using chetah to estimate lower flammable limit, minimum ignition energy, and other flammability...

Using CHETAH to Estimate Lower Flammable Limit

Minimum Ignition Energy and Other Flammability

ParametersLaurence G Brittona and Benjamin Keith Harrisonb

aAIChE Fellow Charleston WV 25314 lbrittonconsultsuddenlinknet (for correspondence)bDepartment of Chemical and Biomolecular Engineering University of South Alabama Mobile AL 36688

Published online 8 November 2014 in Wiley Online Library (wileyonlinelibrarycom) DOI 101002prs11721

Britton discovered that with increased ldquonet heat ofoxidationrdquo (DHox) the maximum flame temperatures of CHand CHO fuels in air increase linearly while flame tempera-tures at the lower flammable limit (LFL) decrease linearlyMaximum flame temperature is a major factor determiningthe combustion rate of optimum fuel-air mixtures and rela-tionships were found between DHox and ldquooptimizedrdquo flam-mability parameters such as minimum ignition energy TheLFL is the fuel concentration needed to attain the lower limitflame temperature since less fuel is needed to attain asmaller flame temperature the LFL varies inversely withDHox Simple expressions derived between DHox and parame-ters commonly used in process safety were previously pub-lished in this journal The commercially available computerprogram ldquoCHETAHTMrdquo now solves these expressions and out-puts the flammability parameters plus the internally gener-ated thermodynamic data used in the solutions This articleupdates the original expressions together with new findingsand explanatory material VC 2014 American Institute of Chemical

Engineers Process Saf Prog 33 314ndash328 2014

Keywords fire and explosion analysis hazards evaluationrisk assessment safety management incident investigations

INTRODUCTION

The ASTM E-27 Committeersquos ldquoCHETAHTMrdquo program [1] isnormally used to address chemical instability and performindustrially useful thermodynamic calculations such as theheat of reaction A recently added feature uses calculated heatsof combustion plus ldquoBrittonrsquos Methodrdquo [2] to estimate flamma-bility parameters for fuels burning to CO2 plus H2O The esti-mated parameters are intended for general guidance and not ameans of saving costs at the expense of due diligence CHE-TAH is discussed in greater detail in the Appendix

Applications to gases other than CH and CHO are limitedprimarily by a lack of reliable experimental data plusongoing disparities between definitions and test methodsCHETAH currently treats CHN and CHON fuels as membersof the CHO series neglecting the formation of nitrogen com-bustion product Application to nitro-compounds is allowedfor research reasons but the practical application of derived

parameters such as lower flammable limit (LFL) is discour-aged LFL and limit flame temperature estimates are permit-ted for some organo-chlorides but these are based on aseparate analysis using vinyl chloride rather than methanereference gas

This article reviews CHETAHrsquos ldquoflammabilityrdquo feature withemphasis on CH and CHO fuels Previously published corre-lations are updated using more precise heat of combustiondata Brittonrsquos LFL estimation method is explained in moredetail and compared with a modified estimation method plusa new approach using limit flame temperatures The threemethods are compared with Catoire and Naudetrsquos [3] empiri-cal correlation Itrsquos shown that both quenching distance andmaximum experimental safe gap (MESG) decrease linearly asDHox increases Since the fundamental burning velocity val-ues tabulated in NFPA 68 [4] are considered too high a newdataset and predictive equation are presented Possible CHE-TAH improvements are discussed including estimates for fuelmixtures and adding a new routine for calculating adiabaticflame temperatures

HEAT OF OXIDATION

Nearly 100 years ago it was observed by Thornton [5]that the molar gross heat of combustion per atom of oxygenconsumed is roughly constant at 53 kcal except for nitro-compounds such as nitrobenzene Figure 1 from Britton andFrurip [6] shows ldquonet heat of combustionrdquo (DHc) for a set ofgaseous fuels plotted against the ldquonumber of oxygen mole-cules needed to completely combust one molecule of fuelrdquoThe latter is commonly termed the ldquostoichiometric ratiordquo (S)The gradient (DHcS) depends on whether the fitted line isforced through zero but in both cases is similar to the valuehistorically used to estimate the total heat released by com-bustion of organic material namely 100 kcalmol of molecu-lar oxygen consumed (418 kJmol or 131 MJkg of oxygen)The constancy of heat released by common organic materialsper unit mass of oxygen consumed has long been known asldquoThorntonrsquos Rulerdquo

The net heat of combustion per mole of O2 consumedcan be termed the ldquonet heat of oxidationrdquo DHox 5 DHcSBoth DHc and DHox are negative (exothermic) quantitiesalthough for simplicity the negative signs are usually omittedin this article It was recently discovered by Britton [2] thatDHox is not constant for organic gases but is instead anVC 2014 American Institute of Chemical Engineers

314 December 2014 Process Safety Progress (Vol33 No4)

important thermodynamic variable governing flame tempera-ture and other combustion parameters As discussed in theAppendix ASTMrsquos CHETAH Program [1] uses ldquoBrittonrsquos Meth-odrdquo to estimate a series of such parameters from DHox Forcommon hydrocarbon gases DHox varies from 9589 kcalmol for methane to 12004 kcalmol for acetylene Most CHOfuels have values in the same range although higher valuesapply to unstable materials such as peracetic acid Notableexceptions among CHON fuels are nitrated compounds suchas ethyl nitrate (DHox 169 kcalmol) and nitromethane(DHox 205 kcalmol) If Brittonrsquos Method is applied tonitrated compounds using the same approach used for CHOfuels LFL values are underestimated The error increaseswith the degree of nitration so is most pronounced for lowmolecular weight compounds such as nitromethane Thorn-ton [5] concluded that the oxygen contained in nitro-compounds takes no part in combustion (perhaps due to itsassociation with nitrogen instead of carbon) and suggestedwhat amounts to neglecting the bound oxygen in the mole-cule when calculating ldquoSrdquo DHox has been found to have sep-arate applications in assessing instability hazards of unstableorganic materials such as peroxides and nitrated compounds[6]

The ldquonet heat of oxidationrdquo (DHox 5 DHcS) is a measureof the tendency of a fuel to react with oxygen It also pro-vides a measure of the ldquoreactivityrdquo of the fuel via its enthalpyof formation This is because the numerator (net heat ofcombustion) includes release of bond energy (such as CCand CBC bonds) while the denominator (S) normalizes theheat of combustion according to the oxygen needed strictlyfor combustion to products such as CO2 plus H2O Forhydrocarbons that decompose explosively in the absence ofoxidant DHox also provides a measure of instability Forexample the minimum pressure at which the gas will propa-gate a decomposition flame in pipe of a given diametershould decrease as DHox increases

In the case of CHN and CHON fuels the heat of combus-tion accounts for the heat released by forming the strongNBN bonds in the nitrogen product from weaker bonds inthe fuel Functional isomers with identical stoichiometricreactions and ldquoSrdquo values can have very different DHox valuesowing to differences in bond energy An example is ethyleneoxide versus its functional isomer acetaldehyde DHox is aneasily calculated thermodynamic variable that despite Thorn-

tonrsquos Rule provides a fairly wide scale of heat release fromabout 96 to more than 120 kcal per mole of oxygen con-sumed during combustion For CH fuels larger DHox valuesreflect larger quantities of heat available to activate the stoi-chiometric proportion of oxygen molecules As shown in thenext section it also reflects a higher maximum flame temper-ature For CHO fuels the situation is more complex becauseO atoms in the fuel decrease ldquoSrdquo and hence elevate DHox

independent of the heat available to activate oxygen mole-cules However the complicating effects of bound oxygenare mostly exhibited by the first members of homologousseries such as formaldehyde and methanol

This article includes many ldquofirst members of homologousseriesrdquo Such compounds are widely used in chemical proc-esses However the exaggerated effect of the functionalgroup tends to cause atypical flammability behavior whichmakes it more difficult to estimate commonly used parame-ters such as LFL and burning velocity

MAXIMUM ADIABATIC FLAME TEMPERATURE

Figure 2 shows the maximum adiabatic flame temperature(Tfmax) of CH and CHO fuels in air plotted against net heatsof oxidation (DHox) The graph has been updated versusBritton (2002a) using CHETAH-generated DHox rather thanrounded-off values calculated from net heats of combustionpublished by Kuchta [7] The ldquoCHOrdquo set (lower line) includeshydrogen cyanide but insufficient Tfmax data were calculatedto determine if other CHN or CHON fuels follow the sametrend as CHO For each fuel Tfmax values at 298 K were cal-culated for a series of equivalence ratios between 08 and 13using the Gordon and McBride [8] chemical equilibrium pro-gram Quadratic interpolation was then used to find thepeak Tfmax for each fuel at its ldquooptimumrdquo concentration [2]Both fuel sets show a linear relationship between Tfmax andDHox For equal DHox values CH flame temperatures areabout 100 K higher than CHO flame temperatures

The three hydrocarbon flame temperatures falling slightlyabove and parallel to the trend line belong to toluene ben-zene and styrene all of which are aromatics with positiveheats of formation Methanersquos flame temperature is belowthe hydrocarbon trend line but the first members of homolo-gous series often display anomalous behavior Methane has

Figure 2 Dependence of maximum adiabatic flame temper-ature on net heat of oxidation [Color figure can be viewedin the online issue which is available at wileyonlineli-brarycom]

Figure 1 Modified Thornton plot [6] [Color figure can beviewed in the online issue which is available at wileyonli-nelibrarycom]

Process Safety Progress (Vol33 No4) Published on behalf of the AIChE DOI 101002prs December 2014 315

the lowest DHox of any hydrocarbon (9589 kcalmol) not farabove graphite (9405 kcalmol) Lacking CAC bonds itrsquoshighly resistant to oxidation and its reaction requires a differ-ent kinetic scheme than other alkanes However since themaximum deviations are within 1 of the absolute valuesthe hydrocarbon correlation is remarkably good Hydrocar-bon combustion at high temperatures involves a radical poolwhose growth rate becomes positive above a characteristicldquoignition temperaturerdquo (Tign) which is several hundred Kbelow Tfmax The difference between Tfmax and Tign widenswith increased DHox so the latter should reflect faster growthof the radical pool and faster reaction

The flame temperatures of formaldehyde and methanolare significantly less than predicted by the CHO trend lineand are excluded from the fit Each compound is the firstmember of an homologous series and the HCO and CAOHfunctional groups represent abnormally large proportions ofoxygen Consequently the stoichiometric ratios are verysmall (S 5 10 and 15 respectively) Since DHox 5 DHcSsmall ldquoSrdquo values can result in relatively large heats of oxida-tion that are inappropriate for some applications such as thisone CHETAH could be modified to avoid problems with theatypical behavior of first members of homologous series

LOWEST MINIMUM IGNITION ENERGY

Figure 3 shows the dependence of lowest minimum igni-tion energy (LMIE) on DHox The graph has been updatedfrom the original reference [2] using more precise net heat ofoxidation data Methane is shown as having the largest LMIEof any hydrocarbon and ethylene is the major outlier Theresilience of methane to ignition can be explained by thenearly 10 kcal of additional energy needed to break the firstCAH bond relative to the other CAH bonds in the moleculeor in other hydrocarbons In view of the disparate flame tem-perature (Tfmax) lines shown in Figure 2 it was originallyexpected that both fundamental burning velocity and LMIEdata for CH and CHO fuels would fall on different curvesNeither proposition can yet be supported by reliable testdata and methane has the largest LMIE of any CH or CHOfuel for which reliable test data are available Itrsquos shown laterthat burning velocity data for CH and CHO fuels are corre-lated by a single curve with values scattered in a bandaround the curve with ethylene as the major outlier

Recent European tests have generally indicated largerLMIE values than those shown in Figure 3 For exampleEckhoff et al [9] concluded that the ldquoclassicrdquo US Bureau ofMinesrsquo LMIE result of 024 mJ for propane was obtainedusing an excessively low ignition probability and that thecorrect value is twice as high Their test apparatus neitherconformed to the current ASTM E582 [10] standard nor withany ldquoclassicrdquo apparatus design It used a moving electrodesystem originally designed for dust cloud ignition testing andwhich couldnrsquot produce sparks with the reproducibilityneeded for gas ignition energy measurement The authorsoverlooked an extensive ignition energy study by Calcoteet al [11] which confirmed the US Bureau of Minesrsquo LMIEfor propane (024 mJ) and graphically showed how its MIEdecreases with decreased capacitance at any given gaplength For stoichiometric propane in air the smallest MIEwith a 26-mm gap was found at a capacitance of 77 pFwhich is close to the minimum practical value of about 6 pFfor any two-electrode test system Optimum capacitanceswere far below the 19ndash64 pF range investigated by Eckhoffet al [9] The importance of small capacitance was empha-sized by Britton [12] with reference to Movilliat and Giltaire[13] who showed that the MIEs of hydrogen and methaneboth decrease as capacitance and electrode tip diameter aredecreased Corona discharges limit the use of very small tip

diameters because as storage capacitance decreases a highervoltage must be used to store the same energy

Itrsquos probably unnecessary to report test data at low igni-tion probability as discussed by Eckhoff et al [9] If theflanges are removed from the electrodes the measured LMIEwill decrease by a factor up to about two Eckhoff et al [9]used glass flanged electrodes and this would help explaintheir high LMIE result for propane (048 versus 024 mJ) Itseems unlikely that the US Bureau of Minesrsquo LMIE resultswere obtained with flanges installed even using the little-known plastic version of their test vessel Quenching dis-tance has little practical importance nowadays ASTM E582[10] needs to be amended so that flanges are no longerrequired when measuring minimum ignition energies

Another source of error is exposure of high voltage insu-lation to humid air Early work was done in a large box heldbelow 10 relative humidity With the advent of Teflon insu-lation this precaution became avoidable provided the com-bustion air was thoroughly dried and the insulation wascleaned between tests However there remained the possi-bility of contamination by vapors of electrically conductiveliquids This problem has not previously been described inthe literature ldquoClassicrdquo LMIE work summarized in NACA1300 [14] mainly addressed volatile CH compounds whichare all electrically insulating Of CHO fuels tested results forthe polar solvents methyl ethyl ketone (028 mJ) and ethylacetate (048 mJ) fall above the curve shown in Figure 3whereas values for methanol diethyl ether ethylene oxideand propylene oxide lie close to the curve Ethyl ether is avolatile insulating liquid while ethylene oxide is a gas Val-ues for methanol propylene oxide and tetrahydropyranwere extrapolated from test data measured at 100 and 200mmHg using a correlation developed by the NACA LewisLaboratory The procedure is described by Metzler [15] Lowpressure measurements minimized the likelihood of formingconductive monolayers The extrapolated LMIE value forpropylene oxide which is as volatile as diethyl ether (530mmHg at 298 K) was within 001 mJ of the atmosphericvalue measured by Calcote et al [11] Metzlerrsquos [15] extrapo-lated LMIE values were all larger than available reference val-ues so this is an unlikely source of large underestimates

Figure 3 Dependence of lowest minimum ignition energyon net heat of oxidation [Color figure can be viewed in theonline issue which is available at wileyonlinelibrarycom]

DOI 101002prs Process Safety Progress (Vol33 No4)316 December 2014 Published on behalf of the AIChE

Recently reported LMIE values for acetone (055 mJ)methanol (020 mJ) and ethanol (028 mJ) tabulated in IEC60079-32-1 [16] are questionable for the same reasons as Cal-cote et alrsquos [11] values for methyl ethyl ketone (028 mJ) andethyl acetate (048 mJ) All of these CHO fuels are vapors ofpolar solvents If the high reported LMIE values are correctand not due to charge leakage across conductive films orother errors caused by condensation the ldquoclassicrdquo values forother CHO fuels look too small by comparison The IEC tab-ulation contains a value of 038 mJ for acetaldehyde whichas noted by Britton [2] was measured at stoichiometric con-centration instead of the optimum concentration and is there-fore not the LMIE

Methanolrsquos published LMIE of 014 mJ [15] made it themost easily ignitable common solvent vapor among aliphaticand aromatic hydrocarbons aliphatic alcohols estersketones amines or mixtures of these Britton Holdstockand Pappas [17] consequently developed a standardized igni-tion test for Flexible Intermediate Bulk Containers (FIBC)using a 54 mol ethylene air mixture with ignition energyof 014 mJ to simulate an optimum methanol-air mixtureEthylene was used owing to its low LMIE low toxicity andrelatively flat MIE versus concentration curve This work isthe basis for IEC 61340-4-4 [18] If methanolrsquos LMIE is actually020 mJ as tabulated in [16] the standard 54 6 01ethylene-air mixture required by IEC 61340-4-4 loses its prac-tical significance However consider Figure 2 Methanol andformaldehyde are the highly oxygenated first members ofthe aliphatic alcohol and aldehyde homologous series whosemaximum flame temperatures are underestimated using Brit-tonrsquos Method Consequently burning velocities are likely tobe overestimated and LMIE values underestimated As dis-cussed below methanolrsquos burning velocity lies below the fit-ted curve An elevated LMIE is therefore consistent withmethanolrsquos relatively low burning velocity just as ethylenersquoshigh burning velocity is consistent with its low LMIE

As discussed later under ldquoRelationship between BurningVelocity and Ignition Energyrdquo the inverse relationshipbetween LMIE and burning velocity isnrsquot followed by acetoneor ethyl acetate Itrsquos concluded that the reported LMIE valuesare too high especially in the case of acetone All polar sol-vents lie above the trend line of the inverse relationship withonly methanol and methyl ethyl ketone (MEK) lying withinthe scatter of other data Ethanolrsquos burning velocity isnrsquotavailable although any reasonable burning velocity estimateplaces it above the trend line

Test mixtures are normally made up in the test vessel asdescribed in ASTM E582 [10] although Calcote et al [11]used an external vessel to make up dry test mixtures underpositive pressure This avoided shot-to-shot compositionchanges Water produced by combustion plus accumulationof decomposition products on the test vessel walls create theneed for careful cleaning and periodic confirmatory tests ofinsulation performance This is true for both CH and CHOfuels However conductive material can be deposited assome CHO test mixtures are made up Condensation errorsarenrsquot only caused by allowing internal surfaces to fall belowthe normal dew-point of the test liquid To make up avapor-air mixture by the method of partial pressures liquidis added to an evacuated vessel until the desired partial pres-sure is obtained As air is subsequently added it expands andcools which may cause fogging and condensation of the testvapor If the test liquid contains any heavier contaminantstraces can remain on insulation after the mixture has beenmade up at atmospheric pressure As a separate issue if theapparatus contains any crevices (such as capillary tubingleading to transducer housings) a significant mass of con-densed liquid can become trapped and the gas mixture willbe leaner than calculated In some cases test mixtures are

consistently leaner than indicated by the measured partialpressure of the vapor prior to air addition

Since standard MIE test apparatus measure ldquototal storedenergyrdquo it ought to be impossible to underestimate the LMIEalthough very easy to overestimate it Itrsquos quite possible theLMIE values for polar solvents lie on a separate curve fromthat shown in Figure 3 but the test apparatus must first beshown to give the ldquoclassicrdquo results for at least (conductive)propylene oxide and diethyl ether which is insulating buthas essentially the same DHox value as acetone As discussedabove the LMIE of propylene oxide was confirmed by twodifferent laboratories Diethyl ether was very carefully inves-tigated by the Bureau of Mines owing to its former use as ananesthetic

QUENCHING DISTANCE AND MAXIMUM EXPERIMENTAL SAFE GAP

There is a limited database of minimum quenching distan-ces for CH and CHO fuels at optimum concentration in airFigure 4 shows that available values decrease linearly withincreased DHox [2] Kuchta [7] reviewed previous Bureau ofMines research showing that the MIE of various mixturesover a wide range of pressures and oxygen concentrationsvaries with approximately the square of quenching distanceHence the minimum quenching distance can be estimatedeither from DHox or from LMIE Quenching distance was for-merly used for flame arrester design although these days themaximum experimental safe gap (MESG) is used instead

Figure 4 shows MESG values taken from NFPA 497 [19]Where NFPA values differed from IEC 60079-20-1 [20] the lat-ter database was preferred MESG values for both CH andCHO fuels decrease linearly with increased DHox althoughsignificant data scatter is apparent The stated reproducibilityof IEC 60079-20-1 is 5 and much of the data scatter in Fig-ure 4 is at least twice the expected reproducibility so thecorrelation cannot be used for design purposes Howeverwhere MESG values conflict with the ranking expected fromheat of oxidation considerations it should be worth investi-gation especially if expensive electrical installations areinvolved

Some MESG values in NFPA 497 differ from IEC 60079-20-1 by far more than the supposed 5 reproducibility Plus

Figure 4 Dependence of quenching distance and MESGwith net heat of oxidation [Color figure can be viewed inthe online issue which is available at wileyonlinelibrarycom]


the ldquoDefinitionsrdquo in NFPA 497 allow Zone Groups to bedetermined either from MESG or minimum igniting current(MIC) Ratio Although MIC Ratio is relevant to design ofintrinsically safe circuits it has nothing to do with flamespropagating through narrow gaps MESG is measured inmillimeters while MIC Ratio is the dimensionless ratio of twocurrents each measured in amperes MESG and MIC Ratiojust happen to have similar magnitudes The use of MICRatio in place of MESG was introduced in the 1980s as astop-gap measure owing to the shortage of MESG data com-patible with the new IEC apparatus This situation haschanged and therersquos no longer a reason for chemicals toexist in two different Zone Groups simultaneously such asmethyl ethyl ketone (MEK) which is Group IIA by MIC Ratioand IIB by MESG The definitions should be changed soMESG takes precedence when designing ldquoExplosion ProofEnclosuresrdquo The listed MESG of 084 mm for MEK is muchsmaller than reported by Lunn [21] whose value of 092 mmis consistent with MIC Ratio and with the MESGs of othersimple ketones Unfortunately a typo caused Lunn to listMEK as nonexistent 2-butane instead of 2-butanone and hisresult became lost NFPA 497 defines Group IIB atmospheresas including those containing acetaldehyde but then tabu-lates acetaldehyde as Group IIA based on a 092 mm MESGwhich was also measured by Lunn [21] Based simply onheat of oxidation considerations the 092 mm value is toohigh Lunn reported formaldehydersquos MESG as 057 mm andpropionaldehydersquos as 084 mm The MESG of acetaldehydeshould lie between these values rather than coincide withthe 092 mm MESG of butyraldehyde

LOWER FLAMMABLE LIMIT

As reviewed by Britton [2] it was discovered over 100years ago that the molar heats of combustion (kcalmol) atthe LFL are approximately constant

LFL3DHc=100 K kcal=mol mixtureeth THORN (1)

If K is assumed constant the LFL of any fuel can be esti-mated from the LFL of a reference fuel

LFL5fLFL3DHcgethrefTHORN=DHc (2)

Subsequent studies showed that K is not constantAlthough K is usually 105 6 05 kcalmol for CHON fuelsvalues reported by Kuchta [7] range from about 75 for acety-lene to more than 20 kcalmol for certain ldquoCHClrdquo com-pounds This means the right-hand side of Eq 2 needs theadditional term (KKref) to account for K variation

Britton [2] used published LFL values to calculate and plotK values against DHox The K data were scattered aroundtwo roughly parallel lines that both showed negative lineardependence on DHox Multiplying Eq 2 by the ratioDHoxrefDHox was shown to compensate for most of thenegative linear dependence of K on DHox and give goodagreement between calculated and reported LFL values ofhydrocarbons

LFL 5 fLFL3DHc3DHoxgethrefTHORN=fDHc3DHoxg (3)

Both the reactants and products at the LFL are almostentirely air and so minor changes in number of moles andthermal capacity can be neglected The case was made byBritton [22] that methanersquos large and well-established LFL of50 mol makes it suitable as a reference gas Letrsquos assumemethane is used as the reference gas First the heat of com-bustion ratio adjusts methanersquos LFL in proportion to howmuch heat is needed to raise 1 mole of fuel-air mixture to

the lower limit flame temperature (Eq 2) If the fuel of inter-est has a greater heat of combustion than methane less fuelneeds to be burned to achieve the lower limit flame temper-ature and so the LFL is decreased proportionally The esti-mated LFL is then multiplied by the DHox ratio toapproximately compensate for variation of K (Eq 3) Asshown later this largely compensates for any difference inthe lower limit flame temperature versus methane If the fuelhas a lower flame temperature than methane the LFL isagain decreased proportionally

Figure 5 shows a plot of K versus DHox for hydrocarbonswhose LFL values were recently measured and consideredreliable Reference data are summarized in Table 2 Methanepropane and ethylene were measured in the NIOSH 120-Lsphere using a 7 pressure rise to denote ignition [23] Eth-ane and ethylene were measured by Wong [24] and acetyleneby Zhao [25] using the same vertical 10-cm diameter closedsteel tube with thermal detection of flame propagation Noneof these studies had been made when Brittonrsquos Method waspublished in 2002

For this dataset Figure 5 shows a negative linear depend-ence of K on DHox with a gradient of 2110 Extrapolationof the equation of fit shows the intercept on the DHox scalehas 10 times the numerical value of the intercept on the Kscale Methane is at the midpoint of the DHox axis Figure 5therefore represents part of an isosceles right triangle sonear the midpoint on the DHox axis the ratio (Y2Y1) (X1X2) If the K value of the reference gas is Y1 all the K values(Y2) can be made approximately equal to that of the refer-ence gas using the multiplier (X1X2) This means multiplyingK by the factor DHoxDHoxref The result is shown in Figure6 The gradient is decreased by 75 and the corrected K val-ues all fall within the error bounds caused by a roughly 5LFL error such as LFL 5 20 6 01 mol From Eqs 1 and 2the inverse ratio DHoxrefDHox is applied to correct the LFLand this procedure results in Eq 3 This correction methodfor a variable K is used in the current CHETAH Version 90

The error represented by the residual gradient in Figure 6can be nullified using a modified K correction ratio(DHox(ref)DHox)

128 Increasing the power exponent from100 to 128 has an increasingly greater effect at higher DHox

values There is almost no change of calculated LFL valuesfor ldquolow energyrdquo gases such as propane but the LFL

Figure 5 K plotted against heat of oxidation using recentLFL values [Color figure can be viewed in the online issuewhich is available at wileyonlinelibrarycom]


predictions for gases such as ethylene and acetylene becomesmaller and closer to the reported ldquoreferencerdquo values shownin Table 2 While trigonometry demands a nonlinear correc-tion to offset the approximation (Y2Y1) (X1X2) it wouldbe remarkable if the LFL varied completely linearly with boththermodynamic ratios in Eq 3 It should be appreciated thatselection of the correct exponent depends on availability ofa reliable dataset Of the data shown in Figure 5 only meth-anersquos LFL was considered reliable in 2002 Other availabledata had been measured decades earlier using the standard5-cm vertical tube method which was known to be subjectto flame quenching Methane had been tested in a variety oflarge vessels and its 50 mol LFL was widely accepted [22]Since the LFL predictions of Eq 3 were found to be adequateand in the absence of a reliable set of LFL data no attemptwas previously made to null the error The modified Eq 3 is

LFL5LFL3 DHcethrefTHORN=DHc

3 DHoxethrefTHORN=DHox

128(3a)

If CHO data are added to Figure 5 a second line isobtained above the CH line The lines are approximatelyparallel so methane reference gas can also be used for CHOfuels [2] If the lines are assumed to be parallel itrsquos only nec-essary to increase all the values obtained using Eq 3 by aconstant correction factor ldquoFrdquo This third adjustment yields

LFL5F3fLFL3DHc3DHoxgethrefTHORN=fDHc3DHoxg (4)

LFL5F3fLFL3 DHcethrefTHORN=DHc


128(4a)

Using methane reference gas the correction factor is unityfor hydrocarbons Using Eq 4 the correction factor F 5 112for CHO fuels This was determined from the ratio of theuncorrected K values of CHO versus CH fuels [2] Using Eq4a the correction factor F 5 117 for CHO fuels Otherhomologous sets apart perhaps from CHON need either adifferent correction factor or a different reference gas In thecase of organo-chlorides vinyl chloride was used as the ref-erence gas [6] Since this article focuses on CH and CHOfuels this topic isnrsquot discussed further CHETAH 90 currentlyuses Eq 4 to calculate LFL values If Eq 4a were used the

calculated lower limit flame temperatures discussed in thenext section would decrease with increased DHox

Figure 7 shows LFL values of 13 CH fuels plus 20 CHOfuels estimated using Eq 4 [6] Of the two outliers vinyl ace-tylenersquos reported LFL was probably estimated using LloydrsquosRule since no original measurement has been found Cyclo-propanersquos reported value is probably also too high and thisis discussed later under ldquoCatoire and Naudetrsquos LFL EquationrdquoOther than these two examples LFL values estimated usingEq 4 are generally within typical measurement error of 01ndash02 mol and most are within 01 mol of reported values

LOWER LIMIT FLAME TEMPERATURES

It follows from Eq 1 that if K is constant all flames musthave the same temperature at the LFL Since K is not con-stant neither is the lower limit flame temperature (LLFT)constant The LLFT of CH and CHO fuels generally varies inthe range 1400 6 150 K Other fuels have a much widerrange of limit temperatures from less than 700 K to above1600 K [6] It follows that a globally constant LLFT assump-tion has the potential to either overestimate or underestimatethe LFL An extreme case is the 1700 K assumed by Ma [26]This exceeds the LLFT range of CH and CHO fuels and LFLoverestimation will be especially large for energetic fuelssuch as ethylene and acetylene Apart from highly halogen-ated compounds ammonia is one of very few fuels having aLLFT above 1600 K

Figure 8 shows adiabatic lower limit flame temperatures(LLFTs) for three disparate sets of fuels calculated using theGordon and McBride Chemical Equilibrium Program [8] plot-ted against DHox In each case therersquos a negative lineardependence of LLFT on DHox and the lines are approxi-mately parallel especially the CH and CHO lines The LLFTvalues were all based on LFL values calculated using Eq 4This is because reported experimental LFL data exhibit fartoo much scatter to calculate flame temperatures especiallyat small LFL values For example while a 01 mol error inmethanersquos LFL creates a LLFT error of only 24 K the sameabsolute error in styrenersquos LFL creates a LLFT error of 126 KAs shown in Table 2 obtaining LFL to within 01 mol is notcurrently feasible The existence of several disparate standarddefinitions and test methods only makes matters worse TheLLFT data for organo-chlorides were obtained in a similar

Figure 6 Variation of hydrocarbon K values before and aftercorrection [Color figure can be viewed in the online issuewhich is available at wileyonlinelibrarycom]

Figure 7 Reported versus calculated lower flammable limitsof CH and CHO fuels [Color figure can be viewed in theonline issue which is available at wileyonlinelibrarycom]


manner using vinyl chloride as the reference fuel [6] Theorgano-chloride line is beyond the scope of this article andis shown only for reference purposes

Figure 8 is similar to Figure 5 and it can be shown thatthe ldquoDHox ratiordquo correction for ldquoKrdquo is the inverse of a limitflame temperature correction From Figure 8 the depend-ence of LLFT on DHox is

LLFT Keth THORN521722736353DHox CH fuelseth THORN (5)

LLFT Keth THORN522932768573DHox CHON fuelseth THORN (6)

Equation 6 is given for ldquoCHON fuelsrdquo although most of thedata points were for CHO fuels As discussed later more workis needed to refine the relationships Only the interceptschange if 298 K is subtracted from both sides of Eqs 5 and 6This yields the temperature increase above standard tempera-ture ldquoDTlimrdquo during upward propagation of a flame at its LFL

DTlim Keth THORN518742736353DHox CH fuelseth THORN (7)

DTlim Keth THORN519952768573DHox CHON fuelseth THORN (8)

LFL increases linearly with increased ldquoKrdquo but decreaseslinearly with decreased flame temperature A ldquoKrdquo correctionbased on LLFT is therefore the inverse of the DHox ratio usedin Eqs 3 and 4 If the DHoxrefDHox term in Eq 3 isreplaced by DTlimDTlimref the ldquonewrdquo LFL expression for CHand CHO fuels becomes

LFL5LFLref3DTlim3 DHcf gethrefTHORN=fDHc3ethDTlimTHORNrefg (9)

Equation 9 corrects first for heat of combustion ratio thenfor the DTlim ratio relative to the LFL of methane measuredat the 298 K reference temperature A set of results using thethree versions of Brittonrsquos Method is shown in Table 1 Nocorrection factor is needed for CHO versus CH fuels becauseDTlimDTlimref gives a direct ratio of the amount of fuelneeded to be burned relative to methane The only otherfactors are the DHcrefDHc ratio and the LFL of the referencegas Comparison of Eqs 4 and 9 helps to explain why LFL

depends on the net heat of oxidation Since Eq 9 relies onLLFT values calculated from LFL values that are themselvescalculated from Eq 4 it has no independent use It wouldbe a different matter if LLFT values could be calculated inde-pendently of measured LFL values but this is not possibleFigure 8 can be improved as more reliable LFL data becomeavailable since LLFT calculations can be made with highaccuracy This will improve the LFL temperature correctionmethod described next

LFL TEMPERATURE CORRECTION METHOD

CHETAH users can input the temperature at which a LFLvalue is needed The temperature correction method isexplained in detail by Britton and Frurip [6] The LLFT equa-tions shown in Figure 8 are first solved for the fuel of inter-est Since LLFT is a constant the LFL decreases linearly withincreased temperature and becomes zero at the LLFT ForLFL values measured at standard temperature (298 K) theLFL at temperature ldquoTrdquo is

LFLTeth THORN5 LFLeth THORN2983ethLLFT2298THORN=ethLLFT2TT THORN (10)

In addition to estimating LFL values at temperatures otherthan 298 K using CHETAH Eq 10 can also be used manuallyto adjust LFL values measured at nonstandard temperaturesIn principle the method could be improved using LFL esti-mates from Eq 4a rather than Eq 4 However Table 1 showsthat Eq 4a provides little improvement over Eq 4 in calculat-ing LFL Equation 4a is dependent on the dataset being con-sidered and the exponent could vary between CH and CHOfuel sets There are no LFL ldquoreferencerdquo data for CHO fuelscomparable to the NIOSH data in Table 2

Catoire and Naudet [3] used a power relationship inwhich the LFL decreases nonlinearly with increased tempera-ture This decision appears to have been based on experi-mental findings that might have been in error PreviouslyHustad and Soslashnju [27] using a 10-cm vertical tube found lin-ear temperature dependence of LFL for a range of fuels andmixtures They reported for methane and butane that ldquoTheextrapolated LFL becomes zero at 1200C which is somewhatless than the calculated values in the literature (1300ndash1400C)rdquo Their extrapolation agrees well with the LLFT val-ues in Figure 8 Methanersquos LLFT is 1484 K (1211C) at 50mol and n-butanersquos is 1448 K (1175C) at 149 mol How-ever Hustad and Sonju noted reactant depletion at highertemperatures which might account for nonlinear tempera-ture dependence Wierzba and Ale [28] showed that meth-anersquos LFL decreases linearly with increased temperature upto 350C while other gases (hydrogen ethylene and pro-pane) exhibited linearity at first but nonlinearity at highertemperatures The extent of the nonlinearity increased withincreased residence time which was believed due to cata-lytic depletion on the test vessel surfaces

CATOIRE AND NAUDETrsquoS LFL EQUATION

Catoire and Naudet [3] claimed that their empirical regres-sion equation outperformed all other LFL predictive equa-tions they had examined including Brittonrsquos Method asexpressed by Eq 4 using methane as the reference gas Theirequation is

LFL moleth THORN55199573X0709363n01973T 051536 (11)

In this equation ldquoXrdquo is the mole fraction of the fuel in thecorresponding stoichiometric fuelair mixture ldquonrdquo is thenumber of carbon atoms in the molecule and ldquoTrdquo is the tem-perature (K) Inspection of Eq 11 shows itrsquos incapable of dis-tinguishing between structural isomers including functional

Figure 8 Calculated lower limit flame temperatures [Colorfigure can be viewed in the online issue which is availableat wileyonlinelibrarycom]


isomers Ethylene oxide will have the same estimated LFL asacetaldehyde and 14-dioxane the same as ethyl acetate (orbutyric acid methyl propanoate etc) This is a serious short-coming The nonlinearity of the temperature dependencehas already been discussed

The authors correctly observed that Brittonrsquos Method per-forms poorly for nitro-compounds They also suggested Brit-tonrsquos Method needs a different ldquoFrdquo factor for cyclichydrocarbons This was based mostly on the differencebetween the calculated and reported LFLs of cyclopropaneCyclopropane has a highly strained ring while cyclohexanehas no ring strain owing to the ideal staggering of its chairconformation Cyclopropane is therefore much less stablethan other cycloalkanes and this is reflected in its elevatedDHox relative to its propylene isomer Since a higher DHox inany homologous series corresponds to a smaller LLFT cyclo-propanersquos LFL should be smaller than that of propylene Brit-tonrsquos 19 mol LFL estimate for cyclopropane (Eq 4) is quitereasonable versus 20 mol for propylene Since these arestructural isomers Eq 11 yields the same LFL for both chem-icals (237 mol) The reported 24 mol LFL of cyclopro-pane dates from 1942 at which time the chemicalrsquos principalcontaminants were propylene (as expected) but also cyclo-hexane resulting from its manufacture by ldquoRingschlussrdquochemical reaction (eg zinc acting on 13-dichloropropane)Neither of these impurities would increase the measured LFLA 5-cm vertical tube about 2-m tall was used which is con-sistent with the US Bureau of Minesrsquo standard method [29]The ignition source generally used was an induction sparkHowever smaller LFL values were reported for propylene

(20 vs 24 mol) when a larger diameter glass tube closedat the bottom was used Propylenersquos LFL is variouslyreported between 18 mol and 24

Table 1 compares Catoire and Naudetrsquos equation (Eq 11)with the three versions of Brittonrsquos Method (Eqs 4 4a and9) The ldquooldrdquo Britton Method (Eq 4) corrects LFL using theratio DHoxrefDHox

100 while the ldquonewrdquo Britton Method (Eq9) corrects LFL using LLFT values calculated from solutionsof Eq 4 Figure 9 shows that the ldquooldrdquo and ldquonewrdquo LFL esti-mates are almost identical and that both outperform Eq 11The modified ldquooldrdquo Britton Method (Eq 4a) corrects LFLusing the ratio DHoxrefDHox

128 in order to nullify a resid-ual dependence of K on DHox The effect of the elevatedexponent increases as DHox increases and as shown inTables 1 and 2 results in better agreement with reported LFLvalues of energetic fuels such as ethylene and acetyleneTable 1 shows all three versions of Brittonrsquos method outper-form Eq 11 for this particular set of fuels many of which areenergetic in terms of DHox Some fuels are paired with dis-parate functional isomers (ethylene oxide and acetaldehydepropylene oxide and propionaldehyde cyclopropane andpropylene) Additional isomers could have been contrastedsuch as dimethyl ether versus ethanol and propylene oxideversus vinyl methyl ether Equation 11 predicts the same LFLfor all chemicals sharing the same molecular formula andneglects functional variations that affect the LFL

LIMITING OXYGEN CONCENTRATION

As described by Bodurtha [30] the limiting oxygen con-centration (LOC) can be estimated with reasonable accuracy

Table 1 Data used to compile Figure 9

FuelDHc

(kcalmol) SDHox

(kcalmol)LLFT(K)

BrittonEq 4

(mol)

BrittonEq 4a(mol)

BrittonEq 9

(mol)

ReportedPre-2002(mol)

CampNEq 11(mol)

Methane 19179 2 9589 1484 500 500 500 500 519Styrene 10188 10 10188 1419 089 087 089 090 116Ethylene 31625 3 10542 1397 276 269 281 270 347Propylene 46026 45 10228 1415 195 192 196 200 244Acetylene 30009 25 12004 1293 255 240 268 250 392Methyl acetylene 44207 5 11052 1354 188 181 193 170 264Cyclopropane 46829 45 10407 1412 189 184 192 240 244Propadiene 44367 4 11092 1356 187 179 193 220 264Formaldehyde 12415 1 12415 1310 668 649 659 700 796Acetaldehyde 26394 25 10558 1481 370 376 362 400 391Propionaldehyde 41102 4 10276 1503 244 250 237 260 264Acrolein 38243 35 10927 1453 246 248 244 280 289Ethylene oxide 29112 25 11645 1391 304 301 304 300 391Propylene oxide 43338 4 10834 1453 219 221 215 230 264Dimethyl ether 31751 3 10584 1475 306 311 300 340 347Methanol 16157 15 10771 1461 592 598 582 600 622

Table 2 Comparison of post-2002 ldquoReferencerdquo LFL data

FuelDHc

(kcalmol) SDHox

(kcalmol)

BrittonEq 4

(mol)

BrittonEq 4a(mol)

Closed10-cm Tube

(mol)

120-L Sphere(NIOSH)(mol)

Methane 19179 2 9589 500 500 523 (Wong) 525 (Zhao) 50Ethane 34144 35 9755 276 275 272 (Wong) ndashPropane 48834 5 9767 193 192 209 (Wong) 20Ethylene 31625 3 10542 276 269 271 (Wong) 281 (Zhao) 27Acetylene 30009 25 12004 256 240 242 (Zhao) ndash


using the expression LOC 5 LFL 3 S where ldquoSrdquo is the stoichi-ometric oxygenfuel ratio This simple relationship is used byCHETAH The expression ought to underestimate the LOCsince it neglects the ldquonoserdquo of the flammable envelop How-ever as discussed by Britton [31] large errors can accumulatewhen LFL values are estimated especially in the case of mix-tures Any error in LFL is multiplied by S when it comes toestimating the LOC Consequently if the LFL is overesti-mated further multiplication by a large ldquoSrdquo may offset theconservatism of the simple LOC expression For examplethe S value of benzene is 75

MAXIMUM LAMINAR (FUNDAMENTAL) BURNING VELOCITY

Most tabulated data in NACA 1300 [14] were measuredusing the NACA tube but some were from Bunsen burnermeasurements using shadowgraph or Schlieren imaging ofthe flame cone Since burner techniques give higher burningvelocity values than the NACA tube NACA 1300 does not listactual burning velocities but only the percentage of the pro-pane value

Gibbs and Calcote [32] measured the maximum laminar(fundamental) burning velocities of 77 compounds using theBunsen burner shadowgraph method They found 46 cmsfor propane 45 cms for methane and 74 cms for ethyleneThese values were all considerably higher than those foundusing the NACA tube especially methane and propane sincedeviations between tube and burner methods are greatest atlow burning velocities However the propane value plus thevalues found for methane and ethylene were consistent withvalues measured in the 1970s using contemporary ldquostate-of-the-artrdquo techniques such as the ldquodouble kernelrdquo method Theburning velocity table in NFPA 68 [4] was taken from theNACA 1300 [14] compilation using a reference value of46 cms for propane and a summary of the selection of thisvalue including values used for comparison taken from Brit-ton [33] are still given in NFPA 68

For this article the NFPA 68 values have been recalcu-lated from NACA 1300 using a smaller reference value of39 cms for propane Additionally a value of 37 cms hasbeen adopted for methane rather than the smaller value of34 cms calculated from NACA 1300 using the 39 cms pro-pane reference value The 39 cms propane reference value

is consistent with the value measured in the NACA tube andis consistent with currently accepted values Based on flatflame burner results Rallis and Garforth [34] considered37 cms to be the ldquobenchmarkrdquo burning velocity of methaneA 37 6 1 cms value for methane was determined by Taylor[35] and a value of 367 cms can be arrived at by averagingthe ldquocorrectedrdquo results of 14 different burner studies summar-ized in his thesis Taylorrsquos correction method involved adjust-ing the reference surface to the luminous zone of the flameand is contrary to the previous correction method wherebyvarious measured cone surface areas were ldquocorrectedrdquo togive cold boundary values Taylorrsquos reverse adjustmentdecreased the calculated flame cone areas and yielded lowerburning velocities

Accepted burning velocity values have declined since1980s owing to recognition of errors caused by flow diver-gence flame stretch and heat losses not only in burnermethods but also in more sophisticated techniques such asthe double kernel and counterflow methods Taylorrsquos meas-ured values for methane (37 6 1 cms) ethane (41 cms)propane (39 6 1 cms) ethylene (660 cms) and hydrogen(285 cms) are all considerably lower than most burnerderived values but compare well with those of Gerstein Lev-ine and Wong [36] who used NACArsquos ldquorevised tuberdquo methodTo compile data for Figure 10 one would ideally use a con-stant correction factor to adjust the large and internally con-sistent database of Gibbs and Calcote [32] downwardHowever relative to Taylorrsquos values a variable correctionfactor is needed decreasing from 090 (ethylene) to 083(methane) As observed relative to NACA tube data the cor-rection needs to be larger for fuels having smaller burningvelocities (see ldquoFurther Workrdquo)

Figure 10 shows the revised correlation between burningvelocity and DHox The second-order polynomial fit capturesthe relatively constant burning velocity of about 40 cmsexhibited by paraffins and other ldquolow energyrdquo CH and CHOfuels However the correlation exhibits a minimum atDHox 5 9724 kcalmol-oxygen The occurrence of a mini-mum could be avoided using a power fit but this wouldcause methanersquos predicted burning velocity (39 cms) to beless than the ldquobenchmarkrdquo value (37 cms) and decrease to34 cms This is the value calculated from the NACA 1300

Figure 9 Old and revised Britton methods versus ldquoCampNrdquoequation [Color figure can be viewed in the online issuewhich is available at wileyonlinelibrarycom]

Figure 10 Dependence of revised NFPA 68 burning velocitydata on net heat of oxidation [Color figure can be viewed inthe online issue which is available at wileyonlinelibrarycom]


[14] database using 39 cms as the reference burning velocityof propane While the second-order polynomial is unsatisfac-tory itrsquos unlikely that methanersquos ldquoacceptedrdquo burning velocitywill be decreased in the future to 34 cms This minimum isa minor problem for CHETAH [1] which estimates funda-mental burning velocities for mixtures at optimumconcentration

Some justification for a second-order polynomial relation-ship was given by Britton [2] Burning velocity depends pri-marily on reaction rate This is mainly driven by flametemperature which increases with increased DHox Burningvelocity depends on other factors besides reaction rate Ofthese thermal diffusivity is weakly dependent on the type offuel unless the optimum concentration is high as with ethyl-ene and acetylene The burning velocities of most CH andCHO fuels increase in a similar exponential fashion withincreased flame temperature [37] although itrsquos long beenknown that ethylenersquos burning velocity is unexpectedly highrelative to its flame temperature [38] NFPA 68 [4] lists ethyl-enersquos burning velocity as 80 cms whereas the most com-monly reported value is 68 cms As noted in NFPA 68 the80 cms value had been recommended in an influential 1972critical review of burning velocities and the same value iscalculated from NACA 1300 using a propane reference valueof 46 cms However itrsquos much higher than reported by mostworkers A tabulation made by Gaydon and Wolfhard [37]shows values close to 68 cms were obtained from four outof seven studies using different methods Taylor [35] reporteda value of 66 cms which is close to the majority of meas-ured values and is based not only on a technique designedto minimize errors but also a more precise definition ofburning velocity

Burning velocities do not generally follow a simple mix-ing rule although CH and CHO mixtures should be betterbehaved than mixtures with hydrogen since hydrogen mix-tures fall on a different burning velocity versus flame temper-ature curve Addition of few mole percent of a hydrocarbonsuch as butane is known to inhibit the burning velocity ofhydrogen [37] Ibaretta [39] considered direct application ofBrittonrsquos Method for mixtures using the calculated net heatsof oxidation of both the pure components and the mixtureHe compared the results with Le Chatelierrsquos mixing rule andalso with Hirasawa et alrsquos [40] mixing rule which requiresflame temperature calculations Results for methane plus pro-pylene were similar for all three mixing rules Ibarettarsquos pre-sentation was however biased by using the ldquoestimatedrdquomethane endpoint for Brittonrsquos Method while using the NFPA68 value (40 cms) for the other two mixing methods Thesource of propylenersquos burning velocity was not divulged (itrsquosoddly missing from NFPA 68) but the same value of 52 cmswas used for all three methods Results for butane plus ethyl-ene were then compared with a set of published burningvelocity data for mixtures Again the results were biased byusing ldquoestimatedrdquo burning velocities for Brittonrsquos Method butidentical published values for the other mixing methodsBurning velocities of 414 cms for n-butane 685 cms forethylene plus intermediate values for mixtures wereobtained by Hirasawa et al using a counterflow techniqueBoth endpoints are much less than the values given in NFPA68 and closer to the revised values in this article BrittonrsquosMethod significantly underestimates the burning velocity ofethylene which is the farthest outlier on Figure 10 With thedifferent endpoints itrsquos impossible to evaluate the merits ofusing a ldquonet heat of oxidationrdquo mixing rule versus Le Chate-lierrsquos mixing rule Ibarettarsquos final test case was methane plushydrogen Since hydrogen does not form carbon dioxidewhen it burns Brittonrsquos Method cannot be applied to hydro-gen mixtures The mixture data for methane plus hydrogenwere calculated using a numerical model and the endpoints

(40 and 237 cms) differ from the reference values (37 and285 cms) recommended by Taylor Ibaretta did not recog-nize the disparities between the sets of burning velocity datahe was using In the case of methane plus propylene theranges of reported endpoints are 34ndash45 cms for methaneand 44ndash52 cms for propylene That is the ranges ofreported endpoint data overlap one another Ibaretta con-cluded that Hirasawa et alrsquos mixing rule is excellent forbinary mixtures but requires a substantial amount of calcula-tion plus the burning velocities of both components Le Cha-telierrsquos mixing rule was thought to give a good butconservative approximation of the burning velocities of mix-tures Since Ibaretta had made no direct comparison of acombined ldquonet heat of oxidationrdquo mixing rule versus Le Cha-telierrsquos mixing rule no conclusions can be drawn based onhis analysis It was decided to use Le Chatelierrsquos rule in CHE-TAH for combining burning velocities estimated using Brit-tonrsquos Method A possible improvement would be to allowusers to enter burning velocity data where the data are confi-dently known (and consistent with the reference data) orcannot be reliably estimated

RELATIONSHIP BETWEEN BURNING VELOCITY AND IGNITION ENERGY

Metzler [15] found that with the exception of carbon disul-fide the LMIE varies inversely with burning velocity raised tosome power Figure 11 shows a plot of LMIE versus burningvelocity using data from the present article Metzler reportedan inverse power relationship with exponent 2083 whileFigure 11 shows an exponent of 2174 Itrsquos unclear how Met-zler obtained an exponent only about half this number Inany case Figure 11 shows that the ldquohigh burning velocityrdquo ofethylene (Figure 10) is quite consistent with its ldquolow LMIErdquo(Figure 3) and neither value is an erroneous outlier Figure12 shows that the apparently high LMIE values for polar sol-vent vapors discussed earlier are not consistent with theirreported burning velocities and this supports the contentionthat these reported values are too high especially acetoneand ethyl acetate Although itrsquos beyond the scope of this arti-cle Figure 12 includes carbon disulfide which is renownedfor exceptional behavior Owing to its extremely low LMIEof 0009 mJ CS2 is expected to have a very large burningvelocity However its burning velocity relative to 39 cms forpropane is only 49 cms A little-known study by Gibbs

Figure 11 Dependence of LMIE on fundamental burningvelocity [Color figure can be viewed in the online issuewhich is available at wileyonlinelibrarycom]


et al [41] shows that quite contrary to whatrsquos found withcarbon monoxide the burning velocity of CS2 is inhibited bymoisture The ignition energy is also affected but to a lesserdegree Using a Bunsen burner technique the burning veloc-ity was about 50 cms with humid air (3 mol) The burn-ing velocity increased exponentially with decreasingconcentrations of water and violent flash-back occurred withextremely dry air No tests were made with hydrogen-free airsince dried lab air contained 100 ppm hydrogen and evensynthetic air contained 8 ppm hydrogen The burning veloc-ity of hydrogen-free CS2 isnrsquot known but is considerablyhigher than the reported value Further experimental work isneeded to determine if CS2 is an exception to the generallyinverse relationship depicted by Figures 11 and 12

FURTHER WORK

ldquoBrittonrsquos Methodrdquo using net heats of oxidation to estimateflammability parameters of CHON fuels was published in2002 [2] and some additional features were published in2003 [6] The estimation methods were later incorporatedinto CHETAH Since 2003 some progress has been made inobtaining reference LFL data (Table 2) but this represents thebare minimum just for hydrocarbons To address the fullrange of DHox values it would be very helpful for the LFLsof acetylene and perhaps propadiene to be measured in thestandard NIOSH vessel along with a range of CHO CHNand CHON fuels Ideally this should be continued for otherfuel sets such as organo-chlorides etc The data should beadded to Figure 5 to obtain accurate adjustments to the LFLof the reference fuel (Eq 4 or 4a) The estimated LLFTs ofdifferent fuel sets in Figure 8 should be examined withrespect to new reference LFL test data In particular itshould be determined whether the CHO line also representsCHN and CHON fuels (other than nitrated compounds) ascurrently assumed

Recent test work with acetylene using a vertical 10-cmtube suggests that some LFL data from the ldquoclassicrdquo standard5-cm vertical tube apparatus are too high [25] Howevermethane was unable to propagate an upward flame below52 mol This means the 10-cm vertical tube used by Zhaois too small to determine a standard set of LFL data compati-ble with methanersquos 50 mol LFL Rather than define flamma-

ble limits by the occurrence of a small overpressure Britton[22] had recommended a closed vertical tube apparatus 20ndash30 cm in diameter to minimize flame quenching This wasconsidered too bulky for laboratory work and a vertical 10-cm steel tube was constructed instead [24] Hustad and Soslashnju[27] had previously constructed a 10 cm by 3-m high steeltube and had obtained a 53 mol LFL for methane muchthe same as found in the 5-cm vertical tube The alternativeof using closed vessels and a small (5ndash7) pressure rise forthe ignition criterion has proven to be impractical for mostlaboratory work As shown in Table 2 reference work usinga 120-L sphere was carried out by NIOSH for methane pro-pane and ethylene using ASTMrsquos pressure rise criterion of17 [23] A 7 pressure rise is equivalent to 1 psi above 1standard atmosphere (147 psia) which has been deemedcapable of destroying the average brick building If the dis-parity between the NIOSH sphere and the 10-cm tube isunique to methane and a few other ldquolow energyrdquo fuels muchof the test work could be done with less effort using thetube Table 2 shows the two methods gave the same LFL forethylene

The burning velocity correlation shown in Figure 10 givesestimates that are lower than values given in NFPA 68 Asdiscussed earlier both NFPA 68 and the correlation shown inFigure 10 are based on NACA 1300 However to obtain bet-ter agreement with current reference values Figure 10 isbased on a burning velocity of 39 cms instead of 46 cmsfor propane Most of the NACA 1300 dataset were measuredusing the NACA tube and this method tends to give less con-sistent results than burner methods The correlation shownin Figure 10 might be revised after applying a variable cor-rection factor to the burner data of Gibbs and Calcote [32]and determining whether the fit can be improved by incor-porating a thermal diffusivity term Le Chatelierrsquos mixing rulewill be adopted Where common fuels are known to exhibitunusual behavior such as ethylene an internal databasecould be used to replace the estimated value

DISCLAIMER

The charts theories and information (Information) givenin this article provide only a general guide to the actualbehavior of chemicals and should be applied with all duediligence in conjunction with the current versions of allapplicable Regulations and Standards together with allrequirements and limitations only some of which are incor-porated herein by reference In any event the authors andall entities affiliated or related to them (Authors) hereby dis-claim all liability arising from your use application or reli-ance upon the Information provided in this article Thisarticle has been prepared with care and diligence but theinnumerable variables associated with the many parametersaddressed in this article preclude the Authorsrsquo acceptance oryour expectation of the Authorsrsquo acceptance of any blameliability or fault of any kind in relation to any damages youincur or may cause by applying any of the Information inthis article

APPENDIX FLAMMABILITY FEATURES OF ASTMrsquoS CHETAH PROGRAM

LFL as Calculated by CHETAHThe CHETAH computer program has been in existence in

some form since the mid 1970s It is a volunteer generatedproduct of the ASTM E27 Committee on Hazard Potential ofChemicals It has historically been widely used to predictthermodynamic properties of chemicals and to assess possi-ble reactive hazards It may be purchased from ASTM

Figure 12 Linearized power fit from Figure 11 illustratingunusual LMIE results [Color figure can be viewed in theonline issue which is available at wileyonlinelibrarycom]


International Inc and a web site describing the CHETAHprogram in more detail is available wwwchetahusouthaledu

The computer program ASTM CHETAHTM Version 9 [1]allows for convenient calculation of the LFL at 298 K and athigher temperatures for a wide variety of chemicals usingthe method described in this article The flammability calcu-lations are limited to compounds composed of C O H Nand Cl Mixtures of compounds are also allowed The pro-gram has an extensive database of the thermodynamic prop-erties of a wide variety of species allowing convenient

calculations involving common chemicals and their mixtures(about 1500 chemical species) However CHETAH also hascapacity to make calculations for chemicals not in the data-base by the use of Bensonrsquos estimation procedure [42]Chemicals of interest may be constructed from a library ofmolecular fragments or groups that has been greatlyexpanded through the years (presently about 1000 groups)This may conveniently be accomplished by a direct selectionof groups within the CHETAH program or by a cut and pasteof a text string in a Simplified Molecular-Input Line-EntrySystem (SMILES) [43] representation of a molecule There are

Figure A1 CHETAH flammability results for sample mixture of chemicals


a variety of computer applications that allow a user to drawmolecules and save a representation of the molecule as aSMILES text string CHETAH has been designed to work wellin this regard with the CHEMDRAWTM program Once a mol-ecule is described thermodynamic properties are predictedand the molecule is available for flammability calculationsThe user has simply to indicate flammability calculations aredesired and calculations are made for LFL and a variety ofother flammability parameters

In applying the LFL calculation method described in thisarticle a quantity termed the heat of oxidation is described[2] Calculation of the heat of oxidation within CHETAH isdependent on the obtaining a value for the heat of combus-tion The method of calculation of the heat of combustion inCHETAH [44] deserves some description The heat of com-bustion method used in CHETAH is very general being ableto make calculations for compounds and mixtures composedof 71 different elements and uses a somewhat complexalgorithm It is based on the common set of stoichiometricrules for combustion for C O H N and halogens plus analgorithm for determining energetically favored combustionproducts for cases involving additional elements Howeverfor the Britton LFL calculations in CHETAH only theelements C O H N and Cl are allowed Thus for thesespecific elements the method in CHETAH uses the followinglogic

Ample oxygen is available to form any potential oxidationproduct

If nitrogen is present it will be converted to the molecularform N2 It is assumed that if carbon is present it will be converted

to carbon dioxide If chlorine is present with hydrogen also present it will

be converted to HCl This is the highest priority use theavailable hydrogen If hydrogen is present in excess to that needed to form

HCl it will be converted to water

This set of assumptions is consistent with the widely usedconventional stoichiometry for combustion [7] However therewill be cases in which combustion products in reality are dif-ferent than described and the actual heat of combustion willbe different than that calculated As Britton [2] points out this isgenerally not a problem but is more likely for halogen contain-ing reactants However halogens other than chlorine are notallowed at present in the calculation for LFL within CHETAHThis accuracy problem will surface for example for methyl-ene chloride trichloroethylene and tetrachloroethylene inCHETAH In such unusual cases the heat of oxidation basedon conventional stoichiometry for combustion would not beaccurate and the prediction of LFL from CHETAH will be inerror There are plans to code CHETAH to allow overrideentries for the heat of combustion but this is not presentlyimplemented CHETAH does however allow the user to spec-ify a chemical reaction including a combustion reaction andcalculate a heat of reaction or combustion for such a reactionThus the CHETAH program in its present form does facilitatein such cases a hand calculation of the LFL using BrittonrsquosMethod if it is desired to make such a calculation

CHETAH also is capable of making a LFL calculation formixture of compounds in varying amounts This is accom-plished by calculation of the LFL using the appropriate pro-cedure for each of the pure species and then combining theLFL results using Le Chatelierrsquos mixing rule

Other Flammability Related Calculations in CHETAHA number of flammability parameters are calculated using

methods outlined by Britton In addition to the LFL at 298 K

the following calculations are made by CHETAH (symbolsrefer to those used on CHETAH output report)

Limiting Oxygen Concentration (LOC)Lower Limit Flame Temperature (LLFT)Maximum Flame Temperature (T-Max)Fundamental Burning Velocity (Su) of Single and Mixed

FuelsQuenching Distance (qd)Lowest Minimum Ignition Energy (LMIE)Lower Flammable Limit (LFLT) at Temperatures Other

than 298 K

Values for pure components are calculated for all theabove Mixture calculations are available for LFL and LOC

For Chlorine containing compounds calculations are madefor LFL LLFT and LOC but not for the other parameters asappropriate correlations are not available

There is also an older simple method by Bothwell [1]included as an altenative in CHETAH for LFL calculations Ithas the advantage of offering results for a greater variety ofelements compared to Brittonrsquos method The method byBothwell is similar to the DIPPR method [45] but modifiesthe DIPPR method for greater accuracy and range of use

Example of a Flammability Calculation in CHETAHIt may be informative to show an example of the output

of a flammability calculation from CHETAH For exampleconsider the flammability calculations for a gas mixture of02 moles tetrahydropyran 04 moles ethylene and 04 molesof ethane in with air as the oxidizing agent at an initial tem-perature of 298 K After the user chooses these compoundsto make up the mixture in the proper amount and executesthe flammability calculation the results shown in Figure A1result Note the flammability results are shown for each ofthe three pure chemicals as well as giving results for the mix-ture The results shown are current solutions from the pro-gram The results for the next version of CHETAH willchange somewhat to reflect updating of the underlyingequations

Planned Future Developments in CHETAH Related toFlammability

There are plans to enhance CHETAH to provide improvedcalculations relative to flammability and to provide conven-ience for explorations for further improvements in relatedtechnology A typical example follows of developmentalactivities that are envisioned to strengthen the usefulness ofCHETAH in this technology area

It is planned to include an ability to calculate an adiabaticflame temperature for a given input fuel concentrationdirectly from the thermodynamic data and correlationsalready included in the CHETAH program This would bepreferable to the present scheme of estimating a value basedon the heat of oxidation Given a fuel concentration corre-sponding to a lower flammable limit (LFL) CHETAH wouldbe able to calculate its adiabatic flame temperature using theenergy release of the combustion reaction in conjunctionwith change in enthalpy calculations for combustion prod-ucts The solution for the adiabatic flame temperature wouldinvolve a search for the value that would satisfy the energybalance CHETAH already accomplishes something quitesimilar to this planned calculation in its present routinethat determines a maximum adiabatic decompositiontemperature for a described composition of chemicals thatneed to be evaluated for possible chemical energy releasehazards

It is planned to refine the correlation in CHETAH for LLFTsas better experimental data become available For example


new data measured for acetylene for LFL (hence LLFT) byZhao [25] in an improved vertical apparatus for measuringflammable limit concentrations differs significantly from thepreviously accepted value

It is planned to continually refine the Britton LFL methodusing only the most reliable LFL data available in CHETAHThe modified Britton LFL method would then be pro-grammed into CHETAH

It is planned to investigate the possibility to improve thecalculation of burning velocity with an additional thermaldiffusivity term Burning velocity is proportional to reactionrate but also proportional to the thermal diffusivity in thepreheat zone of the flame

It is planned to include a calculation for the MESG forpure chemicals and mixtures MESG is more widely usedthan the quenching distance and perhaps should replace itin the program CHETAH results for MESG would not besuitable however for regulated applications like design ofelectrical equipment but only for preliminary safetyassessment

It is planned to extend the flammability calculations usingBrittonrsquos Method to compounds that include halogen sub-stituents This is dependent on development of suitable cor-relations that are of sufficient accuracy to allow reliableresults

It is planned to implement mixture calculations for burn-ing velocity and LMIE for CH and CHO fuels There appearsto be considerable evidence that the use of Le Chatelierrsquosrule for calculating these mixture properties provides reason-able results

It has been noted that the 1st members of homologoussets often exhibit flammability properties that do not followthe trends of later larger members of the same set [2]Providing general correlations to include this abnormalbehavior is problematic It has been suggested that CHETAHshould provide a database of experimental values for suchspecies as opposed to calculating their values from acorrelation

The eventual objective to is provide a robust and compre-hensive tool for flammability-related calculations energyrelease evaluation calculations combustion calculationschemical reaction thermodynamic calculations and for gen-eral chemical thermodynamic predictions and calculationsCHETAH provides a ldquosnapshotrdquo of a chemicalrsquos behaviorcomprising both thermodynamic quantities plus estimatedvalues for complex parameters used in process safetyassessment

ASTM makes no warranty express or implied regardingCHETAH and it is expressly agreed that ASTM will not beliable or in any way responsible for the content of or anerror or omission in this product

LITERATURE CITED

1 BK Harrison CHETAH 90 Users Manual The ASTMComputer Program for Chemical Thermodynamics andEnergy Release Evaluation ASTM West ConshohockenPA (2009) 200 p

2 LG Britton Using heats of oxidation to evaluate flamma-bility hazards Process Saf Prog 21 (2002) 31ndash54

3 L Catoire and V Naudet Estimation of temperature-dependent lower flammability limit of pure organic com-pounds in air at atmospheric pressure Process Saf Prog24 (2005) 130ndash137

4 NFPA 68 Standard on Explosion Protection by Deflagra-tion Venting National Fire Protection AssociationQuincy MA 2013

5 WM Thornton The Relation of Oxygen to the Heat ofCombustion of Organic Compounds Philosophical Maga-

zine Vol XXXIII Series 6 Number CXCIV Paper XVFebruary 1917

6 LG Britton and D Frurip Further uses of the heat ofoxidation in chemical hazard assessment Process SafProg 22 (2003) 1ndash19

7 JM Kuchta Investigation of Fire and ExplosionAccidents in the Chemical Mining and Fuel-RelatedIndustries ndash A Manual US Bureau of Mines Bulletin 6801985

8 S Gordon and BJ McBride Interim Revision NASA SP-273 Computer Program for Computation of ComplexChemical Equilibrium Compositions Rocket PerformanceIncident and Reflected Shocks and Chapman-JouguetDetonations 1976 NASA Glenn Research Center 21000Brookpark Rd Cleveland OH 44135

9 RK Eckhoff M Ngo and W Olsen On the minimumignition energy (MIE) for propaneair J Hazard Mater 175(2010) 293ndash297

10 Standard Test Method for Minimum Ignition Energy andQuenching Distance in Gaseous Mixtures ASTM E582ASTM International 2013

11 HF Calcote CA Gregory CM Barnett and RBGilmer Spark ignition Effect of molecular structure IndEng Chem 44 (1952) 2656ndash2662

12 LG Britton Avoiding Static Ignition Hazards in ChemicalOperations AIChE-CCPS Concept Book 1999 AIChENew York NY

13 P Movilliat and M Giltaire Mesure de lrsquoenergie drsquoinflam-mation de melanges gazeux par decharge capacitiveinflammation par decharge drsquoune personne chargeedrsquoelectricite statique J Electrostat 6 (1979) 307ndash331

14 National Advisory Committee on Aeronautics (NACA)Report 1300 Tables 31ndash32 1959

15 AJ Metzler Minimum Spark-Ignition Energies of 12 PureFuels at Atmospheric and Reduced Pressure NationalAdvisory Committee for Aeronautics (NACA) Report RME53 H3 Washington DC October 29 1953

16 Explosive Atmospheres ndash Part 32-1 Electrostatic HazardsGuidance IEC 60079-32-1 2013

17 LG Britton P Holdstock and RJ Pappas Standardizedignition test procedure for evaluating antistatic flexible inter-mediate bulk containers (FIBC) Process Saf Prog 24 (2005)213ndash222

18 Standard Test Methods for Specific Applications ndash Electro-static Classification of Flexible Intermediate Bulk Contain-ers (FIBC) IEC 61340-4-4 2005

19 National Fire Protection Association NFPA 497 Recom-mended Practice for the Classification of FlammableLiquids Gases or Vapors and of Hazardous Locations forElectrical Installations in Chemical Process AreasNational Fire Protection Association Quincy MA 2012

20 Explosive Atmospheres - Part 20-1 Material Characteris-tics for Gas and Vapor Classification - Test Methods andData IEC 60079-20-1 Ed 10 2010

21 GA Lunn An apparatus for the measurement of maxi-mum experimental safe gaps at standard and elevatedtemperatures J Hazard Mater 6 (1982) 329ndash340

22 LG Britton Two hundred years of flammable limits Pro-cess Saf Prog 21 (2002) 1ndash11

23 IA Zlochower and GM Green The limiting oxygenconcentration and flammability limits of gases and gasmixtures J Loss Prev Process Ind 22 (2009) 499ndash505

24 WK Wong Measurement of flammability in a closedcylindrical vessel with thermal criteria PhD ThesisTexas AampM University College Station TX 2006

25 F Zhao Experimental measurements and modeling pre-diction of flammability limits of binary hydrocarbon mix-tures MSc Thesis Texas AampM University CollegeStation TX 2008


26 T Ma Using critical flame temperature for estimatinglower flammable limits of a mixture Process Saf Prog 32(2013) 387ndash392

27 JE Hustad and OK Soslashnju Experimental studies oflower flammability limits of gases and mixtures of gasesat elevated temperatures Combust Flame 71 (1988) 283ndash294

28 I Wierzba and BB Ale The effect of time of exposureto elevated temperatures on the flammability limits ofsome common gaseous fuels in air Trans ASME 121(1999) 74ndash79

29 HF Coward and GW Jones Limits of Flammability ofGases and Vapors US Bureau of Mines Bulletin 503Washington DC 1952

30 FT Bodurtha Industrial Explosion Protection and Protec-tion McGraw-Hill New York 1980

31 LG Britton Operating atmospheric vent collection head-ers using methane gas enrichment Process Saf Prog 15(1996)

32 GJ Gibbs and HF Calcote Effect of molecular structureon burning velocity J Chem Eng Data 4 (1959) 226ndash237

33 LG Britton New Compilation of Fundamental BurningVelocities in Air Union Carbide Memorandum File No33529 February 27 1985 Submitted to NFPA 68Committee

34 CJ Rallis and AM Garforth The determination of lami-nar burning velocity Prog Energy Combust Sci 6 (1980)303ndash329

35 SC Taylor Burning velocity and the influence of flamestretch PhD Thesis Department of Fuel and EnergyUniversity of Leeds Leeds UK 1991

36 M Gerstein O Levine and EL Wong Flame propaga-tion II The determination of fundamental burning veloc-ities of hydrocarbons by a revised tube method J AmChem Soc 73 (1951) 418

37 AG Gaydon and HG Wolfhard Flames Their StructureRadiation and Temperature Revised 3rd Edition Chap-man and Hall London 1970

38 P L Walker and CC Wright Hydrocarbon burningvelocities predicted by thermal versus diffusional mecha-nisms J Am Chem Soc 74 (1952) 3769ndash3771

39 AF Ibaretta Explosion hazards of multicomponent com-bustible gas mixtures Global Congress on Process Safety2012

40 T Hirasawa CJ Sung A Joshi Z Yang H Wang andCK Law Determination of laminar flame speeds usingdigital particle image velocimetry Binary fuel blends ofethylene n-butane and toluene Proc Combust Inst 29(2002) 1427ndash1434

41 GJ Gibbs IR King and HF Calcote Carbon DisulfideFlames ndash Influence of Moisture Texaco Experiment IncReport TM-642 May 1 1954

42 SW Benson Thermochemical Kinetics Wiley NewYork 1968 320 p

43 DJ Weininger SMILES 1 Introduction and encodingrules J Chem Inf Comput Sci 28 (1988) 31

44 WH Seaton and BK Harrison A new general methodfor estimation of heats of combustion for hazard evalua-tion J Loss Prev Process Ind 3 (1990) 311ndash320

45 RP Danner and TE Daubert (Editors) Manual for Pre-dicting Chemical Process Design Data American Instituteof Chemical Engineers New York 1987


l

l

l

important thermodynamic variable governing flame tempera-ture and other combustion parameters As discussed in theAppendix ASTMrsquos CHETAH Program [1] uses ldquoBrittonrsquos Meth-odrdquo to estimate a series of such parameters from DHox Forcommon hydrocarbon gases DHox varies from 9589 kcalmol for methane to 12004 kcalmol for acetylene Most CHOfuels have values in the same range although higher valuesapply to unstable materials such as peracetic acid Notableexceptions among CHON fuels are nitrated compounds suchas ethyl nitrate (DHox 169 kcalmol) and nitromethane(DHox 205 kcalmol) If Brittonrsquos Method is applied tonitrated compounds using the same approach used for CHOfuels LFL values are underestimated The error increaseswith the degree of nitration so is most pronounced for lowmolecular weight compounds such as nitromethane Thorn-ton [5] concluded that the oxygen contained in nitro-compounds takes no part in combustion (perhaps due to itsassociation with nitrogen instead of carbon) and suggestedwhat amounts to neglecting the bound oxygen in the mole-cule when calculating ldquoSrdquo DHox has been found to have sep-arate applications in assessing instability hazards of unstableorganic materials such as peroxides and nitrated compounds[6]

The ldquonet heat of oxidationrdquo (DHox 5 DHcS) is a measureof the tendency of a fuel to react with oxygen It also pro-vides a measure of the ldquoreactivityrdquo of the fuel via its enthalpyof formation This is because the numerator (net heat ofcombustion) includes release of bond energy (such as CCand CBC bonds) while the denominator (S) normalizes theheat of combustion according to the oxygen needed strictlyfor combustion to products such as CO2 plus H2O Forhydrocarbons that decompose explosively in the absence ofoxidant DHox also provides a measure of instability Forexample the minimum pressure at which the gas will propa-gate a decomposition flame in pipe of a given diametershould decrease as DHox increases

In the case of CHN and CHON fuels the heat of combus-tion accounts for the heat released by forming the strongNBN bonds in the nitrogen product from weaker bonds inthe fuel Functional isomers with identical stoichiometricreactions and ldquoSrdquo values can have very different DHox valuesowing to differences in bond energy An example is ethyleneoxide versus its functional isomer acetaldehyde DHox is aneasily calculated thermodynamic variable that despite Thorn-

tonrsquos Rule provides a fairly wide scale of heat release fromabout 96 to more than 120 kcal per mole of oxygen con-sumed during combustion For CH fuels larger DHox valuesreflect larger quantities of heat available to activate the stoi-chiometric proportion of oxygen molecules As shown in thenext section it also reflects a higher maximum flame temper-ature For CHO fuels the situation is more complex becauseO atoms in the fuel decrease ldquoSrdquo and hence elevate DHox

independent of the heat available to activate oxygen mole-cules However the complicating effects of bound oxygenare mostly exhibited by the first members of homologousseries such as formaldehyde and methanol

This article includes many ldquofirst members of homologousseriesrdquo Such compounds are widely used in chemical proc-esses However the exaggerated effect of the functionalgroup tends to cause atypical flammability behavior whichmakes it more difficult to estimate commonly used parame-ters such as LFL and burning velocity

MAXIMUM ADIABATIC FLAME TEMPERATURE

Figure 2 shows the maximum adiabatic flame temperature(Tfmax) of CH and CHO fuels in air plotted against net heatsof oxidation (DHox) The graph has been updated versusBritton (2002a) using CHETAH-generated DHox rather thanrounded-off values calculated from net heats of combustionpublished by Kuchta [7] The ldquoCHOrdquo set (lower line) includeshydrogen cyanide but insufficient Tfmax data were calculatedto determine if other CHN or CHON fuels follow the sametrend as CHO For each fuel Tfmax values at 298 K were cal-culated for a series of equivalence ratios between 08 and 13using the Gordon and McBride [8] chemical equilibrium pro-gram Quadratic interpolation was then used to find thepeak Tfmax for each fuel at its ldquooptimumrdquo concentration [2]Both fuel sets show a linear relationship between Tfmax andDHox For equal DHox values CH flame temperatures areabout 100 K higher than CHO flame temperatures

The three hydrocarbon flame temperatures falling slightlyabove and parallel to the trend line belong to toluene ben-zene and styrene all of which are aromatics with positiveheats of formation Methanersquos flame temperature is belowthe hydrocarbon trend line but the first members of homolo-gous series often display anomalous behavior Methane has

Figure 2 Dependence of maximum adiabatic flame temper-ature on net heat of oxidation [Color figure can be viewedin the online issue which is available at wileyonlineli-brarycom]

Figure 1 Modified Thornton plot [6] [Color figure can beviewed in the online issue which is available at wileyonli-nelibrarycom]













































128(3a)





128(4a)









































FuelDHc

(kcalmol) SDHox

(kcalmol)LLFT(K)

BrittonEq 4

(mol)

BrittonEq 4a(mol)

BrittonEq 9

(mol)


CampNEq 11(mol)



FuelDHc

(kcalmol) SDHox

(kcalmol)

BrittonEq 4

(mol)

BrittonEq 4a(mol)

Closed10-cm Tube

(mol)
























FURTHER WORK





DISCLAIMER


























than 298 K




















LITERATURE CITED

















































l

l

l












































128(3a)





128(4a)









































FuelDHc

(kcalmol) SDHox

(kcalmol)LLFT(K)

BrittonEq 4

(mol)

BrittonEq 4a(mol)

BrittonEq 9

(mol)


CampNEq 11(mol)



FuelDHc

(kcalmol) SDHox

(kcalmol)

BrittonEq 4

(mol)

BrittonEq 4a(mol)

Closed10-cm Tube

(mol)
























FURTHER WORK





DISCLAIMER


























than 298 K




















LITERATURE CITED

















































l

l

l
































FuelDHc

(kcalmol) SDHox

(kcalmol)LLFT(K)

BrittonEq 4

(mol)

BrittonEq 4a(mol)

BrittonEq 9

(mol)


CampNEq 11(mol)



FuelDHc

(kcalmol) SDHox

(kcalmol)

BrittonEq 4

(mol)

BrittonEq 4a(mol)

Closed10-cm Tube

(mol)
























FURTHER WORK





DISCLAIMER


























than 298 K




















LITERATURE CITED

















































l

l

l





















FURTHER WORK





DISCLAIMER


























than 298 K




















LITERATURE CITED

















































l

l

l




















than 298 K




















LITERATURE CITED

















































l

l

l










LITERATURE CITED

















































l

l

l






















l

l

l

using chetah to estimate lower flammable limit, minimum ignition energy, and other flammability...

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