LITMIR.BIZ

Figure 4‐12 Light scattering from large particles (r/λ ≥1) where geometrical optics apply.

      Scattering phenomena have been emphasized here, but it should be noted that particles can also absorb light energy, as do gaseous molecules. When light of a specific wavelength resonates with the molecular electrons contained in the particle, it will cause the electrons to jump from one energy state to another. As stated earlier, only light wavelengths that correspond exactly to the molecular energy levels will be absorbed to impart energy to the molecule. As a result, light is again lost from the incident beam.

      Opacity and Transmittance

      Transmission of light through a flue gas that contains particulate matter will be reduced through a combination of scattering and absorption processes. Scattering and absorption of light by a stack plume gives rise to its opacity, its opaqueness to light transmission.

      If light is not able to penetrate through a plume, the plume is said to be opaque – the opacity of the plume is 100%. Transmittance and opacity can be related as follows:

      (4‐7)

      Therefore, if a plume or object is 100% opaque, the light transmittance through it is zero. If it is not opaque, but has zero percent opacity, the light transmittance would correspondingly be 100%. A stack gas or plume will rarely have either zero or 100% opacity, but will have some intermediate value. Opacity standards are typically set at 20%, but can range from 0 to 40% opacity, depending upon the policies of the regulatory agency.

      Bouguer's Law

Particle scattering and absorption effects can be treated in a manner similar to that in the previous discussion on light absorption by gas molecules. Similar to the Beer–Lambert law, Bouguer's law is used when discussing particle scattering. Bouguer's law states that transmittance decreases exponentially by the product naQL, as shown in Equation 4‐8.

(4‐8)

      where n = number concentration of the particles

      The expression was first stated by P. Bouguer in 1760 and later rediscovered by Lambert. In deference to the earlier work of Bouguer, it has become customary in the field of opacity monitoring to call it Bouguer's law (Middleton 1968).

      Q is the particle extinction coefficient, which is dependent on the wavelength and expresses how the particle of size a scatters and absorbs light of wavelength λ. It is analogous to the absorption cross section σ(λ), discussed previously. Theoretically, it should be possible to calculate the opacity from first principles using Equation 4‐8. Because there are usually particles with more than one size in a flue gas, the particle size distribution and the Mie scattering coefficients need to be determined for each size particle. The data demands and calculation difficulties make this approach impractical although attempts have been made in the past (Ensor and Pilat 1971; Pilat and Ensor 1970; Thielke and Pilat 1978). Equation 4‐8 is overly simplified, being expressed for particles of only one size (see Jahnke (1984) for more detailed expressions).

      Bouguer's law is an exponential relationship between transmittance and particulate matter concentration and is somewhat difficult to use in stack emission calculations. Another expression, called “optical density,” is used in opacity monitor specifications and calculations. It is related to opacity as follows:

      (4‐9)

      Optical density is useful in emission calculations because it is directly proportional to the particulate concentration, as shown in the following derivation.

First, taking the natural logarithm of both sides of Equation 4‐8 gives

      (4‐10)

      and rearranging gives