SGX Sensortech is often confronted with requests of relative response figures while using its pellistors for more exotic gases and non-straight-chain hydrocarbons. A paper from Jones, Jones and Firth provides the theoretical response figures for more than ninety different materials and is considered as the first reference point.
This article discusses the calculation of the relationship ΔH0298D12 [LEL] so that readers are able to estimate values from basic information if required.
Pellistor Relative Response Measurements
Standard heats of formation of the reactants and products can be used to determine the values of ΔH0298. Benson's group additivity theory can be used to estimate the heat of formation of the required molecule when the value is not available.
It is necessary to consider the correct combustion products in the estimation of ΔH0298. Vapor pressure at the flash point can be considered as a first approximation to estimate the LEL for a target molecule when its LEL value is not available in the literature.
The evaluation of D12 is the major problem in the estimation of pellistor relative response. Equation 1 is the basic equation for the binary diffusion coefficient:
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Where,
M1 and M2 = The molecular weights of the reactants
fD = Second order correction with a value close to 1.00,
n = The number density of the molecular mixture,
σ12 = The Lennard-Jones force constant for the mixture
ΩD = The collision integral
ΩD relies on kT/ε012, a dimensionless ratio where k is the Boltzmann constant.
The empirical relationship expressed in Equation 2 can help estimate the ΩD:
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The combining rules can be used to estimate the values of σ12 and ε012/kT for a gas pair:
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Values for ε01/k, ε02/k, σ1 and σ2 can be derived from the second virial coefficient or viscosity measurements and are tabulated for some gases. If not tabulated, the values can be derived utilizing the Stiel and Thodos estimations:
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Where,
TCc = The critical temperature,
VC = The critical volume
ZC = The critical compressibility factor for the component molecule and is expressed as ZC= PCVC/RTC.
Transforming to usual technical units with n expressed by the ideal gas law, σ expressed in Angstroms and dropping fC modifies equation 1 to:
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Where,
D12 = Square centimeters per second
P is in atmospheres and T is in Kelvin.
D12 can be estimated as follows:
- ε01/k, ε02/k, σ1 and σ2 values can be obtained from tabulated values or by calculation using the critical parameters for each component employing Equations 5 and 6.
- Force constant values must be derived from the same source wherever possible to reduce errors
- ε012/k and σ12 values are then derived for the gas pair by employing the combining rules expressed in Equations 3 and 4
- Using Equation 2, ΩD is then calculated from the derived value for ε012/k at the required temperature in Kelvin
- The derived values for σ12 and ΩD are then substituted into Equation 7 to calculate the theoretical value for D12
For D12, the values provided by Jones, Firth, and Jones are in arbitrary units and vary from the values derived by the aforementioned approach by roughly a factor of 40. After determining the values for ΔH0298, D12 and LEL, the response factor for the right molecule can be derived in kJ mole-1C cm2 sec-1 from the value of ΔH0298 [LEL] D12.
The following expression can be used to evaluate the response corresponding to a calibration molecule:
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The aforementioned relative response estimation does not involve pressure and temperature values and therefore assuming complete combustion on the pellistor for both reference and target gas is mandatory, especially when running a pellistor at temperatures below optimum temperatures and in the case of pellistor poisoning.
The pellistor will generate peak responses to many hydrocarbons at temperatures lower than that for methane. As a result, a pellistor running cool will generate considerably lower signal levels for methane, making the aforementioned equations invalid due to less chance for complete combustion of methane.
Pellistor relative responses will also be affected by the effect of inhibitors and poisons due to reduction in methane response. This is especially critical in the calibration of a pellistor with a non-methane hydrocarbon for use in environments consisting of methane owing to the fact that the reduced methane response would not be revealed in the non-methane calibration of a partially poisoned sensor.
Using the aforementioned equations, response factors ΔH0298 [LEL] D12 can be derived for an extended range of molecules. The response factors for some of the molecules are given in the following table:
Molecule |
LEL %vol |
ΔH0298 kJmole—1 |
[email protected] 300 °C cm2Sec— 1 |
ΔH0298D12LEL |
Response Rel to CHS4 |
Gain Adjust |
ammonia |
15 |
317 |
0.7286 |
3465 |
1.43 |
0.70 |
hydrazine |
4.7 |
579 |
0.4780 |
1301 |
0.54 |
1.86 |
methylhydrazine |
2.5 |
1304 |
0.3578 |
1167 |
0.48 |
2.07 |
dimethylhydrazine |
2.4 |
1978 |
0.3255 |
1545 |
0.64 |
1.57 |
cyanogen |
6 |
1096 |
0.3953 |
2599 |
1.07 |
0.93 |
hydrogen cyanide |
5.4 |
448 |
0.5159 |
1248 |
0.52 |
1.94 |
acetonitrile |
3 |
1265 |
0.3266 |
1239 |
0.51 |
1.95 |
methylamine |
4.2 |
977 |
0.4598 |
1887 |
0.78 |
1.28 |
ethylamine |
2.68 |
1585 |
0.3558 |
1521 |
0.63 |
1.59 |
trimethylamine |
2 |
2244 |
0.3151 |
1414 |
0.58 |
1.71 |
triethylamine |
1.2 |
4075 |
0.2228 |
1090 |
0.45 |
2.22 |
n-propylamine |
2 |
2199 |
0.3020 |
1328 |
0.55 |
1.82 |
aniline |
1.2 |
3295 |
0.2346 |
928 |
0.38 |
2.61 |
nitromethane |
7.3 |
664 |
0.2719 |
1318 |
0.54 |
1.84 |
hydrogen |
4 |
242 |
2.2898v |
2216 |
0.81 |
1.241 |
methane |
4.4 |
803 |
0.6851v |
2421 |
1.00 |
1.00 |
ethane |
2.5 |
1428 |
0.4613v |
1646 |
0.68 |
1.47 |
propane |
1.7 |
2044 |
0.3574v |
1242 |
0.51 |
1.95 |
n-butane |
1.4 |
2657 |
0.3383v |
1258 |
0.52 |
1.92 |
iso-butane |
1.3 |
2649 |
0.3148v |
1084 |
0.45 |
2.23 |
pentane - mixed isomers |
1.4 |
3272 |
0.2717v |
1245 |
0.51 |
1.94 |
iso-pentane |
1.4 |
3262 |
0.2618 |
1110 |
0.46 |
2.18 |
neo-pentane |
1.4 |
3250 |
0.2532v |
1152 |
0.48 |
2.10 |
hexane - mixed isomers |
1.0 |
3887 |
0.2511v |
1171 |
0.40 |
2.48 |
methylpentane |
1.1 |
3877 |
0.2385 |
1017 |
0.42 |
2.38 |
dimethlybutane |
1.1 |
3865 |
0.2412 |
1025 |
0.42 |
2.36 |
heptane - mixed isomers |
1.1 |
4502 |
0.2065 |
1023 |
0.42 |
2.37 |
methylhexane |
1.2 |
4492 |
0.2147 |
1158 |
0.48 |
2.09 |
ethylpentane |
1.2 |
4492 |
0.2168 |
1169 |
0.48 |
2.07 |
dimethylpentane |
1.2 |
4480 |
0.2208 |
1187 |
0.49 |
2.04 |
trimethylbutane |
1.2 |
4471 |
0.2233 |
1198 |
0.49 |
2.02 |
n-octane |
0.8 |
5116 |
0.1884 |
771 |
0.32 |
3.14 |
n-nonane |
0.7 |
5731 |
0.1713 |
687 |
0.28 |
3.52 |
decane - mixed isomers |
0.7 |
6345 |
0.1588 |
705 |
0.29 |
3.43 |
ethylene |
2.3 |
1323 |
0.5010v |
1524 |
0.63 |
1.59 |
propene |
2 |
1927 |
0.3886v |
1498 |
0.62 |
1.62 |
1-butene |
1.6 |
2541 |
0.3153 |
1282 |
0.53 |
1.89 |
cis-but2ene |
1.6 |
2534 |
0.3058 |
1240 |
0.51 |
1.95 |
trans-but2ene |
1.8 |
2529 |
0.3211 |
1462 |
0.60 |
1.66 |
isobutylene |
1.8 |
2528 |
0.3100 |
1411 |
0.58 |
1.72 |
1-pentene |
1.4 |
3156 |
0.2652 |
1172 |
0.48 |
2.07 |
1,3-butadiene |
1.4 |
2410 |
0.3203 |
1081 |
0.45 |
2.24 |
1,4-hexadiene |
2 |
3644 |
0.2509 |
1828 |
0.76 |
1.32 |
acetylene |
2.3 |
1256 |
0.5262v |
1520 |
0.63 |
1.59 |
propyne |
1.7 |
1850 |
0.3796 |
1194 |
0.49 |
2.03 |
cyclopropane |
2.4 |
1959 |
0.3854v |
1812 |
0.75 |
1.34 |
cyclohexane |
1.2 |
3689 |
0.2494v |
1104 |
0.46 |
2.19 |
methylcyclohexane |
1.15 |
4293 |
0.2178 |
1075 |
0.44 |
2.25 |
benzene |
1.2 |
3169 |
0.2879v |
1095 |
0.45 |
2.21 |
toluene |
1.1 |
3772 |
0.2460 |
1020 |
0.42 |
2.37 |
o-xylene |
1 |
4376 |
0.2097 |
918 |
0.38 |
2.64 |
m-xylene |
1.1 |
4374 |
0.2123 |
1021 |
0.42 |
2.37 |
p-xylene |
1.1 |
4375 |
0.2062 |
992 |
0.41 |
2.44 |
ethylbenzene |
1 |
4390 |
0.2252 |
989 |
0.41 |
2.45 |
styrene monomer |
1.1 |
4267 |
0.2199 |
1032 |
0.43 |
2.35 |
methyl alcohol |
5.5 |
676 |
0.5069v |
1885 |
0.78 |
1.28 |
ethyl alcohol |
3.1 |
1277 |
0.3859v |
1527 |
0.63 |
1.58 |
n-propyl alcohol |
2.2 |
1892 |
0.3437v |
1430 |
0.58 |
1.69 |
iso-propyl alcohol |
2.0 |
1874 |
0.2814 |
1055 |
0.44 |
2.30 |
n-butyl alcohol |
1.7 |
2508 |
0.2575 |
1098 |
0.45 |
2.20 |
iso-butyl alcohol |
2.0 |
2499 |
0.2548 |
1273 |
0.53 |
1.90 |
tert-butyl alcohol |
2.4 |
2471 |
0.2609 |
1547 |
0.64 |
1.56 |
dimethyl ether |
2.7 |
1327 |
0.4032v |
1445 |
0.60 |
1.68 |
ethyl methyl ether |
2 |
1932 |
0.3089 |
1193 |
0.49 |
2.03 |
diethyl ether |
1.7 |
2531 |
0.2797v |
1204 |
0.50 |
2.01 |
diiso-propyl ether |
1.0 |
3735 |
0.2247 |
839 |
0.35 |
2.88 |
11,4 dioxane |
1.9 |
2223 |
0.2591 |
1095 |
0.45 |
2.21 |
tetrahydrofuran |
1.5 |
2636 |
0.2860 |
1131 |
0.47 |
2.14 |
acetone |
2.5 |
1690 |
0.3429v |
1449 |
0.60 |
1.67 |
methyl ethyl ketone (butanone) |
1.8 |
2303 |
0.2523 |
1046 |
0.43 |
2.31 |
methyl propyl ketone (pentan-3one) |
1.6 |
2918 |
0.2333 |
1089 |
0.45 |
2.22 |
acetaldehyde |
4 |
1105 |
0.3483 |
1540 |
0.64 |
1.57 |
acetic acid |
4 |
836 |
0.2410 |
806 |
0.33 |
3.00 |
acetic anhydride |
2.0 |
1723 |
0.2791 |
962 |
0.40 |
2.52 |
n-butyric acid |
2 |
2062 |
0.2741 |
1130 |
0.47 |
2.14 |
methyl formate |
5 |
921 |
0.3217 |
1481 |
0.61 |
1.63 |
methyl acetate |
3.2 |
1492 |
0.2758 |
1317 |
0.54 |
1.84 |
methyl propionate |
2.5 |
2135 |
0.2465 |
1316 |
0.54 |
1.84 |
ethyl formate |
2.7 |
1540 |
0.2786 |
1159 |
0.48 |
2.09 |
ethyl acetate |
2.2 |
2109 |
0.2423 |
1124 |
0.46 |
2.15 |
butyl acetate |
1.3 |
3325 |
0.2254 |
974 |
0.40 |
2.48 |
carbonyl sulphide |
6.5 |
552 |
0.4061v |
1457 |
0.60 |
1.66 |
carbon disulphide |
0.6 |
1104 |
0.3473v |
230 |
0.10 |
10.5 |
hydrogen sulphide |
4.0 |
518 |
0.5319v |
1102 |
0.46 |
2.20 |
dimethyl sulphide |
2.2 |
1722 |
0.3125 |
1184 |
0.49 |
2.04 |
methyl mercaptan |
3.9 |
1151 |
0.3824 |
1717 |
0.71 |
1.41 |
ethyl mercaptan |
2.8 |
1764 |
0.3183 |
1572 |
0.65 |
1.54 |
methyl bromide |
10 |
701 |
0.3718v |
2606 |
1.08 |
0.93 |
methyl chloride |
7.6 |
672 |
0.4154v |
2122 |
0.88 |
1.14 |
methylene chloride |
15.5 |
542 |
0.3192v |
2681 |
1.11 |
0.90 |
ethyl bromide |
6.7 |
1308 |
0.3331 |
2919 |
1.21 |
0.83 |
ethyl chloride |
3.6 |
1280 |
0.3416v |
1574 |
0.65 |
1.54 |
vinyl chloride |
3.6 |
1171 |
0.3218 |
1357 |
0.56 |
1.78 |
ethylene dichloride |
7.3 |
1046 |
0.2695 |
2058 |
0.85 |
1.18 |
n-propyl chloride |
2.4 |
1897 |
0.3085 |
1405 |
0.58 |
1.72 |
chlorobenzene |
1.3 |
3018 |
0.2356 |
924 |
0.38 |
2.62 |
carbon monoxide |
10.9 |
283 |
0.6235v |
1923 |
0.79 |
1.26 |
ethylene oxide |
2.6 |
1220 |
0.3723 |
1181 |
0.49 |
2.05 |
1,2-propylene oxide |
2.1 |
1814 |
0.2785 |
1061 |
0.44 |
2.28 |
Notes:
v =D12 evaluated using values of s and E as derived from viscosity data[8] .
All other values of D12 are derived from estimated values of s and E via the Stiel and Thodos method[5] using published critical data[6].
LEL values taken from Firth, Jones and Jones[1] and EN61779-1-2000[4].
Monitoring Kerosene-Based Products with Pellistors
SGX Sensortech is often approached for advice on the application of pellistors to detect kerosene based product spillages. The LEL of kerosene vapor is 0.7% and its very high flash point causes problem in employing a gas detection system for spillage monitoring. Moreover, the flash point of virgin kerosene is lower than that of older kerosene.
This ageing of kerosene also poses difficulty to determine a relative response value in the calibration of a pellistor due to the presence of small amount of vapor above the liquid at normal temperatures. As a result, for effective pellistor operation, it is necessary to calibrate the pellistor with a lower alarm level when compared to other flammable vapors.
SGX Sensortech recommends the use of a calibration factor like that of a pentane and the lowest possible alarm level for kerosene spillage monitoring with a pellistor. The possibility of false alarms will be based on the stability of both the pellistor and the equipment in which it is mounted. A decision must be taken on that basis.
The SGX Sensortech VQ41TSB is an ideal pellistor for kerosene spillage monitoring. It was originally developed to monitor low LEL levels of ammonia. However, with very stable zero and repeatable response to heavy hydrocarbons, the VQ41TSB has been demonstrated in the field to provide satisfactory results. The output of the sensor for 20% LEL pentane is 20–30mV with zero stability on bench tests of ±0.5mV.
Conclusion
It is possible to evaluate relative responses between different gases and vapors using the response factors (ΔH0298 [LEL] D12) derived from the aforementioned equations. However, these factors are theoretical values, and therefore calibration with the gas being analyzed is always recommended.
About SGX Sensortech (IS) Ltd
SGX Sensortech is a market leader in innovative sensor and detector devices that offer unrivalled performance, robustness and cost- effectiveness.
SGX have been designing and manufacturing gas sensors for use in industrial applications for over 50 years, offering excellent applications support for an extensive range of gas sensors and the expert capability for custom design or own label.
As an independent OEM supplier of gas sensors, we pride ourselves on providing customers with unrivalled product reliability and personal product support via specialist engineers.
SGX gas sensors are built to the highest standards with all pellistor and infrared gas sensors achieving ATEX and IECEx certification, SGX gas sensors are also UL and CSA approved.
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- Industrial area protection
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This information has been sourced, reviewed and adapted from materials provided by SGX Sensortech (IS) Ltd.
For more information on this source, please visit SGX Sensortech (IS) Ltd.