapor-air mixture above the liquid is ilammable, in accord­<::lce with Le Chatelier's r\lle. In the discussion up to this point the various flamma­bility functions were assumed to iJe at constant temperature, and (except for flam~a­bility ;ndex) this temperature was 25°C. The concept of flash point bringS in temperatureas an additional nriable.

For a flar.:J.mable, multicomponent liquid solution at its flash point temperature t LMthe derived form of Le Chatelier's rule (Eq. (35» becomes

(41)

where Pit and Lit are the vapor pressure and lower flammability limit value", respec­tively, of each component at the flash point temperature of the solution.

From Eq. (19)

(42)

where L i is the lower flammability limit of a given fuel lOomponent at 25°C. Substitutingthe right side of Eq. (42) for L i t in Eq. (41),

(43)

which on rearranging becomes

(44)

For a two-component fuel Eq. (44) becomes

(45)

For a solution of pure hydrocarbon components of known concentrations" i and assumingthat tae lower flammability limits of each fuel component L i at 25°C are also known, itis then necessary to k.'lOW the vapor-pressure-vs-temperature functions of each compo­nent Pi t in order to solve Eq. (44), or Eq. (45), for the flash point temperature t LM "

Vapor-pressure-vs-temperature data for the hydrocarbons are readily available (14-161.For purposes of this work the familiar Antoine type Eq. (15) was foum! to be a useful andgood approximation:

(46)

where b i and Mi are constants, varying from hydrocarbon to hydrocarbon. In general, avalue of 230 was found to be a good approximation for C for the n-alkanes. The valuesof b i and Mi may be estimated from the literature (14-16). With values of b i and Miknown for each fuel component, solution of Eq. (44) for t LM can be attempted with the aidof Eq. (46). For approximate purposes this solution can be done graphically by the fol­lowing eleml::ntaTy treatment.

From Eq. (44-i, let

(47)

14 W. A. AFFENS

The solution involves finding its roots (Y = 0) which can be done graphkally by plotting Yvs t LM , at various values of t L..,. For ~ach t LM the value of Pit in Eq. (46) is deter­mined and.substituted in Eq. (47) for each component, which yields the solution for Y.This procedure was done for three separate binary solutions of n-hexane, n-octane, andn-decane, respectively, in n-undecane. Tte results are shown in Fig. 11. This figurealso illustrates the large influence of higher volatile compone.ats in a flammable liquidsolution.

Fig. 11 - Theoretical lower flash-pointtemperatures of binary liquid solution.s ofn-alkanes and n-undecane in air

The combination of Eqs. (44) and (46) (eliminating Pit i eh-preSSes t LM as a functionof Li , Mi , b i , and :-Ii' It would be useful to be able to express tL'l as a function of theflash points of the individual pure components (tLi ) rather than that of the lower limits.This transformation was done by algebraic manipulation, which is summarized here.

For a pure liquid hydrocarbon at its flash point t Li , Eq. (43) becomes, on re­arranging,

where p~ t is the vapor pressure at t Li • Soh:ion of Eq. (48) for Li gives

L i = 100 p~t/(1.02 - 0.000721 t Li ) .

(48)

(49)

Substitution of ~ and Q i for the temperature terms in Eqs. (43) and (49), respectively,gives

(50)

and(51)

Substituting the value of Li from Eq. (51) in Eq. (50) and simplifying,

where

and

NRL REPORT 6617

Qi = 1. 02 - O. 0007:11 t L , '

Ot.! = 1. 02 - O. OOOi 21 t LM '

15

(52)

(53)

(54)

(55)

(46)

We now have a combination of five equations (Eqs. (46), (52)-(55)) by which we canexpress the lower flash point of the solution (tLM ) as a function of the flash points of thecomponents Ct L ;). By algebraic manipulation these five equations may be combined intoa single equation. Subtraction of Eq. (55) from Eq. (46) gives

(56)

(57)

(58)

where T' = t + 230.

EqU:ltio!l (52) may be rewritten as

~ [CQi/QM)(Pit/P~t)N;] = 1.

Substituting for the ratios Qi 1'4" from Eqs. (53) and (54) and Pi t"P~ t from the e>..-ponen­tial forol of Eq. (56), and using T' for temperature, Eg. (57) becomes

~ ([C1642-T{i):'I;lC1642 -TiM)]" IOMi(T{;-Ti.,,/T{iTLM1} = 1.

Th'i! values in Fig. 11 were calculated by this equation and the results <;.greed withthe graphical solution.

SUMMARY AND CONCLUSIONS

A theoretical study has been made of flammability properties of vapor and liquidmulticomponent fuel mixtures in air, and mathematic:u equations have been derived whichexpress these findings. The most important conclusion demonstr:ated by the derivedequations is that a very small amount of a highly volatile contaminant in a rElatively non­flammable fuel may make it flammable. Although precise relationships h2ve belm derivedabout relatively simple solutions of pure hydrocarbons, the concepts they imply are ap­plicable to more complex mixtures, such as gasoline, jet and diesel fuels, and the like.

It would be interesting to investigate solutions which deviate appreciably fromRaoult's law, especicll.y those which might form azeotropes. Solutions with, for exam­ple, flash points below that of the lowest component would be of particular interest.

Experimental work is under way to test the theoretical equations.

16 W. A. AFFENS

REFERENCES

1. Affens, W.A., J. Chern. Eng. Data 11:197 (1966)

2. Affens, W.A., "Flammability Properties of Hydrocarbon Fuels, Part 1 - Interrela­tions of Flammability Properties of n-Alkanes in Air," NRL Report 6270, [\/f.ay 25,1965

3. Le Chatelier, H., Ann. Mines 19:388 (1891)

4. Coward, H.F., Carpenter, C.W., and Payman, W., J. Chern. Soc. 115:27 (1919)

5. Coward, H.F. and Jones, G.W., U.S. Bur. Mines, Bulletin 503,1952

6. Zabetakis, M.G., U.S. Bur. Mines, Bulletin 627, 1965

7. Payman, W., J. Chern. Soc. 115:1436, J.446 (1919)

e. Jones, G.W., U.S. Bur. Mines Tech. Paper 450 (19291

9. MeUan, 1., Industrial Solvents, 2nd ed., New York:Rei.:1hold, 1950

10. Zabetakis, M.G., Cooper, J.C., and Furno, A.L., U.S. Bur. MJ'les, Rept. of Investi­gation 6048, 1962

11. Thiele, E.W., Ind. Eng. Chem. 19:259 (1927)

12. Butler, RM., Cooke, G.M., Lukk, G.G., and Jameson, B.G., Ind. Eng. Chern. 48:808(1956)

13. Mullins, B.P., "Explosions, Detonations, Flammability and Ignition," Part II, Chap.11, New York:Pergamon Press, 1959

14. Dreisbach, RR, Advan. Chern. Ser. 22, 1959

15. Jordan, T.E., "Vapor Pressure of Organic Compounds," New York:Interscience,1954

16. American Institute 01 Physics Handbook, 2nd ed., New York:McGraw-Hill, 1963

17. Fenn, J.E., Ind. Eng. Chem. 43:2865 (1951)

18. Federal Test Method Standard 791a, Method 1151.1, Dec. 30, 1961, "ExplosiveVapors in Boiler Fuel Oil"

DOCUMENT CONTROL DATA - R&D

,O~~~,ii~i~ry r',~o:: 'U~cl~~'''i:;d''O'_1

, ;~~~~~ILITY PROPERTIES OF HYDROCARBON FUELS, PART 3 - FLAM~BILITY PROPERTIES OF HYDROCARBON SOLUTIONS IN AIR I

.:.. OC.SCR1F"TI 11'£ NOTES rT}'pl!' of ,....port dnd inclw:i~',· darr::;)

This is an interim report; work is continuing on ~::.:e;.....o;:.p:;.r:;.o;:.b;:.le:.:m;;:';"' ---I~ AU' I-lO~(~'J (Fint nllme:, micdlr initial. [ilst naml'")

Wilbur A. Aliens

c· REPOR,. ~".TE:

November 21, 1967~.I_ CONTRAC'T OR GR"N1" NO

NRL Problem COl-03b. P~OJECT NO.

SROOl-06-02-U600NRL Report 6617

RR 010-01-44-58509r. OT~£Q REPO"lT NOI';', r.... tW oth~,. ""mb~r:.. ,bar ma~'LJr:- a,.... ":mrod

rht~ ",p~rt) .

d.

,c, OISTQ.tSU;\O"" S""''TE.MEN''

This document has been approved for public release and sale; its distribution isunlimited.

11. SUPs;;JLE:MEN'rARV NOTES

D~p~t~en1,corffieCN~ary(Office of NavalResearch and Navy Ship Systems Com­mand), Washir.gton, D.C. 20360

Previous work on the interrelatj"~sof the flammability properties of n­

alkanes in air nave been extended to both vapor and liquid fuel mixtures. Based onthe application of Raoult's and Dalton's laws governing vapor pressure and compo­sition above a solution of two or more liquid hydrocarbons to Le Chatelier'srulegoverning the flammability limits of vapor mixtures, eCluC'.tions have been derivedwhich make i.t possible to predict overall flammability properties of mixtures fromthe properties and proportions of the individual components. The flammabilityproperties which were studied include; lower and upper flammability limits, heatof combustion, stoichiometric concentratiQ!l, flash p~int, and flammability iL"ldex("explosiveness"). The derived ectuations demonstrate, quantitatively, why vaporpressure of individual constituents plays II more important role than concentrationon the overall flammability properties of liquid hydrocarbon solutions, and L'1at avery small amount of a highly volatile contaminant in a relatively nonflammablefuel may make it flammable.

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~OL.E: W" ~O'-E WT ~OLt: .. "Hydrocarbon fuelsFlammabilityFlammability limitsFlash point IFlammability index

IiI

n-AlkanesJet fuels IVapor pressure of fuel mixture

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Liquid fuel solutionsFuel vapor mixtures

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