Relative Response Measurements for Pellistors

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:

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:

The combining rules can be used to estimate the values of σ12 and ε012/kT for a gas pair:

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:

 

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:

 

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:

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.

Our product portfolio has continued to expand in technology and detectable gases used in a wide range of applications including:-

  • Mining
  • Oil and gas
  • Confined space entry
  • Indoor air quality
  • Industrial area protection
  • Leak detection

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.

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