NBSIR 76-1076

Flammability Limits:

Thermodynamics and Kinetics

Center for Fire Research

Institute for Applied Technology

National Bureau of Standards

Washington. D. C. 20234

May 1976

Final Report

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU Of STANDARDS

Andrej Macek

NBSIR 76-1076

FLAMMABILITY LIMITS:

THERMODYNAMICS AND KINETICS

Andrej Macek

Center for Fire Research

Institute for Applied Technology

National Bureau of Standards

Washington, D. C. 20234

May 1976

Final Report

U.S. DEPARTMENT OF COMMERCE, Elliot L. Richardson, Secretary

Dr. Betsy Ancker-Johnson. Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS. Ernest Ambler, Acting Director

CONTENTS

Page

LIST OF FIGURES iv

LIST OF TABLES iv

Abstract 1

1. INTRODUCTION 1

2. PREMIXED SYSTEMS 3

3. THE OXYGEN INDEX TEST 4

4. THERMODYNAMIC EQUILIBRIUM — ADIABATIC FLAME TEMPERATURES. . 6

5. THE METHANE ANOMALY, BURNING VELOCITIES, AND REACTION RATES. 11

6. DEVIATIONS FROM THERMODYNAMIC EQUILIBRIUM 13

7. ACKNOWLEDGMENTS 21

8. REFERENCES 21

iii
LIST OF FIGURES

Page

Figure 1. Flammability Limits of Propane-Nitrogen-Air

Mixtures at 25 °C and Atmosphere Pressure 5

Figure 2. Computed (Equilibrium) Flame Temperatures

at Flammability Limits for n-Alkanes 9

Figure 3. Computed Flame Temperature Along the Lower

Branch of the Flammability Limits of Propane 14

Figure 4. Flammability Limits of Fuel/Nitrogen/Air

Mixtures 17

LIST OF TABLES

Table 1. Thermodynamic Equilibrium Properties at Extinction. . . 8

Table 2. Oxygen Mole Fractions, Y, and Flame Temperatures at

Extinction Computed on the Basis of the CO

Stoichiometry 20

iv
FLAMMABILITY LIMITS: THERMODYNAMICS AND KINETICS

Andrej Macek

Abstract

Extinction limits for both premixed and diffusion flames

for n-alkanes and n-alcohols found in the literature are assembled. Several sets of theoretical flame temperatures

corresponding to the limits are defined and presented. The

implications of the view that flames fail to propagate at

temperatures at which reaction rates become too low to overcome the dissipation processes are discussed. Equilibrium

flame temperatures indicate that at lean limits the excess oxygen does not act merely as a diluent but takes an active

part in promoting the kinetics of flame reactions. The

burning-rate data and the results of ignition experiments

are shown to be pertinent to the interpretation of flammability limits. Extinction characteristics of methane are shown to be atypical (compared to other alkanes and alcohols)

and demand a special explanation. It is also shown that the

assumption of thermodynamic equilibrium at the limits is

unrealistic, so there is need for experimental temperature

and concentration measurements in both premixed and diffusion flames. When the assumption of equilibrium is removed,

the chemical kinetic considerations suggest a simple qualitative explanation of the limit phenomenon, based on the

stipulation of incomplete combustion. Quantitative data are presented in support of this view.

Key words: Chemical kinetics; diffusion flames; flame

extinction; flame temperature; flame velocity; f lammability

flammability limits; Oxygen Index Test; thermodynamics.

1 . INTRODUCTION

The question of flame extinction and flammability limits has been

recognized for a long time as one of great interest, both theoretical

and practical. In particular, measurements have been made over many

years on flammability limits in premixed gaseous systems because of

obvious applications to the explosion safety problem. While measurements of flammability limits for various diffusion flames are of more

recent date, they are even more broadly applicable to fire safety problems, because they can be made with gaseous, liquid, or solid fuels.

The common feature of diffusion flames for all fuels is that the principal source of energy is the gas-phase combustion. The distinguishing

feature of flames and fires fueled by condensed materials is the existence of a vaporization process, probably endothermic and often involving pyrolysis, which precedes the gas-phase mixing and combustion.

1
However, once the gaseous pyrolysis product is generated, it forms an analogue to the fuel source in gaseous diffusion flames.

This paper deals with the fundamental phenomena of flammability

limits in both premixed and diffusion-controlled systems. While the

underlying principles no doubt apply more generally, the discussion is

restricted to limits (a) at atmospheric pressure, (b) with oxygen gas

(O2) as the only oxidant, and (c) with nitrogen (N 2

) as the diluent.

Furthermore, for the sake of simplicity, all quantitative data used for

illustration purposes are drawn from experiments with two homologous

series of fuels: n-alkanes and n-alcohols. Thus the discussion is

limited to simple systems, the elemental composition of which is restricted

to carbon, hydrogen, oxygen and nitrogen. Under these restrictive con- ditions, a complete set of experimental data needed for our purposes is

available.

Flammability limits in premixed gaseous systems have been discussed

extensivelyj in the combustion literature. A recent critical review of -1 the subject was published by Lovachev et al. [1] . An even more recent

paper by Burgess and Hertzberg [2] summarizes the dissipation processes

which convene to determine the limiting conditions; these include both

heat loss and several aerodynamic effects. However, while causes of

extinction at limits are complex, Burgess and Hertzberg [2] emphasize

that at least one experimental parameter, burning velocity at the lean

limit, tends to about the same value for many fuels. It has also been

common knowledge for a long time that the computed (equilibrium) adiabatic flame temperatures for lean-limit mixtures in air cluster near

1500 or 1600 K for many hydrocarbon- type fuels. Since burning velocities

are determined by a combination of chemical kinetics and of transport

processes, and since transport properties do not vary much in these fuel

systems, a frequently accepted view is that flames fail to propagate at

temperatures at which reaction rates become too low to maintain the burning velocity required to overcome the dissipation processes; see the

historical outline by Burgess [3]. The fact that addition of small

amounts of chemical inhibitors (e.g., halogens), which affect primarily

the chemical kinetics of the flame, raises the lean limits — i.e.,

increases the theoretical flame temperature at the limit — supports

that view. The main purpose of this paper is to bring out some fundamental implications of that view. It will be shown that a re-examination

of experimental f lammability-limit data for simple hydrocarbon fuels

(without chemical inhibitors), and the theoretical computations of flame

temperatures corresponding to these data, can clarify the thermodynamic

and chemical-kinetic aspects of near-limit systems for both premixed

flames and diffusion flames.

Numbers in brackets refer to the literature references listed at the

end of this paper.

2
Flammability-limit data for gaseous diffusion flames are not quite

so extensive as in the case of premixed systems, but they are also

entirely adequate for our purposes. The best developed and standardized

experimental procedure for diffusion flames is the Oxygen Index Test,

which was developed for gases and liquids by Wolfhard and coworkers [4,

5,6], and for solids by Fenimore and Martin [7]. In all cases the

Oxygen Index is defined as the limiting mole fraction of oxygen in an oxygen/nitrogen mixture necessary to maintain a diffusion flame. In the

recent years, many solids have been rated by the test, but these data

will not be discussed. The discussion will be restricted to thermodynamic

aspects of the results obtained for gases and liquids, and will center

around the comparison of these with the results obtained with premixed

gaseous systems. A natural limitation imposes itself immediately on the

extent to which such a comparison can be made: While in premixed systems

one can obtain a set of f lammability-limit data for each fuel, corresponding to a wide range of f uel/oxidant/diluent proportions, this is not

true of diffusion flames each of which determines its own unique stoichiometry

.

In addition to results of these standardized tests, it will be

shown that useful information toward a better understanding of thermodynamics and chemical kinetics of flammability limits can be drawn from

ignition and burning rate data.

To prevent confusion in the mind of the reader, we must emphasize

at the outset that the discussion will be on two distinct levels.

Firstly, quantitative calculations and reasoning will be presented based

on the assumption that thermodynamic equilibrium obtains in all flames.

This is the usual assumption. Secondly, we shall give qualitative con- clusions based on the realization that we are dealing with processes

where attainment of full equilibrium should not be expected. The distinction is important, because the conclusions differ depending on whether one does or does not assume attainment of full thermodynamic

equilibrium.

2. PREMIXED SYSTEMS

The comprehensive compilation by Zabetakis [8], which presents

detailed data on flammability limits in premixed systems obtained from

upward flame propagation experiments will be used in all tabulations and

calculations. Since it is known that upward limits are broader than for

the downward case, they are certainly appropriate for fire and explosion

safety purposes, but one may question whether they are entirely so for

the purpose of basic correlations. Burgess and Hertzberg [2] point out

that buoyancy helps the upward and impedes the downward flame propagation;

hence, horizontal propagation, or perhaps an average of upward and

downward limits, may be a more logical basis for a fundamental discussion.

However, while the numerical flame temperature values derived from such

alternative experiments (downward or horizontal) would be somewhat different, it appears probable that our general conclusions would remain

3
substantially unchanged, especially for heavier fuels, because the spread

between upward and downward lean limits decreases with increased molecular weight of the fuel. The case of methane is something of an exception,

and will be discussed in section 5.

The f lammability-limit diagram for propane [8] is reproduced in

figure 1. Propane is chosen for illustration purposes here and in subsequent discussion. The choice is arbitrary, but convenient. Propane

is a very common fuel, for which many data are available and, since its

molecular weight is higher than that of oxygen, complications associated

with selective diffusional demixing are not prominent in lean mixtures —

see the article by Burgess and Hertzberg [2] and section 5 of this paper.

Plots analogous to figure 1 are available for most fuels which will be

discussed. The nomenclature for three key points on the flammability

limit curve — lean limit (LL), upper limit (UL) , and nitrogen peak

(NP) — is conventional and self-explanatory. The term "stoichiometric"

is also used in the conventional sense: it refers to mixtures containing

just enough oxygen to be able to oxidize all of the carbon to C0 2 and

all of the hydrogen to H2 0. The intersection of the stoichiometric line

with the limit curve is denoted SL. In thermodynamic equilibrium the

enthalpy release per unit mass of the mixture is maximized along the

stoichiometric line, so if an adiabatic flame temperature coordinate

were added perpendicular to the plane of figure 1, the stoichiometric

line would appear as a high ridge with downward slopes toward both the

upper and the lower f lammability-limit branches.

A point concerning the distribution of combustion products should

be emphasized. Generally, the term "stoichiometric" refers merely to a simple way of specifying the oxygen/fuel ratio necessary for complete

oxidation of the fuel; it should not be taken to imply that such com- plete oxidation actually takes place or is even predicted by thermodynamics. However, along the stoichiometric line in the region of interest

to us thermodynamic computations show that the equilibrium combustion

products (at the adiabatic flame temperature) do consist largely of C0 2 , H 2 0, and N2 . Dispropor tionations of C0 2 to CO and 02 , etc., occur to some extent at relatively high temperatures near the ordinate, but are negligible near the flammability limit. A fortiori, thermodynamics

predicts virtually full formation of C0 2 and H 2 0 everywhere below the

stoichiometric line, the excess oxygen remaining as free 0 2 ; thus the

thermodynamically-predicted reaction is in fact stoichiometric not only

at, but also everywhere below the line. The only consideration of

importance is whether the dilution is entirely by nitrogen (along the

line) , or also partly by excess oxygen (below the line)

.

3. THE OXYGEN INDEX TEST

Oxygen- index (01) data have been reported for two different experimental test arrangements. The simpler and more commonly used geometry

is that of a cylindrical column of fuel (solid stick or cup filled with

liquid) having a diameter of the order of 1 cm, and surrounded by an oxygen-nitrogen mixture flowing upward at a velocity of a few centimeters

4
Figure 1. Flammability

Air Mixtures at 25 °C

(from reference [8]).

Limits of Propane-Nitrogenand Atmosphere Pressure

5
per second [7]. While, in principle, one can use this geometry also

with gaseous fuels, Simmons and Wolfhard [5] report having obtained more

reproducible data both for gases and for liquids by a somewhat different

geometric arrangement, utilizing an inverted porous-hemisphere burner.

For internal consistency, we shall use the Simmons-Wolfhard data for all

numerical illustrations of diffusion flames.

Adiabatic flame temperatures corresponding to the 01 (i.e. extinction)

conditions were calculated by Simmons and Wolfhard [5], but it must be

recognized that they rest on two assumptions. The first assumption is

that flame products come to thermodynamic equilibrium. In a diffusion

flame this means that the reactants fully consume each other, i.e., that

they enter the flame in very nearly stoichiometric proportions (providing

the temperature is so low that dissociation is negligible — see section

2. While the assumption of thermodynamic equilibrium, hence of complete

reaction, is probably not realistic near flammability limits, it must be

pointed out that the same assumption is made also in conventional computations of premixed flame temperatures. The second assumption is that

the N2/O2 ratio in the flame is the same as at the cold boundary. Again,

this may not be quite true, because in diffusion flames one generally

expects to find concentration gradients of all species, including diluents, but the assumption is probably good in cases where the inert gas

is present in very large amounts (over 80% at 01 for alkanes and alcohols).

These two assumptions suffice for a complete thermodynamic definition of

the experimental 01; furthermore, the thermodynamic state so defined

corresponds to a point along the stoichiometric line in the f lammabilitylimit diagram for premixed systems, discussed in section 2. Indeed,

Simmons and Wolfhard [5] call the ratio 02/(02 + N2) at premixed flammability limits also "oxygen index from limits of inflammability," with

the implication that one can define an infinite set of oxygen indices

along a single f lammability-limit curve, such as the one for propane

shown in figure 1; the relation between the two oxygen indices so defined — by diffusion and by flammability — presumably offers a measure of similarity, or differences, in flammability requirements for

premixed and diffusion flames. Since in the recent years the term

Oxygen Index has become firmly associated with diffusion experiments, it

will not be applied to premixed systems in this discussion. However, we shall proceed along the path indicated by Wolfhard and coworkers [4,5,6]

and examine closely the relation of calculated flame temperatures cor- responding to experimental 01 data, T(0I), and temperatures calculated

along the premixed f lammability-limit curves, e.g., T(LL), T(SL), or T(NP)

.

4. THERMODYNAMIC EQUILIBRIUM — ADIABATIC FLAME TEMPERATURES

This section explores the implications of the assumption that

thermodynamic equilibrium is attained in f lammability-limit experiments.

6
Table 1 lists values of LL, SL, and NP for premlxed systems from

Zabetakis [8] , 01 from diffusion experiments of Simmons and Wolfhard

[5], and the respective computed adiabatic flame temperatures for each.

LL is given as the mole percent of fuel, a standard practice in the

combustion literature. SL and NP are given in terms of oxygen mole

fractions, Y, which is convenient for the subsequent discussion. Note

that 01, being defined as the mole fraction of oxygen in oxygen/nitrogen

mixtures without fuel, is always slightly higher than the mole fraction

Y(0I) in the corresponding premixed system used for calculations of

T(0I). Note also that, in the Oxygen Index experiment, only 01 = [02/(02 + N2)]i-j m

is an experimental quantity; the values of both Y(0I)

and T(0I) depend on the thermodynamic assumptions stated in section 3.

Thermodynamic data for temperature computations were taken from JANAF

Tables [9] and from Stull et al. [10].

Consider first the series of alkanes. As pointed out originally by

Simmons and Wolfhard [5] , the states 01 and SL coincide quite closely;

furthermore, all temperatures pertaining to these two sets of data —

T(0I) and T(SL) — cluster in the same range, except for ethane, the

values for which are somewhat low. The apparent implication is that in

the 01 test, and in the premixed limit test at the stoichiometric point,

ethane is somehow more flammable than other alkanes. This matter will

now be pursued somewhat beyond the extent of earlier discussions.

Figure 2 shows the plots of T(0I) and T(LL) for alkanes versus the

number of carbon atoms in the fuel molecule. Two aspects of these plots

deserve attention. Note first that both T(0I) and T(LL) decrease smoothly

with decreasing molecular weight of the fuel, T(0I) for methane being

the only gross exception. Following the T(0I) curve down the rungs of

carbon atoms, one would perhaps expect to find methane in the familiar

region around 1500 K; instead, it appears about 300 K higher. Thus the

suggestion of the T(0I) curve is not so much that the 01 test rates

ethane as unusually flammable, but that it rates methane as anomalously

nonflammable. This problem will be discussed in section 5.

The second point of interest is a quantitative comparison of the

two curves in figure 2. Note that the T(0I) values are on the average

about 150 K higher than T(LL) — less than average for ethane, much more

so for methane. One may be tempted to ascribe the temperature difference

to the fact that the upper curve relates to diffusion experiments and

the lower to premixed flames. Surely, this would be incorrect. One

need not go at all to diffusion experiments to demonstrate the difference

between T(LL) and temperatures of limiting mixtures at or near the

stoichiometric, as an inspection of table 1 will show: the T(SL) values,

while somewhat more scattered than their T(0I) counterpart, are clearly

in the domain of the upper curve of figure 2 and substantially above the

lean-limit data. Yet, these SL temperatures are derived from the same source of premixed flammability data as T(LL). The difference, then, is

not one between premixing and diffusion, but one of stoichiometry : it

is the difference between excess oxygen (at LL) and the bare sufficiency

thereof (01 and SL) . In figure 1, as one proceeds from LL along the

limit curve, the equilibrium flame temperature necessary to maintain the

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flame increases. Now, if one accepts the general explanation of the

role of chemical kinetics near flammability limits, as stated in the

introduction, the clear implication is that SL conditions are kinetically less favorable than at the LL, and therefore demand higher temperatures for viability of the flame.

An attempt to use the data in table 1 to reach a conclusion also

about differences in flammability requirements between premixed and

diffusion flames creates something of a dilemma. On one hand, a comparison of T(OI) and T(SL), or of the respective oxygen mole fractions Y(OI)

and Y(SL) — which is entirely appropriate in the light of the foregoing

discussion — shows virtually no differences. If anything, the indication is that in some cases the diffusion flames have slightly lower

thermal and oxygen requirements (see the entries in table 1 for pentane,

hexane, and methyl alcohol), which in itself is somewhat puzzling; one would rather expect the opposite. On the other hand, there is the

experimental fact, unencumbered by the thermodynamic assumptions used to

calculate Y(OI), T(OI), and T(SL), that the maximum dilution which a diffusion flame can tolerate is less than for premixed flames: a com- parison of 01 with NP appears to give a more reasonable idea of the

differences in flammability requirements, than the comparison of 01 with

SL. This was recognized by Simmons and Wolfhard [5] who, after establishing a close correspondence of 01 and SL, still used the dilution effect,

i.e. a comparison of 01 with NP, to reach their conclusion: it is the

fact that a premixed flame can be diluted with more nitrogen than a diffusion flame that points to fundamental differences between the two

types of flames. A resolution of this dilemma will be given at the end

of the paper, after a discussion of non-equilibrium effects.

An additional comment regarding the flammability limits in premixed

systems, having practical consequences, is in order here. To wit, the

effect of oxygen in shifting the limiting equilibrium flame temperature

in these systems, although qualitatively understandable, appears sur- prisingly large; for example, in the case of propane there is a 190 K

temperature increase upon a modest decrease of oxygen mole fraction from

0.204 at LL to 0.125 at SL. This means that the assumption of thermodynamic equilibrium strongly indicates that practical explosion and fire

safety problems must be approached with care. In particular, even if

the hazard occurs because of rising mole fraction of the fuel (i.e., if

there is threat of crossing the lower branch of the f lammability-limit

curve, which is a common practical case), one should be careful not to

identify potential problems of gas-phase explosion and flammability

indiscriminately and exclusively with lean limits, because the oxygen/

nitrogen ratio also matters. Lean-limit thermodynamics will indeed be

applicable if the 0 2 /N 2 ratio is that of air, but the thermodynamics may

be significantly different if that ratio is lower. It is obviously

different in 01 experiments. Oxygen depletion may occur also in practical fire and explosion situations. In such cases, increase of mole

fraction of oxygen (without change in mole fraction of the fuel) may be

hazardous: as the above discussion shows, oxygen in excess of the

stoichiometric does not merely act as a diluent but takes an active part

10
in promoting flame reactions and thus lowering the thermodynamic requirement for establishment of a flame. However, it should be mentioned here

that non-equilibrium considerations admit the possibility that the effect

of oxygen is somewhat less than indicated by the discussion so far; this

is an important matter, and it will be taken up in section 6.

5. THE METHANE ANOMALY, BURNING VELOCITIES, AND REACTION RATES

As seen in table 1 and figure 2, the 01 test gives methane a relatively low flammability rating, compared to other alkanes and alcohols.

In particular, its flammability is substantially lower than those of its

neighbor alkanes, ethane and propane, and very much lower than that of

methyl alcohol. Other combustion experiments indicate that this low

rating by the 01 test is in fact realistic. For example, Vanpee and

Wolfhard [6] report ignition temperatures for a hot air jet into fuel as 1310 K for methane, but only 1110 K for ethane, 1160 K for propane, and

1180 K for butane. We shall now discuss some burning velocity (Su ) experiments which indicate the same relative ranking and, moreover, give

additional insight into reactivity and kinetics of hydrocarbon oxidation

at high temperatures.

The data of Gibbs and Calcote [11] show that lean methane-air mixtures generally have Su values lower than other alkanes; only high homologues on the rich side show Su values somewhat below that of methane.

Ethane and propane always burn faster than methane.

Kaskan [12] made an especially interesting study of burning velocities as functions of flame temperature by means of a quenched- flame

technique which allows controlled flame temperature variation for a fixed stoichiometry . He found that methane-air mixtures not only burn

more slowly than either ethane or propane, but that S u for methane has a higher temperature coefficient, hence a higher "overall activation

energy." According to Kaskan' s own interpretation [12], which is most

useful for the purposes of this discussion, the differences among the

burning velocities of various hydrocarbons must be sought in the differences of primary oxidation rates to CO and H2O. This is so because the

final stage of flame reactions, which is known to be oxidation of CO to

C0 2 [13], must be common to all hydrocarbons. The interpretation is

bolstered by the fact that C0/H2 mixtures, in which the primary oxidation

of carbon is eliminated, burn very rapidly: burning velocities of all

hydrocarbons which Kaskan [12] studied — ethane, propane, ethylene, and

acetylene — were found to be intermediate between those of methane

(slow) and carbon monoxide/hydrogen mixtures (fast). Thus, hydrocarbons

which burn slowly do so because their primary oxidation rates to CO are relatively slow. Kaskan' s activation energies (from burning velocities

in air, stoichiometric ratios), which must relate in some fashion to the

kinetics of primary oxidation to CO and H 2 0, rank the five fuels in the

following increasing order: C2H2, C2H1+, C2H5, C3H8, CH^. This is also

the order of increasing T(0I) values.

11
Thus, several independent combustion measurements agree with the

f lammability-limit ranking of the 01 test. For alkanes, this means that

fuels become progressively more flammable with decreasing molecular

weight, with sudden reversal of the trend in the case of methane. The

key to low flammability of methane must be in the fundamental kinetic

mechanism of oxidation of methane, more specifically in differences

between oxidation mechanisms of methane and ethane. This problem has

not been resolved, but two points may be mentioned indicating that it is

reasonable to expect methane oxidation to be relatively slow. First,

methane is a very stable molecule, so the initial attack upon it (by

hydrogen abstraction) will be relatively slow. Second, despite much

work, no kinetically easy route has been found for subsequent oxidation

of the CH3 radical in flames. Recent studies by Peeters and Mahnen [14]

indicate that oxidation of CH3 by oxygen atoms is the key step — a radical-radical reaction, hence necessarily relatively slow. Attachment

of oxygen to the C-C bond in higher hydrocarbons may be kinetically

easier. If this reasoning is correct, one should expect that fuel

molecules containing a single carbon atom which is already oxidized will

be substantially more flammable than methane. Two such molecules are formaldehyde, which in fact is usually assumed to be an intermediate in

the oxidation of methane, and methyl alcohol. Rough high-temperature

01 data for formaldehyde [4] indeed indicate it to be much more flammable

than methane, but the data cannot be quantitatively compared to the

results of Simmons and Wolfhard [5] . Methyl alcohol, on the other hand,

does provide the comparison and it fulfills the expectation: as shown

in table 1, the T(0I) value for methyl alcohol, 1530 K, is substantially

lower than for ethyl alcohol, and very much lower than for methane.

T(0I) values for alcohols higher than methyl are aligned along the upper

curve in figure 2 showing that, with the sole exception of methane,

alkanes have about the same thermal requirements for flammability as the

corresponding alcohols.

In view of the considerable weight of evidence that methane is a gas of unusually low flammability, it is surprising that the lean-limit

data indicate the opposite to be true: the lower curve in figure 2 descends uniformly down to methane, indicating it to be the most flammable of alkanes. We believe this apparent behavior to be caused by the

phenomenon of selective diffusional demixing, which has been known for a long time to influence the f lammability-limit behavior of hydrogen

because of its low molecular weight. Alone among the alkanes (and

alcohols), methane has the molecular weight only half that of O2. Thus,

it must be expected that the actual mole fraction of methane in the

flame, hence also the flame temperature, is higher than that calculated

on the basis of complete mixedness. It has been pointed out by Burgess

and Hertzberg [2] that the phenomenon has less of an effect on downward

than on upward propagation of the flame. Indeed, a comparison of T(LL)

for downward propagation, listed in table 1, shows methane to be slightly

less flammable than ethane. Thus, while the lean limits for methane

given in the literature [8,15] no doubt give a good measure of flammability for safety purposes, they are not representative for the purpose

of thermodynamic comparisons.

12
6. DEVIATIONS FROM THERMODYNAMIC EQUILIBRIUM

The preceding pages have discussed some implications of the assumption of thermodynamic equilibrium at flammability limits, both for premixed and for diffusion flames. We now return to a subject, first

brought up in section 4, which pertains to premixed limits only; to wit,

the role of oxygen along the lower branch of the f lammability-limit curve

(fig. 1). We pointed out that as the mole fraction of oxygen decreases,

the equilibrium flame temperature at the limit increases quite substantially; and following earlier thoughts, we interpreted this to mean that

the decreasing availability of oxygen chemical kinetic conditions for

oxidation becomes less favorable, demanding increasing temperatures for

viability of the flame. The reader will have noted, however, that the

word so far has been only about the segment of the limit curve between

the lean limit and the stoichiometric point. An attempt to extend this

reasoning over the short, but extremely important, segment to the nitrogen peak, at once, reveals an apparent failure of the interpretation and

gives a clue as to what can and what cannot be expected from thermodynamic

equilibrium calculations.

The upper curve in figure 3 shows the equilibrium temperature variation along the entire lower branch of the limit curve for propane, from

LL to NP plotted against added nitrogen as in figure 1 (fig. 3 should be

inspected in conjunction with fig. 1); the mole fraction of oxygen in

the unburnt mixture is also indicated on the abscissae. Similar temperature curves are obtained from flammability limits of other hydrocarbons.

The precipitous temperature drop from SL to NP, amounting to 260 K for

propane and as much as 400 K for pentane, is striking — and unrealistic.

It does not appear reasonable that gradual deprivation of oxygen, without an identifiable discontinuity, should suddenly benefit the flame to

the point where it becomes viable even at temperatures below those at

the lean limit where oxygen abounds. The opposite should be expected,

namely an increase of limit temperatures beyond SL, where oxygen becomes

deficient. We conclude that the negative slope, and hence the entire

stoichiometric hump in figure 3, cannot have the kinetic-thermodynamic

significance postulated in the discussion thus far, and may not arise in

reality at all.

The cause of the sharp rise in equilibrium temperature from NP to

SL is easily seen by inspection of the two respective stoichiometries

At SL:

C 3 H8 + 5.0 0 2 + 33.1 N2 ^2.9 C0 2 + 0.1 CO + 4.0 H2 0 + 33.1 N2 ; T(SL) = 1730 K.

At NP:

C 3 H8 + 3.7 0 2 + 27.8 N2 —1.5 C0 2 + 1.5 CO + 2.9 H2 0 + 1.1 H2 + 27.8 N2 ; T(NP) = 1470 K.

13
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14
The enthalpy responsible for the temperature difference T(SL) - T(NP) comes largely from oxidation of CO, present at NP, to CO2, with a smaller

contribution from oxidation of H2 • However, if chemical kinetics becomes

limiting near extinction, it is precisely the oxidation of CO to CO2,

the final stage of the flame reaction requiring a relatively long time

at high temperatures, which will be affected. Therefore, one can cer- tainly not assume that equilibrium amounts of CO2 (which would mean com- plete oxidation of carbon at all points to the left of SL in figures 1

and 3) will form at extinction. Rather, one should expect incomplete

reaction.

Since it appears that, at least in the region between SL and NP,

the equilibrium thermodynamics does not give a realistic representation,

one must turn to the experiment for information about the chemical com- position and temperature of combustion products near limits; the available reaction rate data, of course, are totally inadequate to be of

quantitative use. Unfortunately, the experimental information is also

extremely limited. We are aware of no temperature measurement or chemical analysis in premixed f lammability-limit tests. Since the flame

front in these tests is moving, and the reaction tube has to be open on both ends, such measurements would be difficult to make. As far as the

01 test is concerned, Fenimore and Jones [16] made both analytical and

temperature measurements for polymeis at reduced pressures, and concluded

that, even significantly above the extinction (01) values, formation of

CO and C0 2 in equal amounts — i.e., substantially incomplete

combustion — is a reasonable assumption for estimates of heat release.

At limits, one should probably expect even less complete combustion.

Evidently, much more experimental information is needed on both the

composition and temperature of the flame reaction products as flammability limits are approached.

Besides the meager data from f lammability-limit tests, more extensive

and detailed experimental data from burner experiments are on record,

and some of these may be of indirect use for our purposes. Such, for

example, are the early findings of Friedman and Cyphers [13] that the

CO/H2 ratio in low-pressure lean propane flames is much in excess of the

equilibrium value, indicating that the formation of H2 in the water-gas

equilibrium,

H2 0 + CO^H.2 + C0 2 ,

cannot keep up with generation rates of H2O and CO. Relative rates of

formation for these and other species in low-pressure methane flames

have also been reported by several workers [14,17].

In the absence of adequate experimental information, one must resort

to conjecture. If, as appears to be the case, both C0 2 and H2 are late

products, their concentrations will tend to remain low as the late reaction stages are affected at extinction. Therefore, we shall attempt to use the simple CO stoichiometry — i.e., oxidation of hydrogen to H2 0,

but carbon to CO only — as a rough first approximation to the distribution of products formed at limits. The implied assumption is that

15
oxidation of CO to C0 2 , if any, will take place sufficiently downstream

of the main reaction zone not to affect extinction (or the processes

determining the flame velocity) . The extent of such oxidation will

depend on the residence time of partly oxidized products at high temperatures, i.e., on the geometry of a particular burner. In the case of

experiments discussed in this paper it is probable that the extent of

oxidation to C0 2 near extinction is always low, and especially for stoichiometrics near NP.

Several consequences of the assumption of partial combustion can be

made evident easily. Adiabatic flame temperatures calculated on the

assumption of the CO stoichiometry are plotted in figure 3 (lower curve)

along with the equilibrium temperatures. As expected, these temperatures

increase monotonically with decreasing availability of oxygen. In

particular, the very steep temperature increase as the ultimate dilution

by nitrogen is approached, appears qualitatively reasonable. Figure 4

is even more interesting. It shows the f lammability-limit curves for

several higher hydrocarbons from the literature [8], in which, however, we have indicated not only the conventional full-combustion stoichiometry, but also the deficient CO stoichiometry. It is most instructive

to see that the CO-stoichiometry lines intersect the limit curves near

NP in all four cases, showing that the maximum allowable dilution by

nitrogen is attained when there is just enough oxygen for oxidation to

H2 0 and CO; beyond that point a truly fuel-rich situation obtains,

corresponding to the upper branch of the f lammability-limit curve.

Thus, the fact that nitrogen peaks usually lie well to the fuelrich side of "stoichiometric" mixtures does not necessarily imply a peculiar preference by flames for fuel-rich conditions, occasionally

hinted at in the literature. Rather, the a priori expectation that maximum allowable dilution by nitrogen will coincide with the stoichiometry

corresponding to the maximum heat release may well be true, after all.

It is just that the choice of this stoichiometry should be based on

estimates of realistic flame reactions, not simply on the assumption of

complete oxidation. As our discussion shows, both the experimental

f lammability-limit data (see especially fig. 4) and the conjecture about

chemical kinetics suggest that for many fuels the CO stoichiometry may

be a more realistic first guess.

It is doubtful whether any special significance should be attached

to the fact that some nitrogen peaks (fig. 4) are a little on the lean

and others on the rich side of the CO-stoichiometry. It is generally

agreed that the flammability limit is not a sharply defined fundamental

phenomenon. Thus even at LL the definition of the limit composition may

be a bit diffuse. At NP the uncertainty is apt to be more, because the

definition of the peak is very sensitive to the exact shape of the curve. This causes a problem in calculation of flame temperatures

around NP, especially in cases where NP corresponds to a composition

even richer than the CO stoichiometry: in the case of pentane, for

example, the construction of curves analogous to those given in figure 3

becomes well nigh impossible, because both curves become virtually

16
Figure 4. Flammability Limits of Fuel/Nitrogen/Air Mixtures.

Percent Fuel vs Percent Nitrogen Added to Air (from ref. [8]).

17
vertical as NP is approached, tending to meet around 1400 K. In fact,

all adiabatic flame temperatures calculated on the basis of the CO

stoichiometries approach values near 1400 K as nitrogen peaks are approached

.

Nitrogen peaks of both methane and ethane differ somewhat from

those of higher alkanes: they are intermediate between the CO stoichiometry and the fully oxidized C0 2 stoichiometry . ' While methane displays

sufficient anomalous behavior (section 5) to explain the difference

between it and the higher alkanes, the explanation for ethane is not

obvious. The N-peaks for both methyl and ethyl alcohol are close to,

but a little to the lean side of the CO stoichiometry.

It follows that, until adequate experimental data become available,

only extremely rough estimates can be made of actual temperatures at

extinction. From what was said above, it appears that the adiabatic

flame temperature most likely will be somewhere between the two curves

in figure 3 (although there is no fundamental reason why it could not

fall even below the CO-stoichiometry curve) . This means that it is

reasonably well bracketed only at the nitrogen peak (about 1400 K)

.

Beyond that, we may surmise that it will decrease monotonically toward

the lean limit, and thus fall somewhere below 1400 K at LL. To be sure,

it should not be assumed that it will follow the lower curve, even though

this curve does predict qualitatively reasonable behavior. Quite apart

from the fact that the CO stoichiometry is only a first approximation

which can hardly be given quantitative credence at any point, one might

guess that increasing availability of oxygen will favor some formation

of CO2 toward the lean limit. Thus, the quantitative value of the

temperature difference between LL and NP remains in question (cf. discussion in section 4)

.

The above estimates concerning adiabatic flame temperatures must,

of course, be further modified by a downward correction for the heat

loss. Quantitative estimates of heat losses at limits are available in

the literature — see for example the text by Mullins and Penner [19] —

but this subject will not be pursued here.

The discussion by Lewis and von Elbe [18] indicates otherwise, because

it assumes that the NP composition for methane is fuel-lean, corresponding to an equivalence ratio ER = 0.88. However, this value of ER is

due to an error in arithmetic. According to the data of Coward and

Jones [15], used by Lewis and von Elbe, the NP composition for methane

is in fact slightly fuel-rich (ER = 1.03). According to the more recent

compilation by Zabetakis [8], which we have adopted for all our calculations, the NP compositions for both methane and ethane are substantially fuel-rich having ER values of 1.12 and 1.14 respectively. The

discussion of the N-peak region by Lewis and von Elbe [18], which is

partly based on the erroneous value for methane, would have to be amended.

18
We conclude with a brief and tentative discussion of the applicability of this interpretation to diffusion flames. On the assumption of

the CO stoichiometry the 01 point will lie somewhere on the line appropriate to that stoichiometry (upper straight lines in figure 4). The

relevant data for higher alkanes and the two alcohols for which the

f lammability-limit curves are available are listed in table 2. It can be seen that both thermal and oxygen requirements are always somewhat

higher for diffusion flames than for their premixed counterpart. Graphically, this means that, in all cases, in order to find the extinction

limit for a diffusion flame one must move from the premixed limit along

the CO stoichiometry line to a point inside the flammability peninsula

(see fig. 4). This is entirely reasonable. By contrast, it will be

recalled that thermodynamic equilibrium (table 1) would place the 01

state either at SL, or even shift it along the "stoichiometric" line to a lower temperature at a point outside the premixed limit. This does

not appear reasonable. Thus for diffusion flames, just as for premixed

flames, the CO stoichiometry describes behavior which is qualitatively

more credible than that predicted by the assumption of equilibrium.

Table 2 also allows another quantitative comparison. It can be seen

that differences in extinction temperatures among the fuels, within

either the premixed or the diffusion column, are larger than the differences between the two columns; compare especially the data for alkanes

with those for methyl alcohol. This would indicate that in diffusion

flames, just as in premixed flames (see Introduction), the extinction

temperature is determined primarily by chemical kinetic requirements.

Increments of extinction temperatures in the 01 experiment over those

found with premixed flames — presumably due to the additional requirements of interdif fusion of the fuel and the oxidant — are noticeable,

but small (20 to 100 K)

.

It should be noted that reasonable comparisons can be made from the

data in table 2 because for all fuels listed in that table the CO stoichiometry lines intersect the f lammability-limit curves near NP; when

this is the case the CO stoichiometry appears to be a useful rule of

thumb, and it can be invoked to resolve the dilemma about relative

flammability requirements in the two types of flames (see section 4)

.

It shows that it is indeed the location of NP — not of SL — relative

to 01 that gives a meaningful measure of the difference. No broad generalizations should be made, however, because there is no assurance that

any given experimental situation will always be so simple; for example,

in the case of ethane neither the full equilibrium stoichiometry nor the

CO stoichiometry appears to fit the facts. Only further experiments

aimed at elucidating realistic combustion stoichiometries can tell.

19
Table 2. Oxygen Mole Fractions, Y, and Flame Temperatures

at Extinction Computed on the Basis of the CO Stoichiometry

Premixed Flammability Limits Oxygen Index (Diffusion)*5"

Y T(°K) Y T(°K)

C 3 H 8 0.114 1400 0.123 1470

n-Ci^Hjo 0.120 1420 — —

n-C 5 H 12 0.116 1390 0.130 1480

n-C 6 H llf 0.117 1420 0.131 1480

n-C 8 H 18 0.119 1380 0.131 1480

n_C 10 H 22 0.119 1390 0.132 1480

CH3OH 0.098 1260 0.100 1280

C 2 H 5 OH 0.107 1330 0.119 1380

From experimental data complied by Zabetakis [8]

.

From experimental data of Simmons & Wolfhard [5].

20
7 . ACKNOWLEDGMENTS

The author wishes to express thanks to Dr. Clayton Huggett of the

Center for Fire Research who suggested that a re- examination of flame

temperatures at limits may give additional insight into mechanisms of

flame propagation and extinction; also to Drs. David Burgess and Martin

Hertzberg of the U.S. Bureau of Mines, and Professor Felix Weinberg of

the Imperial College (London) for clarifying comments.

[1

[2

[3

[4

[5

[6

[7

[8

[9

8. REFERENCES

Lovachev, L. A., Babkin, V. S., Bunev, V. A., V'yun, A. V.,

Krivulin, V. N. and Bartov, A. N. , Combustion and Flame, Vol. 12,

259 (1973).

Burgess D. and Hertzberg, M., 20th Annual ISA Instrumentation Symp.,

Pittsburgh, Pa. (1974).

Burgess, D., 62nd Annual Meeting A.I.Ch.E., Washington, D.C. (1969).

Hall, A. R. , McCoubrey, J. C. and Wolfhard, H. G. , Combustion and

Flame, Vol. 1, 53 (1957).

Simmons, R. F. and Wolfhard, H. G. , Combustion and Flame, Vol. 1,

155 (1957).

Vanpee, M. and Wolfhard, H. G., ARS Journal 29, 517 (1959).

Fenimore, C. P. and Martin, Combustion and Flame, Vol. 10, 135 (1966)

Zabetakis, M. G. , U. S. Bureau of Mines Bulletin 627 (1965).

JANAF Thermochemical Tables, NSRDS — NBS Document 37 (1971).

[10] Stull, D. R. , Westrum, E. F. and Sinke, G. C, The Chemical

Thermodynamics of Organic Compounds (John Wiley & Sons, Inc., 1969).

[11] Gibbs, G. J. and Calcote, H. F., J. Chem. Eng. Data 5, 226 (1959).

[12] Kaskan, W. E., 6th Symposium (International) on Combustion, 134

(1957).

[13] Friedman, R. and Cyphers, J. A., J. Chem. Phys., Vol. 23, 1875

(1955).

[14] Peeters, J. and Mahnen, G. , 14th Symposium (International) on Combustion, 133 (The Combustion Institute, 1973).

[15] Coward, H. F. and Jones, G. W. , U. S. Bureau of Mines Bulletin

503 (1952).

21
[16] Fenimore, C. P. and Jones, G. W. , Combustion and Flame, Vol.10,

295 (1966).

[17] Fristrom, R. and Westenberg, A. A., Flame Structure, (McGraw-Hill,

1965).

[18] Lewis, B. and von Elbe, G., Combustion, Flames and Explosions

of Gases, 2nd ed., 317ff (Academic Press, 1961).

[19] Mullins, B. P. and Penner, S. S., Explosions, Detonations,

Flammability and Ignition (Pergamon Press, 1959).

22
NBS-114A (REV. 7-73)

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBSIR 76- 1076

2. Gov't Accession

No.

3. Recipient's Accession No.

A TfTI P AVn sl'RT[Tl tZ Ill LE AiNU jLd 1 1 I Lt

FLAMMABILITY LIMITS: THERMODYNAMICS AND KINETICS

5. Publication Date May 1976

6. Performing Organization Code

7. AUTHOR(S) v

Dr. Andre j Macek

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WAjnmv 1 UN, U.^.. 1\j1jA

10. Project. Task. 'Work Unit No. 491 4679

11. Contract /Grant No.

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)

Same as No. 9

13. Type of Report & Period C ov e r e d Final Report

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less [actual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.) Extinction limits for both premixed and diffusion flames for n-alkanes

and n-alcohols found in the literature are assembled. Several sets of

theoretical flame temperatures corresponding to the limits are defined and

presented. The implications of the view that flames fail to propagate at

temperatures at which reaction rates become too low to overcome the dissipation

processes are discussed. Equilibrium flame temperatures indicate that at lean

limits the excess oxygen does not act merely as a diluent but takes an active

part in promoting the kinetics of flame reactions . The burning-rate data and

the results of ignition experiments are shown to be pertinent to the interpretation of flammability limits. Extinction characteristics of methane are shown

to be atypical (compared to other alkanes and alcohols) and demand a special

explanation. It is also shown that the assumption of thermodynamic equilibrium

at the limits is unrealistic, so there is need for experimental temperature and

concentration measurements in both premixed and diffusion flames . When the

assumption of equilibrium is removed, the chemical kinetic considerations

suggest a simple qualitative explanation of the limit phenomenon, based on the

stipulation of incomplete combustion. Quantitative data are presented in

support of this view.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons) chemical kinetics; diffusion f lames ; flame extinction;

flame temperature; flame velocity; flammability; flammability limits; Oxygen Index

Test; thermodynamics.

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