Application of Thermochemical Energy Hazard Criteria to the Prediction of Lower Flammability Limits of Hydrocarbons in Air
Oil & Gas Science and Technology - Rev. IFP, Vol.
Application of Thermochemical Energy Hazard Criteria to the Prediction of Lower Flammability Limits of Hydrocarbons in Air
D. Dalmazzone 1
J.C. Laforest 0
J.M. Petit 0
0 Institut national de recherche et de sécurité , 30, rue Olivier-Noyer, 75680 Paris Cedex 14 - France
1 Laboratoire chimie et procédés, École nationale supérieure de techniques avancées , Chemin de la Hunière, 91761 Palaiseau Cedex - France
- Application of Thermochemical Energy Hazard Criteria to the Prediction of Lower Flammability Limits of Hydrocarbons in Air - The energy hazard criteria of ASTM program CHETAH have been tested as criteria of flammability of gaseous mixtures containing an hydrocarbon vapour and air as oxidiser, at lean concentrations. A method for calculating the lower flammability limits in air, at atmospheric pressure and ambient temperature, is proposed as a result of a statistical study, which involved 67 combustible compounds. CHETAH's fourth energy hazard criterion was found to be the most reliable flammability criterion. The method is predictive since all the input data may be obtained with very good accuracy using a group contribution method. It is reliable, predicted limits being more frequently underevaluated, by 0.11 mol% on average, than overevaluated. The method is also precise, with a standard deviation of the estimates of 0.14 mol%. It is easily applicable to fuel mixtures and gives the same results as Le Chatelier's law.
Flammability is defined as the capability of a gas mixture to
unlimitedly sustain the autonomous propagation of a flame.
Generally, a fuel-oxidiser mixture is only flammable within a
limited range of compositions. The minimum and maximum
fuel concentration limits of this range are known as the lower
and upper flammability limits, respectively. They are
expressed in fuel mole percent in the total mixture.
Flammability limits are properties of a particular fuel and
oxidiser couple, and also depend on temperature and pressure
conditions. The most frequently used are flammability limits
in air, at ambient temperature and atmospheric pressure. The
most useful for safety purposes is the lower flammability
limit, which indicates the fuel vapour concentration that
should not be exceeded, in order to avoid any explosion
Flammability limits are important data in the field of fire
and explosion prevention, in any human activity handling
potentially flammable substances. Unfortunately, very few
among the thousands of chemicals produced by the industry
have their flammability limits known precisely. Measuring
flammability limits is an expensive and time-consuming
process, especially when good accuracy has to be achieved,
because flame propagation in very lean compositions is
largely dependent on experimental conditions. The values
available are therefore highly subject to uncertainties.
It is thus interesting to develop a computational method to
evaluate the flammability limits of a wide variety of organic
compounds in air, with an accuracy comparable to the
experimental methods, and if possible with total
predictability. Several methods of prediction using empirical
correlations between the fuel’s chemical structure and the
flammability limits have been proposed by
Hilado and Cumming
. Other authors, such as
Shebeko et al. (1983)
proposed some group contribution methods. All these
methods involve some parameters which depend on the
chemical nature of the combustible. Since only limited sets of
parameters have been published, most of these methods have
a restricted field of application.
Ducros et al. (1981)
proposed an original application
of ASTM (American Society for Testing and Materials)
computer program CHETAH (Chemical Thermodynamics
and Energy Hazard Evaluation program)
(Seaton et al.,
. CHETAH uses thermochemical criteria to
predictively evaluate the explosion potential hazard of a compound
or a mixture of organic compounds. The idea was that criteria
originally intended to predict the explosiveness of solid
or liquid compounds could also be used as flammability
criteria for gaseous mixtures. Some encouraging results were
published, even though the method needed further
optimisation, and many uncertainties remained about the
(Ducros and Sannier, 1988)
1 THE ENERGY HAZARD CRITERIA OF CHETAH
CHETAH was developed by the ASTM to evaluate the
potential explosion hazard of pure substances and mixtures,
using four predictive criteria based on thermochemical
(Seaton et al., 1974)
. The criteria provide a
thermal hazard rating based upon correlations evidenced by
The criteria, and the equations used to compute them in
the case of lean fuel-air mixtures, are described in the
1.1 First Criterion: C1
For the first criterion, CHETAH uses the enthalpy ∆ Hmax, in
kilocalories per gram of mixture, of the most exothermic
reaction that could occur, given the composition of the
– If 0 > ∆ Hmax > –0.3 kcal/mol, the thermal potential hazard
is rated as low.
– If –0.3 > ∆ Hmax > –0.7 kcal/mol, it is rated as medium.
– If ∆ Hmax < –0.7 kcal/mol, it is rated as high.
The only input data required to compute ∆ Hmax are the
enthalpies of formation of all the reactants in the gas phase,
and the final composition having the lowest possible
enthalpy, given the overall elemental composition. The
unknown enthalpies of formation are calculated using
Benson’s group contribution method
enthalpies of formation of all possible products are included
in a data bank. A linear programming method is used to
minimise the final enthalpy.
1.2 Second Criterion: C2
The second criterion uses the difference between the heat
of combustion of the reactants in an excess of oxygen
∆ Hc and the maximum heat of reaction ∆ Hmax defined above:
∆ Hc – ∆ Hmax, in kilocalories per gram.
– If ∆ Hc – ∆ Hmax > 5 kcal/mol, the thermal potential hazard
is rated as low.
– If 5 > ∆ Hc – ∆ Hmax > 2 kcal/mol, it is rated as medium.
– If 2 > ∆ Hc – ∆ Hmax > 0 kcal/mol, it is rated as high.
In the case of lean fuel-air mixtures, C2 has no meaning
because the combustion is the most exothermic possible
reaction, and ∆ Hc – ∆ Hmax would always be zero. Therefore,
we did not use this criterion in this study.
1.3 Third Criterion: C3
The third criterion is based on the oxygen balance of the
mixture, in gram percent:
OB = nO − 2nC − 2 M
D Dalmazzone et al. / Application of Thermochemical Energy Hazard Criteria to the Prediction of Lower Flammability Limits 367
– If OB > 160% or OB < –240%, the thermal potential
hazard is rated as low.
– If –120% < OB < –240% or 80% < OB < 160%, it is rated
– If –120% < OB < 80%, it is rated as high.
C3 was tested for flammability limit prediction, but gave
(Ducros and Sannier, 1988; Dalmazzone, 1995)
which will not be reported here.
1.4 Fourth Criterion: C4
C4 is represented by the empirical function:
C 4 = 10 ⋅ ∆ H m2ax n
where ∆H max is the same maximum energy of reaction as
used in the computation of C1 and C2, n is the number of
gram-atoms contained in a mass M of the reacting mixture.
– If C4 < 30 kcal2·g, the thermal potential hazard is rated as
– If 30 < C4 < 110 kcal2·g, it is rated as medium.
– If C4 > 110 kcal2·g, it is rated as high.
1.5 Application to Near-Limit Mixtures
We define those fuel-air mixtures that have a fuel mole
fraction close to the lower flammability limit, at 25°C and
atmospheric pressure, as near-limit mixtures. We considered
that the most exothermic reaction that could take place in that
case was the total combustion of the fuel, leaving the excess
oxidiser unchanged. Thus, the computation of CHETAH
thermal hazard criteria is particularly easy. Let the fuel’s
formula be CaHb. Its molecular weight is: MF = 12a + b, and
it contains nF = a + b gram-atoms per mole. We assume that
air is composed of 21% oxygen and 79% nitrogen, has a
molecular weight of 28.84 g·mol–1, and contains 2
gramatoms per mole. The reaction equation is:
1 b 0.79
C a H b + 2 2a + 2 O 2 + 0.21
N (+ excess air) →
aCO 2 +
H 2O + 2 2a +
N 2 (+ excess air)
As the reaction takes place at atmospheric pressure, its
enthalpy is equal to the standard enthalpy of combustion. For
one mole of fuel, it is given by:
∆ 0c H = ∆ a 0f H (CO2 ) +∆
0f H (H 2O∆ ) −
0f H (F)
where ∆ 0f H(F), ∆ 0f H(CO2) and ∆ 0f H(H2O) stand for the
standard enthalpies of formation of the fuel, and of the
combustion products, respectively.
Criterion C1 is equal to the enthalpy of combustion of 1 g
of fuel-air mixture. If x is the mole fraction of the fuel in the
mixture, it is given by:
x∆ 0c H
xM F + 28.84(1 − x)
And C4 is given by:
C 4 =
10( x∆ 0c H )
( xM F + 28.84(1 − x))( xnF + 2(1 − x))
2 STATISTICAL ANALYSIS
2.1 Experimental Data
Our literature sources for flammability limit data were the
bulletin 503 of the US Bureau of Mines
(Coward and Jones,
, the handbook on explosive mixtures published by the
French National Institute for Research and Safety (INRS)
(Cleuet and Gros, 1989)
, and the Hazardous Chemical Data
In addition, we used values determined in our laboratory
, using a specially designed apparatus,
featuring several improvements from the device described by
Coward and Jones (1952)
. The 67 test molecules selected are
listed in Table 1.
The standard enthalpies of formation of carbon dioxide
and water in the gaseous state, which are needed to compute
the enthalpies of combustion, were found in the NBS
(National Bureau of Standards) tables
(Wagman et al.,
– ∆ 0f H(CO2) = –94.051 kcal·mol–1
– ∆ 0f H(H2O) = –57.796 kcal·mol–1
at 298 K.
The standard enthalpies of formation of the fuels, ∆ 0f H(F),
were mostly found in Pedley’s Thermochemical Data of
(Pedley et al., 1986)
. When not
available they were estimated using the Benson’s method, the
group contributions being taken from a data base available at
, that considerably extends
original Benson’s one.
2.2 Principle of the Analysis
Criteria C1 and C4 have been expressed in Equations (1) and
(2) as functions of the fuel mole fraction in the mixture x.
Each of these functions is defined within the interval x = 0
The S column contains the source for experimental data:
Coward and Jones (1952)
Cleuet and Gros (1989)
The Exp column lists the experimental lower flammability limits.
For both criteria C1 and C4, the Pred column gives the predicted value, and the Err column the difference between predicted and experimental values.
(pure air) to x = stoichiometric mole fraction, and depends on
the parameters ∆ 0cH, MF and nF, which are all properties of
the fuel. That particular value, noted C*i, taken by the
criterion Ci(i = 1, 4) at the exact mole fraction x corresponding
to the lower flammability limit, may be considered as the
frontier between non-hazardous and hazardous mixtures. In
the following, we assume that these values C*i are
independent of the nature of the fuel. Therefore, the
prediction of the lower flammability limit of a given fuel in
air is equivalent to the determination of the mole fraction x
corresponding to Ci = C*i. Given the fuel properties, x is
expressed by the following equations:
– first criterion, from Relation (1), it comes:
where Err stands for the estimation error: predicted limit –
experimental limit. For each criterion, the following iterative
process was applied:
– choosing a value C*i;
– computing the 67 estimates using the proper equation, and
the 67 estimation errors;
– computing the standard deviation;
– going back to the first step until a minimum is found.
Average prediction error (mol%)
Standard deviation (mol%)
Most negative error (mol%)
Most positive error (mol%)
3 RESULTS AND DISCUSSION
The complete set of molecules is listed in Table 1, together
with the experimental and predicted limits. The results are
summarised in Table 2, in which each row corresponds to one
criterion. The first column contains the optimal value of C*i,
the second and third columns give the average absolute error
and the standard deviation of the estimates. The fourth and
fifth columns give the minimum and the maximum error
Lower flammability limits predicted using C4 are
statistically lower than those obtained with C1, by 0.04 mol%
on average. This is confirmed by the histogram in Figure 1,
which presents the distribution of the two series of estimates in
seven classes of error. With both criteria, 65 estimates over 67
have a deviation comprised between –0.5 and +0.1 mol%. C1
estimates are in majority (37 over 67) precise to ±0.1 mol%,
while the majority (35 over 67) of C4 estimates have a
negative deviation of –0.3 to –0.1 mol%. Only acetylene has
its lower limit overestimated by more than 0.5 mol%, the error
being slightly greater using C1 than using C4.
3.1 Precision and Reliability of the Method
Experimental limits are usually known with a precision of
only 0.1 mol%. Furthermore, values reported by diverse
<-0.5 -0.5 -0.3 -0.1 0.1 0.3 0.5
Prediction error (mol%)
sources often differ by several tenths of a mole percent for
the same fuel. The precision of the predictive method is thus
comparable to most experimental determinations.
Hilado and Cumming (1979)
described one of the most precise predictive methods of
flammability limit estimation, reported a standard deviation
of 0.26 mol% for a set of compounds of carbon, hydrogen
and oxygen. This may be compared to the standard deviation
of our estimates (0.14 mol%).
The reliability of the estimates depends not only on the
standard deviation, but also on the sign of the errors. A
negative error means that non-flammable mixtures will be
considered as flammable, resulting in an excess of
cautiousness. A positive error means exactly the opposite,
resulting in potentially dramatic consequences. For safety
purposes, it is always preferable to overestimate the hazard.
Therefore, C4 can be considered as the best of CHETAH
criteria for predicting the lower flammability limits of
hydrocarbons in air.
3.2 Application to Fuel Mixtures
It is easy to apply this method to the prediction of
flammability limits of fuel mixtures. The thermal hazard
criteria of a fuel blend mixed with air at lean concentration
may be obtained using Equations (1) and (2) as well as for
pure fuels. The following equations may be used in that case
to compute the required data:
∆ 0c H = ∑ υ∆ 0 H
i i c i
M F = ∑ υiM i
nF = ∑ υini
where υi stands for the mole fraction of fuel i in the blend.
Using these definitions, we implicitly assume that the fuels
behave as ideal gases, neglecting excess properties such as
enthalpies of mixing.
When dealing with fuels having close properties and
chemical structures, such as mixtures of hydrocarbons, the
additive law known as Le Chatelier’s law
(Cleuet and Gros,
allows to compute flammability limits of mixtures,
given the individual limits of each fuel:
where Li stands for the individual flammability limit of fuel i,
expressed in the same unit as L. Le Chatelier’s law is useful
for predicting both lower and upper flammability limits of
any mixture of several fuels with a single oxidiser. The
results are generally better for lower limits.
Le Chatelier’s law is based on the assumption that
flammability limits are additive properties. In other words,
mixing in any proportion several gas mixtures, each of them
being composed of air and a fuel at its exact limit
concentration, at given temperature and pressure, should
result in a mixture whose concentration is equal to the
blend’s flammability limit, at the same temperature and
pressure. Because the data used to compute the hazard
criteria are also defined by additive relations in Equations (3),
(4) and (5), applying the thermochemical method to fuel
mixtures should logically be equivalent to applying Le
Chatelier’s law, using predicted values as individual limits.
We can easily demonstrate this equivalence for criterion
C1. From Equations (1), (3) and (4), it comes:
∑ υi∆ 0c H i − C*1 ∑ υiM Fi − 28.84
1 = i i
x 28.84 ⋅ C*1
By definition ∑ υi = 1, thus:
∑ υi∆ 0c H i − C*1 ∑ υiM Fi − ∑ υi ⋅28.84
1 = i i i
x 28.84 ⋅ C*1
= ∑i υi
∆ 0c H i − C*1(M Fi − 28.84)
28.84 ⋅ C*1
If we represent the predicted limit of each fuel i alone in
air by xi, this is equivalent to:
1 = ∑ υi
x i xi
which is the same as Equation (6).
For the estimates computed using criterion C4, the
equivalence with Le Chatelier’s law can be illustrated
graphically. As an example, Figure 2 reports three sets of
estimates of lower flammability limits for a mixture of
1-hexane and 1-nonane in air, at 25°C and 1 atm. The first
set, represented by a dashed line, was obtained using Le
Chatelier’s law with the experimental values as individual
limits, that is, respectively for 1-hexane and 1-nonane, 1.18
and 0.83 mol% in air. The second set, represented by a solid
line, was obtained using Le Chatelier’s law with the values
predicted using criterion C4 as the individual limits: 1.06 and
Le Chatelier, experimental values Le Chatelier, predicted values Predicted
Fraction of 1-nonane in the blend (mol%)
Lower flammability limit estimates of blends of 1-hexane and
1-nonane in air.
0.72 mol%, respectively. The third set, represented by points,
was obtained using C4 to estimate the flammability limit of
each blend, from pure hexane to pure nonane with a step of
10 mol%. It is obvious that the second and third sets of
estimates are equivalent.
A new method for predicting the lower flammability limits of
hydrocarbon gases and vapours in air, at atmospheric
pressure and ambient temperature, has been developed. It
uses the fourth thermochemical hazard criterion of ASTM
program CHETAH as a flammability criterion. All data
necessary to the criterion computation may be obtained from
the chemical structure of the compound, by the Benson’s
group contribution method. As the Benson’s contributions
for hydrocarbon groups are all well known, the method can
be predictively applied to virtually any hydrocarbon
molecule and mixture. It is consistent with the additive rule
of Le Chatelier, usually used to compute the flammability
limits of mixtures.
The method is more precise than the most accurate
predictive methods already existing. Also, the estimates are
on average slightly lower than the experimental limits, which
is preferable for safety purposes.
The authors wish to thank the INRS for its financial support
to this study.
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