Analysis of Principlesof Remote Sensing and Characterization of Stack Gases by Infrared Spectroscopy Shih H. Chan,’ Chuen C. Lin, and M. J. D. Low Departments of Mechanical Engineering and Chemistry, N e w York University, N e w York, N.Y. 10453
The remote sensing of stack gases by infrared emission spectroscopy has been studied analytically. An expression is derived relating the concentration of gaseous pollutants to the infrared band parameters and the mean temperature of the stack gases. The band parameters employed are independent of the resolution of spectrometers used in remote sensing or in laboratory measurements undertaken to define the spectral characteristics of the gases. Consequently, existing data obtained under various conditions of resolution can be applied directly to remote sensing. A method is proposed by which the temperature of the stack gases can be estimated from the spread of the peak of the P or R branch of a vibration-rotation band of the remotely observed emission spectrum. The application of the principles to the remote sensing of SO2 by measuring the V I SO2 emission band is discussed. Considerable interest has been evidenced in the remote sensing of air pollutants (Low and Clancy, 1967; Williams and Kolitz, 1968; Barringer and Moffat, 1969; Hanst, 1970; Menzies, 1971) because it would be desirable and useful to detect the presence of pollutants and to measure their concentrations under conditions where direct physical access to the polluted area or to the source of pollution is not feasible or practical. The qualitative aspects of remote sensing by infrared emission spectroscopy have been explored by Low and Clancy (1967), who used a Fourier transform spectrometer to record the infrared emission spectra of stack gases. They showed that spectra could be recorded from a position remote from the source of pollution, and the discharge of pollutants not observable by direct visual inspection could be detected. Significantly, this could be done at night, when surveillance by other methods becomes difficult if not impossible. The feasibility of qualitatively detecting pollutants by infrared sensing has thus been established. It has, however, not been possible so far to carry out quantitative measurements by which the concentration levels of pollutants could be established. To make quantitative measurements it is necessary to know the stack-to-sensor distance, the atmospheric absorption over that distance, the field of view, instrument characteristics, the nature of the pollutant and its infrared band parameters, and the temperature of the stack gases. Some items are trivial or easy to obtain, so that the requirement is reduced to computing the amount of gas present, given the strength of the specific signal which was detected, the emission characteristics specific to the gas, and the temperature-i.e., in its simplest terms, calculating the amount of gas from its temperature. It has, however, not been feasible so far to use infrared remote sensing to provide the crucial information about the temperature of the gas, so that it has not been possible to carry out quantitative infrared remote sensing of pollutants. It may be surmised that it should be possible to estimate the temperature of an emitting gas if the spectro-
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Environmental Science & Technology
scopic information and the gas concentration are known. That has been the approach of the astrophysicists, who measure spectral emission a t selected frequencies, assume that gas concentrations are known from the distribution of gases in the atmosphere, and then invert the ill-conditioned integral equation to obtain the temperature distribution. Similarly, in engineering studies of rocket exhausts, remote temperature determinations are carried out by assuming that the concentrations of exhaust gases are known from the stoichiometry of the reactions. However, numerous studies have shown that there i s no unique solution to the equations, so that the required temperature information could not be extracted for remote sensing purposes. It would thus appear that the approach of using a gas as its own “thermometer” in the manner outlined is not a potentially fruitful one for remote sensing; in the latter case, both the temperature and the concentration are unknown. We have analyzed the theoretical aspects of the remote sensing problem in a search for alternative procedures which might make it possible to carry out quantitative infrared remote sensing of air pollutants. Such a procedure is described.
Remote Sensing of Concentrations of Stack Gases Consider a suitable spectrometer system incorporating a dual infrared detector. The latter consists of two sensors connected differentially. The field of view of one sensor observes the stack plume, and that of the other sensor observes the atmosphere in the proximity of the plume. The net radiation flux perceived by the dual detector is simply the difference between the fluxes of the two fields of view. Assume that the concentration of the pollutant in the plume is much larger than that of the immediate surrounding atmosphere, and that the background radiation -i.e., the radiation originating in the sky and atmosphere behind the plume and in the proximity of the plume, which reaches the sensors is the same for both fields of view. The net radiation flux can then be approximated as follows (Chan et al., 1971):
where Aut i.s the resolution of the spectrometer. The temperature has been assumed to be constant across the plume; this is not far from realistic near the exit of the stack because the plume usually is highly turbulent. Physically, the right-hand side of Equation 1 means that the emission of the gaseous pollutant in the plume is attenuated by the atmosphere between the plume and the sensor. The absorber thickness of the pollutant, u , in Equation 1 is related to the concentration of the pollutant, C,by u = CL (2) It is the purpose of the present study to find an explicit expression of concentration from the integral Equation 1 so that the concentration of a pollutant can be easily predicted from the measurement carried out by the remote sensor. The integral Equation 1 is basically the same as the equation in inverting the atmospheric temperature or
ozone distribution in the upper atmosphere in astrophysics; it is a mathematically unstable integral equation, and has received considerable attention in astrophysics literature (Wark and Fleming, 1966). Because it is difficult even to invert the concentration from the equation numerically, to invert it analytically will certainly require the introduction of some simplifying assumptions. In general, the solid angle of the field of view is small and, consequently, all the quantities on the right-hand side of Equation 1 can be approximated by their mean values in performing the integration with respect to the solid angle. Furthermore, the spectral region useful for remote sensing lies in the atmospheric window regions; in other words, the sensor should be operated in the window regions. For example, a method of remote sensing of SO2 in the exhaust of smokestacks involves measuring emission spectra in the 1050-1250 cm-1 (8-9.5 ym) region. The u 1 fundamental band of SO2 centered near 1151 (8.69 ym) falls in that region, but there are practically no bands due to carbon dioxide or water vapor. Therefore, the atmospheric path between the sensor and the plume is very transparent, and the spectral transmittance of the atmospheric path is relatively constant in the window region. The atmospheric spectral transmittance, T a $ , in Equation l can then be assumed to be independent of Equation 1can be simplified to the following IJ.
where Tabis the average value of Tavin the region &vi. In the conventional remote-sensing technique, the absorption coefficient, K", must be known a priori and is obtained from laboratory measurements. Generally, K" is a function of temperature, pressure, wavenumber, and the resolution of the spectrometer. As the temperature of the stack gases is unknown, it is difficult to know which appropriate K~ value should be used. Besides, the resolution of the sensor must be constantly adjusted to match the resolution of the laboratory spectrometer which produced the K " data. In view of all these difficulties, it is proposed here to use a complete infrared band spectrum for inversion purposes such that the absorption coefficient is to be replaced by a band parameter independent of the resolution and which has been correlated semiempirically as a continuous function of path length and temperature, and so forth. In other words, the radiation flux is integrated over the whole band to yield
erature, the continuous correlation (Tien and Lowder, 1966) appears to be the easiest one to use. It is given by
where
G' =
4
p
Pe = [(P,
e
u =
c,u/c,
+ ~ P , ) / P ~ ]f " = y
exp ( 2
-
y)
C1, C Z , and Ca are functions of temperature. For S o n , the latter have been determined by Chan and Tien (1971b). Therefore, the integral equation has been reduced to the algebraic Equations 5 and 7 from which u (or C) can be solved easily in terms of other quantities which are known, except for the temperature of the stack gases which will be determined by the method presented in the next section. In actual applications, K ~ U> 1, Wien’s approximation can be employed to yield an explicit expression for the temperature as follows:
+
where - and signs apply to P and R branches, respectively. On the other hand, for hCv/kt
