Theoretical
flammability diagrams

 

Tingguang Ma

Fire
Protection and Safety Technology

Oklahoma
State University

492 Cordell
South, Stillwater, OK 74078

Tingguang.ma@gmail.com

 

Abstract

Flammability diagrams play an important role on guiding
dilution and purging operations. Recently, a theoretical flammability diagram,
generic to Coward?s diluted flammability diagram, is proposed to check the
dilution requirement under various diluent/oxygen/temperature conditions. This
method is based on the enthalpy conservation at the critical flame temperature,
still a hand-calculation method with simple treatment of fuel/oxygen/diluent.
Any gaseous mixtures involving flammable gases, will
be presented in the flammability diagram, with quadrant information on
flammable state, dilution requirement to non-flammable state, and variations
due to oxygen or temperature. It will find more applications in gas-handling
industry for safety-related operations.

 The role of
flammability limits on determining the fire and explosion potential of a
flammable gas mixture has long been recognized since Sir Humphrey Davy?s
classical experiments (1816). Starting from Davy?s work, Britton (2002)
reviewed 200 years of experimental work, especially identified some debatable
topics on flammability measurements, such as ignition strength, wall heat loss,
ignition criteria, incompleteness of reactions, etc. This fact calls for a
theoretical view on flammability, without any ambiguity from experimental methods.

Flammability theory started by Le Chatelier?s (1898) ?mixture
law?, while his work was mostly empirical and its derivation was given almost a
century later (Mashuga et al. 2000). Burgess and
Wheeler (1911) first proposed that the lower limit of flammability should vary
inversely as the calorific value of the gas, which is adopted by many
correlations (Ma et al. 2003). They also proposed the temperature dependence of
flammability limits, which is termed as Burgess-Wheeler?s law. Thornton (1917)
proposed that the upper limit bears a direct relationship to the amount of
oxygen needed for perfect combustion, which lay the foundation for the concept
of heat of oxidation (Britton, 2002). White (1925) confirmed the net calorific
value of the vapor, and further proposed that the critical adiabatic flame
temperature is unchanged by the presence of raised ambient temperature or added
fuels. Jones (1938) noticed the ratio of the lower limit to the amount of
combustible needed for complete combustion is approximately constant. This is
termed as the Jone?s rule or Lloyd?s rule (1948). Coward
et al. (1952) first proposed the diluted flammability diagram, which used the
diluent/fuel ratio as the primary variable. Zabetakis (1965) instead proposed a
ternary diagram, which gained wide acceptance in industry. The last
contribution is Huggett?s oxygen calorimetry (1978),
which is not directly related to flammability but useful to understand the role
of oxygen at ignition.

Based on previous experience on Le Chatelier's Rule,
Burgess Wheeler's law, Jone's (or Lloyd) rule, White's
principle, Coward Diagram, Zabetakis? ternary diagram, Huggett?s
oxygen calorimetry, a theoretical flammability diagram is proposed based on the
thermal balance at the critical flammable limits (Ma, 2013). This thermal
balance method has been applied to solve the flammability limits of a mixture
(Ma, 2011), check and propose correlations (Ma et al. 2013), determine the
dilution requirements to safety (Ma, 2013). It will be summarized here with several
solved example to show the utility of flammability diagram in solving flammable
mixture problems.

 

Reference:

1.       
H. Davy,  On the Fire-Damp of Coal Mines, and on
Methods of Lighting the Mines So as to Prevent Its Explosion,  Philosophical Transactions of the Royal
Society of London, Vol. 106 (1816), pp. 1-22

2.       
L.G. Britton,
Two-hundred years of flammable limits, Prog. Safe. Prog. 21 (1) (2002) 1?11.

3.       
H. Le Chatelier, O. Boudouard, On the Flammable Limits of Gas Mixtures, Bull Soc Chim, 1898

4.       
C.V. Mashuga,
D.A. Crowl, Derivation of Le Chatelier?s Mixing Rule
for Flammable Limits, Process Safety. Progress. 19(2) (2000)112-117.

5.       
MJ., Burgess, RV.,
Wheeler, The lower limit of Inflammation of Mixtures of the Paraffin
Hydrocarbons with air, Journal of Chemical society, 1911

6.       
W.M. Thornton XV.
The relation of oxygen to the heat of combustion of organic compounds, Philosophical Magazine Series 6, Vol. 33, Iss. 194,
1917

7.       
A.G. White, Limits for the propagation of flame in inflammable
gas?air mixtures. III. The effect of temperature on the limits, J. Chem. Soc.
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8.       
GW. Jones, Inflammation Limits and Their Practical Application in
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Lloyd, P. The Fuel Problem in Gas Turbines. Inst. Mech. Eng. Proc., War
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10.     H.F. Coward, G.W. Jones, Limits of Flammability of
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11.     M.G.
Zabetakis, Flammability characteristics of combustible gases and vapors,
Bulletin 627, Bureau of Mines, Washington, 1965.

12.     B. Huggett, Estimation of
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13.     V. Babrauskas, Ignition
Handbook, Fire Science Publishers, 2003, Appendix.

14.     T. Ma, Q. Wang, M. Larrañaga, Correlations for
estimating flammability limits of pure fuels and fuel-inert mixtures, Fire
Safety Journal 56 (2013) 9?19

15.     T. Ma, Q. Wang, M. Larrañaga, A thermal balance method
for estimating the flammability limits of a mixture, FW-World, Fall 2012.

16.     T. Ma, A thermal Theory for Estimating the Flammability
limits of a Mixture, Fire Safety Journal, 46 (2011) 558-567