Journal of Applied Spectroscopy, Vol. 79, No. 1, March, 2012 (Russian Original Vol. 79, No. 1, January–February, 2012)
SPECTRONEPHELOMETRIC METHODS TO DETERMINE MICROPHYSICAL CHARACTERISTICS OF DUST IN ASPIRATION AIR AND OFF-GASES IN CEMENT PLANTS S. A. Lisenko and M. M. Kugeiko*
UDC 551.508
The information value of spectral directional scattering coefficients of cement dust released into both the atmosphere and aspiration air during cement production is analyzed in terms of the concentration and effective dust particle size based on a regression approach to solving the inverse problem. The most effective layouts of dust meters that combine ease of implementation with high accuracy over the entire range of physicochemical properties of dust are considered. Keywords: cement dust, mass concentration, effective size, spectronephelometric measurements, inverse problem, multiple regression. Introduction. The activity of cement plants is unavoidably connected with extensive release of gas-dust streams into the atmosphere. The high concentration of solid pollutants (dust) in the releases inflicts enormous damage on the environment and causes irreversible loss of a large amount of raw material and finished product and premature deterioration of living quarters, etc. In addition to this, high dust concentrations in workplace air degrade the health conditions of the workers and reduce their productivity. In several instances they can cause occupational diseases. Therefore, an important problem for modern industry is protection of the environment from releases of dust and hazardous gases. Various dust-trapping apparatuses such as electric filters, sleeve filters, cyclones, inertial dust-traps, etc. are currently used to remove dust from workplace air of industrial facilities and gases released into the atmosphere [1–3]. However, in many instances the dust concentration of industrial releases exceed by several times the maximum allowed concentrations defined by regulations [2]. According to current rules and standards, the mass concentration of dust in off-gases is used to monitor the effectiveness of existing dust-trapping apparatuses and to evaluate the throughput of designed ones [2]. This parameter is also applicable to health and epidemiological services for quantitative estimation of industrial atmospheric dust releases [4, 5]. Methods for measuring dust concentration are divided into two groups. Those of the first group are based on preliminary precipitation of dust particles and a study of the precipitate. Those of the second group do not include preliminary precipitation [3]. The principal advantage of the first group is the capability for direct measurement of the dust mass concentration. Its disadvantages are the labor-intensiveness of the measurements and the need for strict observance of lengthy procedures that required highly qualified personnel. As a result, air pollution becomes apparent only after the passage of a significant time period after its occurrence. Advantages of the second group are the capability for direct measurements in the gas-dust stream itself without the use of a sampling device, continuous measurements, high sensitivity, and the ability for total automation of the measurement process. The stream is not subjected to aerodynamic distortion during the measurements. Furthermore, these methods provide continuous information about the instantaneous dust concentration in the stream and trends in its change. This enables, first, the operating modes of the dust-trap to be controlled automatically; second, an alarm to be activated if the dust concentration rises above the limit; and third, the production to be halted in emergencies where the purification apparatus breaks down. ∗
To whom correspondence should be addressed.
Belarusian State University, 4 Nezavisimosti Ave., Minsk, 220030, Belarus; e-mail:
[email protected]. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 79, No. 1, pp. 66–76, January–February, 2012. Original article submitted June 28, 2011. 0021-9037/12/7901-0059 ©2012 Springer Science+Business Media, Inc.
59
Optical methods are the leading types of continuous monitoring of gas-dust releases. They are very simple and reliable. Therefore, industrial dust meters that are used in many countries to monitor releases from cement plants, power plants, etc. have been developed based on them. Optical methods for measuring the dust mass concentration are based on recording the attenuation (photometric) or scattering (nephelometric) of a light beam upon its passage through a volume with dust particles [6–8]. The principal drawbacks of photometric methods are their low sensitivity 3 3 for measuring low concentrations (10 g/m ) because of strong attenuation of the light [9]. Furthermore, this method is susceptible to a sharp loss of sensitivity when measuring the concentration of particles of diameter >8.0–10.0 μm. This limits considerably the ability to use them in several industrial sectors. Nephelometric methods turn out to be more effective for monitoring dust in industrial cement-production processes. As a rule, the conversion from the scattering coefficient β(θ) at an angle θ to the mass concentration M of the aerosol is carried out using a calculated or empirical coefficient Kθ that relates these parameters. The coefficient Kθ is not strictly determined and can vary over broad limits depending on the aerosol microstructure. Therefore, the accuracy and precision of the dust monitoring results are determined mainly by the consistency of the dust-particle properties if nephelometric measuring devices are used. For example, there are limitations on the dust composition dispersion, which should not vary with oscillations of its concentration [3]. The effect of the dust physicochemical properties on the result of its mass concentration measurement can be avoided by measuring light scattered at several angles and(or) at several wavelengths. The inverse problem, i.e., finding the aerosol particle-size distribution f(r) from optical measurements, reduces to the solution of a system of integral equations of the following form [7]: ∞
β (θ, λ) = N ∫ Cθ (m (λ), x) f (r) dr , 0
(1)
where N is the calculated particle concentration (cm–3); Cθ, the light scattering cross section at wavelength λ and angle θ, which is known from light diffraction theory for a separate particle [10, 11]; m, the complex refractive index of the particles; and x = 2πr ⁄ λ. o The range of angles θ < 15 provides the most information regarding the size distribution of large dust particles because their scattering indicatrix is elongated in the forward direction [12, 13]. Furthermore, the light scattering intensity in this range of θ depends least on the shape of the scattering particles and their refractive index. This enables the amount of a priori information required to solve the inverse problem to be reduced. Numerous systems for laser analysis of the granulometric composition of suspensions, emulsions, and powders o are mass produced today and are based on measurements of the scattered light intensity at angles θ < 15 [14–16]. However, they all are expensive and suitable exclusively for laboratory analysis. High flow rates and temperatures of the monitored gas-dust streams are typical of industrial dust monitoring. This makes it impossible to use such systems and requires the development of new inexpensive and operationally reliable measuring devices for continuous industrial monitoring that are stable to variations in the dust physicochemical properties. Herein a regression approach is used to solve the inverse problems [17, 18]. The optical probe wavelengths and scattered light recording angles are selected so that they are optimal with respect to their information value regarding the cement dust microphysical parameters (mass concentration and effective particle size) and their stability to optical measurement uncertainty for solving the inverse problem. The problem of designing nephelometric dust measurements that are stable to variation of its chemical and size composition is being solved. A statistically representative set of optical and microphysical properties of cement dust released into the atmosphere and aspiration air during various industrial processes for producing various grades of cement is required in order to solve the aforementioned problems. Such a set is obtained based on a developed statistical microphysical model of cement dust, the parameters of which are discussed in the next section. Statistical Microphysical Model of Cement Dust in Industrial Releases. A theoretical calculation of the directional scattering coefficient β(θ, λ) of a dispersed medium presupposed knowledge of its properties such as the particle shape, their concentration and size-distribution function, and the spectral dependence of the complex refractive index (CRI) of the particle substance. Results of numerous mathematical experiments on the modeling of light scattering by particles of various shapes demonstrate a weak influence of the particle shape on their small-angle scattering indicatrix (for angles 60
TABLE 1. Ranges of Variations in Bulk Concentrations (%) of Cement Components and Water (due to hygroscopicity) in Dust Particles Component
Portland cement
Aluminous cement
CaO Al2O3 SiO2 Fe2O3 MgO H2O
52–70 2.6–7.0 15.7–25.0 0.26–5.00 0.09–4.50 0.2–12.6
26.2–45.0 26.2–70.0 3.5–15.0 1.5–10.0 0.09–1.00 0.2–12.6
θ < 15o) [10, 19]. This indicates that diffraction effects play the main role in this range of scattering angles. Considering this and the high information value of small-angle scattering for large particles, namely this range of angles is examined below. Scattering by cement-dust particles is calculated using the known Mie formulas [11] for spherical particles of equivalent volume. The spectrum of sizes of dispersed industrial aerosols is described well by a logarithmic normal distribution [2, 3, 6]: 2 1 ⎡ 1 ⎛ ln (r ⁄ rm) ⎞ ⎤ f (r) = exp ⎢− ⎜ (2) ⎟ ⎥, r√ ⎯⎯⎯⎯ 2πσ σ ⎠⎦ ⎣ 2⎝ where r is the radius of a spherical particle with equivalent volume; rm, the median particle radius; and σ, the standard deviation for ln r. The ranges of the distribution parameters of Eq. (2) (rm = 0.1–5.0 μm and σ = 0.2–1.0) were selected based on literature data for the dispersed composition of cement dust released into aspiration air and the atmosphere at various processing stages (unloading, loading, packaging cement, dry mulling of raw material mixtures in grinders, roasting clinker in rotating furnaces, mulling clinker with an additive and gypsum in grinders) [1, 3, 6] and at the exit of sleeve filters of gas-purification facilities [20, 21]. Uniform distributions requiring only an indication of the range of possible parameter variations were used as models for the variations of parameters rm and σ. The mass fraction of particles of radius r > 30 μm was held to less than 1% of the total particle mass [1, 3]. The CRI of the cement-dust particles was determined by the cement chemical composition, which was rather complicated and could vary significantly depending on the used raw material and clinker production method. The principal cement components were lime (CaO), silica (SiO2), aluminum oxide (Al2O3), and hematite (Fe2O3) [1, 22]. The chemical composition of Portland cement was mainly lime and silica. Aluminous cement contained calcium and aluminum oxides and small amounts of iron, magnesium (MgO), titanium (TiO2), and other oxides. Table 1 presents the ranges of total contents of principal components of Portland and aluminous cements that were chosen based on an analysis of the literature on the chemical composition of various grades of cement [1, 22, 23]. Rather detailed information on CRI spectra of cement components such as SiO2, Al2O3, Fe2O3, and MgO are currently available in the literature (and the electronic media) [24–26]. However, data on the CRI of CaO are limited to the spectral range 0.43–0.66 μm only [27] whereas the CaO content in Portland cement typically shows the greatest variations and is responsible for the greatest variability of its CRI. Therefore, the CRI spectrum of CaO mCaO(λ) for λ > 0.66 μm was given as a linear function for statistical modeling of the CRI spectra of cement dust m(λ):
λ − λ0.66 , mCaO (λ) = mCaO (λ0.66) + ⎡ξ − mCaO (λ0.66)⎤ ⎣ ⎦ λmax − λ0.66
(3)
where λ0.66 = 0.66 μm; λmax = 1.6 μm is the upper limit of the spectral range examined herein; mCaO(λ0.66) = 1.83 [27]; parameter ξ, which represented the CRI of CaO at wavelength λmax, was selected randomly from the range 1.65– 1.80. The CRI of cement dust was calculated as a linear combination of the CRIs of the separate cement components and water (because of hygroscopicity) taking into account their bulk concentrations vi: 61
Fig. 1. Spectra of real (a) and imaginary (b) parts of complex refractive indices of the principal cement components: Fe2O3 (1), CaO (2), Al2O3 (3), MgO (4), SiO2 (5), and H2O (6) that were used in the calculations.
m (λ) = vCaOmCaO (λ) + vSiO mSiO (λ) + vAl O mAl O (λ) 2
2
2
3
2
3
+ vFe O mFe O (λ) + vMgOmMgO (λ) + vH OmH O (λ) . 2
3
2
3
2
2
Figure 1 shows spectral dependences of the real n(λ) and imaginary χ(λ) parts of the CRIs of cement components and water that were used in the present work (the imaginary parts of the CRIs of CaO, Al2O3, and MgO are small and were set equal to zero in the calculations). Weak absorption and an almost neutral dependence n(λ) were characteristic of the examined components with the exception of hematite at λ ≤ 0.5 μm. Therefore, it was obvious that the variations noted above for the spectral dependence mCaO(λ) at λ ≥ 0.66 μm could be adequately taken into account as an uncertainty in the literature data for this dependence or chemical components present in the cement (in small quantities) that were not examined in the present work. The bulk concentrations of SiO2, Al2O3, Fe2O3, MgO, and H2O for Portland cement dust were varied independently in the ranges given in Table 1. The CaO concentration was calculated as vCaO = 1 – vSiO2 – vAl2O3 – vFe2O3 – vMgO – vH2O. The obtained value vCaO was checked for excursion beyond the range of values characteristic of Portland cement (Table 1). The concentrations of CaO, SiO2, Fe2O3, MgO, and H2O were varied analogously andwas calculated for aluminous cement. The mass concentration M of dust in aspiration air and off-gases at cement plants changes by several orders 3 3 of magnitude from 0.01 g/m to 60 g/m depending on the technical process and throughput of the equipment [1–3, 6, 20, 21]. Because of this, the logarithm of the mass concentration and not the concentration itself was varied in our model. The effective density ρ of the particle substance was determined analogously to their CRIs according to the 3 bulk contents of the cement components and water in the particles. The following component densities (g/cm ) were 3 3 used: ρCaO = 3.35 g/cm , ρSiO2= 2.65, ρAl2O3 = 4.0, ρFe2O3 = 5.24, ρMgO = 3.58, and ρH2O = 1.0 g/cm . The calculated particle concentration N with size-distribution function f(r) was related to their mass concentration M by the equation: −1
∞ ⎞ ⎛ 3 ⎜ N = 3M ⎜4πρ∫ r f (r) dr⎟⎟ . ⎟ ⎜ 0 ⎠ ⎝
Thus, the microphysical model of cement dust was defined by nine parameters: M, rm, σ, the bulk contents of the dust components (SiO2, Al2O3, Fe2O3, MgO, and H2O for Portland cement; CaO, SiO2, Fe2O3, MgO, and H2O for aluminous cement), and parameter ξ of the spectrum mCaO(λ). A set of parameters was selected and β(θ, λ) was 62
Fig. 2. Spectral transmission of a homogeneous gas-dust cloud along a path of length L = 10 m; concentrations of gas components H2O, 76 g/cm3; CO, 5.2; CO2, 300; and NO, 0.21; parameters of dust-particle size-distribution function rm = 1.4 μm, σ = 0.7, and dust mass concentration M = 0.5 g/m3; wavelengths for which the attenuation coefficients were calculated (). calculated according to known rules for modeling evenly distributed random quantities. The size of the set of optical 3 and microphysical characteristics of cement dust was 10 values, half of which corresponded to Portland cement; the other half, to aluminous cement. Selection of Probe Spectral Portions. The wavelengths for optical probing of cement dust were selected based on, firstly, the availability of effective laser sources at these wavelengths and, secondly, the requirement that absorption by gaseous components in the off-gases at the cement plants had a minimal influence on the optical measurements. It should be noted with respect to the first criterion that a large variety of semiconducting lasers with practically any wavelength in the range from the near UV to the near IR is currently available. Therefore, only the requirement that these radiation sources fall within the "window of transparency" of the off-gases at cement plants will dictate the selection of the probe spectral portions for them. Off-gases can contain components such as H2O, N2, O2, CO, CO2, SO2, SO3, NO, and NO2 depending on the cement production method and the used fuel (natural gas, coal, fuel oil, etc.) [1]. Of these, only four gases (H2O, CO, CO2, NO) absorb at λ < 1.6 μm [25]. The spectral transmittance T(λ) was calculated taking into account the aforementioned gaseous components for the gas-dust stream released into the atmosphere in order to select the window of transparency. The molecular transmittance Tm(λ) was calculated using a line-by-line method by summing the absorption coefficients kij(λ) for separate absorption lines (index j) of the various gases (index i): ⎧ ⎡ ⎤ ⎫⎪ ⎪ Tm (λ) = ∏ ⎨exp ⎢⎢− ρi L ∑ kij (λ, t, p, ρi)⎥⎥ ⎬ , ⎪ ⎢ ⎥ ⎪⎭ j i=1 ⎩ ⎣ ⎦ 5
where L is the path length; t and p, the temperature and pressure in the release; and ρi, the gas concentrations (g/m3). The fine structure parameters of the gas absorption bands were taken from the database HITRAN 2004 [25]. Figure 2 shows the transmission spectrum of a homogeneous gas-dust cloud. It can be seen that the gas components have no strong absorption bands in the spectral ranges 0.4–0.5, 0.60–0.64, 0.86–0.88, 1.00–1.07, 1.24–1.26, and 1.55–1.56 μm. This means that attenuation of the radiation is due mainly to dust particles. Thus, optical probing should be carried 63
out at wavelengths in these ranges. We selected λ = 0.44, 0.62, 0.87, 1.04, 1.25, and 1.56 μm for calculating β(θ, λ) because existing laser sources can generate radiation at these wavelengths. Selection of Optical Measurements and Solution of the Inverse Problem. Direct calculation of the dust mass concentration as a function of the measured optical characteristics [spectral and(or) angular directional scattering coefficients β(θ, λ)] is of interest from the viewpoint of automated monitoring. Obviously such a deterministic functional dependence is non-existent. However, a statistical function (regression) can be easily produced based on the aforementioned set of optical and microphysical characteristics of the dust. Such a function is actually a solution of the inverse problem [Eq. (1)]. However, a priori information is not required to reproduce the dust mass concentration using it if the actual dust characteristics are within the limits of the set used to produce the function. Another important attribute of such an approach to solving the inverse problem is the automatic elimination of a multitude of equivalent solutions that reproduce the measurements equally well within experimental accuracy by averaging them. Obviously the wavelengths λ and angles θ for recording scattered light for which the quantities β(θ, λ) are least correlated must be chosen in order to solve the inverse problem. Otherwise the system of Eqs. (1) will be poorly specified and small errors in measuring δβ will cause significant errors in reproducing mass concentration δM. This applies fully to the sensitivity of regression dependences between M and β(θ, λ) to errors of δβ. Therefore, it is important to analyze the number of independent components contained in variations of β(θ, λ) that are due to changes of the dust microphysical characteristics. As a rule, such an analysis is performed by examining the eigen values of a normalized covariant matrix of measurements x = β(θ, λ): Sij =
1 σiσj
K
_
_
∑ (xi − xi) (xj − xj) , k
k
(4)
k=1
_ where K = 10 is the size of the set of optical and microphysical characteristics of the cement dust; x and σ, the average and scatter of x. In our instance the vector of measurements x = (xi) contains 96 components corresponding to λ = 0.44, 0.62, 0.87, 1.04, 1.25, and 1.56 μm and θ = 5, ... , 15o (angles θ < 5o were not examined because of the complicated practical feasibility of measuring the scattering signals corresponding to them). An analysis of the relationship of the eigen values of the covariant matrix [Eq. (4)] to its trace SpSij = 3
Σ Sii revealed that 99.4% of the total scatter of β(θ, λ) over the whole examined range of θ and λ was due to the i
three first eigen vectors of the matrix [Eq. (4)] corresponding to the largest eigen values. The size of the fourth eigen value μ4 relative to SpSij was 0.38%, which according to the theory of the principal component method [28] means that the examined optical measurements for δβ > √ ⎯⎯⎯⎯⎯⎯⎯⎯⎯ μ4 ⁄ SpSij⎯ ≈ 6.2% contain at most three independent components. Considering this, the statistical relationship between M and β(θ, λ) is approximated by polynomials of the form: ln M =
∑
i
j
k
aijk [ln β (λ1, θ1)] [ln β (λ2, θ2)] [ln β (λ3, θ3)] ,
(5)
0≤i+j+k≤3
where aijk are coefficients that are found by a least squares method for given values of θi and λi (i = 1, 2, 3) using a model set of optical and microphysical dust characteristics. It is noteworthy that increasing N by k times should produce simultaneously the same increase of M and β(θ, λ) because of the linear dependence of M and β(θ, λ) on the calculated concentration of particles N. Hence it follows that the relationship between M and β(θ, λ) should be described by a homogeneous first-power function that is the sum of terms of the type β(θi, λi)F(h), where F(h) is a certain function that depends on the ratios h = β(θi, λi)/β(θj, λj). However, the range of variations of N covers several orders of magnitude. As a result, the same error in the approximation of the statistical relationship between M and β(θ, λ) over the whole range of N cannot be attained. Therefore, logarithms of M and β(θ, λ) are used in Eq. (5) because in this instance values of the same order are used and the M values obtained from Eq. (5) will always be positive. The effect of errors in optical measurements of δβ on the result of reproducing M was evaluated using a model set of optical and microphysical dust characteristics in a closed numerical experimental. The quantity M was calculated for each instance of dust parameters using Eq. (5) with the imposition of random deviations on β(θ, λ) in 64
Fig. 3. Optical-microstructural correlations of cement dust: correlation coefficient between β(θ, λ) and M for λ = 0.44 (1), 0.87 (2), and 1.56 μm (3) (a); correlation relationship between β (5o, 1.56 μm) and M (b).
the range of δβ. The resulting M values were compared with the "exact" (model) values. The average errors of δM over the set were calculated after enumerating all instances. It is important to analyze the spectral and angular dependences of the paired correlation coefficients between M and β(θ, λ) in order to select the most informative wavelengths for optical probing and angles for recording scattered light. Figure 3 shows the correlation coefficient between these parameters. As expected, the small-angle indicatrix was most informative with respect to the particle mass concentration. This was explained by the predominant contribution to it of large dust particles that also determined the dust mass concentration. However, as noted above, o measuring β(θ, λ) at angles θ < 5 was complicated by several technical difficulties. It can be seen from Fig. 3 that these difficulties could be obviated by using a light source with wavelength λ = 1.56 μm (the correlation coefficient o maximum corresponded to θ = 5 ) and greater. This was also explained by the dependence of the scattering indicatrix on diffraction parameter x = 2πr ⁄ λ. The elongation of the dust particle (including large ones) scattering indicatrix decreased with increasing λ. This led to a shift of the maximum of the correlation coefficient between β(θ, λ) and M to greater θ values. o The existence of the close correlation between M and β (5 , 1.56 μm) that is shown in Fig. 3 made it possible to construct a very simple nephelometer of cement dust concentration that was based on measurement of scattering for –3 3 one angle at one wavelength only. In the simplest instance, the conversion coefficient K = 1.55⋅10 g⋅km⋅sr/m can be used to convert from β(θ, λ) to M. Its mean-square deviation was 19%. However, it was more preferred to use the polynomial regression 2
−4
3
ln M = − 6.3035 + 0.9121 ln β + 0.0137 [ln β] − 7.033⋅10 [ln β] ,
(6)
which allows M to be reproduced from the average optical and microphysical aerosol parameters of the model set with an error of 12.5%. As noted above, the influence of the dust particle size-distribution function and their complex refractive index on the measured M can be decreased by using three optical measurements and the multiple regressions [Eq. (5)] corresponding to them. The optimum set of optical characteristics in Eq. (5) for reproducing M was determined by a computerized search of all possible combinations of θ and λ in the aforementioned ranges and an estimation of the o o errors in reproducing M for δβ = 5%. The values were λ1 = 0.62 μm, θ1 = 15 ; λ2 = 1.56 μm, θ2 = 5 ; and λ3 = o 1.56 μm, θ3 = 8 . Table 2 lists the regression coefficients [Eq. (5)] for this set of θ and λ. The average error over the set for reproducing M was 8.5% for δβ = 5%. 65
TABLE 2. Regression Coefficients of Eq. (5) aijk
λ1 = 0.62 μm
λ1 = 1.56 μm
a000 a100 a200 a300 a010 a020 a030 a001 a002 a003 a110 a210 a120 a101 a201 a102 a011 a021 a012 a111
–6.1843 0.1338 0.2049 0.0257 –0.0499 4.4180 –1.6256 0.8253 5.5356 1.5740 1.0265 –0.0211 0.0215 –1.4349 –0.0598 0.0625 –9.7374 4.8255 –4.8033 –2.70⋅10−8
—6.3196 –0.6047 7.2673 –2.7563 2.2994 9.3838 3.0146 –0.7716 –0.5478 –0.3029 –17.1917 8.3353 –8.3048 2.7427 –0.0922 0.0808 –1.6442 –0.7866 0.8117 –2.21⋅10−8
Despite the fact that the difference in the reproduced M values that resulted from the use Eqs. (5) and (6) taking into account the range of M values was not significant, the nephelometer taking three measurements of β(θ, λ) had an important advantage. The characteristics of the dust particle size-distribution, in particular, the effective size of the dust particles ref could be determined {the ratio of the third term in the distribution function [Eq. (1)] to the second}. This parameter had to be estimated in order to select the most suitable dust-trapping apparatuses for removing dust from aspiration air and off-gases during cement production [1–3]. In contrast with the mass concentration, the effective radius is a dust quality parameter. Therefore, it made sense to use the relationship β(θ, λ) for various θ and λ that were independent of the calculated dust particle concentration to reproduce ref. Two dimensionless parameters can be obtained from the three values of β(θ, λ). These are R12 = β(λ1, θ1)/β(λ2, θ2) and R23 = β(λ2, θ2)/β(λ3, θ3). As a result, the polynomial regression between ref and β(θ, λ) becomes: ln ref =
∑
n
m
anm [ln R12] [ln R23] .
(7)
0≤n+m≤3
Table 3 presents coefficients anm from Eq. (7). The average error over the set for reproducing ref using Eq. (7) for δβ = 5% was 3.3%. Two semiconducting laser sources (0.62 and 1.56 μm) are required for nephelometric measurement of cement dust using the aforementioned method. Obviously a nephelometer taking scattering measurements at several angles but one wavelength is economically more preferred. The optimum set of angles for λ = 1.56 μm (with respect to their information value relative to M and the stability of the solution of the inverse problem to optical measurement errors) o o o includes θ1 = 5 , θ2 = 8 , and θ3 = 15 . The error of reproducing M corresponding to this set is 8.8% and is practically the same as the error corresponding to the optimum measurements (at least for δβ ≥ 5% and a lack of informa66
Fig. 4. Reproduction of mass concentration (a, c) and effective size (b, d) of cement dust particles from β(θi, λi) (i = 1, 2, 3) for λ1 = 0.62 μm, θ1 = 15o; λ2 = 1.56 μm, θ2 = 5o; λ3 = 1.56 μm, θ3 = 8o (a, b) and for λ = 1.56 μm, θ1 = 5o, θ2 = 8o, θ3 = 15o (c, d) corresponding to δβ = 5%.
TABLE 3. Regression Coefficients of Eq. (7) anm
λ1 = 0.62 μm
λ1 = 1.56 μm
a00 a10 a20 a30 a01 a02 a03 a11 a21 a12
–0.3896 –0.6725 –0.3256 –0.1077 –1.5577 0.9586 –1.4143 –2.0941 –0.8622 –1.1339
–0.9285 –5.9556 7.1601 –1.9414 4.4862 –3.2398 0.7705 3.7480 –1.6818 –0.8427
tion on the spectral dependence of the CRI). However, parameter ref in this instance is reproduced worse with an error of 6.7%. This is ~2 times greater than the error of the optimum measurements. Figure 4 shows results of reproducing M and ref for a model set of cement dust parameters using the examined regressions. It can be seen that the results are practically the same for M whereas differences are observed for ref only in the range ref < 2.0 μm, i.e., for finely dispersed dust released into the atmosphere [20, 21]. These differences are easily explained physically. The examined set of optical measurements differ only by one measurement, i.e., in the o o o first instance β (15 , 0.62 μm); in the second, β (15 , 1.56 μm). In both instances the scattering at 15 is due primar67
ily to medium and fine particles. However, scattering theory suggests that the dependence of β(θ, λ) on λ is expressed through the parameter x = 2πr ⁄ λ and particle sizes r corresponding to a single x value for λ = 0.62 μm are ≈2.5 times less than for λ = 1.56 μm. This causes the first set of measurements to be highly sensitive to the presence of fine particles in the medium scattering volume. Conclusion. The polynomial regressions established between the scattering characteristics of cement dust and its microphysical parameters (mass concentration and effective size) provided a basis for constructing a highly accurate and operationally reliable spectronephelometer for dust in aspiration air and off-gases at cement plants. The instrument enabled monitoring of dust over a wide range of chemical compositions and dispersions. This eliminated the need for recalibration of the instrument during its use to monitor dust released by various industrial operations and to perform automated monitoring of dust in real time.
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