Application of Thermochemical Energy Hazard Criteria to the Prediction of Lower Flammability Limits of Hydrocarbons in Air

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.


INTRODUCTION
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 hazard.
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 Zabetakis (1965), Shimy (1970), or Hilado (1975), Hilado and Cumming (1979).Other authors, such as Shebeko et al. (1983), have 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., 1974).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 application range (Ducros and Sannier, 1988).

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 properties (Seaton et al., 1974).The criteria provide a thermal hazard rating based upon correlations evidenced by statistical studies.
The criteria, and the equations used to compute them in the case of lean fuel-air mixtures, are described in the following.

First Criterion: C1
For the first criterion, CHETAH uses the enthalpy ∆H max , in kilocalories per gram of mixture, of the most exothermic reaction that could occur, given the composition of the reacting mixture.
-If 0 > ∆H max > -0.3 kcal/mol, the thermal potential hazard is rated as low.
-If ∆H max < -0.7 kcal/mol, it is rated as high.
The only input data required to compute ∆H max 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 (Benson, 1976).The enthalpies of formation of all possible products are included in a data bank.A linear programming method is used to minimise the final enthalpy.

Second Criterion: C2
The second criterion uses the difference between the heat of combustion of the reactants in an excess of oxygen ∆H c and the maximum heat of reaction ∆H max defined above: ∆H c -∆H max , in kilocalories per gram.
-If ∆H c -∆H max > 5 kcal/mol, the thermal potential hazard is rated as low.-If 5 > ∆H c -∆H max > 2 kcal/mol, it is rated as medium.
In the case of lean fuel-air mixtures, C2 has no meaning because the combustion is the most exothermic possible reaction, and ∆H c -∆H max would always be zero.Therefore, we did not use this criterion in this study.
C3 was tested for flammability limit prediction, but gave poor results (Ducros and Sannier, 1988;Dalmazzone, 1995) which will not be reported here.

Fourth Criterion: C4
C4 is represented by the empirical function: 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.

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 C a H b .Its molecular weight is: M F = 12a + b, and it contains n F = 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: 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: where ) 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: (1) And C4 is given by: (2)

Experimental Data
Our literature sources for flammability limit data were the bulletin 503 of the US Bureau of Mines (Coward and Jones, 1952), 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 Book (Weiss, 1980).
In addition, we used values determined in our laboratory (Dalmazzone, 1995), 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., 1982): The standard enthalpies of formation of the fuels, ∆ 0 f H(F), were mostly found in Pedley's Thermochemical Data of Organic Compounds (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 the laboratory (Dalmazzone, 1995), that considerably extends original Benson's one.

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: 1: Coward and Jones (1952) 2: Cleuet and Gros (1989) 3: Weiss (1980) 4: Dalmazzone (1995) 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 ∆ 0 c H, M F and n F , 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: -fourth criterion, Relation (2) gives: The positive root of this equation is the fuel mole fraction that corresponds to C4 = C*4.
The aim of the optimisation was to find the values C*1 and C*4, that give statistically the best estimates of flammability limits, by minimising the standard error of the 67 predicted limits: where Err stands for the estimation error: predicted limitexperimental 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.

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 observed.
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.

Precision and Reliability of the Method
Experimental limits are usually known with a precision of only 0.1 mol%.Furthermore, values reported by diverse F F 2 28 84 28 84 2 2 28 84 0 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 (1975) and Hilado and Cumming (1979), who 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.

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: (3) (4) (5) where υ i 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, 1989) allows to compute flammability limits of mixtures, given the individual limits of each fuel: (6) where L i 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: By definition , thus: leading to: If we represent the predicted limit of each fuel i alone in air by x i , this is equivalent to: And finally: 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 .
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.

CONCLUSION
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.
Figure 1Distribution of prediction errors.

TABLE 1
Flammability limit estimation results for the 67 test molecules used in the study