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Calculation of degree of mineral matter liberation in coal from sink–float separation data
Minerals Engineering 17 (2004) 39–51 This article is also available online at: www.elsevier.com/locate/mineng
Calculation of degree of mineral matter liberation in coal from sink–float separation data T. Oki a
a,*
, H. Yotsumoto a, S. Owada
b
National Institute of Advanced Industrial Science and Technology, Onogawa, Tsukuba 305-8569, Japan b Waseda University, Shinjyuku-ku, Tokyo 169-8555, Japan Received 20 May 2003; accepted 16 September 2003
Abstract A method for calculating the degree of mineral matter liberation by the sink–float separation data of coal was studied. The mineral composition was estimated by norm calculation using the results of elemental analyses of sink–float separated coals. The content of the inherent ash from the lowest density fraction and the minimum limit of the locked particle rate from the highest density fraction were also estimated, and the degree of the maximum mineral matter liberation (MLmax ) was calculated from these results. The MLmax can be easily measured by carrying out sink–float separation at only two density points, and by measuring the weight, ash content, and ash element of these three density fractions. Because coal properties such as particle size and mineral composition are well reflected in the value, the MLmax is useful as a substitute index of the true degree of liberation. 2003 Elsevier Ltd. All rights reserved. Keywords: Coal; Liberation analysis; Dense medium separation; Grinding
1. Introduction The degree of liberation is one of the most important and basic indices in particle separation processes such as mineral processing and waste treatment, and is used to estimate selectively of grinding and the sharpness of separation. In addition, in coal preparation, the limits of demineralization and desulfurization depend on the degree of mineral matter liberation. The degree of liberation has been generally measured by counting the liberated and locked particles using a microscope. However, because coal has a complicated structure, it is very difficult to discriminate useful components from ones that are not useful by microscope. Recently, methods of analyzing coal particles using scanning electron microscope-based automated image analysis (SEM-AIA) (Straszheim and Markuszewski, 1990; Straszheim and Markuszewski, 1992), CCSEM (Ward, 2002; Huggins, 2002), and X-ray CT (Lin et al., 1991; Lin and Miller, 1996; Lin and Miller, 2002) instead of optical microscopes have been studied. Not only the strict dis-
* Corresponding author. Tel.: +81-298-618475; fax: +81-298618472. E-mail address: [email protected] (T. Oki).
0892-6875/$ - see front matter 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.mineng.2003.09.009
crimination of mineral matter (inorganic matter) from coal substance (organic matter) was attained, but a lot of information on the existent states of the minerals, such as size and shape distribution for mineral domains, was obtained by direct observation using this equipment. However, in order to acquire highly accurate and reliable measurements of a cross-section of a sample (2D), a large number of measurements must be carried out same as the conventional microscopic method. Although the resolution of the equipment used for 3D measurements has increased recently (Lin and Miller, 2002), the microscopic structure of coal under 5 lm cannot be observed even by the latest equipment. Moreover, these measurement methods are not widely utilized, because special equipment is needed. Estimation methods using a matrix model (Hsih et al., 1995) and simulation (King and Schneider, 1998; Wei and Gay, 1999) are other important methods by which liberation measurements can be made. These methods greatly evolved the calculation technique for liberation. However, a huge database and number of calculations are required to estimate the accurate structure and grinding of coal, which has a complicated structure, and no example for coal has been reported, as far as the authors know. For coal liberation, methods of calculating the liberation index by sink–float separation data (washability
40
T. Oki et al. / Minerals Engineering 17 (2004) 39–51
Nomenclature ML CC CM CMþX CA 1 CA CAþX CPþX i j
degree of mineral matter liberation rate of coal substance in feed sample rate of mineral matter in feed sample (¼ 1 CC ) rate of mineral matter in the density fraction over X g/cm3 rate of ash in feed sample (ash content) rate of combustible matter in feed sample rate of ash in the density fraction over X g/ cm3 rate of particles with density over X g/cm3 rate of inherent ash in coal substance (inherent ash content) rate of ash in mineral matter (mineral ash content)
data) have been studied. One method reported by Austin et al. (Austin, 1994; Austin et al., 1994; Austin, 1995) was to quantify the extent of ash liberation by the route the results would take between the Mayer curves of complete liberation and no liberation. However, since the original sink–float separation data is based upon the ash after combustion, this method does not express the state of mineral matter liberation before combustion. Holland-Batt (1994) reported a method of calculating the liberation index based upon the ratio of mineral matter and coal substance before combustion, from sink–float separation data. He provided a reasonable concept for the relation of coal components before and after combustion. However, several unfounded assumptions, such as the density range of the locked materials, and the ash content of liberated particles were included in the calculations. Moreover, since special liberation indices were used in these studies, it is unclear what kind of state of particles the values express, and how the values should be related mathematically to ash rejection or separation efficiency. Although sink–float separation data does not include information for each particle and domain, the data is highly accurate and can be obtained easily without using a special equipment. If the degree of liberation (not special liberation index) could be easily calculated by using the sink–float separation data, this calculation method would be useful as the way to add new information to the original sink–float separation data. Sink–float separation data is particle information according to density, and is expressed as a result in which the density of each component included in a particle is reflected. However, it has been conventionally assumed that each particle in sink–float separation data consists of two uniform components of ash and combustible
RM dC dM dp
rate of mineral matter in a particle density of coal substance density of mineral matter (density of whole minerals) mean density among each density fraction
Abbreviations MM mineral matter CS coal substance A ash CM combustible matter Subscripts x kinds of mineral phase (ex. x ¼ 1: pyrite, x ¼ 2: anatase. . .) X density
matter, and that only the ratio of these components in each density fraction is important. In order to calculate the degree of mineral matter liberation from sink–float separation data, it is important to effectively pull out the particle information which is latent in these data, by taking the density of components into consideration. Although the degree of liberation can be calculated for mineral matter and coal substance, respectively, the degree of mineral matter liberation, which has a rather deep relation with the de-ashing property, was investigated in this study. In this report, the concept that gives the degree of mineral matter liberation from the sink–float separation data and from the elemental data by XRF has been investigated, and one example of simple analysis/ calculation method has been provided.
2. Experimental methods 2.1. Sample When the percentage of mineral matter in coal is high, namely, when coal includes a lot of ash, an appropriate degree of liberation can be easily acquired using any estimation method. However, if it is possible to estimate the little difference of the degree of liberation of coal with low ash content, a more highly accurate estimation will be guaranteed in coal with a high ash content. In this study, in order to check if the degree of liberation which differs according to particle size and mineral composition could be evaluated appropriately, coal with a low ash content was used. The samples used in this study consisted of N coal from China and H coal from Australia. Both samples were clean coals imported to Japan after coal preparation. The massive coal sam-
T. Oki et al. / Minerals Engineering 17 (2004) 39–51
ples were divided, ground by ball mill, and sieved to the size range of 38–300 lm. The samples prepared to these size ranges were expressed as NM and HM samples (M: middle size), respectively. A portion of the NM and HM samples was further ground using a vibrating mill to a fine size, which was under 5 lm in average. These fine samples were called NF and HF samples (F: fine size), respectively. The results of the proximate and ultimate analyses for the N and H coals are shown in Table 1. The results of the elemental analysis of the ash of both coals by the XRF measurements, which will be described in the next subsection, are shown in Table 2. Table 3 shows the particle sizes at 50 vol.% for the samples of different sizes, which were measured by continues-flow particle image analyzer (Nireco: Luzex SE-SPL). Although the ash content and coal composition of both samples are relatively close, the ash components were different. In the N coal, SiO2 and Al2 O3 had almost the same percentage of ash elements, and kaolinite was identified as the major mineral phase by XRD. However in the H coal, three-fourths of the ash consisted of SiO2 , and the main mineral was identified as quartz.
41
Table 3 50 vol.% particle size of samples Sample
50 vol.% particle size (lm)
NM NF HM HF
167.2 2.6 166.6 4.9
After the sink–float separation was conducted, the separated samples were weighed, and the ash content was measured according to JIS M8812. However, ashing was carried out at 815 C for 2 h (1 h in JIS) to prevent unburned combustibles from remaining. The glass bead samples of the ashes were made and the ash components of them were measured by a wavelength dispersive XRF (Philips: PW-2404). The calibration curves for the major elements in ash were drawn by using the standard samples of geological survey of Japan. Then, the oxide concentration by the computer application of XRF were corrected by the calibration curves. The correlation of the calibration curves for the eight major elements shown in Table 2 were from r2 ¼ 0:9989 to r2 ¼ 0:9996. It was possible to conduct a very highly accurate analysis for solid particles.
2.2. Experiment The samples were separated using heavy media prepared to the density of 1.25, 1.30, 1.35, 1.40, 1.50, 1.70, 2.50, and 2.96 g/cm3 . For densities under 1.70 g/cm3 , a zinc chloride solution was used as the heavy media. A mixture of tetraboromoethane and tetracholoroethylene was used in the density range of 1.70–2.50 g/cm3 , and undiluted tetraboromoethane was used at 2.96 g/cm3 . One percent of anion surfactant (Kao: DemorN) was added as a dispersant to the zinc chloride solution. Onehundred grams of sample was made into one unit, and the NM and HM samples were placed in a separation funnel for 24 h to carry out the sink–float separation. The NF and HF samples were separated using a centrifugal separator at 3500 rpm for 1 h. Separation was repeated at the same density until nothing floated anymore or nothing sank anymore (usually three times).
3. Estimation of degree of mineral matter liberation 3.1. Outline The components in coal that are not useful are generally shown by the ash content for convenience, and the sink–float separation data is based on the ash content. However, needless to say, coal preparation is a process which treat the particles before combustion (mineral matter (MM) and coal substance (CS)). It is also important to treat the components on a mineral matter base when estimating the degree of liberation. HollandBatt (1994) explained the fundamental concept for coal components before and after combustion in detail. Fig. 1 shows his concept arranged as interpreted by the authors. Fig. 1(a) shows the components on a mineral
Table 1 Proximate and ultimate analysis of coal samples Sample
A (%, db)
VM (%, db)
FC (%, db)
C (%, daf)
H (%, daf)
N (%, daf)
S (%, daf)
O (%, daf)
N H
7.1 9.2
36.3 39.7
56.6 51.1
81.7 81.4
6.0 6.2
1.6 1.9
0.4 0.6
10.2 10.0
Table 2 Elemental analyses of ash from coal samples by XRF Sample
SiO2 (%)
Al2 O3 (%)
Fe2 O3 (%)
TiO2 (%)
CaO (%)
MgO (%)
Na2 O (%)
K2 O (%)
Others (%)
N H
49.0 75.0
36.4 19.8
4.2 2.1
1.5 0.6
3.0 0.6
1.7 0.3
1.1 0.4
0.6 0.6
2.5 0.6
42
T. Oki et al. / Minerals Engineering 17 (2004) 39–51
(a)
(b)
Coalsubstance Coal substance (CS) (CS) [Organic matter] [Organic matter]
Combustible matter Combustible matter (CM) (CM)
Mineral matter (MM) [Inorganic matter]
Ash (A) (A)
on the ash content and elemental data among each density fraction. It is impossible to know what the true degree of liberation from the sink–float separation data is without information on each particle, but it would be possible to estimate MLmax by calculating the percentage of particles that would certainly become locked from the sink–float separation data. In this study, MLmax is treated as the representative index for the degree of mineral matter liberation. 3.2. Estimation of mineral base composition
(c) Exist as liberated CS (CS)
(MM)
(CM)
(CM)
(A)
(A)
Exist as locked particles Exist as liberated MM
Fig. 1. Relation between the components of coal before combustion and after combustion: (a) before combustion, (b) after combustion; (c) contents in CS and MM.
matter base, and Fig. 1(b) shows those on an ash base. Since some minerals are decomposed to other phases during combustion, and the ash contents of these are not 100%, mineral matter also includes combustible matter (moisture, sulfur, carbon) in the calculation. And, ash in coal is not also 0%, because some metal elements such as alkaline metals included in coal substance remain as ash after combustion. This ash is called inherent ash. Thus, coal substance and mineral matter have their own characteristic ash content, and exist as three kinds of particles, that is, as liberated coal substance, liberated mineral matter, and locked particles of both components (Fig. 1(c)). Here, the degree of mineral matter liberation (ML) can be obtained by the following equation: Liberated MM 100 ð1Þ MM If the proportion of each mineral among each density fraction becomes clear, sink–float separation data based on the ash content (CM and A) could be converted to the data based on the mineral percentage before being combusted (CS and MM). Also, it would be possible to find out the minimum percentage of locked particles which can be permitted in each density fraction (the concept will be described in Section 3.3). Although the minimum value of ML (MLmin ) is expected to always be 0%, except for the case when the mineral rate is 100%, as will be mentioned later (Section 3.3), the maximum value of ML (MLmax ), which is expected in cases where the proportion of locked particles is minimum, depends
Table 4 is an example of the sink–float separation results of an NM sample. At first, it was necessary to determine the proportion of each mineral among every density fraction from these data for calculating the MLmax . Fig. 2 shows the coal composition expressed by the rate of the components before and after combustion, which are shown in Fig. 1(c). Here, CC is the rate of coal substance, CM is the rate of mineral matter, i is the inherent ash content (ash content of the inherent ash), and j is the mineral ash content (ash content of the
Table 4 Sink–float separation data of NM sample Specific gravity fraction )1.25 1.25–1.30 1.30–1.35 1.35–1.40 1.40–1.50 1.50–1.70 1.70–2.50 2.50–2.96 +2.96
Weight (%) 0.74 21.89 41.13 19.73 10.34 3.44 2.48 0.22 0.02
Total
Ash content (%)
Ash content in feed (%)
1.50 1.53 2.85 7.33 15.27 28.92 53.67 82.16 72.82
0.01 0.34 1.17 1.45 1.58 0.99 1.33 0.18 0.02
100.00
–
7.07
i
(CC i) Inherent Inherentash ash C i)
ML ð%Þ ¼
CC
CM
(CM j)Mineral ash ash M j)Mineral j Ash (CA) Combustible matter(1-CA)
Fig. 2. Coal components before and after combustion.
T. Oki et al. / Minerals Engineering 17 (2004) 39–51 Minimum ash content 0
0 10
10 20
20 30 40 50
Float (%)
30 40 50 60
0012345 1
70
2
3
4
5
80 90 100 0
10
20
30
40
50
60
70
80
90 100
Ash content (%) Fig. 3. Characteristic curve in H–R diagram of NM sample.
mineral matter). Since a method for measuring i has not been established, the ash content of the intercept on 0% of the float of a washability diagram (H –R diagram) (extrapolated by a characteristic curve in H –R diagram as shown in Fig. 3), which is the minimum ash content, is substituted for i in many cases. The minimum ash content of the NM sample is about 1.5%, and is almost the same for the other three samples. Although further discussion on the method of measuring inherent ash is required, 0.75%, which is the mean value between 0% and 1.5%, was set to i in this study, because of the reason explained later (refer to Section 4.2). As the ash content (CA ) of N coal is known as 7.07%, the percentage of ash in mineral matter (CMj ) among the whole amount of coal can be calculated from the following equation if the value of CC is known (the percentage was converted into a decimal in the following calculations). CMj ¼ CA CCi
ð2Þ
However, since the value of CC cannot be known at this point, the percentage of combustible matter (1 CA : 92.93%) was used instead of CC as a primary approximate value. CMj ¼ C ð1 CA Þi
based on reference information (Tsunekawa et al., 1994; Hirajima et al., 1994; Vassilev et al., 1999; Demir et al., 2001; Ward, 2002), are shown in Table 5. Minerals can be classified into those whose weight decreases by dehydration and decomposition during combustion, and those whose weight does not change after combustion. Although these are just theoretical values and there are various opinions on the mineral phases after combustion, and although jx of real sample would differ according to the opinion, the values of this table were used here for convenience. It is also difficult to determine CMx . The most simple determination method is to carry out a norm calculation based on the results of the elemental analysis of ash. Various ways of calculating the norm calculation can be considered, and authors have used the following methods. Seven minerals were identified as the major minerals in N coal from the results of XRD and the main elements which are contained or may be contained in these minerals are shown in Table 6. Norm calculation was done first from illite. Illite is the general term for dioctahedral mica; it is difficult to identify the mineral phase because various
Table 5 Typical mineral phases in coal and their ash content after combustion Density
Mineral in coal (before combustion)
Component in ash (after combustion)
2.61
Kaolinite Al2 Si2 O5 (OH)4 Quartz SiO2 Calcite CaCO3 Illite Dolomite CaMg(CO3 )2 Anatase TiO2 Siderite FeCO3 Pyrite/Marcasite FeS2
Metakaolinite Al2 Si2 O7 Quartz SiO2 Lime CaO ÆAmorphousæ
2.65 2.71 2.75a 2.94 3.90 3.94 5.03b
ð3Þ a
The CM j of N coal was calculated to be about 6.37% from Eq. (3). CM can be estimated by dividing 6.37% by j. Because j differs by the difference between mineral phases before and after combustion in each mineral, it is necessary to find out the ash content in each mineral (jx ) and the percentage of each mineral among the whole amount of coal (CMx ). x represents the kinds of minerals (ex. x ¼ 1: quartz, x ¼ 2: kaolinite. . .). j¼
n X
ðjx CMx Þ
ð4Þ
x¼1
The mineral phases before and after combustion and the ash content for typical minerals in coal, which are
43
b
CaO Æ MgO Anatase TiO2 Hematite Fe2 O3 Hematite Fe2 O3
Ash content (%) 93.5 100.0 56.0 95.5 60.9 100.0 69.0 66.7
Typical density. Average density from 4.95 to 5.1.
Table 6 Elements in mineral phases included in N coal Illite Kaolinite Quartz Pyrite Anatase Dolomite Calcite
Si
Al
Fe
Ti
Ca
Mg
Na
K
·
·
·
·
· not counted in this study.
T. Oki et al. / Minerals Engineering 17 (2004) 39–51
elements may exist. Since only illite may contain Na and K among the minerals identified in this sample, the chemical composition was assumed to be (Na,K)Al3 Si3 O12 H2 , and the whole amounts of Na and K in the mineral matter were assumed to have arisen from illite. Next, the Al which remained was subtracted from illite was considered to have arisen from kaolinite. In addition, the Si which remained was subtracted from illite and kaolinite was considered to have arisen from quartz. Since only pyrite contains Fe in N coal, all Fe was considered to have arisen from pyrite. When other Fe containing minerals such as siderite exist together, a pyritic sulfur analysis should be carried out to determine the amount of pyrite. All Ti was considered to have arisen from anatase. Also, all Mg was considered dolomite, and the Ca which remained was subtracted from dolomite was considered calcite. The element of the )1.25 g/cm3 fraction based on that of the 1.25–1.30 g/cm3 fraction was calculated here, because there was a small amount of )1.25 g/cm3 fraction in the sample, and the ash elements could not be analyzed. In addition, the average ash content of the minerals, except for the ‘‘Others’’, was used for the ash content of the ‘‘Others’’. The j of N coal was calculated to be 86.4% by Eq. (4) using jx obtained from Table 5, and CMx obtained by norm calculation, as mentioned above. By dividing CMj (6.37%) by j, the CM of N coal becomes 7.37%. This is a primary approximate value calculated by Eq. (3) using 1 CA instead of CC , as described in the beginning of this subsection. When 92.63% (100–7.37) was substituted to the CC of Eq. (2) here, the result became CM ¼ 7:38%, and the difference with the primary approximate value was only 0.006%. Even when norm calculation was done again using this value, CM became the same value as 7.38%. Therefore, it became clear that repeating this calculation twice was sufficient to obtain an accurate CM . Moreover, a large error would not be given even if the primary approximate value was used. The components of the N coal before and after combustion are shown in Fig. 4. The results of the calculation, described in this subsection, applied to each density fraction of the NM sample are shown in Table 7. 3.3. Degree of liberation In this subsection, MLmax was estimated using the calculation data mentioned in the previous subsection. The concept of liberation calculation is shown in Fig. 5(a) and (b) and the calculation sheet for the MLmax of NM sample is shown in Table 8. The density of liberated minerals in coal generally ranges from about 2.5 to 5 g/ cm3 (refer to Table 5). Therefore, in this study, liberated minerals existed only in density fractions over 2.5 g/cm3 , and every mineral included in a density fraction less than 2.5 g/cm3 existed as locked particles. Fig. 5(a) shows the concept of liberation by using, as an example,
i=0.75%
91 . 9% 91.9%
CC = 92.6%
CM=7.4%
1. 0% 1.0%
0. 7% 0.7%
44
6. 4% 6.4% j=86.4%
Ash content=7.1% Combustible matter=92.9% Fig. 4. Components before and after combustion of N coal.
the 2.50–2.96 density fraction of the NM sample. About 3% by weight of coal substance was included in this fraction (refer to Table 7), which was equal to about 6% by volume. This means that if all particles are uniform, they will measured as locked particles of mineral rate 0.94 by microscopic method (minimum liberation case). In this case, since there is no liberated particle, MLmin becomes 0%. MLmin becomes 0% similarly in all cases, except when the mineral rate is 100%. However, the degree of liberation becomes highest when the density of all particles, except for the liberated mineral matter, is the minimum in each density fraction (maximum liberation case). In this calculation, in order to make the mineral rate that exists as locked particles the lowest, the mineral matter is allocated as locked particles in the order of higher density minerals to lower ones. In the case of Fig. 5(a), the case in which the density of locked particles made of pyrite and coal substances is 2.50 g/cm3 is considered first. In the NM sample, since all coal substances were allocated to the locked particles with pyrite, it was considered that the remainder were liberated minerals. Here, the density of coal substance (dC ) has to be decided for the calculations. The dC in this study was obtained by the following equation using the average density of mineral matter (dM ) in each density fraction, which was computed by the data in Table 7. dC ¼
dP dM CC dM dP CM
ð5Þ
Here, dP is the mean density among each density fraction. Since the exact density could not be calculated for the density fraction over 2.50 g/cm3 which included little coal substance, the coal substance density 1.34 g/cm3 of the 1.50–1.70 fraction, whose density was comparatively high and included lots of coal substance, was used here. As the density of pyrite and coal substance are 5.03
2.66 2.67 2.63 2.64 2.64 2.68 2.69 2.80 3.88 86.4 6.38 0.69 MM: mineral matter, CS: coal substance, mineral ash: ash content of mineral matter, CC ¼ 100 CM . a Inherent ash was estimated as 0.75%. b Mineral composition calculated from the oxide data of 1.25–1.30 fraction.
7.07 92.62 7.38 0.03 0.20 0.05 0.05 0.36 0.11 6.04 Feed
0.56
85.7 85.6 86.6 87.0 86.8 86.5 85.5 84.9 73.2 0.76 0.79 2.12 6.63 14.65 28.42 53.39 82.14 72.81 0.74 0.74 0.73 0.69 0.62 0.50 0.28 0.02 0.00 1.50 1.53 2.85 7.33 15.27 28.92 53.67 82.16 72.82 99.2 99.1 97.5 92.4 83.1 67.2 37.6 3.2 0.6 0.8 0.9 2.5 7.6 16.9 32.8 62.4 96.8 99.4 0.0 0.0 0.0 0.0 0.1 0.3 0.4 1.8 1.6 0.0 0.0 0.1 0.1 0.3 0.9 2.0 8.0 64.9 0.0 0.0 0.0 0.0 0.0 0.1 0.9 3.4 2.9 0.0 0.0 0.0 0.0 0.0 0.7 1.3 3.8 0.0 0.0 0.0 0.0 0.3 0.5 3.0 4.7 4.1 0.0 0.0 0.0 0.0 0.0 0.1 0.4 1.9 7.8 2.2 0.7 0.8 2.3 6.6 14.7 24.2 47.0 44.5 26.6 )1.25b 1.25–1.30 1.30–1.35 1.35–1.40 1.40–1.50 1.50–1.70 1.70–2.50 2.50–2.96 +2.96
0.1 0.1 0.1 0.6 1.2 3.2 4.2 23.4 1.2
Anatase (%) Dolomite (%) Illite (%) Calcite (%)
RMx2:50 ¼
Kaolinite (%)
Quartz (%)
45
(dM1 ) and 1.34 g/cm3 (dC ), respectively, the weight percentage of pyrite for a 2.50 g/cm3 particle (RM12:50 ) was decided as 63.2% by the following equation:
Fraction
Table 7 Mineral composition of NM sample calculated by norm calculation
Pyrite (%)
Others (%)
Total (CM ) (%)
CS (CC ) (%)
Ash content (CA ) (%)
Ash in org. (CC i) (%)a
Ash in inorg. (CA CC i) (%)
Mineral ash (ðCA CC iÞ=CM ) (%)
Density of MM (dM ) (g/cm3 )
T. Oki et al. / Minerals Engineering 17 (2004) 39–51
dMx ð2:50 dC Þ 2:50ðdMx dC Þ
ð6Þ
Since the pyrite content in this fraction is 8.0%, 4.7% (8:0 ðð1 0:632Þ=0:632Þ) of coal substance is necessary in order to allocate the whole amount of pyrite as locked particles. However, as the coal substance (CC ) in this fraction is 3.2%, the allocation ends halfway for pyrite as mentioned above. Therefore, all of the coal substance (3.2%) and 5.5% (3:2 ð0:632=ð1 0:632ÞÞ) of pyrite exist as locked particles. This result shows that at least 8.7% (3.2 + 5.5) of the particles among the 2.50– 2.96 g/cm3 fraction must be locked particles (refer to Fig. 5(a)). By the same calculations, 2.2% of the particles must be locked particles for the +2.96 g/cm3 fraction. 91.3% of mineral matter in the 2.50–2.96 g/cm3 fraction and 97.8% of mineral matter in the +2.96 g/cm3 fraction could be expected to exist in maximum as liberated particles, so MLmax was calculated as 3.0% (2:93 0:913 þ 0:34 0:978) from the mineral percentage of both fractions for the total mineral matter, which were 2.93% and 0.34% (refer to Table 8). In the case of another sample, if coal substance remains even after it is allocated to locked particles with pyrite of a density of 2.50 g/cm3 , then the locked particles of 2.50 g/cm3 with anatase, which has the second highest density, will be considered next. The allocation of coal substance continues one by one in order to lower the density minerals until all coal substance is allocated (refer to Fig. 5(b)). In addition to this, if the threshold value is except 100% (liberated) in this calculation, the percentage of locked particles whose mineral rate is more than the threshold value can be calculated. Therefore, the mineral rate distribution of locked particles can also be acquired by repeating the calculation with different threshold values. The details are abbreviated here from the limit of space in this paper. The calculation results of MLmax computed in the same way for the four samples used in this study are shown in Fig. 6. The MLmax of each sample was N coal < H coal among the same particle sizes. This shows that the MLmax of H coal, whose main mineral is quartz, becomes higher than that of N coal, which includes kaolinite as the main mineral. Among the same kinds of coal, each MLmax shows the same relation of coarse particles < fine particles. The relation of MLmax in these samples reflects the property of coal by coal kinds and particle size well. It is impossible to obtain more detailed particle information for liberation from the sink–float separation data. Although MLmax is not the true degree of liberation, it can be utilized as a substitution value, because the value shows that the acquirable information of
46
T. Oki et al. / Minerals Engineering 17 (2004) 39–51
(b) Example
(a) NM sa sample
Locked mineral particles
Liberated 91.3%
Locked 8.7%
100 Mineral percentage in each particle
100 Mineral percentage in each particle
Liberated mineral particles
95
Minimum liberation liberat ion case
(Every (Every mineral mineral exists exists as as locked locked particles) particles)
90 85 80
Maximum liberation case
75 70
Locked mineral particles (coal substance and pyrite)
65
95 Coal substance and calcite
90 85
Coal substance and dolomite
80 75 70 65
Coal substance and anat anatase ase
Coal substance and pyrite
60
60 0
10
200
330
400
550
60
700
880
900 100 0
Weight percentage
1 10 20 30 40 50 60 70 80 900 100 Weight percentage
Fig. 5. Calculation diagram of maximum and minimum degree of mineral matter liberation in 2.50–2.96 specific gravity fraction: (a) NM sample, (b) example.
locked particles is not contradictory to the true information.
4. Effect of condition and accuracy of each parameter on MLmax
group. Therefore, the error of norm calculation mainly arises from the rate of mineral phases inside each group, and it is thought that errors beyond groups cannot easily occur. From these results, it is expected that the influence of the error on the accuracy of the MLmax is comparatively small, in spite of the low accuracy of the norm calculation.
4.1. Effect of accuracy of norm calculation Different values of MLmax will be obtained using the computing method of norm calculation and inherent ash, and by the density of fractions, because the accuracy of locked particle information changes according to which method and densities are employed. In this section, the error factors by different measuring processes are investigated. The accuracy of norm calculation was verified first. Since determining mineral phases by norm calculation is not very accurate, different values are obtained using a different calculation process. However, the parameters that contribute to the accuracy of MLmax consists of only the ash content and the density of the mineral matter. Therefore, even if an error exists in the percentage of each mineral phase, it will not lead to a lessening of the accuracy of MLmax when the ash content and the density are the same. Table 9 shows the classified results of the mineral phases mentioned in this study according to ash content and density. The minerals can be classified into four groups. The main components in each group are the characteristic elements, namely, Si and Al in the high ash–low density group, Ti in the high ash–high density group, Ca and Mg in the low ash–low density group, and Fe in the low ash–high density
4.2. Estimation of inherent ash and effect of low density fraction The error of the estimated value which has been derived from the intercept of the extrapolated line is verified here. The estimated value in the NM sample when the density of the minimum density fraction was changed to 1.25, 1.30, and 1.35 g/cm3 is shown in Fig. 7. Although the estimated value was 1.5% in the case of the minimum density fraction at 1.25 g/cm3 , it changed to 1.3% at 1.30 g/cm3 and 0.2% at 1.35 g/cm3 . This means that a lower value was shown as the estimated value by mistake, with the increase of density of the minimum density fraction. This is because the estimated value is strongly influenced by the change of the amount of ash in fractions of the higher density side, with the increase of the density in the minimum density fraction. Thus, since the estimated value by the intercept of the extrapolated line changes by the minimum density of fraction, the minimum density fraction of each sample needs to be as small as possible in order to compare the MLmax of a different sample in the same accuracy. More accurate data is required to determine the standard of the minimum density for the sink–float separated frac-
Table 8 Calculation sheet of MLmax for NM sample Calculation steps 1
2
3
4
Theoretical ratio (wt.%) in a particle with the lowest density in each fraction
Wt.% of CS or each mineral in each density fraction
Wt.% of liberated and locked components in each density fraction
Wt.% of each components for final calculation of MLmax
Locked-2; . . . ; nb
Locked-1
Density fraction (g/cm3 ) 2.50– 2.96 +2.96 a
Pyrite
d
e
f
g (f b=a)
h
i (h d=c)
j (f þ h ¼ 100)e)
l k (e a=b)a ( ¼ e)
m (k þ l)
n 100 m
o
CS (CC )
Pyrite (CM1 )
CS allocated to pyrite
Other MM (CM2; . . . ; n)
CS allocated to other MM
Total MM (CM )c
Locked MM a
Locked CS
Locked particles
Liberated MM
5.03e (RM1 )f
CS 1.34 e (1 RM1 )
– – (RM2; . . . ; n)
CS 1.34 (1 RM2; . . . ; n)
63.25
36.75
–
–
3.20
8.02
4.66
88.78
–
96.80
5.51
3.20
8. 71
91. 29
74.60
25.40
–
–
0.57
64.87
22.09
34.56
–
99.43
1.67
0.57
2.24
97. 76
General formula of the locked MM is ( " ) # n1 n1 X X 1 RMn 1 RMx RMn Locked MM ¼ CC ; ðCMx Þ þ CMn CMx RMn RMx 1 RMn x¼1 x¼1
p
q (p j=o)
r (n q)
s P ( r)
MM in Weight feed in each (CM )d fraction
MM/ MM in feed
Liberated MM
MLmax
7.38
0.223
2.925
2.67
3.00
0.025
0.337
0.33
T. Oki et al. / Minerals Engineering 17 (2004) 39–51
Symbol for calculation a b c
RM1 Mn but, when CC < CM1 1R , namely, e < g is satisfied like NM sample, the equation can be simplified to ¼ CC 1R is, e ab in this table. RMn M1 b No data for NM sample in this study. c CM in each density fraction. d CM in feed sample. e Density of CS and each mineral (g/cm3 ). f RMx : theoretical ratio (wt.%) of a mineral phase locked with coal substance in a particle with the lowest density in each density fraction.
47
48
T. Oki et al. / Minerals Engineering 17 (2004) 39–51
1.5
0.2% 1.3% 0
1.25
10
1.30
Float (%)
20 30
1.35
40 50 60
1.40
70 80 0
1
2
3
4
Fig. 6. The maximum degree of mineral matter liberations.
tion. However, estimating from these results, when the weight of the minimum density fraction is less than 10%, it can be considered that the intercept value of the extrapolated line, namely, the inherent ash content, can be estimated just as accurately. In this study, since the minimum density fraction of every sample was 1.25, an extremely precise value was obtained for an estimated value by extrapolation. The estimated value of the NM sample was around 1.5%, and was also almost the same for other samples. However, is this ash content really the value of particles containing only inherent ash? The main elements of inherent ash have been considered to be Ca, Na, K, Mg, Ti, etc. (Joseph and Forrai, 1992; Ward, 2002); however, the main components of ash in the 1.25–1.30 g/cm3 fraction, which had almost the same ash content (1.53%) as the estimated value, were SiO2 (0.64%) and Al2 O3 (0.60%). Since most of the inherent ash is considered to consist of clay minerals, the estimated value of 1.5% would be too large for inherent ash. Therefore, from the data in this study, the only certain thing is that the inherent ash is between 0% and 1.5%. In this study, 0.75% of that mean value was adopted as the inherent ash temporarily. If the
5
6
7
8
9
Fig. 7. Estimation by extrapolation of ash content of the minimum ash particle in NM sample.
real inherent ash is somewhere between 0% and 1.5%, the range of MLmax can be computed to be 3.0% ± 0.3% in the NM sample, and to be 16.4% ± 1.2% in the HF sample, when inherent ash was set as 0.75%. As the possibility of true inherent ash being 0% or 1.5% is very low, it is presumed that the actual error range is even smaller. Although further study is necessary to determine the accurate inherent ash content, the influence on the MLmax is comparatively small for every value in the predicted range of inherent ash. 4.3. Effect of the highest density fraction The maximum density of heavy media is usually around 1.7–2.0 g/cm3 . However, separating at around 2.5 g/cm3 is effective in strictly limiting the density fraction, including liberated particles. The MLmax was calculated when only one density point at 1.70 or 2.50 g/ cm3 was set as the separation density in the higher density side. The results are shown in Fig. 8. In the previous section, MLmax was calculated by two density
Table 9 Classification of mineral groups in coal to estimate the degree of liberation Mineral groups
Density
Mineral phases
Ash content (%)
Si
Al
Fe
Ti
Ca
Mg
Na
K
High ash–low density
2.61 2.65 2.75a
Kaolinite Quartz Illite
93.5 100.0 95.5
·
·
·
·
High ash–high density
3.90
Anatase
100.0
Low ash–low density
2.71 2.94
Calcite Dolomite
56.0 60.9
3.94 5.03b
Siderite Pyrite/Marcasite
69.0 66.7
Low ash–high density
(·) Not counted in this study. a Typical density. b Average density of pyrite from 4.95 to 5.1.
10
Ash content (%)
T. Oki et al. / Minerals Engineering 17 (2004) 39–51
49
Fig. 8. The MLmax estimated using several specific gravity fractions.
points of 2.50 and 2.96 g/cm3 . But the MLmax calculated by only one density point at 2.50 g/cm3 also shows almost the same accuracy. When 1.70 g/cm3 was set as the maximum density fraction, the HF sample, which showed a relatively high MLmax , showed a good MLmax value, but in other samples of the lower MLmax , higher values were calculated, and an accurate value could not be acquired. This is because the theoretical top limit of the degree of liberation was evaluated from the percentage of particles that certainly exist as locked particles in this estimation method. When the MLmax is estimated at 1.70 g/cm3 of the maximum density fraction in a sample with low MLmax , the accuracy of the MLmax becomes lower because the rate of the locked particles increases a great deal. Next, the difference between the MLmax determined in this study and simple indices customarily used in other estimating methods were compared. Table 10 shows each commonly used index and the MLmax when the
maximum density fraction is 1.70 and 2.50 g/cm3 . CPþX =CA is the index assumed that all particles of densities more than X (1.70 or 2.50 g/cm3 in this study) are liberated mineral matter, and the percentage of that to total ash is defined as the degree of mineral matter liberation. CAþX =CA is the index used when the ash percentage included in the density fraction over X to total ash is defined as the degree of mineral matter liberation. These two are the indices on ash base. CMþX =CM is the index used when the mineral percentage included in the density fraction over X to total mineral is defined as the degree of mineral matter liberation, using data in the mineral base which has been computed in the previous section. In addition, the fourth index is MLmax , which takes into consideration the kind of mineral phases. The upper four cases in the table (NM , NF , HM , HF ) show the results for the samples used in this study. Setting the MLmax at 2.50 g/cm3 of the maximum density fraction (bold letter) as a standard value, each index at 1.70 g/
Table 10 Comparison of the results of rough estimations of the degree of mineral matter liberation and the results of MLmax Sample
Maximum specific gravity fraction: 1.70 CPþ1:70 =CA
CAþ1:70 =CA
CMþ1:70 =CM
MLmax
CPþ2:50 =CA
CAþ2:50 =CA
CMþ2:50 =CM
MLmax
NM NF HM HF
38.6 47.2 25.9 60.3
21.7 25.4 16.3 34.1
24.2 28.7 18.5 38.0
12.5 13.3 13.1 16.8
3.5 6.5 7.1 16.0
2.9 5.4 5.7 15.1
3.3 6.2 6.8 16.5
3.0 5.9 5.9 16.4
16.6 16.6 16.6
11.6 11.6 11.6
13.0 13.4 13.8
5.0 33.6 63.7
M1 M2 M3
Maximum specific gravity fraction: 2.50
50
T. Oki et al. / Minerals Engineering 17 (2004) 39–51
cm3 shows a value which is greatly different from it. Also, at 1.70 g/cm3 of the maximum density fraction, although even the order of the degree was not correct for the three indices, only the MLmax showed the same order as the standard (NM < NF ¼ HM < HF ). However, when the maximum density fraction was set to 2.50 g/cm3 , every index indicated a value near to the MLmax . This is because most mineral matter in every sample in this study belonged to the ‘‘high ash–low density group’’ of Table 9, so the ash content of the +2.50 g/cm3 fraction was near 100%. Accordingly, the value of each index was calculated using imaginary samples for cases in which the samples included many kinds of minerals from different groups. In each model sample (M1 , M2 , M3 ), it was assumed that the particles with a density of less than 2.50 g/cm3 was completely the same component as the HF sample, and that the ash contents in the fraction more than 2.50 g/cm3 were 70% (the HF sample was 94.7%). The mineral phases of the model samples were assumed to consist only of quartz and pyrite. In the M1 sample, the ash content of 70% in the density fraction greater than 2.50 g/cm3 consisted of 60% of SiO2 and 10% of Fe2 O3 . Similarly, it was assumed that M2 was 55% of SiO2 and 15% of Fe2 O3 , and that M3 was 50% of SiO2 and 20% of Fe2 O3 , respectively. All other conditions, such as the density of the coal substance and inherent ash content, were set the same as the HF sample. From the results of the calculation, since the MLmax showed a completely different value from the other indices in the model samples, it was shown that the commonly used indices cannot show the true value when a lot of mineral matter, except for the mineral matter in the ‘‘high ash–low density group’’ in the fraction more than 2.50 g/cm3 , is included. From the above results, it was concluded that while it is important to take the maximum density fraction around 2.5 g/cm3 in order to estimate the degree of mineral matter liberation with high accuracy, it is crucial to compute the MLmax , in order to investigate the coal samples with various mineral compositions. In this section, the usefulness of MLmax and the effect of each parameter on MLmax have been investigated. But the model sample whose ML is known has not been investigated here. The error range of the data of each analysis for sink–float separation and mineral composition has neither been included into the consideration. Therefore, the real accuracy of MLmax could not be strictly evaluated and these will be a future work of our study.
5. Discussion and conclusions Here, the most convenient operation process was investigated by assuming the actual MLmax of an unknown sample. To calculate the MLmax , sink–float sep-
arations in the low density side have to be carried out to estimate the inherent ash content, and ones in the high density side have to be done to finally fix the MLmax . As the investigations here show, accurate measurement of the inherent ash content is essentially difficult, and there is no other choice but to improve the accuracy of the estimation by the intercept of the extrapolated line. When a density less than about 10% in weight percentage of the minimum density fraction was taken, the inherent ash content could be estimated by separation at only one density in the low density side, since it could be considered that the ash content of that density fraction is almost the same as the estimated value by the intercept of the extrapolated line. In the high density side, just one separation at around 2.50 g/cm3 was required, as mentioned in the previous subsection. Thus, the simplest process of measuring the MLmax is to obtain the weight percentage, ash content, and ash element data by XRF for three density fractions separated at one density point in the low and high density side (ex. 1.30 and 2.50 g/cm3 ). Here, the density of coal substance is calculated from the intermediate density fraction (ex. 1.30–2.50 g/ cm3 ). The MLmax can be obtained by this easy procedure, and this is useful as a new index to assist the original sink–float separation data. The results are summarized as follows. (1) The content of inherent ash was estimated by the intercept of an extrapolated line of the characteristic curve in the washability diagram. However, since it was judged that the estimated value was too large, the real inherent ash could not be simply measured. In this study, the mean value between 0% and the estimated value was temporally used as the inherent ash content. When the percentage of the minimum density fraction was 10% or less, the ash content in that fraction could be regarded as the estimated value, and it was possible to estimate the inherent ash content with sufficient accuracy by the separation at one density point. (2) It is generally difficult to determine mineral phases with high accuracy by norm calculation. However, only the distribution of the ash content and the density of the mineral matter influences the degree of liberation. Since the main ash elements of the four mineral groups which are classified by ash content and density are different, the effect of the determination error by norm calculation on the accuracy of the degree of liberation is small. (3) For separation in the high density side, separation at one density point around 2.5 g/cm3 , which is close to the minimum density of the mineral phase in coal, is sufficient. The MLmax , which is the theoretical maximum degree of mineral matter liberation, can be obtained by computing the rate of particles that would certainly become locked particles among the particles in the maximum density fraction. Although the true degree of liberation would surely become smaller than this, the MLmax is an index which accurately reflects the particle
T. Oki et al. / Minerals Engineering 17 (2004) 39–51
size, coal kinds, and mineral kinds in coal, and is useful as a substitution index for the true degree of liberation. Acknowledgements The authors would like to thank T. Kimura (CCUJ) for guiding the determination by XRF. References Austin, L.G., 1994. Patterns of liberation of ash from coal. Minerals and Metallurgical Processing (August), 148–159. Austin, L.G., Kalligeris-Skentzos, A., Woodburn, E.T., 1994. Ash liberation in fine grinding of a British coal. Powder Technology 80, 147–158. Austin, L.G., 1995. The graphical representation of ash liberated in milled coal. The Chemical Engineering Journal 59, 23–31. Demir, I., Hughes, R.E., DeMaris, P.J., 2001. Formation and use of coal combustion residues from three types of power plants burning Illinois coals. Fuel 80, 1659–1673. Hirajima, T., Wang, N., Tsunekawa, M., 1994. Mineral composition of coals and their minimum ash content attainable by gravity separation. Study on removal characteristics of mineral matter from coal by physical separation (1st Report). Journal of the Mining and Material Processing Institute of Japan 110 (6), 461–466. Holland-Batt, A.B., 1994. Estimating liberation in coals. Coal Preparation 15, 1–24. Hsih, C.S., Wen, S.B., Kuan, C.C., 1995. An exposure model for valuable components in comminuted particles. International Journal of Mineral Processing 43, 145–165.
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Huggins, F.E., 2002. Overview of analytical for inorganic constituents in coal. International Journal of Coal Geology 50, 169–214. Joseph, J.T., Forrai, T.R., 1992. Effect of exchangeable cations on liquefaction of low rank coals. Fuel 71 (January), 75–80. King, R.P., Schneider, C.L., 1998. Mineral liberation and the batch comminution equation. Minerals Engineering 11, 1143–1160. Lin, C.L., Miller, J.D., Cortes, A.B., Galery, R., 1991. Coal washability analysis by X-ray computed tomography. Coal Preparation 9, 107–119. Lin, C.L., Miller, 1996. Cone beam X-ray microtomography for threedimensional liberation analysis in the 21st century. International Journal of Mineral Processing 47, 61–73. Lin, C.L., Miller, 2002. Cone beam X-ray microtomography: a new facility for 3D analysis of multiphase materials. Minerals and Metallurgical Processing 19 (2), 65–71. Straszheim, W.E., Markuszewski, R., 1990. Automated image analysis of minerals and their association with organic components in bituminous coals. Energy & Fuels 4 (6), 748–754. Straszheim, W.E., Markuszewski, R., 1992. SEM-AIA measurement of the association of mineral matter with the organic coal matrix for predicting fine coal cleanability. Coal Preparation 10, 59–75. Tsunekawa, M., Seo, S., Hirajima, T., 1994. Influence of carbon dioxide on flotation and deashing characteristics of coal: on Datong, Wandoan and Illinois coals. Resources Processing 41 (1), 18–27. Vassilev, S.V., Braekman-Danheux, C., Laurent, P., 1999. Characterization of refuse-derived char from municipal solid waste. 1. Phasemineral and chemical composition. Fuel Processing Technology 59, 95–134. Ward, C.R., 2002. Analysis and significance of mineral matter in coal seams. International Journal of Coal Geology 50, 135–168. Wei, X., Gay, S., 1999. Liberation modeling using a dispersion equation. Minerals Engineering 12, 219–227.
Calculation of degree of mineral matter liberation in coal from sink–float separation data T. Oki a
a,*
, H. Yotsumoto a, S. Owada
b
National Institute of Advanced Industrial Science and Technology, Onogawa, Tsukuba 305-8569, Japan b Waseda University, Shinjyuku-ku, Tokyo 169-8555, Japan Received 20 May 2003; accepted 16 September 2003
Abstract A method for calculating the degree of mineral matter liberation by the sink–float separation data of coal was studied. The mineral composition was estimated by norm calculation using the results of elemental analyses of sink–float separated coals. The content of the inherent ash from the lowest density fraction and the minimum limit of the locked particle rate from the highest density fraction were also estimated, and the degree of the maximum mineral matter liberation (MLmax ) was calculated from these results. The MLmax can be easily measured by carrying out sink–float separation at only two density points, and by measuring the weight, ash content, and ash element of these three density fractions. Because coal properties such as particle size and mineral composition are well reflected in the value, the MLmax is useful as a substitute index of the true degree of liberation. 2003 Elsevier Ltd. All rights reserved. Keywords: Coal; Liberation analysis; Dense medium separation; Grinding
1. Introduction The degree of liberation is one of the most important and basic indices in particle separation processes such as mineral processing and waste treatment, and is used to estimate selectively of grinding and the sharpness of separation. In addition, in coal preparation, the limits of demineralization and desulfurization depend on the degree of mineral matter liberation. The degree of liberation has been generally measured by counting the liberated and locked particles using a microscope. However, because coal has a complicated structure, it is very difficult to discriminate useful components from ones that are not useful by microscope. Recently, methods of analyzing coal particles using scanning electron microscope-based automated image analysis (SEM-AIA) (Straszheim and Markuszewski, 1990; Straszheim and Markuszewski, 1992), CCSEM (Ward, 2002; Huggins, 2002), and X-ray CT (Lin et al., 1991; Lin and Miller, 1996; Lin and Miller, 2002) instead of optical microscopes have been studied. Not only the strict dis-
* Corresponding author. Tel.: +81-298-618475; fax: +81-298618472. E-mail address: [email protected] (T. Oki).
0892-6875/$ - see front matter 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.mineng.2003.09.009
crimination of mineral matter (inorganic matter) from coal substance (organic matter) was attained, but a lot of information on the existent states of the minerals, such as size and shape distribution for mineral domains, was obtained by direct observation using this equipment. However, in order to acquire highly accurate and reliable measurements of a cross-section of a sample (2D), a large number of measurements must be carried out same as the conventional microscopic method. Although the resolution of the equipment used for 3D measurements has increased recently (Lin and Miller, 2002), the microscopic structure of coal under 5 lm cannot be observed even by the latest equipment. Moreover, these measurement methods are not widely utilized, because special equipment is needed. Estimation methods using a matrix model (Hsih et al., 1995) and simulation (King and Schneider, 1998; Wei and Gay, 1999) are other important methods by which liberation measurements can be made. These methods greatly evolved the calculation technique for liberation. However, a huge database and number of calculations are required to estimate the accurate structure and grinding of coal, which has a complicated structure, and no example for coal has been reported, as far as the authors know. For coal liberation, methods of calculating the liberation index by sink–float separation data (washability
40
T. Oki et al. / Minerals Engineering 17 (2004) 39–51
Nomenclature ML CC CM CMþX CA 1 CA CAþX CPþX i j
degree of mineral matter liberation rate of coal substance in feed sample rate of mineral matter in feed sample (¼ 1 CC ) rate of mineral matter in the density fraction over X g/cm3 rate of ash in feed sample (ash content) rate of combustible matter in feed sample rate of ash in the density fraction over X g/ cm3 rate of particles with density over X g/cm3 rate of inherent ash in coal substance (inherent ash content) rate of ash in mineral matter (mineral ash content)
data) have been studied. One method reported by Austin et al. (Austin, 1994; Austin et al., 1994; Austin, 1995) was to quantify the extent of ash liberation by the route the results would take between the Mayer curves of complete liberation and no liberation. However, since the original sink–float separation data is based upon the ash after combustion, this method does not express the state of mineral matter liberation before combustion. Holland-Batt (1994) reported a method of calculating the liberation index based upon the ratio of mineral matter and coal substance before combustion, from sink–float separation data. He provided a reasonable concept for the relation of coal components before and after combustion. However, several unfounded assumptions, such as the density range of the locked materials, and the ash content of liberated particles were included in the calculations. Moreover, since special liberation indices were used in these studies, it is unclear what kind of state of particles the values express, and how the values should be related mathematically to ash rejection or separation efficiency. Although sink–float separation data does not include information for each particle and domain, the data is highly accurate and can be obtained easily without using a special equipment. If the degree of liberation (not special liberation index) could be easily calculated by using the sink–float separation data, this calculation method would be useful as the way to add new information to the original sink–float separation data. Sink–float separation data is particle information according to density, and is expressed as a result in which the density of each component included in a particle is reflected. However, it has been conventionally assumed that each particle in sink–float separation data consists of two uniform components of ash and combustible
RM dC dM dp
rate of mineral matter in a particle density of coal substance density of mineral matter (density of whole minerals) mean density among each density fraction
Abbreviations MM mineral matter CS coal substance A ash CM combustible matter Subscripts x kinds of mineral phase (ex. x ¼ 1: pyrite, x ¼ 2: anatase. . .) X density
matter, and that only the ratio of these components in each density fraction is important. In order to calculate the degree of mineral matter liberation from sink–float separation data, it is important to effectively pull out the particle information which is latent in these data, by taking the density of components into consideration. Although the degree of liberation can be calculated for mineral matter and coal substance, respectively, the degree of mineral matter liberation, which has a rather deep relation with the de-ashing property, was investigated in this study. In this report, the concept that gives the degree of mineral matter liberation from the sink–float separation data and from the elemental data by XRF has been investigated, and one example of simple analysis/ calculation method has been provided.
2. Experimental methods 2.1. Sample When the percentage of mineral matter in coal is high, namely, when coal includes a lot of ash, an appropriate degree of liberation can be easily acquired using any estimation method. However, if it is possible to estimate the little difference of the degree of liberation of coal with low ash content, a more highly accurate estimation will be guaranteed in coal with a high ash content. In this study, in order to check if the degree of liberation which differs according to particle size and mineral composition could be evaluated appropriately, coal with a low ash content was used. The samples used in this study consisted of N coal from China and H coal from Australia. Both samples were clean coals imported to Japan after coal preparation. The massive coal sam-
T. Oki et al. / Minerals Engineering 17 (2004) 39–51
ples were divided, ground by ball mill, and sieved to the size range of 38–300 lm. The samples prepared to these size ranges were expressed as NM and HM samples (M: middle size), respectively. A portion of the NM and HM samples was further ground using a vibrating mill to a fine size, which was under 5 lm in average. These fine samples were called NF and HF samples (F: fine size), respectively. The results of the proximate and ultimate analyses for the N and H coals are shown in Table 1. The results of the elemental analysis of the ash of both coals by the XRF measurements, which will be described in the next subsection, are shown in Table 2. Table 3 shows the particle sizes at 50 vol.% for the samples of different sizes, which were measured by continues-flow particle image analyzer (Nireco: Luzex SE-SPL). Although the ash content and coal composition of both samples are relatively close, the ash components were different. In the N coal, SiO2 and Al2 O3 had almost the same percentage of ash elements, and kaolinite was identified as the major mineral phase by XRD. However in the H coal, three-fourths of the ash consisted of SiO2 , and the main mineral was identified as quartz.
41
Table 3 50 vol.% particle size of samples Sample
50 vol.% particle size (lm)
NM NF HM HF
167.2 2.6 166.6 4.9
After the sink–float separation was conducted, the separated samples were weighed, and the ash content was measured according to JIS M8812. However, ashing was carried out at 815 C for 2 h (1 h in JIS) to prevent unburned combustibles from remaining. The glass bead samples of the ashes were made and the ash components of them were measured by a wavelength dispersive XRF (Philips: PW-2404). The calibration curves for the major elements in ash were drawn by using the standard samples of geological survey of Japan. Then, the oxide concentration by the computer application of XRF were corrected by the calibration curves. The correlation of the calibration curves for the eight major elements shown in Table 2 were from r2 ¼ 0:9989 to r2 ¼ 0:9996. It was possible to conduct a very highly accurate analysis for solid particles.
2.2. Experiment The samples were separated using heavy media prepared to the density of 1.25, 1.30, 1.35, 1.40, 1.50, 1.70, 2.50, and 2.96 g/cm3 . For densities under 1.70 g/cm3 , a zinc chloride solution was used as the heavy media. A mixture of tetraboromoethane and tetracholoroethylene was used in the density range of 1.70–2.50 g/cm3 , and undiluted tetraboromoethane was used at 2.96 g/cm3 . One percent of anion surfactant (Kao: DemorN) was added as a dispersant to the zinc chloride solution. Onehundred grams of sample was made into one unit, and the NM and HM samples were placed in a separation funnel for 24 h to carry out the sink–float separation. The NF and HF samples were separated using a centrifugal separator at 3500 rpm for 1 h. Separation was repeated at the same density until nothing floated anymore or nothing sank anymore (usually three times).
3. Estimation of degree of mineral matter liberation 3.1. Outline The components in coal that are not useful are generally shown by the ash content for convenience, and the sink–float separation data is based on the ash content. However, needless to say, coal preparation is a process which treat the particles before combustion (mineral matter (MM) and coal substance (CS)). It is also important to treat the components on a mineral matter base when estimating the degree of liberation. HollandBatt (1994) explained the fundamental concept for coal components before and after combustion in detail. Fig. 1 shows his concept arranged as interpreted by the authors. Fig. 1(a) shows the components on a mineral
Table 1 Proximate and ultimate analysis of coal samples Sample
A (%, db)
VM (%, db)
FC (%, db)
C (%, daf)
H (%, daf)
N (%, daf)
S (%, daf)
O (%, daf)
N H
7.1 9.2
36.3 39.7
56.6 51.1
81.7 81.4
6.0 6.2
1.6 1.9
0.4 0.6
10.2 10.0
Table 2 Elemental analyses of ash from coal samples by XRF Sample
SiO2 (%)
Al2 O3 (%)
Fe2 O3 (%)
TiO2 (%)
CaO (%)
MgO (%)
Na2 O (%)
K2 O (%)
Others (%)
N H
49.0 75.0
36.4 19.8
4.2 2.1
1.5 0.6
3.0 0.6
1.7 0.3
1.1 0.4
0.6 0.6
2.5 0.6
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T. Oki et al. / Minerals Engineering 17 (2004) 39–51
(a)
(b)
Coalsubstance Coal substance (CS) (CS) [Organic matter] [Organic matter]
Combustible matter Combustible matter (CM) (CM)
Mineral matter (MM) [Inorganic matter]
Ash (A) (A)
on the ash content and elemental data among each density fraction. It is impossible to know what the true degree of liberation from the sink–float separation data is without information on each particle, but it would be possible to estimate MLmax by calculating the percentage of particles that would certainly become locked from the sink–float separation data. In this study, MLmax is treated as the representative index for the degree of mineral matter liberation. 3.2. Estimation of mineral base composition
(c) Exist as liberated CS (CS)
(MM)
(CM)
(CM)
(A)
(A)
Exist as locked particles Exist as liberated MM
Fig. 1. Relation between the components of coal before combustion and after combustion: (a) before combustion, (b) after combustion; (c) contents in CS and MM.
matter base, and Fig. 1(b) shows those on an ash base. Since some minerals are decomposed to other phases during combustion, and the ash contents of these are not 100%, mineral matter also includes combustible matter (moisture, sulfur, carbon) in the calculation. And, ash in coal is not also 0%, because some metal elements such as alkaline metals included in coal substance remain as ash after combustion. This ash is called inherent ash. Thus, coal substance and mineral matter have their own characteristic ash content, and exist as three kinds of particles, that is, as liberated coal substance, liberated mineral matter, and locked particles of both components (Fig. 1(c)). Here, the degree of mineral matter liberation (ML) can be obtained by the following equation: Liberated MM 100 ð1Þ MM If the proportion of each mineral among each density fraction becomes clear, sink–float separation data based on the ash content (CM and A) could be converted to the data based on the mineral percentage before being combusted (CS and MM). Also, it would be possible to find out the minimum percentage of locked particles which can be permitted in each density fraction (the concept will be described in Section 3.3). Although the minimum value of ML (MLmin ) is expected to always be 0%, except for the case when the mineral rate is 100%, as will be mentioned later (Section 3.3), the maximum value of ML (MLmax ), which is expected in cases where the proportion of locked particles is minimum, depends
Table 4 is an example of the sink–float separation results of an NM sample. At first, it was necessary to determine the proportion of each mineral among every density fraction from these data for calculating the MLmax . Fig. 2 shows the coal composition expressed by the rate of the components before and after combustion, which are shown in Fig. 1(c). Here, CC is the rate of coal substance, CM is the rate of mineral matter, i is the inherent ash content (ash content of the inherent ash), and j is the mineral ash content (ash content of the
Table 4 Sink–float separation data of NM sample Specific gravity fraction )1.25 1.25–1.30 1.30–1.35 1.35–1.40 1.40–1.50 1.50–1.70 1.70–2.50 2.50–2.96 +2.96
Weight (%) 0.74 21.89 41.13 19.73 10.34 3.44 2.48 0.22 0.02
Total
Ash content (%)
Ash content in feed (%)
1.50 1.53 2.85 7.33 15.27 28.92 53.67 82.16 72.82
0.01 0.34 1.17 1.45 1.58 0.99 1.33 0.18 0.02
100.00
–
7.07
i
(CC i) Inherent Inherentash ash C i)
ML ð%Þ ¼
CC
CM
(CM j)Mineral ash ash M j)Mineral j Ash (CA) Combustible matter(1-CA)
Fig. 2. Coal components before and after combustion.
T. Oki et al. / Minerals Engineering 17 (2004) 39–51 Minimum ash content 0
0 10
10 20
20 30 40 50
Float (%)
30 40 50 60
0012345 1
70
2
3
4
5
80 90 100 0
10
20
30
40
50
60
70
80
90 100
Ash content (%) Fig. 3. Characteristic curve in H–R diagram of NM sample.
mineral matter). Since a method for measuring i has not been established, the ash content of the intercept on 0% of the float of a washability diagram (H –R diagram) (extrapolated by a characteristic curve in H –R diagram as shown in Fig. 3), which is the minimum ash content, is substituted for i in many cases. The minimum ash content of the NM sample is about 1.5%, and is almost the same for the other three samples. Although further discussion on the method of measuring inherent ash is required, 0.75%, which is the mean value between 0% and 1.5%, was set to i in this study, because of the reason explained later (refer to Section 4.2). As the ash content (CA ) of N coal is known as 7.07%, the percentage of ash in mineral matter (CMj ) among the whole amount of coal can be calculated from the following equation if the value of CC is known (the percentage was converted into a decimal in the following calculations). CMj ¼ CA CCi
ð2Þ
However, since the value of CC cannot be known at this point, the percentage of combustible matter (1 CA : 92.93%) was used instead of CC as a primary approximate value. CMj ¼ C ð1 CA Þi
based on reference information (Tsunekawa et al., 1994; Hirajima et al., 1994; Vassilev et al., 1999; Demir et al., 2001; Ward, 2002), are shown in Table 5. Minerals can be classified into those whose weight decreases by dehydration and decomposition during combustion, and those whose weight does not change after combustion. Although these are just theoretical values and there are various opinions on the mineral phases after combustion, and although jx of real sample would differ according to the opinion, the values of this table were used here for convenience. It is also difficult to determine CMx . The most simple determination method is to carry out a norm calculation based on the results of the elemental analysis of ash. Various ways of calculating the norm calculation can be considered, and authors have used the following methods. Seven minerals were identified as the major minerals in N coal from the results of XRD and the main elements which are contained or may be contained in these minerals are shown in Table 6. Norm calculation was done first from illite. Illite is the general term for dioctahedral mica; it is difficult to identify the mineral phase because various
Table 5 Typical mineral phases in coal and their ash content after combustion Density
Mineral in coal (before combustion)
Component in ash (after combustion)
2.61
Kaolinite Al2 Si2 O5 (OH)4 Quartz SiO2 Calcite CaCO3 Illite Dolomite CaMg(CO3 )2 Anatase TiO2 Siderite FeCO3 Pyrite/Marcasite FeS2
Metakaolinite Al2 Si2 O7 Quartz SiO2 Lime CaO ÆAmorphousæ
2.65 2.71 2.75a 2.94 3.90 3.94 5.03b
ð3Þ a
The CM j of N coal was calculated to be about 6.37% from Eq. (3). CM can be estimated by dividing 6.37% by j. Because j differs by the difference between mineral phases before and after combustion in each mineral, it is necessary to find out the ash content in each mineral (jx ) and the percentage of each mineral among the whole amount of coal (CMx ). x represents the kinds of minerals (ex. x ¼ 1: quartz, x ¼ 2: kaolinite. . .). j¼
n X
ðjx CMx Þ
ð4Þ
x¼1
The mineral phases before and after combustion and the ash content for typical minerals in coal, which are
43
b
CaO Æ MgO Anatase TiO2 Hematite Fe2 O3 Hematite Fe2 O3
Ash content (%) 93.5 100.0 56.0 95.5 60.9 100.0 69.0 66.7
Typical density. Average density from 4.95 to 5.1.
Table 6 Elements in mineral phases included in N coal Illite Kaolinite Quartz Pyrite Anatase Dolomite Calcite
Si
Al
Fe
Ti
Ca
Mg
Na
K
·
·
·
·
· not counted in this study.
T. Oki et al. / Minerals Engineering 17 (2004) 39–51
elements may exist. Since only illite may contain Na and K among the minerals identified in this sample, the chemical composition was assumed to be (Na,K)Al3 Si3 O12 H2 , and the whole amounts of Na and K in the mineral matter were assumed to have arisen from illite. Next, the Al which remained was subtracted from illite was considered to have arisen from kaolinite. In addition, the Si which remained was subtracted from illite and kaolinite was considered to have arisen from quartz. Since only pyrite contains Fe in N coal, all Fe was considered to have arisen from pyrite. When other Fe containing minerals such as siderite exist together, a pyritic sulfur analysis should be carried out to determine the amount of pyrite. All Ti was considered to have arisen from anatase. Also, all Mg was considered dolomite, and the Ca which remained was subtracted from dolomite was considered calcite. The element of the )1.25 g/cm3 fraction based on that of the 1.25–1.30 g/cm3 fraction was calculated here, because there was a small amount of )1.25 g/cm3 fraction in the sample, and the ash elements could not be analyzed. In addition, the average ash content of the minerals, except for the ‘‘Others’’, was used for the ash content of the ‘‘Others’’. The j of N coal was calculated to be 86.4% by Eq. (4) using jx obtained from Table 5, and CMx obtained by norm calculation, as mentioned above. By dividing CMj (6.37%) by j, the CM of N coal becomes 7.37%. This is a primary approximate value calculated by Eq. (3) using 1 CA instead of CC , as described in the beginning of this subsection. When 92.63% (100–7.37) was substituted to the CC of Eq. (2) here, the result became CM ¼ 7:38%, and the difference with the primary approximate value was only 0.006%. Even when norm calculation was done again using this value, CM became the same value as 7.38%. Therefore, it became clear that repeating this calculation twice was sufficient to obtain an accurate CM . Moreover, a large error would not be given even if the primary approximate value was used. The components of the N coal before and after combustion are shown in Fig. 4. The results of the calculation, described in this subsection, applied to each density fraction of the NM sample are shown in Table 7. 3.3. Degree of liberation In this subsection, MLmax was estimated using the calculation data mentioned in the previous subsection. The concept of liberation calculation is shown in Fig. 5(a) and (b) and the calculation sheet for the MLmax of NM sample is shown in Table 8. The density of liberated minerals in coal generally ranges from about 2.5 to 5 g/ cm3 (refer to Table 5). Therefore, in this study, liberated minerals existed only in density fractions over 2.5 g/cm3 , and every mineral included in a density fraction less than 2.5 g/cm3 existed as locked particles. Fig. 5(a) shows the concept of liberation by using, as an example,
i=0.75%
91 . 9% 91.9%
CC = 92.6%
CM=7.4%
1. 0% 1.0%
0. 7% 0.7%
44
6. 4% 6.4% j=86.4%
Ash content=7.1% Combustible matter=92.9% Fig. 4. Components before and after combustion of N coal.
the 2.50–2.96 density fraction of the NM sample. About 3% by weight of coal substance was included in this fraction (refer to Table 7), which was equal to about 6% by volume. This means that if all particles are uniform, they will measured as locked particles of mineral rate 0.94 by microscopic method (minimum liberation case). In this case, since there is no liberated particle, MLmin becomes 0%. MLmin becomes 0% similarly in all cases, except when the mineral rate is 100%. However, the degree of liberation becomes highest when the density of all particles, except for the liberated mineral matter, is the minimum in each density fraction (maximum liberation case). In this calculation, in order to make the mineral rate that exists as locked particles the lowest, the mineral matter is allocated as locked particles in the order of higher density minerals to lower ones. In the case of Fig. 5(a), the case in which the density of locked particles made of pyrite and coal substances is 2.50 g/cm3 is considered first. In the NM sample, since all coal substances were allocated to the locked particles with pyrite, it was considered that the remainder were liberated minerals. Here, the density of coal substance (dC ) has to be decided for the calculations. The dC in this study was obtained by the following equation using the average density of mineral matter (dM ) in each density fraction, which was computed by the data in Table 7. dC ¼
dP dM CC dM dP CM
ð5Þ
Here, dP is the mean density among each density fraction. Since the exact density could not be calculated for the density fraction over 2.50 g/cm3 which included little coal substance, the coal substance density 1.34 g/cm3 of the 1.50–1.70 fraction, whose density was comparatively high and included lots of coal substance, was used here. As the density of pyrite and coal substance are 5.03
2.66 2.67 2.63 2.64 2.64 2.68 2.69 2.80 3.88 86.4 6.38 0.69 MM: mineral matter, CS: coal substance, mineral ash: ash content of mineral matter, CC ¼ 100 CM . a Inherent ash was estimated as 0.75%. b Mineral composition calculated from the oxide data of 1.25–1.30 fraction.
7.07 92.62 7.38 0.03 0.20 0.05 0.05 0.36 0.11 6.04 Feed
0.56
85.7 85.6 86.6 87.0 86.8 86.5 85.5 84.9 73.2 0.76 0.79 2.12 6.63 14.65 28.42 53.39 82.14 72.81 0.74 0.74 0.73 0.69 0.62 0.50 0.28 0.02 0.00 1.50 1.53 2.85 7.33 15.27 28.92 53.67 82.16 72.82 99.2 99.1 97.5 92.4 83.1 67.2 37.6 3.2 0.6 0.8 0.9 2.5 7.6 16.9 32.8 62.4 96.8 99.4 0.0 0.0 0.0 0.0 0.1 0.3 0.4 1.8 1.6 0.0 0.0 0.1 0.1 0.3 0.9 2.0 8.0 64.9 0.0 0.0 0.0 0.0 0.0 0.1 0.9 3.4 2.9 0.0 0.0 0.0 0.0 0.0 0.7 1.3 3.8 0.0 0.0 0.0 0.0 0.3 0.5 3.0 4.7 4.1 0.0 0.0 0.0 0.0 0.0 0.1 0.4 1.9 7.8 2.2 0.7 0.8 2.3 6.6 14.7 24.2 47.0 44.5 26.6 )1.25b 1.25–1.30 1.30–1.35 1.35–1.40 1.40–1.50 1.50–1.70 1.70–2.50 2.50–2.96 +2.96
0.1 0.1 0.1 0.6 1.2 3.2 4.2 23.4 1.2
Anatase (%) Dolomite (%) Illite (%) Calcite (%)
RMx2:50 ¼
Kaolinite (%)
Quartz (%)
45
(dM1 ) and 1.34 g/cm3 (dC ), respectively, the weight percentage of pyrite for a 2.50 g/cm3 particle (RM12:50 ) was decided as 63.2% by the following equation:
Fraction
Table 7 Mineral composition of NM sample calculated by norm calculation
Pyrite (%)
Others (%)
Total (CM ) (%)
CS (CC ) (%)
Ash content (CA ) (%)
Ash in org. (CC i) (%)a
Ash in inorg. (CA CC i) (%)
Mineral ash (ðCA CC iÞ=CM ) (%)
Density of MM (dM ) (g/cm3 )
T. Oki et al. / Minerals Engineering 17 (2004) 39–51
dMx ð2:50 dC Þ 2:50ðdMx dC Þ
ð6Þ
Since the pyrite content in this fraction is 8.0%, 4.7% (8:0 ðð1 0:632Þ=0:632Þ) of coal substance is necessary in order to allocate the whole amount of pyrite as locked particles. However, as the coal substance (CC ) in this fraction is 3.2%, the allocation ends halfway for pyrite as mentioned above. Therefore, all of the coal substance (3.2%) and 5.5% (3:2 ð0:632=ð1 0:632ÞÞ) of pyrite exist as locked particles. This result shows that at least 8.7% (3.2 + 5.5) of the particles among the 2.50– 2.96 g/cm3 fraction must be locked particles (refer to Fig. 5(a)). By the same calculations, 2.2% of the particles must be locked particles for the +2.96 g/cm3 fraction. 91.3% of mineral matter in the 2.50–2.96 g/cm3 fraction and 97.8% of mineral matter in the +2.96 g/cm3 fraction could be expected to exist in maximum as liberated particles, so MLmax was calculated as 3.0% (2:93 0:913 þ 0:34 0:978) from the mineral percentage of both fractions for the total mineral matter, which were 2.93% and 0.34% (refer to Table 8). In the case of another sample, if coal substance remains even after it is allocated to locked particles with pyrite of a density of 2.50 g/cm3 , then the locked particles of 2.50 g/cm3 with anatase, which has the second highest density, will be considered next. The allocation of coal substance continues one by one in order to lower the density minerals until all coal substance is allocated (refer to Fig. 5(b)). In addition to this, if the threshold value is except 100% (liberated) in this calculation, the percentage of locked particles whose mineral rate is more than the threshold value can be calculated. Therefore, the mineral rate distribution of locked particles can also be acquired by repeating the calculation with different threshold values. The details are abbreviated here from the limit of space in this paper. The calculation results of MLmax computed in the same way for the four samples used in this study are shown in Fig. 6. The MLmax of each sample was N coal < H coal among the same particle sizes. This shows that the MLmax of H coal, whose main mineral is quartz, becomes higher than that of N coal, which includes kaolinite as the main mineral. Among the same kinds of coal, each MLmax shows the same relation of coarse particles < fine particles. The relation of MLmax in these samples reflects the property of coal by coal kinds and particle size well. It is impossible to obtain more detailed particle information for liberation from the sink–float separation data. Although MLmax is not the true degree of liberation, it can be utilized as a substitution value, because the value shows that the acquirable information of
46
T. Oki et al. / Minerals Engineering 17 (2004) 39–51
(b) Example
(a) NM sa sample
Locked mineral particles
Liberated 91.3%
Locked 8.7%
100 Mineral percentage in each particle
100 Mineral percentage in each particle
Liberated mineral particles
95
Minimum liberation liberat ion case
(Every (Every mineral mineral exists exists as as locked locked particles) particles)
90 85 80
Maximum liberation case
75 70
Locked mineral particles (coal substance and pyrite)
65
95 Coal substance and calcite
90 85
Coal substance and dolomite
80 75 70 65
Coal substance and anat anatase ase
Coal substance and pyrite
60
60 0
10
200
330
400
550
60
700
880
900 100 0
Weight percentage
1 10 20 30 40 50 60 70 80 900 100 Weight percentage
Fig. 5. Calculation diagram of maximum and minimum degree of mineral matter liberation in 2.50–2.96 specific gravity fraction: (a) NM sample, (b) example.
locked particles is not contradictory to the true information.
4. Effect of condition and accuracy of each parameter on MLmax
group. Therefore, the error of norm calculation mainly arises from the rate of mineral phases inside each group, and it is thought that errors beyond groups cannot easily occur. From these results, it is expected that the influence of the error on the accuracy of the MLmax is comparatively small, in spite of the low accuracy of the norm calculation.
4.1. Effect of accuracy of norm calculation Different values of MLmax will be obtained using the computing method of norm calculation and inherent ash, and by the density of fractions, because the accuracy of locked particle information changes according to which method and densities are employed. In this section, the error factors by different measuring processes are investigated. The accuracy of norm calculation was verified first. Since determining mineral phases by norm calculation is not very accurate, different values are obtained using a different calculation process. However, the parameters that contribute to the accuracy of MLmax consists of only the ash content and the density of the mineral matter. Therefore, even if an error exists in the percentage of each mineral phase, it will not lead to a lessening of the accuracy of MLmax when the ash content and the density are the same. Table 9 shows the classified results of the mineral phases mentioned in this study according to ash content and density. The minerals can be classified into four groups. The main components in each group are the characteristic elements, namely, Si and Al in the high ash–low density group, Ti in the high ash–high density group, Ca and Mg in the low ash–low density group, and Fe in the low ash–high density
4.2. Estimation of inherent ash and effect of low density fraction The error of the estimated value which has been derived from the intercept of the extrapolated line is verified here. The estimated value in the NM sample when the density of the minimum density fraction was changed to 1.25, 1.30, and 1.35 g/cm3 is shown in Fig. 7. Although the estimated value was 1.5% in the case of the minimum density fraction at 1.25 g/cm3 , it changed to 1.3% at 1.30 g/cm3 and 0.2% at 1.35 g/cm3 . This means that a lower value was shown as the estimated value by mistake, with the increase of density of the minimum density fraction. This is because the estimated value is strongly influenced by the change of the amount of ash in fractions of the higher density side, with the increase of the density in the minimum density fraction. Thus, since the estimated value by the intercept of the extrapolated line changes by the minimum density of fraction, the minimum density fraction of each sample needs to be as small as possible in order to compare the MLmax of a different sample in the same accuracy. More accurate data is required to determine the standard of the minimum density for the sink–float separated frac-
Table 8 Calculation sheet of MLmax for NM sample Calculation steps 1
2
3
4
Theoretical ratio (wt.%) in a particle with the lowest density in each fraction
Wt.% of CS or each mineral in each density fraction
Wt.% of liberated and locked components in each density fraction
Wt.% of each components for final calculation of MLmax
Locked-2; . . . ; nb
Locked-1
Density fraction (g/cm3 ) 2.50– 2.96 +2.96 a
Pyrite
d
e
f
g (f b=a)
h
i (h d=c)
j (f þ h ¼ 100)e)
l k (e a=b)a ( ¼ e)
m (k þ l)
n 100 m
o
CS (CC )
Pyrite (CM1 )
CS allocated to pyrite
Other MM (CM2; . . . ; n)
CS allocated to other MM
Total MM (CM )c
Locked MM a
Locked CS
Locked particles
Liberated MM
5.03e (RM1 )f
CS 1.34 e (1 RM1 )
– – (RM2; . . . ; n)
CS 1.34 (1 RM2; . . . ; n)
63.25
36.75
–
–
3.20
8.02
4.66
88.78
–
96.80
5.51
3.20
8. 71
91. 29
74.60
25.40
–
–
0.57
64.87
22.09
34.56
–
99.43
1.67
0.57
2.24
97. 76
General formula of the locked MM is ( " ) # n1 n1 X X 1 RMn 1 RMx RMn Locked MM ¼ CC ; ðCMx Þ þ CMn CMx RMn RMx 1 RMn x¼1 x¼1
p
q (p j=o)
r (n q)
s P ( r)
MM in Weight feed in each (CM )d fraction
MM/ MM in feed
Liberated MM
MLmax
7.38
0.223
2.925
2.67
3.00
0.025
0.337
0.33
T. Oki et al. / Minerals Engineering 17 (2004) 39–51
Symbol for calculation a b c
RM1 Mn but, when CC < CM1 1R , namely, e < g is satisfied like NM sample, the equation can be simplified to ¼ CC 1R is, e ab in this table. RMn M1 b No data for NM sample in this study. c CM in each density fraction. d CM in feed sample. e Density of CS and each mineral (g/cm3 ). f RMx : theoretical ratio (wt.%) of a mineral phase locked with coal substance in a particle with the lowest density in each density fraction.
47
48
T. Oki et al. / Minerals Engineering 17 (2004) 39–51
1.5
0.2% 1.3% 0
1.25
10
1.30
Float (%)
20 30
1.35
40 50 60
1.40
70 80 0
1
2
3
4
Fig. 6. The maximum degree of mineral matter liberations.
tion. However, estimating from these results, when the weight of the minimum density fraction is less than 10%, it can be considered that the intercept value of the extrapolated line, namely, the inherent ash content, can be estimated just as accurately. In this study, since the minimum density fraction of every sample was 1.25, an extremely precise value was obtained for an estimated value by extrapolation. The estimated value of the NM sample was around 1.5%, and was also almost the same for other samples. However, is this ash content really the value of particles containing only inherent ash? The main elements of inherent ash have been considered to be Ca, Na, K, Mg, Ti, etc. (Joseph and Forrai, 1992; Ward, 2002); however, the main components of ash in the 1.25–1.30 g/cm3 fraction, which had almost the same ash content (1.53%) as the estimated value, were SiO2 (0.64%) and Al2 O3 (0.60%). Since most of the inherent ash is considered to consist of clay minerals, the estimated value of 1.5% would be too large for inherent ash. Therefore, from the data in this study, the only certain thing is that the inherent ash is between 0% and 1.5%. In this study, 0.75% of that mean value was adopted as the inherent ash temporarily. If the
5
6
7
8
9
Fig. 7. Estimation by extrapolation of ash content of the minimum ash particle in NM sample.
real inherent ash is somewhere between 0% and 1.5%, the range of MLmax can be computed to be 3.0% ± 0.3% in the NM sample, and to be 16.4% ± 1.2% in the HF sample, when inherent ash was set as 0.75%. As the possibility of true inherent ash being 0% or 1.5% is very low, it is presumed that the actual error range is even smaller. Although further study is necessary to determine the accurate inherent ash content, the influence on the MLmax is comparatively small for every value in the predicted range of inherent ash. 4.3. Effect of the highest density fraction The maximum density of heavy media is usually around 1.7–2.0 g/cm3 . However, separating at around 2.5 g/cm3 is effective in strictly limiting the density fraction, including liberated particles. The MLmax was calculated when only one density point at 1.70 or 2.50 g/ cm3 was set as the separation density in the higher density side. The results are shown in Fig. 8. In the previous section, MLmax was calculated by two density
Table 9 Classification of mineral groups in coal to estimate the degree of liberation Mineral groups
Density
Mineral phases
Ash content (%)
Si
Al
Fe
Ti
Ca
Mg
Na
K
High ash–low density
2.61 2.65 2.75a
Kaolinite Quartz Illite
93.5 100.0 95.5
·
·
·
·
High ash–high density
3.90
Anatase
100.0
Low ash–low density
2.71 2.94
Calcite Dolomite
56.0 60.9
3.94 5.03b
Siderite Pyrite/Marcasite
69.0 66.7
Low ash–high density
(·) Not counted in this study. a Typical density. b Average density of pyrite from 4.95 to 5.1.
10
Ash content (%)
T. Oki et al. / Minerals Engineering 17 (2004) 39–51
49
Fig. 8. The MLmax estimated using several specific gravity fractions.
points of 2.50 and 2.96 g/cm3 . But the MLmax calculated by only one density point at 2.50 g/cm3 also shows almost the same accuracy. When 1.70 g/cm3 was set as the maximum density fraction, the HF sample, which showed a relatively high MLmax , showed a good MLmax value, but in other samples of the lower MLmax , higher values were calculated, and an accurate value could not be acquired. This is because the theoretical top limit of the degree of liberation was evaluated from the percentage of particles that certainly exist as locked particles in this estimation method. When the MLmax is estimated at 1.70 g/cm3 of the maximum density fraction in a sample with low MLmax , the accuracy of the MLmax becomes lower because the rate of the locked particles increases a great deal. Next, the difference between the MLmax determined in this study and simple indices customarily used in other estimating methods were compared. Table 10 shows each commonly used index and the MLmax when the
maximum density fraction is 1.70 and 2.50 g/cm3 . CPþX =CA is the index assumed that all particles of densities more than X (1.70 or 2.50 g/cm3 in this study) are liberated mineral matter, and the percentage of that to total ash is defined as the degree of mineral matter liberation. CAþX =CA is the index used when the ash percentage included in the density fraction over X to total ash is defined as the degree of mineral matter liberation. These two are the indices on ash base. CMþX =CM is the index used when the mineral percentage included in the density fraction over X to total mineral is defined as the degree of mineral matter liberation, using data in the mineral base which has been computed in the previous section. In addition, the fourth index is MLmax , which takes into consideration the kind of mineral phases. The upper four cases in the table (NM , NF , HM , HF ) show the results for the samples used in this study. Setting the MLmax at 2.50 g/cm3 of the maximum density fraction (bold letter) as a standard value, each index at 1.70 g/
Table 10 Comparison of the results of rough estimations of the degree of mineral matter liberation and the results of MLmax Sample
Maximum specific gravity fraction: 1.70 CPþ1:70 =CA
CAþ1:70 =CA
CMþ1:70 =CM
MLmax
CPþ2:50 =CA
CAþ2:50 =CA
CMþ2:50 =CM
MLmax
NM NF HM HF
38.6 47.2 25.9 60.3
21.7 25.4 16.3 34.1
24.2 28.7 18.5 38.0
12.5 13.3 13.1 16.8
3.5 6.5 7.1 16.0
2.9 5.4 5.7 15.1
3.3 6.2 6.8 16.5
3.0 5.9 5.9 16.4
16.6 16.6 16.6
11.6 11.6 11.6
13.0 13.4 13.8
5.0 33.6 63.7
M1 M2 M3
Maximum specific gravity fraction: 2.50
50
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cm3 shows a value which is greatly different from it. Also, at 1.70 g/cm3 of the maximum density fraction, although even the order of the degree was not correct for the three indices, only the MLmax showed the same order as the standard (NM < NF ¼ HM < HF ). However, when the maximum density fraction was set to 2.50 g/cm3 , every index indicated a value near to the MLmax . This is because most mineral matter in every sample in this study belonged to the ‘‘high ash–low density group’’ of Table 9, so the ash content of the +2.50 g/cm3 fraction was near 100%. Accordingly, the value of each index was calculated using imaginary samples for cases in which the samples included many kinds of minerals from different groups. In each model sample (M1 , M2 , M3 ), it was assumed that the particles with a density of less than 2.50 g/cm3 was completely the same component as the HF sample, and that the ash contents in the fraction more than 2.50 g/cm3 were 70% (the HF sample was 94.7%). The mineral phases of the model samples were assumed to consist only of quartz and pyrite. In the M1 sample, the ash content of 70% in the density fraction greater than 2.50 g/cm3 consisted of 60% of SiO2 and 10% of Fe2 O3 . Similarly, it was assumed that M2 was 55% of SiO2 and 15% of Fe2 O3 , and that M3 was 50% of SiO2 and 20% of Fe2 O3 , respectively. All other conditions, such as the density of the coal substance and inherent ash content, were set the same as the HF sample. From the results of the calculation, since the MLmax showed a completely different value from the other indices in the model samples, it was shown that the commonly used indices cannot show the true value when a lot of mineral matter, except for the mineral matter in the ‘‘high ash–low density group’’ in the fraction more than 2.50 g/cm3 , is included. From the above results, it was concluded that while it is important to take the maximum density fraction around 2.5 g/cm3 in order to estimate the degree of mineral matter liberation with high accuracy, it is crucial to compute the MLmax , in order to investigate the coal samples with various mineral compositions. In this section, the usefulness of MLmax and the effect of each parameter on MLmax have been investigated. But the model sample whose ML is known has not been investigated here. The error range of the data of each analysis for sink–float separation and mineral composition has neither been included into the consideration. Therefore, the real accuracy of MLmax could not be strictly evaluated and these will be a future work of our study.
5. Discussion and conclusions Here, the most convenient operation process was investigated by assuming the actual MLmax of an unknown sample. To calculate the MLmax , sink–float sep-
arations in the low density side have to be carried out to estimate the inherent ash content, and ones in the high density side have to be done to finally fix the MLmax . As the investigations here show, accurate measurement of the inherent ash content is essentially difficult, and there is no other choice but to improve the accuracy of the estimation by the intercept of the extrapolated line. When a density less than about 10% in weight percentage of the minimum density fraction was taken, the inherent ash content could be estimated by separation at only one density in the low density side, since it could be considered that the ash content of that density fraction is almost the same as the estimated value by the intercept of the extrapolated line. In the high density side, just one separation at around 2.50 g/cm3 was required, as mentioned in the previous subsection. Thus, the simplest process of measuring the MLmax is to obtain the weight percentage, ash content, and ash element data by XRF for three density fractions separated at one density point in the low and high density side (ex. 1.30 and 2.50 g/cm3 ). Here, the density of coal substance is calculated from the intermediate density fraction (ex. 1.30–2.50 g/ cm3 ). The MLmax can be obtained by this easy procedure, and this is useful as a new index to assist the original sink–float separation data. The results are summarized as follows. (1) The content of inherent ash was estimated by the intercept of an extrapolated line of the characteristic curve in the washability diagram. However, since it was judged that the estimated value was too large, the real inherent ash could not be simply measured. In this study, the mean value between 0% and the estimated value was temporally used as the inherent ash content. When the percentage of the minimum density fraction was 10% or less, the ash content in that fraction could be regarded as the estimated value, and it was possible to estimate the inherent ash content with sufficient accuracy by the separation at one density point. (2) It is generally difficult to determine mineral phases with high accuracy by norm calculation. However, only the distribution of the ash content and the density of the mineral matter influences the degree of liberation. Since the main ash elements of the four mineral groups which are classified by ash content and density are different, the effect of the determination error by norm calculation on the accuracy of the degree of liberation is small. (3) For separation in the high density side, separation at one density point around 2.5 g/cm3 , which is close to the minimum density of the mineral phase in coal, is sufficient. The MLmax , which is the theoretical maximum degree of mineral matter liberation, can be obtained by computing the rate of particles that would certainly become locked particles among the particles in the maximum density fraction. Although the true degree of liberation would surely become smaller than this, the MLmax is an index which accurately reflects the particle
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