PROCEEDINGS
OF THE TOMSK POLYTECHNIC INSTITUTE
NAMED AFTER S. M. KIROV,
ORDER OF THE OCTOBER REVOLUTION AND ORDER
OF THE RED BANNER OF LABOR

Volume 267　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　1975

METHOD FOR DETERMINING GAS CONCENTRATION AND A DEVICE IMPLEMENTING IT

M. S. ALEINIKOV, E. P. KOLTSOV, V. I. LUKOVNIKOV, S. A. GRACHEV,
K. L. PESTEREV, V. S. TITOV

(Presented by the scientific and technical seminar of the Department of Instruments and Devices of Automation Systems)

Known methods for determining gas concentration use infrared (IR) radiation on the basis of negative filtering with the application of positive and negative sensitization [1].

The use of sensitization of both types in the indicated methods leads to complication of the devices implementing these methods and to a reduction in their accuracy.

The method described here is free from these shortcomings. It can be implemented, for example, by means of the block diagram shown in Fig. 1.

Fig. 1. Block diagram of a gas analyzer.

The flux of IR radiation from source 1 is passed through the medium under study in working cell 2, and then is divided into two equal fluxes by divider 3. The divided fluxes pass through cell 4 with vacuum (or with a gas that does not absorb in the IR range) and through reference cell 5 with the limiting concentration of the gas being determined. Measurement of concentration can be carried out by logarithmizing the quotient obtained by dividing signals proportional to the powers of the infrared fluxes that have passed through the cells, or by logarithmizing the difference of these signals.

Indeed, the transmittance of the gas mixture is determined by the expression

\[ T = \int_{\lambda_1}^{\lambda_2} \prod_{i=1}^{n} e^{-\beta_i(\lambda) W_i}\, d\lambda . \tag{1} \]

where \(\beta_i(\lambda)\) is the absorption coefficient of IR radiation of the \(i\)-th gas;
\(W_i\) is the deposited layer of the \(i\)-th gas;
\(\lambda_1 \div \lambda_2\) is the spectral interval in which the IR source radiates.

Thus, the intensity of IR radiation after passing through the working cell with the medium under study and the channel with the vacuum cell will be equal to:

\[ I_1 = 0.5 I_0 \int_{\lambda_1}^{\lambda_2} e^{-\beta_x(\lambda) W_x} e^{-\beta_2(\lambda) W_2} \cdots e^{-\beta_n(\lambda) W_n}\,d\lambda, \tag{2} \]

and the intensity of the IR radiation after passage through the channel with the reference cuvette is

\[ I_2 = 0.5 I_0 \int_{\lambda_1}^{\lambda_2} e^{-\beta_x(\lambda)(W_{x0}+W_x)} e^{-\beta_2(\lambda) W_2} \cdots e^{-\beta_n(\lambda) W_n}\,d\lambda, \tag{3} \]

where \(W_x\) is the deposited layer of the measured gas contained in the working cuvette with the medium under study;

\(W_{x0}\) is the deposited layer of the measured gas at the limiting concentration contained in the reference cuvette;

\(I_0\) is the intensity of the IR radiation from the source.

Since \(W_{x0} \gg W_x\), then \(e^{-\beta(\lambda)(W_{x0}+W_x)} = e^{-\beta(\lambda)W_{x0}}\), and the desired concentration \(W_x\) can then be found from the relation

Fig. 2. Dependence of the output signal on the concentration of carbon monoxide.

Figure labels: \(U_1 \times 0.1; U_2\), rel. units; \(0.9\), \(0.6\), \(0.3\), \(0\); \(U_2\); \(U_1\); \(W_{\mathrm{atm.CO}}^{*} = 10\ \mathrm{atm\cdot cm}\); \(W_{\mathrm{H_2O}}^{*} = 0.02\ \mathrm{rel.\ units\cdot cm}\); \(0.025\); \(0.25\); \(\lg W_{\mathrm{CO}}^{*},\ \mathrm{atm\cdot cm}\).

Fig. 3. Dependence of the output signal on the concentration of water vapor.

Figure labels: \(U_1 \times 0.1; U_2\), rel. units; \(0.8\), \(0.6\), \(0.4\), \(0.2\), \(0\); \(U_2\); \(U_1\); \(W_{\mathrm{atm.CO}}^{*} = 3\ \mathrm{atm\cdot cm}\); \(W_{\mathrm{CO}}^{*} = 0.023\ \mathrm{atm\cdot cm}\); \(0.010\); \(0.014\); \(0.018\); \(W_{\mathrm{H_2O}}^{*},\ \mathrm{rel.\ units\cdot cm}\).

\[ U_1 = \ln \left[ \frac{ \displaystyle \int_{\lambda_1}^{\lambda_2} e^{-\beta_x(\lambda)W_x} e^{-\beta_2(\lambda)W_2} \cdots e^{-\beta_n(\lambda)W_n}\,d\lambda }{ \displaystyle \int_{\lambda_1}^{\lambda_2} e^{-\beta_x(\lambda)W_{x0}} e^{-\beta_2(\lambda)W_2} \cdots } \right], \tag{4} \]

or

\[ U_2 = \ln \left[ \int_{\lambda_1}^{\lambda_2} e^{-\beta_x(\lambda)W_x} e^{-\beta_2(\lambda)W_2} \cdots e^{-\beta_n(\lambda)W_n}\,d\lambda - \right. \tag{5} \]

\[ -\int_{\lambda_1}^{\lambda_2} e^{-\beta_x(\lambda) W_{x0}} e^{-\beta_2(\lambda) W_2}\cdots e^{-\beta_n(\lambda) W_n}\, d\lambda \right]. \]

The expressions obtained, despite their cumbersomeness, are close to linear dependences between \(U_1\), \(U_2\), and \(W_x\). Thus, for example, for a single wavelength of IR radiation \(\lambda_0\), expression (4) reduces to the form

\[ U_1=\beta_x(\lambda_0)\lvert W_{x0}-W_x\rvert . \tag{6} \]

The sufficiently high linearity of the dependences is also evident from Fig. 2, which presents the calculated curves \(U_1(\lg W^*_{CO})\) and \(U_2(\lg W^*_{CO})\), obtained from formulas (4) and (5). The calculation was carried out for the case in which the measured gas is carbon monoxide (CO), and the interfering gas is water vapor \(\mathrm{H_2O}\). In this case, in the working cuvette the pressure is \(P=1\) atm, and the temperature is \(T=293^\circ\mathrm{K}\).

It is interesting to note that variation over wide limits of the concentration of the interfering gas does not lead to a noticeable change in the output signal, as shown by Fig. 3. This indicates the small magnitude of the methodological error possessed by the proposed method of IR gas analysis.

REFERENCES

1. D. Kendall. Applied Infrared Spectroscopy. Moscow, “Mir,” 1970.