Energy & Fuels 1993, 7,860-869
860
Effective Optical Properties of Pulverized Coal Particles Determined from FT-IR Spectrometer Experiments S. Manickavasagam and M. P. Mengiic’ Department of Mechanical Engineering, University of Kentucky, Lexington, Kentucky 40506 Received April 8, 1993. Revised Manuscript Received September 10, 199P
For accurate modelingof radiative transfer in combustion systems, radiative properties of combustion gases and particles are required. The particle properties are usually determined from the LorenzMie theory assuming they are spherical in shape and their optical properties, Le., the complex index of refraction data, are available. In the present study, an FT-IR spectrometer has been used to determine the “effective” optical properties of Blind Canyon and Kentucky no. 9 coals suspended in KBr pellets, within the wavelength interval of 2-20 pm. A detailed inversion analysis based on the Lorenz-Mie theory is employed to reduce the measured transmission data to a complex index of refraction spectra. In the analysis, the effects of both absorption and scattering by coal particles are accounted for. The results obtained for different coal size distributions deviate from each other only slightly, and they are in good agreement with the single-wavelength data determined from in situ scattering experiments. Simple polynomial expressions are developed to represent the spectral variation of the coal absorption indices in a functional form. These relations can readily be used to predict the radiative properties of “spherical” coal particles from the Lorenz-Mie theory.
1. Introduction
Coal is the most abundant fossil fuel on earth. In order to ensure clean and efficient use of it for power production, coal combustion mechanism should be well understood.’ Radiation heat transfer accounts for as much as 90% of total heat transfer in large-scale coal combustion chambers. This requires accurate modeling of radiative transfer equation in corresponding geometry and realistic evaluation of radiative properties of combustion products, which include pulverized-coal, char, fly-ash, and soot particles as well as water vapor and carbon dioxide gases.2 Pulverized coal particles are irregular in shape and nonhomogeneous in nature. If they are assumed to be spherical, their radiative properties, i.e., absorption, extinction, and scattering coefficients, and the phase function can be determined from the Lorenz-Mie theory, provided that their size distribution and spectral complex index of refraction are kn0m.3 Most of the complex index of refraction data available in the literature were obtained from application of classical Fresnel reflection and transmission measurement techniques to thin, compressed wafers. This approach has been employed by various researchers to determine the refractive index of different type and rank coals”l0 and reviewed recently by MenguC Abstract published in Advance ACS Abstracts, October 15, 1993. (1) Smoot, L. D. Fundamentals of Coal Combustion for Clean and Efficient Use, Elsevier; Amsterdam, 1993; Chapter I. (2) Viskanta, R.; MenNg, M. P. Radiation Heat Transfer in Combustion Systems. Prog. Energy Combust. Sci. 1987,13,97-160. (3) Bohren, C. F.; Huffman, E. R. Absorption and Scattering of Light by Small Particles; Wiley: New York, 1983. (4) Huntjens, F. J.; van Krevelen, D. W. Chemical Structures and Properties of Coal: 11-Reflectance. Fuel 1954,33,8&103.
(5) McCartney, J. T.; Ergun, S. Optical Properties of Graphite and Coal. Fuel 1958,37, 272-282. (6) Ergun, S.; McCartney, J. T.; Walline, R. E. Absorption of Ultraviolet and Visible Light by Ultra-thin Sections of Coal. Fuel 1961,40(2), 104-117.
(7)Field, M. A.; Gill, D. W.; Morgan, B. B.; Hawkdey, P. G. W. Combustion of Pulverized Coal; The British Coal Utilization Research Association: Leatherland, 1967.
and Webbll and Im and Ahluwalia.12 All these studies show that the real part of the complex index of refraction (mx = nx-ikx)variesbetween1.6and2.1 withinthespectral range of 1-20 pm for different rank coals. The imaginary part (i.e., absorption index k ) , however, displays a larger variation (and higher uncertainty), as the reported values are between 0.2 and 1.2. For anthracite coal, for example, Blokh’O reported k values of -0.9 at near infrared wavelengths and -0.1 at the visible wavelength spectrum. For bituminous coals, k values given are close to 0.3 up to X = 6 pm and then increase linearly with the wavelength. A different approach was used by Brewster and Kunitomol3 to obtain coal refractive indices. Following an earlier work by Janzen,14they suspended coal particles in a KBr matrix and measured spectral transmission from the samples. Assuming spherical-shaped coal particles, they estimated the size distribution and volume fraction of particles in the sample and predicted the corresponding extinction efficiency factor, Bert. They also measured normal reflectance of highly polished coal samples. Using these two sets of measured data, they estimated the refractive index of coal samples. They reported nx values comparable to those given in the literature; however, the estimated kx values were 1 order of magnitude smaller than those given in the earlier studies (Le., less than 0.05 for X < 7 pm). (8) Foster, C. J.; Howarth, C. R. Optical Constants of Carbons and Coals in the Infrared. Carbon 1968,6,719-729. (9) Blokh, A. G.; Burak, L. D. Radiation Characteristics of Solid Fuels. Teploenergerika 1973,20(8), 48-52. (10)Blokh, A. G. Heat Transfer in Steam Boilers; Hemisphere: Washington, D.C., 1988. (11) Mengas, M. P.; Webb, B. W. Radiative Heat Transfer. In Fundamentals of Coal Combustion: Clean and Efficient Use;Smoot, L. D., Ed.; Elsevier Science Publ. Co.: New York, 1993. (12)Im, K. H.; Ahluwalia, R. K. Radiation Properties of Coal Combustion Products. Int. J. Heat Mass Transfer 1993,36, 293-302. (13) Brewster, M. Q.; Kunitomo, T. The Optical Constants of Coal, Char, and Limestone. J. Heat Transfer 1984,106,678-683. (14) Janzen, J. The Refractive Index of Colloidal Carbon. J. Colloid Interface Sci. 1979, 69(3), 436-447.
0887-0624/93/2507-0860$04.00/0 0 1993 American Chemical Society
Optical Properties of Pulverized Coal Particles Our theoretical studies based on Fresnel equations showed that the normal reflectance from coal pellets may not be sensitive to the imaginary part k,if k is less than 0.3, although it was a somewhat stronger function of the real part n.15 In addition to that, the accuracy of reflectance measurements is dependent not only on the optical properties but also on the sample surface smoothness and homogeneity, which cannot be satisfied unless extensive pressures are used in preparing the waffles.14 These observations suggest that the reflectance of polished samples may not be used to obtain the unique values of k, especially if k is less than 0.3. A recent study by Solomon et al.16 suggested, however, that the Brewster-Kunitomo data may be correct. They suspended coal particles in KBr and CsI pellets and measured the transmittance spectra in the infrared region. Then, they determined the index of refraction data following the Kramers-Konig relation. The comparisons of particle-cloud emission predicted from these refractive index data agreed well with the emission data obtained from FT-IR spectroscopy experiments performed on heated coal particles. In the experiments, they have accounted for scattering in the forward direction within the acceptance angle of the detectors. However, in the analysis they did not use wavelength-dependent phase functions and did not consider the size distribution of coal particles in detail. Depending on both the wavelength and the size distribution, the foward scattered radiation may affect the transmittance data significantly. Therefore, their results need further evaluation before being used to support 1order of magnitude smaller k values. Note that recently Im and Ahluwalialz reported an inconsistency in the optical properties published by Brewster and Kunitomo.13 Almost all of the studies conducted to obtain coal optical properties are based on ex situ measurements. The only exception is probably the study reported by Solomon et al., who compared ex situ results against in situ transmission data. Recently, in a fundamentally different study, MengiiC et a1.17J8measuredeffective extinction and scattering characteristics of suspended coal particles. Using the scattering-phase function coefficients retrieved from the experiments, they estimated the optical parameters of coal particles at X = 10.6 pm. Because the experiments were not conducted using compressed wafers and both transmission and scattering data were employed to arrive at the results, the recovered optical parameters are believed to be more accurate than those published in the literature. Unfortunately, the data sets obtained are at a single wavelength and, therefore, need to be expanded to cover the entire wavelength spectrum for combustion research. The objective of the present study is to introduce a general methodology based on FT-IR spectrometer ex(15)Manickavasagam,S.EffectiveOptical and Radiatiue Properties Ph.D. Dissertation, Department of Mechanical Engineering, University of Kentucky, Lexington, KY, 1993. (16)Solomon, P. R., Carangelo, R. M.; Best, P. E.; Markham, J. R.; Hamblen, D. G. The Spectral Emittance of Pulverized Coal and Char. Twenty-first Symposium (Internationul) on Combustion, The Combustion Institute, pp 437-446. (17).Men#~, M. P.; Manickavasagam,S.; Dsa, D. Determining the Radiative Properties of Pulverized Coal Particles from Experiments. FUEL, in press. (Also presented at the ASME/JSME Joint Thermophysics and Heat Transfer Conference, Reno,NV, Feb 1991;Preceedings Vol. 5, pp 23-34.) (18)Manickavasagam,S.;Merigtic,M. P. EffectiveRadiativeProperties of Coal/Char Particles in Flames at A = 10.6pm. Presented at the ASME NationalHeat Transfer Conference,Atlanta, GA, Aug 1993,ASME HTD, Vol. 250, Heat Transfer in Fire and Combustion Systems, 1993,pp 145154. of Pulverized CoallChar Particles.
Energy & Fuels, Vol. 7,No. 6, 1993 861
Incident Beam
e Transmitted+ Scattered
I 1 ,
Figure 1. Geometry of the FT-IR spectrometer optical alignment.
periments to determine the "effective" radiative and optical properties of pulverized-coal particles over a wide wavelength spectrum. In the analysis, size distribution and both absorption and scattering characteristics of coal particles are considered in detail. An extensive optimization scheme based on the Lorenz-Mie theory is employed to predict the n and k values that would yield the same effective extinction efficiency factors measured from the experiments. The results at X = 10.6 pm are compared against those obtained from the detailed C02 laser nephelometer measurements reported elsewhere.17J8 In the followingsection,we will discuss the experimental system and the procedure followed in the experiments. Then, the theory behind the data reduction algorithm will be outlined. The results and their sensitivity on different physical parameters will be discussed in the fourth section. Finally the conclusions drawn will be listed. 2. Experimental Section 2.1. Fourier Transform Infrared Spectrometer, In the experiments, a Fourier transform infrared (FT-IR) spectrometer (Perkin-Elmer, Model 1600) is used to obtain the infrared spectrum of coal/KBr pellets. This system develops the infrared spectrum of a sample by computing the Fourier transform of an interferogram. The infrared source used in the instrument is a heated wire coil element, which is operated at approximately 1050 OC. It emits a continuous spectrum of infrared radiation. The source is maintained at a constant temperature through a constant voltage supply. The FT-IR spectrometer used contains a polarized He-Ne laser employed to facilitate the optical alignment in the system. The laser emits radiation at a visible wavelength (0.693Mm),makiig the alignment of the beam much easier. During any particular scan, the intensity of the beam is modulated by the interferometer according to the interferogram produced. This modulated beam is collimated and then transmitted through the sample compartment to the IRdetector. The IRdetector converts the incident infrared signal to an electrical signal which is amplified by the IR preamplifier and sent to the analog board. The digitized data is then relayed through a data bus to the CPU where it is processed. In this spectrometer, a high performance deuterated triglycine sulfate detector is used, which is very sensitive to the modulated radiation and has high sensitivity over the entire frequency range. The radiation transmitted through the sample is collected by a parabolic mirror and directed to the detector. The parabolic mirror focusses all the incident light on to its focal point, ensuring that most of the transmitted light is collected by the detector. The dimension of the mirror is critical in determining the solid angle subtended by the optical system. Figure 1 depicts the optical diagram used to evaluate the solid angle of the system. 2.2. Experimental Procedure. In a FT-IR spectrometer, the infrared spectrum of a sample pellet can be measured using either transmitted or reflected radiation. The results presented in this study are based on transmission measurements. The sample pellets are prepared by suspending pulverized coal particles in a KBr matrix, which is transparent in the infrared spectrum. The experimental procedure is relatively simple and
862 Energy & Fuels, Vol. 7,No. 6,1993
Manickavasagam a n d Men&
Table I. Proximate and Elemental Analyses of Coals Blind Canyon Kentucky no. 9 Proximate Analysis 10.35 10.75 % moisture 3.51 10.68 % ash 41.89 34.90 % volatile % fixed carbon 44.25 43.67 Elemental Analysis % carbon 77.20 62.44 % hydrogen 5.85 5.57 % nitrogen 1.48 1.43 0.54 5.09 % total sulfur Table 11. Coal Size Distribution diameter (um) % bvvol % bv no. O.oo00 O.oo00 261.70-160.40 160.70-112.80 112.80-84.30 84.30-64.60 64.60-50.20 50.20-39.00 39.00-30.30 30.30-23.70 23.70-18.50 18.50-14.50 14.50-11.40 11.40-9.00 9.00-7.20 7.20-5.80 5.80
0,1000
0.8oooO 2.6oooO 5.8000 6.6000 9.8000 11.oo00 11.8000 12.6000 9.7000 7.4000 6.3000 6.7000 8.8000
O.oo00 0.0002 0.0015 0.0074 0.0180 0.0570 0.1352 0.3038 0.6784 1.0802 1.6865 2.8670 5.9004 87.2644
not time consuming compared to other experimental techniques (for example, in situ scattering experiments); however, it is not without pitfalls. For example, it is very important to disperse coal particles evenly in the pellets and to be sure that the pellets are free of cracks or undesired inhomogeneities. 2.2.1. Pulverized-Coal Particles and Size Distributions. Two different coal types (UtahBlind Canyon and Kentucky no. 9) were used in the experiments. The proximate and elemental analyses of these coals are given in Table I. Before the experiments, coal received was classified using a commercial shaker into different size groups. Early attempts revealed that the classification does not result in a uniform and narrow size distribution. However, detailed knowledge of particle size distribution is critical in determining the radiative properties from the Lorenz-Mie theory. For this purpose, coal size distributions were obtained from a Malvern size analyzer and are listed in Table I1 for the Blind Canyon coal. The size distribution obtained is biased toward either smaller or larger particles, depending on whether it is expressed in terms of particle number density or volume, respectively. Note that a very similar size distribution was observed for the Kentucky no. 9 coal. In order to simulate small size-range particles, a simple size distribution function was usedl9
Nj(r) = aDa exp(-bDT) (1) where N is the number of particles per unit volume and a, b, a, and y are independent parameters. In this study, the values of these parameters were determined using electron-microscope pictures of coal samples: a = 13.28 b = 1.47 a = 4.68 y=1 (2) The results presented were not sensitive to the size distribution parameters given above. For the sake of consistency, the same parameters were employed to represent the small size coal particles in all samples. Even if the number fraction of larger particles is low, their effect on radiative properties of the particle cloud can be significant and should not be neglected. In order to predict the (19) Mengijc, M. P.; Viskanta, R. On the Radiative Properties of Polydiapersions: A Simplified Approach. Combust. Sci. Technol. 1985, 44,143-159.
Table 111. Details of Size Distribution large sizes small sizes (from eq 1) size group Da2 bm) D (um) Y I 5.2 23 0.2 I1 5.2 27 0.3 111 5.2 0.5 39 IV 5.2 43 0.7 effectivecross-sectionsof different coal particle clouds,we assume a fraction x (by number) of large particles are present. The size distribution given by eq 1 is used to represent the small-size particles, whereas for larger particles a monosize distribution is adapted. The value of fraction x was determined for each size distribution from electron microscope pictures. For example, for coal size I, it is assumed that x = 0.2 % of particles had *mean" diameters of 27 pm. Table I11 provides the details of the size distributions considered in the experiments. 2.2.2. Sample Preparation. In FT-IRexperiments, preparation of the pellets is as important as obtaining and analyzing the spectrum, especiallyfor quantitative studies. Painterm gives a detailed methodology for sample preparation and discusses how to avoid the pitfalls associated with negligence of any of the various factors. The procedure we followed in the experiments is outlined below:15 About 100 mg of KBr is weighed in a chemical balance and mixed with about 1mg of pulverized coal. KBr is hand ground well using a mortar before it is weighed in order to form a homogeneous mixture with coal particles. Note that KBr is hygroscopic in nature; hence, it is kept inside a furnace at a temperature of about 80 O C and is exposed to the surroundings only while the pellets are being prepared. This is necessary because moisture absorbs radiation in the near-infrared region, and its interference with the absorption spectrum of the sample material would result in misinterpretation of data. A part of the mixture is slowly fed into a dye to prepare the pellet. Sufficient care is taken during the process to ensure that the mixture is uniformly spread inside the dye to prevent any nonuniformity in the thickness of the pellet. Particles sticking to the sides of the dye are removed before forming the pellet. The dye is kept under a compression pressure to form the pellet. Since a sudden high compression pressure would yield a nonuniform surface, the required pressure was applied in two steps. First, a 35-MPa (about 5000 psi) pressure is applied for 1 min, followed by a compression pressure of 85 MPa (about 13 OOO psi) for an additional duration of 1 min. The pellet is examined visually for any small cracks or nonuniform dispersion of sample material inside the matrix. Since coal particles are black, it is easier to examine their distribution inside KBr matrix which is predominantly white. If the pellet is found to be defective in any aspect, the whole procedure is repeated. After the pellet is removed from the dye, it is placed in a sample holder of the FTIR spectrometer and the transmittance spectra are measured. The coal/KBr pellet is weighed using a chemical balance after the measurements to estimate the volume fraction of coal particles. In order to account for background scattering and reflection, a pure KBr pellet of approximately the same weight as the sample pellet is prepared and ita spectrum is measured.
3. Theoretical Background 3.1. Application of the Lorenz-Mie Theory to Polydispersed Particles. Before we discuss t h e data reduction scheme, i t is preferable to introduce the no(20) Painter, P.; Starsinic,M.; Coleman, M. Fourier Transform Infrared Spectroscopic Analyeis of Coal Structures. In FTIR: Applicatiom to Chemical System; Ferraro, J. R., Baeile, L. J., Eds.; Academic Press: New York, 1986; Vol. 4.
Optical Properties of Pulverized Coal Particles
Energy & Fuels, Vol. 7, No. 6, 1993 863
menclature and governing equations for particle radiative properties. The extinction, scattering, and absorption coefficients of the particles are functions of the number density and the corresponding efficiencies of particles. For a polydispersed particle cloud, these coefficients are defined as
where PA stands for spectral absorption coefficient KA, spectral extinction coefficient PA, or spectral scattering coefficient UA,Q, represents the corresponding efficiency factor calculated from the Lorenz-Mie theory, f ( D )is the normalized size distribution, N is the number of particles per unit volume, and dD is the infinitesimal diameter interval. Note that these properties are functions of the spectral complex index of refraction mA = nA - ikh. The sum of absorption and scattering coefficients is equal to the extinction (or attenuation) coefficient OX:
PA"m
=
KA"m
+ bA"JV)
(4)
Single scattering albedo W A is defined as W,(P,,N = aA(mA,N)/BA(mA,N)
(5)
Medium optical thickness is based on the variation of extinction coefficient along a line-of-sight 1
transmitted and the forward-scattered radiation. The magnitude of the measured forward scattered radiation depends on the collection angle of the detector, which should be accounted for in interpreting the results. This is possible only if the extinction coefficient obtained from the transmittance measurements is interpreted carefully. With this in mind, we define an effective extinction 3 coefficient j
The left-hand side of eq 11 denotes the experimentally determined extinction coefficient Bexp, whereas the righthand P i , side can be obtained from the Lorenz-Mie theory for a given size distribution and complexindex of refraction data of coal particles. Since the size distribution is already known, out objective is to determine the spectral coal refractive index data which yield the same spectral effective extinction coefficients measured from the FT-IR experiments. This can be achieved using a detailed inversion scheme. Note that the use of Beer's law in eq 11 is acceptable only if the second- and higher-order scattering effects are small, which is a reasonable assumption if the sample optical thickness is less than 0.2.21 It is preferable to perform calculations using more fundamental efficiency factors instead of extinction coefficients. The right-hand side of eq 11 can be expressed in terms of a modified extinction efficiency factor Q,,which takes into account the forward scattered radiation:
For a homogeneous medium, T A is reduced to = Px(m,JV)L (7) For a size distribution of particles, which is given in a series expansion form, the radiative properties can be expressed in a finite series representation
On the other hand, the experimental extinction coefficient can be reduced to an experimental extinction efficiency as
Here, fv is the volume fraction of particles in the pellet and 0 3 2 is the Sauter mean diameter, which is defined as where i is for different diameter intervals. If the size distribution is given for a very narrow diameter range, then the summation term can be dropped and the diameter can be replaced by a mean value. Effective absorption, extinction, or scattering efficiency factors, Q,,,can be defined for polydispersions as n
CN~D'
somD3f (D)NdD D32
=
(14)
cD2f(D)NdD Simple algebraic manipulations are required to write Qe,exp in terms of the measured parameters, which are outlined below. Let M,and k f k be the masses of coal and KBr, mixed for sample preparation. Both M,and Mk can be measured accurately. The mass ratio R is given as (15)
1=1
and the scattering phase function, W), is written as n
i=l
where Qs,i is the scattering efficiency factor for the size distribution interval corresponding to diameter Di and is the scattering phase function for the same interval. In the experiments, the measurements include both the
Let m p be the mass of the pellet, which is also measured with good accuracy. If m, and mk are the masses of coal and KBr in the pellet, respectively, the mass of coal in the pellet is calculated as RmP m, = l+R (21) Agarwal,B. M.; MengQG,M. P. Single and Multiple Scattering of Collimated Radiation in an hisymmetric System. Znt. J. Heat Mass Transfer 1991,34,633-647.
Manickauasagam and MengiiC 3hwI k-0.10, n-1.8
6-e4
k-0.20. k-0.50, &-A-& k-1.00, Q-Q-0 k-0.01, k-0.10, Q-Q-Q k-0.20, O - e - 4 k-0.50,
*-+-+
k-0.10, n-1.e
n-1 .e w1.e n-1.e n-1.6 n-1.8 n-1.6 n-1.6
8-9-9 k-0.20, n-1 .e k-0.50, n-1 .6
Mk-l.W, n-1.e Q-Q-O
k-0.01, n-1.6 n-1.0 Q - Q - Q k-0.20, n-1.e 0 - e - 4 k-0.50, n-1.6 &--A--hk-1.00, n-1.e
++-+k-0.10,
2-
8 1
0
0
2
6
10
14
18
22
26
A (Pm) Figure 2. Theoreticalspectral absorption efficiency factor, Q,,, as a function of real and imaginary parts of the complex index of refraction. For size distribution A.
The number of coal particles in the pellet (N,) is determined from
2
6
10
14
26
4
A-&-& Q-Q-Q
where pcod is the density of coal. The number density of coal (N) in the pellet is found as
22
18
A (Pm) Figure 3. Theoretical spectral scattering efficiency factor, Q,, as a function of real and imaginary parts of the complex index of refraction. For size distribution A.
k-1.00, k-0.01, k=O.lO, k-0.20,
*-+-*
3
Q-Q-Q
n-1.6 n-i.6 n-1.6 n-1.6
where dp and L are the diameter and thickness of the pellet, respectively. Using the measured optical thickness rh = -In Th (19) the mass of the coal particles in the pellet (mc), the diameter of the pellet (d,), and the calculated particle number density (N), QeXp is obtained from eq 8
Since the size distribution of coal particles is already known, 0 3 2 data are readily available for different size distributions considered. 3.2. Theoretical Efficiency Factors. It is useful to investigate the spectral behavior of theoretical efficiency factors of coal particles before attempting to retrieve their complex index of refraction from the experimental data. For this purpose, spectral absorption, scattering, extinction, and modified extinction efficiencies were calculated from the Lorenz-Mie theory for a polydispersed pulverized-coalcloud using size distribution given by eq 1(called size A). The results were obtained fork values of 0.01, 0.1, 0.2,0.5,and 1.0 and for n = 1.6 or 1.8 and plotted in Figures 2-5. Figure 2 shows that the absorption efficiency Qa is a strong function of k. At any given wavelength, it varies
1
0
2
6
10
14
18
22
26
A (Pd Figure 4. Theoretical spectral extinction efficiency factor, Qa, as a function of real and imaginary parta of the complex index of refraction. For size distribution A.
from a value closer to zero to more than 1.0 as k changes from 0.01 to 1.0. The effect of variation of n on Qa is not very significant at all. Figure 3 depicts the variation of the scattering efficiency Q. for different values of n and k. Q, is a strong function of k at all wavelengths; however, it is sensitive to n only at lower wavelengths (A < 7 pm). Similarly, the extinction efficiency QBis a stronger function of both n and k at wavelengths less than 10pm and a weak function of n a t far infrared (see Figure 4).
Optical Properties of Pulverized Coal Particles
Energy & Fuels, Vol. 7, No. 6,1993 865
k-0.01, n-I .8 n-1.8 k-0.20, n-1 .8 k-0.50, n-I ,a Mk-1.W n-1.8 O-Q-O k-0.01, n-1.0 k-0.10, n-1.6 Q-Eb-0k-0.20, n-1.6 4-+-0 k-0.50, n-1.0 *--ti--* k-1.03. n-1.6
mk-0.10,
++-+
3I
.-
0)
€ 2
6
U
1
0
2
6
10
14
18
22
26
A (Fm) Figure 5. Theoretical spectral 'modified" extinctionefficiency (eq 12), as a function of real and imaginary parts factor, Bedmle of the complex index of refraction. For size distribution A.
In the experiments, the modified extinction efficiency is measured; hence, it is also necessary to investigate the sensitivity of Qeqie on n and k. In order to calculate Qe = Qe,mie, an acceptance angle of 6 = 20' is assumed. Figure 5 shows the spectral variation of Qe as a function of n and k within the wavelengths range of 2-24pm. It is interesting to note that the behavior of Qe is similar to Qa a t lower wavelengths ( 7 pm; however, for shorter wavelengths, a more rigorous treatment of n may be preferable. The size distribution data are obtained from the Malvern size analyzer and the electron microscope pictures (see Table 111). The solid angle subtended by the detector is measured from the geometry of the optical system. It is estimated to be about 18', but in the analysis a range of 6 from 18' to 23' is considered to account for multiple and side scattering effects. Once these parameters are estimated, the only unknown to be determined is the imaginary part of refractive index of coal particles. In order to predict its spectral variation the following procedure is employed: Theoretical efficiency factors and phase functions of monosize coal particles are obtained from the LorenzMie theory for particle diameters between 1 and 24 pm, for wavelengths between 2 and 24 pm, for n values of 1.6 and 1.8, and for several discrete values of k between 0.001 and 2.0. The effective radiative properties of coal particles are evaluated for a given size distribution, which accounts for the presence of large particles in addition to the basic, prevailing size distribution in the sample, as a function of n, k, and A. Once the effective radiative properties are estimated, the modified extinction efficiency factor, is determined as a function of n, k, and the acceptance angle of the optical system (18, 20, and 23'). From the experimental measurements, the modified extinction efficiency &e,exp is determined at various wavelengths (between 3 and 22 pm). A minimization routine is used to determine the most likely values of k which would yield the same Qe,exp determined from experiments at a given wavelength. The procedure is repeated to estimate k at the entire wavelength spectrum for different values of n. The effect of uncertainties in the size distribution and the solid angle of the system on the recovered k values is investigated. 4. Results and Discussion 4.1. Infrared Spectrum of Coal. The transmission spectra obtained from the FT-IR spectrometer experiments were analyzed and compared against the available spectra in the literature to match the functional groups with different wavelength bands. The comparisons ensured the qualitative agreement and the repeatability of the method. The FTIR transmission spectrum for Utah Blind Canyon coal for the size ranges considered is shown in Figure 6. (For Kentucky no. 9 coal, the spectrum was similar in nature.) Any variations on these curves are mostly due to the physical differences in pellet thicknesses and the small changes in coal mass (see Table IV for details). The region 3800-3200 cm-1 (2.63-3.13 pm) corresponds to various OH and NH molecules' stretching modes. While non-hydrogen-bonded OH groups absorb near 3600 cm-', hydrogen-bonded OH groups absorb near
Manickavasagam and Mengiic
866 Energy & Fuels, Vol. 7, No. 6,1993 Utah Blind Canyon Coal size 111
80 W
0.41
0 0.2
Utah Blind Canyon
0.0
0 4000
3400
2800
2200
1600
iaoo
Table IV. Details of KBr Pellets
Kentucky no. 9 coal
I I1 I11 IV I1 I11
103.90 111.27 103.52 104.68 180.35 107.48
1.36 1.19 1.37 1.08 2.51 1.16
4
6
8
10
12
14
16
18 20
22
2
4
6
8
10
12
14
16
18
22
400
Wavenumber ( l / c m ) Figure 6. Experimental transmission spectra measured from the FT-IR spectrometer, for Blind Canyon coal. For different size distributions (see Table 111).
Blind Canyon coal
2
49.20 66.10 53.90 71.49 51.60 50.70
3400 cm-l. In addition, NH groups absorb in the range 3200-3400 cm-1. The minimum observed in Figure 6 in this region corresponds to the presence of the OH group in coal. Any presence of moisture in the sample would also have contributed to high absorption in this region. The second most important region in this spectrum is the CH stretching modes. In general, aromatic CH groups have bands between 3100 and 3000 cm-l, whereas aliphatic CH bands fall between 3000 and 2700 cm-l. This is observed as two minima in Figure 6. At 1600 cm-', the minima in the spectrum corresponds to aromatic ring stretch. It is also characteristic of highly conjugated hydrogen bonded C=O. The minima observed at 1060 cm-1 is due to the C=C stretching. Note that the corresponding wavelength for this strong band is 9.4 pm. 4.2. Modified Extinction Efficiency. The transmission spectra measured from the FTIR spectrometer are reduced to determine the modified extinction efficiency factor Qe,exp for different coal samples using eqs 19 and 20. Size distributions of coal particles used in the analysis are given in Tables I1 and 111. Note that the Sauter mean diameter 0 3 2 is 5.22 pm for the basic size distribution A. Because of this, the size parameter ( x = ?rD/X)changes from -7 for X = 2.5 pm to -0.75 for X = 22 bm. Since x is not very large, it is not possible to claim that most radiation scattered is in the forward direction. Figure 7 depicts measured modified extinction efficiency, Qe,exp, spectra for Utah Blind Canyon and Kentucky no. 9 coals. The variations in these curves are mostly due to the samples, which may have slightly different size distributions or optical thicknesses, adding uncertainty due to higher order scattering contributions. For both coals, the extinction approaches a maximum in the wavelength region between 6 and 9 pm. This region, as
0.0 20
(Pm) Figure 7. Experimental spectral"modified"extinction efficiency factor, Qe,exp(eq 13),for Blind Canyon and Kentucky no. 9 coals. For different size distributions (see Table 111).
discussed before, corresponds to CO and C=C stretching modes, respectively. At shorter wavelength range, the size parameter is large and the scattering phase function is steeper in the forward direction more than that for longer wavelength range. This means that more of the forward scattered energy is recovered in the small wavelength range. In summary, the experimental cross-section is closer to the absorption cross-section at shorter wavelengths and approaches the extinction cross-section at longer wavelengths. 4.3. "Effective"RefractiveIndex of Coal Particles. Modified extinction efficiency factors obtained from experiments are used to determine the "effective"complex index of refraction of coal particles, followingthe inversion scheme discussed earlier. These refractive index data account for all the effects of particle inhomogeneities and irregularities, and if used in the Lorenz-Mie algorithms, they would yield the same efficiency factors determined from the experiments. The spectral transmission spectra for different Blind Canyon and Kentucky no. 9 coal samples were reduced to obtain the corresponding optical properties. Representative results are shown in Figures 8 and 9. For all samples, the same basic size distribution A (eq 1)was used to model the small particles, and large particles were considered monodisperse. The details of the size distributions are given in Table 111. The results are for either n = 1.6 or n = 1.8 and for the detector acceptance angles of 18, 20, and 23'. The effect of different parameters on the recovered k values are discussed in the following subsections. 4.3.1. Effect of Different Size Distributions. The results presented for different samples indeed correspond to slightly different size distributions. Coal particles used in the experiments were classified differently. However, as discussed earlier, later size distribution measurements showed that small-size fragmented particles dominated the number density of samples. In order to avoid any complications and any further uncertainty, only a single generic (but representative) size distribution was adapted
Optical Properties of Pulverized Coal Particles
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Energy &Fuels, Vol. 7,No. 6,1993 867 l .ooo >
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Figure 9. “Effective” absorption index k determined from experimentsvs wavelength; for Kentucky no. 9 coal, size groups I1 and 111. Real part n is either 1.6 or 1.8. for small particles in all samples, and the large particle fractions (xs) were determined from the electron-microscope pictures. Therefore, any variation the recovered k values for a fixed n and 8 value is mostly due to the variations in the coal size distributions within the mea-
Figure 10. “Effective”absorption index k spectra for Blind Canyon coal; all size distributions. Real part n = 1.6 or 1.8. See Table V for the coefficients of the best-fit polynomials (thick curve). surement control volume of samples. The cross-comparison of curves in Figure 8 for Blind Canyon coal and Figure 9 for Kentucky no. 9 coal show that the uncertainty due to size distributions is less than f20%. If the size distribution in the samples can be controlled more effectively, it is possible to obtain more accurate k spectra. Note that large particles were assumed to be monosize. I t is clear from the results presented that the effective optical properties determined from different size groups, which have different size large particles, are in good agreement. In other words, the size of the large particle used in the analysis did not affect the outcome significantly. The use of polydispersed size distribution is not expected to change the results significantly. In order to show the range of recovered k spectra more clearly, the results are replotted in Figure 10 for Blind Canyon coal and in Figure 11for Kentucky no. 9 coal for either n = 1.6 or n = 1.8. The upper and lower curves correspond to the maximum and minimum values obtained from different samples for the fixed detector acceptance angle of 0 = 20°. The areas between the upper and lower curves on these figures can be considered as the uncertainty range in the recovered k values, which is due to different samples used. It is clear that the uncertainty range is not wide, and regardless of the choice of n, k values almost overlap for A > 7 pm. The thick curves shown in Figures 10 and 11 are the average k values fit to polynomials given as
k, = c C i X i I
Three different polynomials were considered for each coal for the wavelength intervals of 3-7 pm,7-11 pm, and 1122 pm. The corresponding coefficients are tabulated in Table V for both n = 1.6 and n = 1.8. Either of these relations can be used to determine the spectral “effective” radiative properties of pulverized coal particles from the Lorenz-Mie theory. Also shown in Figure 10is the range of k values predicted from independent in situ COz laser nephelometer exper-
Manickauasagam and Mengiic
868 Energy & Fuels, Vol. 7, No. 6, 1993
Table V. Coefficients of ‘Effective” k Polynomials, Eq 21 coefficients Blind Canyon coal Kentucky no. 9 coal ((fim)-9 n = 1.6 n = 1.8 n = 1.6 n = 1.8 co 0.1001~+015 0.49243+00 0.45883-01 4.10953+00 0.144034 1 0.15773+00 c1 -0.18583+00 0.17943+00 c2 -0.29573-01 -0.58003-01 -0.55833-01 -0.53453+00 cs 0.61943-02 0.73873-02 0.51363-02 0.4580342
wavelength
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co
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0.91243+01 -0.32763+01 0.40343+00 -0.16273-01
-0.84933+01 -0.30993+01 0.38403+00 -0.1555341
0.38493+01 4.1390E+01 0.17213+00 -0.69193-02
0.39143+01 -0.14353+01 0.17643+00 -0.70463-02
-0.24453+02 0.78203+01 -0.97023+00 0.58903-01 -0.17493-02 0.2040344
-0.21993+02 ’0.69733+01 -0.85933+00 0.51833-01 -0.15303-02 0.1772344
-0.73493+00 -0.2250341 0.44313-01 -0.5416342 0.24893-03 -0.39873-05
0.24623+01 -0.11373+01 0.19313+00 -0.1514E-01 0.5604343 -0.78913-05
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1.6, the results were not sensitive to 8 or x because the phase function obtained from the Lorenz-Mie theory was highly forward peaked. This means that, regardless of the 8 or x values used, a significant part of the forwardscattered radiation is included in the modified efficiency factor. On the other hand, if n is 1.8, the scattering is not peaked as much, and depending on the acceptance angle, the contribution of the forward scattered radiation may affect the transmission measurements and the modified extinction efficiency recovered. This suggests that unless the forward scattering is carefully accounted for in these kinds of experiments, the optical properties recovered may not be unique. 4.4. Effect of RetrievedkValues on Coal Radiative Properties. The goal of this study has been to obtain the “effective” complex index of refraction of coal particles such that if these optical parameters are used in theoretical calculations, they would yield a unique set of “effective” radiative properties. As shown in Figures 8 and 9, different sets of n and k values were obtained mostly because of variations in the sample size distributions, as well as because of 8 and n choices. Here, it is instructive to see how these different sets of recovered optical properties affect the efficiency factors. To test this idea, we used a single size distribution for coal particles. Again, the small size range was represented with the size distribution A, and for larger particles 39 pm was chosen as the mean diameter. We considered an arbitrary x fraction of 0.2% and obtained the spectral variation of Qs,Qs,and Qe from the Lorenz-Mie theory for each set of n and lz values obtained for Blind Canyon coals (usingthe results given in Figure 8,as well as those reported by Manickavasagam9. The results from all calculations are depicted in Figures 1 2 and 13. Overall, all efficiency factors follow the average values within roughly f15% in the long-wavelength range. The only significant spread observed is in Qaand Qsspectra if X is less than 7 pm, which is mainly because of the choice of n. It is interesting to note that this spread is opposite in direction in absorption and scattering efficiency factors, such that it does not affect the Qe spectra significantly. It is clear that the “effective”optical properties can be used to determine Qe within the entire wavelength spectrum. The use of a single value for n is likelyto affect the accuracy of scattering coefficient and the single scattering albedo at small wavelengths.
i n=l.8
2
4
6
8
10
12
14
16
18 20
22
A (Pd Figure 11. “Effective”absorption index k spectra for Kentucky no. 9 cod, all size distributions. Real part n = 1.6 or 1.8. See Table V for the coefficients of the beat-fit polynomials (thick curve).
iments.18 The predictions from these fundamentally different experimental studies yield almost identical results. Because the data from ex situ FT-IR spectrometer experiments agree very well with the data from in situ scattering experiments at X = 10.6 pm, we have more confidence in the spectral results presented here. 4.3.2. Effect of Solid Angle Uncertainty. The amount of forward scattered radiation reaching the detector is a function of the solid angle of optical system; hence, it is necessary to consider the effect of uncertainty in acceptance angle on the recovered k values. Due to multiple scattering, as well as increased side-scattering due to coal particle irregularities, the acceptance angle of the detector may be larger than the angle determined from geometry. For this purpose, three different values (18,20, and 23”) were employed to retrieve k values through inverse analysis. Figures 8 and 9 show that the effect of solid angle is minimal on the estimation of k a t larger wavelengths. The effect of 8 is more visible at the shorter wavelength range only if the real part of the refractive index is 1.8. If n is
Optical Properties of Pulverized Coal Particles
Energy & Fuels, Vol. 7, No. 6,1993 869
uncertainties related to particle material inhomogeneity and shape irregularity. They are given in terms of simple polynomials and can be used in the Lorenz-Mie algorithms 1.o to predict the "effective" radiative properties of "spherical" v) coal particles. U The theoretical studies revealed that the forward0.5 scattered radiation affects the estimated n and k values at short wavelengths (A < 7 pm). Unless scattering is 1.5 accounted for accurately in the data reduction scheme, it is not possible to obtain the optical properties with confidence. The estimated absorption index k is between 0.1 and 0.3 at the wavelength of 10.6 pm, if n is 1.8. This is in very good agreement with the results obtained from in situ scattering experiments.15J7 0.0 I The "effective" k values determined from this study 2 4 6 8 10 12 14 16 18 20 22 are, overall, higher than the values reported by Brewster A (Pd and Kunitomo (as much as three times) and smaller than Figure 12. Effect of absorption index (k)band on the absorption those based on Fresnel reflection techniques (almost by (8,) and scattering (Q1)efficiency factor spectra; Blind Canyon a factor of 2). There was no significant difference between coal, for both n = 1.6 and n = 1.8; generic size distribution. optical properties determined for Blind Canyon and Kentucky no. 9 coals. The use of a constant n value for the entire. wavelength spectrum did not affect the accuracy of extinction efficiency factor determined from effective optical properties. However, in the shorter wavelength spectrum, the recovered k values were small and the impact of n on the results, especially on the scattering efficiency factor, was significant. This suggests that at small wavelength range it is desirable to consider the spectral variation of both n and
k. It is observed that the size and number density of particles play a dominant role in determining their radiative properties. This suggests that, in order to determine the particle radiative properties correctly, it is necessary to model the evolution of size and size distribution of particles in combustion systems as realistically as possible.
I a io ia
0.0
2
4
6
12
14
16
20
22
A (in p m ) Figure 13. Effect of absorption index (k)band on the extinction factor (Q.) spectra; Blind Canyon coal; for both n = 1.6 and n = 1.8; generic size distribution.
5. Conclusions In this study, "effective" complex index of refraction spectra for Utah Blind Canyon and Kentucky no. 9 coals have been estimated. The experiments were performed using a FTIR spectrometer, and the data were reduced using a detailed inversion scheme based on the LorenzMie theory. The estimated n and k values include all
Acknowledgment. This research project has been supported by the DOE-PETC Advanced University Coal Research Program Grant Nos. DE-FG22-PC79916and DEFG22-PC92533. Partial support has been received from NSF/BYU Advanced Combustion Engineering Research Center, BYU, Provo, Utah. The authors also acknowledge the help they received from the Chemistry Department at the University of Kentucky, particularly from Dr. David Watt, in conducting the FT-IR experiments.
