Читать книгу Continuous Emission Monitoring - James A. Jahnke - Страница 121

When studying the absorption of light by gases, the Beer–Lambert law can be used to relate the amount of light absorbed to the concentration of the pollutant gas. First, consider the system shown in Figure 4‐8, which is composed of a light source, flue gas, and a sensor that measures light intensity.

The intensity of light passing through a stack (or sample cell) will decrease if gas molecules in the cell become “excited,” that is, if the light embodies wavelengths causing energy transitions in the molecule. Light transmittance, Tr, is the fraction of incident light passing through the cell. This can be expressed as the ratio of the light intensity transmitted through the cell, I, to the initial incident light intensity, I_o, (or the intensity with no absorbing material in the stack or cell), or:

Figure 4‐7 Infrared vibrational–rotational transmittance spectrum for SO₂.

Figure 4‐8 Example system for measuring pollutant gas concentrations.

(4‐5)

The Beer–Lambert law states that the transmittance of light through the medium decreases exponentially by the product α(λ) cL, or

(4‐6)

where

 Tr = the transmittance of the light through the flue gas

 Io = the intensity of the light entering the gas/s

 I = the intensity of the light leaving the flue gas/s

 α(λ) = molecular absorption coefficient (dependent on wavelength)

 c = concentration of the pollutant

 l = distance the light beam travels through the flue gas

The Beer–Lambert law relates light absorbance in a medium, A = α(λ)cl, to the distance the light travels in the medium and the concentration of the light‐absorbing (and or light scattering) species.

[Note: In the conventions of International Union of Pure and Applied Chemistry (IUPAC), the fraction of light not transmitted is termed absorbance, A, and is expressed as A = ɛ(λ)cl, where ɛ(λ) is the “molar absorption” coefficient in L/mol/cm, c is the concentration in mol/L, and l is the pathlength in cm, an expression commonly used for light absorption in liquid solutions. When applied to light absorption by gases, the absorption coefficient is often expressed as A = σ(λ)Nl, where σ(λ) is the “absorption cross section” in cm² and N is the number density of the gas being measured (no./cm³). In the field of continuous emission monitoring, the absorbance has traditionally been expressed as α(λ)cl, where α(λ) is termed the absorption coefficient [used instead of the IUPAC symbol ɛ(λ)], c is the concentration of the gas being measured, and l is the pathlength. [This convention has been used in this book.]

The absorption coefficient α(λ) is dependent upon the light wavelength and the properties of the pollutant molecules. The coefficient is a quantitative expression of the degree to which a molecule will absorb light energy at a given wavelength. If no absorption occurs, α(λ) will be zero, and the transmittance would equal 100%. If an electronic or vibrational–rotational transition occurs at some wavelength, the absorption coefficient will have some value, and the reduction of light energy across the path will also depend upon the pollutant concentration, c, and the pathlength, l.

Based on this principle, an instrument can be designed to measure pollutant gas concentrations. All that is needed is light having a wavelength that will cause some transition in the molecule of interest, a light path through the gas (either through a sample cell or through the stack or duct), and a light detector. I_o is determined by taking a reading from the detector when no pollutant is in the light path of the duct or sample cell. The concentration can be obtained from the Beer–Lambert expression if α(λ) and l are known, but typically a calibration curve is generated with known gas concentrations, rather than using theoretical values for α(λ). Figure 4‐9 shows a calibration plot typical of an instrument designed to measure light absorption by pollutant molecules.

Here, ln(1/Tr) is plotted against concentration instead of plotting transmittance against concentration. This logarithmic plot gives a straight line, from which it is much easier to develop the calibration plot. In the example of Figure 4‐9, a calibration line is generated using three calibration standards of known concentration. Calibration gases are then injected one at a time into a sample cell to obtain values at the detector of I₁, I₂, and I₃. The ratios of I/I_o are calculated, the logarithm is taken, and values of ln(1/Tr) are plotted against the concentration to obtain the line. Injecting an unknown gas into the sample cell gives a value, I_u, at the detector. The unknown concentration can then be determined by drawing a line from the calculated value of ln(1/Tr_u) on the y axis to intersect the calibration line. At the point of intersection, a line is drawn down to the x axis to obtain the concentration of the unknown gas.

Note that it is not necessary to know the value of the absorption coefficient to obtain the unknown concentration value. The use of gas calibration standards avoids that necessity in this type of instrumentation.

Note also that the instrument response can be given as the logarithm to the base ten instead of in Naperian logarithms. The conversion between the two is simply log₁₀(1/Tr) = (1/2.303)ln(1/Tr). Spectroscopists commonly use the base 10 logarithm, A, where absorbance is expressed as A = log₁₀(1/Tr).