Gas Detection 13


combustion, the lower explosive level and the flux of gas in terms of diffusion to the active sites on the detector element. The output of a pellistor at the lower explosive limit (lel) of a fuel was described by the expression:


V(LEL) Where V(LEL) = K D12 ΔH[LEL] is the voltage output at the lel, K is a constant, D12 is the


diffusion coefficient, ΔH is the heat of oxidation and [LEL] is the lower explosive limit of the fuel in air.


The constant K is a function of the pellistor construction and can be considered as being related to ( M x Cp ) in the above equations. It is therefore useful to consider the response relative to a standard gas, i.e. methane, in order that K does not enter into the considerations of relative response.


IEC617792


The lel of many gases are known and listed in standards such as .


The heat of oxidation for several gases were obtained either from reported measurements or by using the group additivity scheme of Benson’s group3,4


. This scheme allows the enthalpy of formation, entropy and heat capacity of a molecule to be quite accurately estimated by using additivity rules whereby contributions from component groups of atoms within a molecule are summed. A group additivity tool is available on line through the NIST Chemistry Webbook at http://webbook.nist.gov/chemistry/grp-add/. The heat of oxidation is essentially the difference between the energy of the products of combustion and the energy of the reactants (fuel and oxygen). It has to be assumed that complete combustion of fuel occurs on the pellistor for this heat of oxidation to be valid.


So with the lel and the heat of oxidation known we need to find the


, the diffusion coefficient, in order to estimate values for the response of a pellistor to a gas. The diffusion coefficient required is that of the gas in air, generally considered as the binary mixture of relevance, and the kinetic theory of gases relates the diffusion to the intermolecular forces acting between the gas and air. The Hirschfelder, Bird and Spotz method5


values of D12 was used by Firth, Jones and Jones to calculate


the diffusion coefficient. This method stems from the kinetic theory of gases which leads to an expression for the diffusion coefficient of:


D12 = b T3/2 / (µ1/2 (σ12)2 Ω(T*) )


Where b is a constant andT is the absolute temperature. The reduced molecular weight of the system µ is: Μ = Ma


Mg Where Ma / (Ma + Mg ) is the mean molecular weight of air and Mg


molecular weight of the gas to be combusted. The collision cross section σ12


parameters using the expression: σ12


Where Vc the gas.


The constant Ω(T*) is a collision integral at a reduced temperature of T*. This reduced temperature T* is:


T* = k T / ε12 Where k is the Boltzmann constant and ε12 ε12 / k = ( (65.3Tc(Zc)3.6 Where Tc is the Lennard-Jones


energy interaction parameter. This molecular interaction para-meter ε12 can be found from viscosity data or estimated from:


= ( 78.6 (65.3Tc(Zc)3.6


)air (65.3Tc(Zc)3.6 )gas )0.5


)gas )0.5 is the critical temperature of the gas.


An approximate equation for the collision integral Ω(T*) for non- polar molecules was published by Neufeld et al6


as: Ω(T*) = 1.06036 / (T*)0.15610 + 0.193 / exp(0.47635T*) + 1.03587 / exp(1.52996T*) + 1.76474 / exp(3.89411T*)


An alternative approximation used by Firth, Jones and Jones is: Ω(T*) = 1.41257*(T*)1.66334


- 0.971012*(T*)1.84982 + 0.994141*(T*)0.141179


So in the absence of published diffusion coefficient for a given gas in air it can be estimated using the above expressions. This leads to a value for the output voltage of a pellistor in an lel concentration of gas and is normally considered relative to the methane response. This is very useful for cases where there is an absence of experimental response data. Some pellistor types are optimised for detecting combustible gases other than methane (ie their catalysts are not optimised for methane combustion) and for those devices the response can be estimated relative to butane.


Relative responses to simple alkanes, calculated using the above expressions, are shown in Table 1.


The response is therefore heavily dependent on the diffusion coefficient of the gas in air and the activity of the catalyst. The diffusion coefficients described above relate to gas diffusing through air but there are additional diffusion barriers present in a typical pellistor arrangement that also affect the overall diffusion rate:


a) There is a “depletion zone” around the pellistor where Methylpentane Dimethylbutane Heptane Methylhexane Ethylpentane Dimethylpentane Trimethylbutane Octane Nonane Decane Mixed Isomers 1 1 1.1 1.1 1.1 1.1 1.1 0.8 0.7 0.7 3877 3865 4502 4492 4492 4480 4471 5116 5731 6345 0.2385 0.2412 0.2065 0.2147 0.2168 0.2208 0.2233 0.1884 0.1713 0.1588 925 932 1023 1061 1071 1088 1098 771 687 705 0.38 0.39 0.42 0.44 0.44 0.45 0.45 0.32 0.28 0.29 N-Pentane Iso-Pentane Neo-Pentane N-Hexane 1.4 1.4 1.4 1 3272 3262 3250 3887 0.2717 0.2618 0.2532 0.2511 1245 1196 1152 976 0.51 0.49 0.48 0.40 Butane Iso-Butane 1.4 1.3 2657 2649 0.3383 0.3148 1258 1084 0.52 0.45 = 0.1866 (Vc)1/3 is the critical volume and Zc (Zc is the can be estimated from critical )-1.2 is the critical compressibility of Methane Ethane Propane 4.4 2.5 1.7 803 1428 2044 0.6851 0.4613 0.3574 2421 1647 1242 1.00 0.68 0.51


combustion products are diffusing away from the bead while fuel and oxygen are diffusing back towards the bead. This zone has a small effect on the diffusion of gas to the active catalytic sites.


b) Some pellistors have fully open cans whilst others have “closed” cans containing a small hole for gas access. Gas diffusion is affected by the restriction of a “closed” can and the output for devices in “closed” cans tends to be less than those of open cans.


c) Flame arrestors are required to be used with pellistor sensors in order to prevent propagation of the combustion to the surrounding environment. These also affect the diffusion of gas since the gas has to diffuse through the flame arrestor before reaching the vicinity of the pellistor. Heavier molecules can give lower responses than expected by the theoretical treatment simply because they have a much lower rate of diffusion through the flame arrestor than the reference gas (normally methane).


d) Some pellistor constructions have porous structures that are used to provide an extremely high surface area of catalyst. This is used to provide some poison resistance where the presence of poisons removes catalytic activity from the outer layers of catalyst but the inner layers are still active and produce a response. However, the gas has to diffuse into the structure of the pellistor itself in order to reach the active catalyst and equally combustion products have to diffuse out of the structure. This results in porous structured pellistors generally having a lower sensitivity that a non porous structure (where the catalyst is available on the outer surface of the bead).


Under normal operation, the rate determining step for the combustion is the diffusion rate of the fuel to the pellistor. The effect of poisons, in particular silicon containing compounds or alkylated heavy metals, is to remove active catalyst sites from the pellistor structure. The mechanism of poisoning is either passivation caused by deposition of solids over the catalyst or passivation caused by chemical bonding to the catalyst. Both remove active catalyst availability.


Poison resistant structures provide a reasonably good level of protection against commonly encountered poisons. However, once sufficient poison has reached the catalyst the rate of reaction becomes dependent on the amount of available catalyst and not the diffusion of gas so the pellistor response therefore starts to reduce.


Moleculeµ LEL %vol - ΔH298 D12 @300'C


ClairAir is a member of CoGDEM, the Council of Gas Detection and Environmental Monitoring. CoGDEM is the trade association representing manufacturers of gas detecting apparatus and sensors, as well as service companies such as calibration gas and hazardous area certification providers. www.cogdem.org.uk


- ΔH298 D12 LEL RR vs CH4


Annual Buyers Guide 2009


IET


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