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

f_D = 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

Ω_D = The collision integral

Ω_D relies on kT/ε0₁₂, a dimensionless ratio where k is the Boltzmann constant.

The empirical relationship expressed in Equation 2 can help estimate the Ω_D:

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,

T_Cc = The critical temperature,

V_C = The critical volume

Z_C = The critical compressibility factor for the component molecule and is expressed as Z_C= P_CV_C/RT_C.

Transforming to usual technical units with n expressed by the ideal gas law, σ expressed in Angstroms and dropping f_C 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, Ω_D is then calculated from the derived value for ε0₁₂/k at the required temperature in Kelvin
• The derived values for σ₁₂ and Ω_D 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:

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.