Thermal conductivity gas analysers

One of the simplest and earliest method for measurement of composition of binary gas mixtures is a method which uses thermal conductivity properties of gases. By passing the gas to be analysed over an electrically heated filament, and thus cooling the filament to an extent that is dependent on the thermal conductivity of the gas under measurement, we can determine the gas composition. The only drawback of this method is that it can be employed only to binary gas mixtures, since this analyser measures the total sample thermal conductivity, and cannot, therefore, distinguish what composition change causes the conductivity variation. However, this technique is widely used in gas chromatography for detection of the constituents of a separated gas mixture. Although they respond to most types of gas samples, thermal conductivity detectors are much less sensitive than flame-ionisation detectors.

Table 7.1 gives values of thermal conductivities of several gases (from Huskins D.J. Quality measuring instruments in on-line process analysis, Ellis Horwood Ltd., NY, 1982, p. 199). In this table k is thermal conductivity of a gas.

Table 7.1. Thermal conductivities of some gases.

A thermal conductivity gas analyser consists of three major parts, namely, measuring cell, regulated power supply and Wheatstone bridge, and a case temperature control. Fig. 7.7 shows a schematic of a four-element thermal conductivity cell. This cell presents a relatively large mass of metal (stainless steel with high thermal conductivity coefficient) to provide a stable heat sink. Flow passages and cavities are drilled in this metal for gas flow and for placement of heat-source-sensing elements, namely, hot wire filaments. These filaments may be made of platinum, platinum alloy materials, or tungsten. The filaments are used in pairs, two filaments are placed in the stream of the sample gas, and two others - in the stream of a reference gas. Increasing the number of filaments (up to eight) will increase the sensitivity of the analyser. Temperatures of these filaments are varied from 200 to 400 Deg C.

The second element of the thermal conductivity gas analyser is a regulated power supply and Wheatstone bridge (see Fig. 7.8). The Wheatstone bridge uses a high-quality regulated power supply, which delivers current between 100 and 300 mA dc. The stability of the analyser depends mostly on the accuracy of a power supply voltage regulation. Electrical terminals of filaments from thermal conductivity cell are connected to the sides of the Wheatstone bridge, filaments which are placed in the sample stream being connected to opposite sides of the bridge, the same refers to the filaments placed in the reference gas stream.

In order to increase stability of the measuring thermal conductivity cell one need to be able to maintain a constant temperature environment in it. For this purpose several types of case temperature control systems utilising on/off thermal switches are used.

Figure 7.7. Four-element thermal conductivity cell.

The four-element thermal conductivity cell is connected to the Wheatstone bridge (see Fig. 7.8). A sample of a gas or a binary gas mixture (flow controlled from 50 to 200 cm3) to be analysed is passed through the measuring cell and across the filaments 1 and 2, placed in the cavities of this cell. A reference gas (usually single component gas representing the major component of the gas mixture under investigation) passes across reference filaments 3 and 4. The flow of the reference gas is controlled from 40 to 100 cm3. The reference gas is used to provide better stability due to variations of temperature and barometric pressure. A current from the regulated power supply 5 is measured by an ampermeter 7, and this current heats the filaments. The surface temperature of filaments increases. When analysing gas passes across the filaments 1 and 2 this heat energy is conducted away from the filaments. The higher the thermal conductivity of the gas under measurement (comparing to that of the reference gas) the more heat energy is removed from the measuring filaments 1 and 2 than from the reference filaments 3 and 4. Therefore, temperature of the measuring filaments will be lower than temperature of the reference filaments, and an electrical resistance of the measuring filaments will be lower that that of the reference ones. This will cause an unbalanced condition of the Wheatstone bridge (current flows through the ampermeter 6), the degree of this unbalance being dependent on the composition of the gas under measurement. To bring the bridge to a new balanced condition a slide resistor 8 is used. The scale 9 of this resistor is calibrated in the units of gas composition.

Figure 7.8. Wheatstone bridge with a thermal conductivity cell.

Development of an equation for output voltage of TCD:
(from Bentley J. P. Principles of Measurement Systems, Longman, 1995, p. 338-340):

Vab is a measure of a gas concentration. Convective heat transfer coefficient U between filament and moving gas is a function of gas thermal conductivity, k , and the average gas velocity. If gas velocity is maintained constant, then

.

The value of a constant self-heating current is determined as follows:

(7.9)

where, I - total bridge current, A.

The steady-state heat balance equation:

where

Since terms involving

are negligible, then

Substitute (7.14) into (7.10):

where,

(7.17)

then :

(7.18)

Resistances of filaments in measuring cells are equal to:

(7.19)

Resistances of filaments in reference cells are equal to:

(7.20)

(7.21)

For a typical system:

, and

, equation (7.21) can be rewritten as follows:

(7.22)

Below is thermal conductivity of a gas mixture:

(7.23)

(7.24)

where, the function of velocity of gas stream can be determined as follows:

(7.25)

Here we used the following parameters:

The resistance measurements tends to drift with time because of vaporisation of a platinum filament and because of reactions between the filament and the gas under measurement. To reduce this drift glass coatings of the filament are used, but this will reduce the response of the analyser. Sample gas temperature may vary from 1.7 to 43 Deg C, ambient temperature - from -1 to 38 Deg C. For binary gas mixtures an accuracy of thermal conductivity gas analysers is equal +/-2% of full scale.

Article Source:: Dr. Alexander Badalyan, University of South Australia