Air & Waste Management Association (A&WMA)

An analysis of extinction coefficients of particles and water moisture in the stack after flue gas desulfurization at a coal-fired power plant


Two important factors that affect in-stack opacity—light extinction by emitted particles and that by water moisture after a flue gas desulfurization (FGD) unit—are investigated. The mass light extinction coefficients for particles and water moisture, kp and kw, respectively, were determined using the Lambert-Beer law of opacity with a nonlinear least-squares regression method. The estimated kp and kw values vary from 0.199 to 0.316 m2/g and 0.000345 to 0.000426 m2/g, respectively, and the overall mean estimated values are 0.229 and 0.000397 m2/g, respectively. Although kw is 3 orders of magnitude smaller than kp, experimental results show that the effect on light extinction by water moisture was comparable to that by particles because of the existence of a considerable mass of water moisture after a FGD unit. The mass light extinction coefficient was also estimated using Mie theory with measured particle size distributions and a complex refractive index of 1.5-ni for fly ash particles. The kp obtained using Mie theory ranges from 0.282 to 0.286 m2/g and is slightly greater than the averaged estimated kp of 0.229 m2/g from measured opacity. The discrepancy may be partly due to a difference in the microstructure of the fly ash from the assumption of solid spheres because the fly ash may have been formed as spheres attached with smaller particles or as hollow spheres that contained solid spheres. Previously reported values of measured kp obtained without considering the effects of water moisture are greater than that obtained in this study, which is reasonable because it reflects the effect of extinction by water moisture in the flue gas. Additionally, the moisture absorbed by particulate matter, corresponding to the effect of water moisture on the particulates, was clarified and found to be negligible.


Opacity is defined as the percentage of transmitted light that is obscured as it passes through a medium. The obscuration is caused by extinction, which consists of absorption and scattering by constituents in the medium. 1,2 In a coal-fired power plant, in-stack opacity is generally measured in situ using light transmission meters as part of a continuous emission monitoring system (CEMS). Opacity is a function of particulate concentrations and many other independent optical and physical variables, such as particle size distribution, particle density, refractive index of particles, and nitrogen dioxide and sulfuric acid concentration in the exhaust gas, as examined in previous studies. The extinction of a constituent is usually expressed in terms of mass extinction coefficient (k),3,4 the extinction coefficient (k multiplied by concentration), or the ratio of specific particulate volume to mass extinction coefficient (K).5–9 The  Lambert-Beer law states that opacity due to constituents that contribute to the decay of intensity in a collimated beam with an optical path length (L) can be expressed as3 where W is the mass concentration, k is the mass extinction coefficient (m2/g), K is the ratio of the volume of a specific particulate to the mass extinction coefficient (cm3/m2),  is the density of the substance, and subscript i denotes the contribution of species i. k and K are dependent on the composition, size distribution, relative refractive index, and the beam wavelength. The Lambert-Beer equation applies at conditions in which multiple scattering is negligible.

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