close

Вход

Забыли?

вход по аккаунту

?

08327823.1996.11688312

код для вставкиСкачать
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
Документ
Категория
Без категории
Просмотров
3
Размер файла
1 932 Кб
Теги
1996, 08327823, 11688312
1/--страниц
Пожаловаться на содержимое документа