Journal of Microwave Power and Electromagnetic Energy ISSN: 0832-7823 (Print) (Online) Journal homepage: http://www.tandfonline.com/loi/tpee20 Determining Dielectric Properties of Coal and Limestone by Measurements on Pulverized Samples S.O. Nelson To cite this article: S.O. Nelson (1996) Determining Dielectric Properties of Coal and Limestone by Measurements on Pulverized Samples, Journal of Microwave Power and Electromagnetic Energy, 31:4, 215-220, DOI: 10.1080/08327823.1996.11688312 To link to this article: http://dx.doi.org/10.1080/08327823.1996.11688312 Published online: 14 Jun 2016. Submit your article to this journal Article views: 2 View related articles Full Terms & Conditions of access and use can be found at http://www.tandfonline.com/action/journalInformation?journalCode=tpee20 Download by: [UNSW Library] Date: 27 October 2017, At: 05:29 D E T E R M IN INDGIE L E C T R IC P R O P E R T IEOSF C O A LA N DL IM E S T O NBEY M E A S U R E M E N T S O N P U L V E R IZ ESDA M P L E S Downloaded by [UNSW Library] at 05:29 27 October 2017 S.O. Nelson Estimatesfor the perrnittivities ofsolid coal and limestone at 11.7 GHz and 20°C are obtained from measurements of the permittivities and bulk densities of pulverized samples and the particle material density. Linear regressions of the cube root of the dielectric constant on sample bulk density provide estimates of the dielectric constants of the solid materials. Since linearity with bulk density of the cube root of the dielectric constant is consistent with the Landau d c Lifshitz, Looyenga dielectric mixture equation, that equation provides estimatesfor both the dielectric constant and lossfactor when the relative complex pennittivities are used for the calculation. Key Words: Dielectric properties, permittivity, coal, limestone, microwave measurements, pulverized samples. in the permittivities or dielectric properties of Interest coals and minerals arises from their influence on electromagnetic wave propagation in exploration [Singh et al., 1979], for control of mining processes [Balanis et al., 1976, 1978, 1980], and possible dielectric heating applications for modifying coal characteristics [Nelson et al, 1980, 1981; Bluhm et a., 1986] or in rock fragmentation [Nelson et al., 19891. Permittivity measurements on pulverized samples of relatively pure materials have been used with dielectric mixture equations to estimate the permittivities of the solid materials [Nelson et al., 1989; Nelson and You, 1990]. Of several well-known dielectric mixture equations tried, the Landau & Lifshitz, Looyenga equation provided the best results for relatively low-permittivity and low-loss materials [Nelson et al., 1989; Nelson and You, 19901. Federal regulations [CFR 30, 1995] require rock dusting to insure that 'The incombustible content of the combined coal dust, rock dust, and other dust shall not be less than 65 percenturn" in coal mines to limit explosion hazards. Recent measurements of permittivities were made on pulverized samples of Pittsburgh coal, rock dust (limestone), and a 35%65% mixture of coal and limestone to learn how different the dielectric properties of these materials might be and whether there might be potential for developing techniques of rapidly sensing coal and rock dust concentrations. Results of initial measurements on these materials are reported in this paper. Materials and Methods ABOUT THE AUTHOR: Stuart 0. Nelson is affiliated with the U. S. Department of Agriculture, Agricultural Research Service, Richard B. Russell Agricultural Research Center, Athens, Georgia, 30604. Manuscript received June 15, 1996. Accepted for publication July 15, 1996. Pulverized samples of Pittsburgh coal and limestone (more than 90% calcium carbonate), with most of the particle diameters ranging from 5 to W O p.m, were furnished for the measurements by the Pittsburgh Research Center, U.S. Bureau of Mines. Moisture content, determined by drying at 105°C for 24 h in an air oven, was 1.4% for the coal and 0.14% for the limestone. A mixed sample, 35% coal and 65% limestone by weight, was also included for the dielectric measurements. Permittivity measurements were made at 11.7 GHz with an X-band measurement system [Nelson, 1972] and the shortcircuited waveguide method [Roberts and von Hippel, 1946; Nelson et al., 19741.Pulverized samples were weighed before International Microwave Power Institute 215 ARWMIMMIMA ia-WAVVMM,-clMMATT Downloaded by [UNSW Library] at 05:29 27 October 2017 they were placed into a 5-cm long, WR-90-waveguide, shortcircuited sample holder for the measurements. Sample length was determined for each of a sequence of measurements at successively increasing sample bulk densities that were determined from sample weight, sample length, and waveguide cross-sectional area. Particle densities, Ps' which correspond to solid material densities, were calculated from sample weights of 15 to 25 g and corresponding particle volumes that were determined by measurements in a Beckman' Model 930 Air-Comparison Pycnometer [Nelson et al., 1989]. Initial pycnometer measurements on pulverized coal samples revealed that the coal was compressible, as indicated by continual drift of the pressure null indicator for several minutes after the sample was placed under 2 atmospheresof air pressure. Therefore the 1-1/2-1 atmosphere mode of operation was used, so the airdisplacement measurement could be determined at a pressure of 1 atmosphere. Pycnometer measurements on limestone samples were made in the 1-to-2 atmosphere compression mode, because both methods gave nearly the same volume values, and the 2-atmosphere mode has better sensitivity for the null pressure determination. Pycnometer measurements on the coal-limestone mixture were made with the 1-1/2-1 atmosphere mode because of the compressibility of the coal. Results and Analysis Results of the permittivity measurements and sample bulk density determinations on the coal and limestone samples are shown in Tables 1 and 2, where the results of analyses are also summarized. It was shown earlier [Nelson, 1983; 1992] that the linearity with bulk density of the cube root of the dielectric constant of the air-particle mixture, e', the real part of the relative complex permittivity, c = c'-je", where E" is the dielectric loss factor, is consistent with the Landau & Lifshitz, Looyenga dielectric mixture equation, which can be stated as follows for a two-phase mixture: 1/ 3 = VI(E1) 1/3 -I- 1/3 v2(e2) (I) where subscripts 1 and 2 refer to the air and the solid particulate material, respectively, and v represents the volume fraction occupied by a component of the mixture. For the twophase (air-particle) mixture, v 1 + v2 = 1, and the permittivity of air is 1-j0. Solving (1) for E2 in terms of E(relative complex permittivity of the mixture) and v2 = vs, the volume fraction occupied by the solid material, provides an expression from which the permittivities of the particulate material can be calculated, Cs = C2 = F c"3 [ 216 + V2 —1_ V2 3 [1 / E. 3 + V, — V, 3 (2) The necessary value for vs can be obtained if the bulk density p of the mixture and the density Ps of the solid particulate material are known, since vs = p/ps. The cube roots of the dielectric constants of the three pulverized samples (see Tables 1 and 2) are shown as functions of sample bulk density in Figure 1. Linear regression analyses showed very high coefficients of determination (r2 values), and the intercepts are very close to the theoretical value of 1, which, for zero bulk density, is the dielectric constant of air. These regression constants are given in Table 3. Since the point (p = 0, = 1) is a valid reference point, it can be included in the regression calculation, and this brings the intercept even closer to c' = 1 at zero bulk density as illustrated in Figure 2. When the linear regression of the cube root of the dielectric constant on bulk density, provides an r2 value so nearly 1 and the zero-bulk-density intercept is so close to the value of 1, the Landau & Lifshitz, Looyenga dielectric mixture equation can be used with confidence to estimate the permittivity of the solid material (see Tables 1 and 2). The linear extrapolation of (e')1/3to the density of the solid material is illustrated for the coal measurements in Figure 2 and for the limestone measurements in Figure 3. Values provided by the regression equations for the dielectric constants of the three material samples are given in Table 4. The mean values of the solid material pennittivities calculated with the Landau & Lifshitz, Looyenga mixture equation for the permittivity measurements at each bulk density, as illustrated for coal in Table 1 and for limestone in Table 2, are also included in Table 4. Discussion and Conclusions Permittivity values for the pulverized coal in Table 1 are in reasonable agreement with those reported for other measurements on coal [Balanis et al., 1976, 1978, 1980; Klein, 1981; Nelson et al., 1980; Nelson et al., 1981]when differences in frequency, moisture content, and density are taken into account. Values obtained check extremely well with those reported earlier for Pittsburgh No. 8 run-of-mine coal at the same frequency and similar densities [Nelson et al., 1980]. It is interesting to check the ps value measured with the air-comparison pycnometer for the 35%-65% (by weight) coal-limestone mixture, by calculating the expected average solid material density from the pycnometer determinations of Ps for the pulverized coal and limestone samples independently. The expected Ps for the mixture can be obtained from the appropriate relationship between these solid densities 1 Ps Journal of Microwave Power and Electromagnetic Energy 0.35 0.65 P se P st (3) Vol. 31 No. 4, 1996 2.0 g C4 I 1.5 -- U at 9.5 - L 0.0 1.0 I I I 1 1 1 1 1.1 1.2 1.3 1.4 9.5 1.0 14 12 1 11 Downloaded by [UNSW Library] at 05:29 27 October 2017 BULKDENSITY,p/401$ 1.7 00 1 0.2 I 1 0.4 04 0.0 1.0 13 1.4 Is BU LKD EN SITYp/cm3 , FIGURE 2: Linear regression of the cube root of the dielectric constant (E')113 of pulverized Pittsburgh coal on bulk density (p) with point (0, 1) included in the regression calculation, showing intersection of regression line with Ps = 1.48 line at 1.615, E's = (1.615)3 = 4.21. where subscripts c and I refer to coal and limestone, respectively. With measured density values of 1.48 for coal and 2.75 for limestone samples, the average solid density for the mixture is given as 2.11 by (3). The measured value was 2.13 (Table 4), which is within the expected accuracy for the pycnometer measurements on these samples. One can note that the E 's values predicted by the regression equations agree better with the mixture equation predic- International Microwave Power Institute I 0.2 I l l i 0.4 0.6 04 1.0 1.2 1.4 1.4 I 1.6 I 2.0 2.2 2.4 23 2 BULK DENSITY, Wm' FIGURE I: Linear relationships between the cube roots of the dielectric constants of pulverized samples and their bulk densities at 20°C and 11.7 GHz. o -Pittsburgh coal, A - 35%-65% coal-limestone mixture, Li - limestone. 1.0 00 FIGURE 3: Linear regression of the cube root of the dielectric constant (0113 of pulverized limestone on bulk density (p) with point (0, 1) included in the regression calculation, showing intersection of regression line with ps = 2.75 line at 1.967, £'5 = ( 1.967)3 = 7.61. tion when the intercept is closer to the value 1. The mixture equation prediction of the dielectric constant is equivalent to that provided by a straight line through the point (0, 1) and the selected single point defined by the cube root of the measured dielectric constant at any particular bulk density. The intersection of that straight line with the vertical line at the solid material density Ps gives the estimate for E's. Thus, if the measured (p e) point is above the regression line (see Figures 2 and 3 for example), the estimated E's value will be high, and if the measured point is below the regression line, the estimated value for es will be low. For the measurements reportedon these samples, the mean values of the permittivities calculated by the Landau & Lifshitz, Looyenga mixture equation, taken over all measured permittivity and bulk density points, should provide the most reliable estimates, and they provide values for both the dielectric constant and the loss factor, which is of greater interest than the dielectric constant for most dielectric heating applications. Values of both the dielectric constants and loss factors of coal and limestone are sufficiently different to justify further studies aimed at determining rock dust content in coal and rock dust mixtures by dielectric sensing techniques. Further measurements of mixtures of different contents, perhaps at different frequencies, and consideration of complicating factors, such as equilibrium moisture contents, and permittivity density relationships for the mixtures will be required to better assess the potential for sufficiently accurate determinations of rock dust content. s•C • 0 ;•4 217 TABLE 1 Measured permittivities and bulk densities of pulverized Pittsburgh coal at 11.7 GHz and 20°C and permittivities of solid coal estimated by the Landau & Lifshitz, Looyenga dielectric mixture equation. Measured values Air-particle permittivity Downloaded by [UNSW Library] at 05:29 27 October 2017 1.894 - j0.035 1.948 - j0.037 1.983 - j0.037 2.012 - j0.039 2.044 - j0.041 2.089 - j0.043 2.113 - j0.046 2.181 - j0.051 2.203 - j0.051 2.229 - j0.054 Bulk density p, g/cm3 0.565 0.598 0.619 0.632 0.648 0.671 0.682 0.716 0.724 0.736 Cube root Volume Estimated values dielectric constant (01/3 fraction Solid particle permittivity es 1.237 1.249 1.256 1.262 1.269 1.278 1.283 1.297 1.301 1.306 vs 0.382 0.404 0.418 0.427 0.438 0.453 0.461 0.484 0.489 0.497 4.262 - j0.157 4.220 - j0.153 4.195 -j0.146 4.208 - j0.149 4.208 - j0.152 4.203 - j0.151 4.208 - j0.158 4.200 - j0.163 4.217 - j0.161 4.218 - j0.166 TABLE 2 Measured perrnittivities and bulk densities of pulverized limestone at 11.7 GHz and 20°C and perrnittivities of solid limestone estimated by the Landau & Lifshitz, Looyenga dielectric mixture equation. Measured values Air-particle permittivity 2.363 -j0.011 2.415 -j0.011 2.519 -j0.011 2.565 - j0.012 2.847 - j0.013 2.961 - j0.014 3.098 - j0.015 3.258 - j0.017 3.462 - j0.020 3.772 - j0.024 3.930 - j0.026 4.154 - j0.031 4.221 -j0.031 218 Bulk density p, g/cm3 0.972 1.008 1.064 1.088 1.228 1.278 1.332 1.395 1.476 1.587 1.642 1.715 1.739 Cube root Volume Estimated values dielectric constant (0113 fraction Solid particle permittivity Cs 1.332 1.342 1.361 1.369 1.417 1.436 1.458 1.482 1.513 1.557 1.578 1.608 1.616 vs 0.353 0.367 0.387 0.396 0.447 0.465 0.484 0.507 0.537 0.577 0.597 0.624 0.632 Journal of Microwave Power and Electromagnetic Energy 7.292 - j0.066 7.212 - j0.062 7.213 - j0.057 7.215 - j0.060 7.240 - j0,054 7.280 - j0.055 7.359 - j0.055 7.427 - j0.058 7.477 - j0.062 7.582 - j0.066 7.624 -j0.068 7.694 - j0.075 7.695 - j0.073 Vol. 31 No. 4, 1996 TABLE 3 for the cube root of the dielectric constant of pulverized coal Linear regression statistics samples as a function of sainple bulk density (e)113= a 4 - bp and limestone Regression without point (0,1) Intercept Slope Coeff. determn. a b r2 Downloaded by [UNSW Library] at 05:29 27 October 2017 Material Regression with point (0,1) included Intercept Slope Coeff. determn. a b r2 Coal 1.0049 0.4083 0.9987 1.0003 0.4152 0.9999 Limestone 0.9612 0.3750 0.9990 0.9877 0.3561 0.9982 35%-65% coal-limestone mixture 0.9823 0.3846 0.9997 0.9965 0.3703 0.9995 TABLE 4 Estimated permittivities of solid materials from measurements on pulverized samples at 20°C and 11.7 GHz. Material Density, g/cm3 e's predicted by linear regression (point (0,1) included) es by mixture equation (mean values) Coal 1.48 4.21 4.21 - j0.156 Limestone 2.75 7.61 7.41 - j0.063 35%-65% coal-limestone mixture 2.13 5.69 5.64 - j0.108 Footnote microwave heating. IEEE Trans. Magn. MAG-22(6): 1887-1890. 'Mention of company or trade names is for purpose of CFR 30. 1995. Code of Federal Regulations, Mineral Resources 30, Part 75, Par. 75.403, p. 492. description only and does not imply endorsement by the U. S. Klem, A. 1981. Microwave determination of moisture in Department of Agriculture. coal: Comparison of attenuation and phase measurement. J. Microwave Power 16(38c4):289-304. References Nelson, S.O. 1972. A system for measuring dielectric properties at frequencies from 82 to 12.4 GHz. Trans. Balanis, C.A., Rice. W.S., and Smith, N.S. 1976. Microwave ASAE 15(2): 1094-1098. measurements of coal. Radio Sci. 11(4): 413-418. Balanis, C.A., Jeffrey, J.L. and Yoon, Y.K. 1978. Electrical Nelson, S.O. 1983. Observations on the density dependence of dielectric properties of particulate materials. J. Microproperties of eastern bituminous coal as a function of wave Power 18(2): 143-152. frequency, polarization and direction of the electromagnetic wave, and temperature of the sample. IEEE Trans. Nelson, S.O. 1992. Estimation of permittivities of solids from measurements on pulverized or granular materials, Ch. 6, Geosci. Electronics GE-16(4): 316-323. Dielectric Properties of Heterogeneous Materials, A. Balanis, C.A., Shepard, P.W., Ting, F.T.C., and Kardosh, Priou, Ed., Vol, 6, Progress in Electromagnetics ReW.F. 1980. Anisotropic electrical properties of coal. search, J. A. Kong, Chief Ed., New York: Elsevier Sci. IEEE Trans. Geosci, Remote Sensing GE-18(3):250Pub. Co. 256. Bluhm, D.D., Fanslow, G.E., and Nelson, S.O. 1986. En- Nelson, S.O., and You, T.-S. 1990. Relationships between microwave perrnittivities of solid and pulverised plastics. hanced magnetic separation of pyrite from coal after International Microwave Power Institute 219 Downloaded by [UNSW Library] at 05:29 27 October 2017 J. Phys. D: Appl. Phys. 23: 346-353. Nelson, S.O., Beck-Montgomery, S.R., Fanslow, G.E., and Bluhm, D.D. 1981. Frequency dependence of the dielectric properties of coal Part H. J. Microwave Power 16(3&4): 319-326. Nelson, S.O., Fans low, G.E., and Bluhm, D.D. 1980. Frequency dependence of the dielectric properties of coal. J. Microwave Power 15(4): 277-282. Nelson, S .0., Lindroth, D.P., and Blake, R.L. 1989. Dielectric propertiesof selected minerals at 1 to 22 GHz. Geophys. 54(10): 1344-1349. Nelson, S.O., Stetson, L.E., and Schlaphoff, C.W. 1974. A general computer program for precise calculation of dielectric properties from short-circuited-waveguide measurements. IEEE Trans. Instr. Meas, IM-23(4): 455-460. Roberts, S. and von Hippel, A. 1946. A new method for measuring dielectric constant and loss in the range of centimeter waves. J. Appl. Phys. 17(7): 610-616. Singh, R., Singh, K.P., and Singh, R.N. 1979. Microwave measurements on some Indian coal samples. Proc. Indian Nat. Sci. Acad. 45A: 397-405. 220 Journal of Microwave Power and Electromagnetic Energy Vol. 31 No. 4, 1996

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