ON THE ISSUE OF FRACTIONAL ANALYSIS OF COAL FINES

B. A. ZEMLYAKOV, N. K. BELOGLAZOV

(Presented by the scientific seminar of the Department of Mineral Beneficiation)

Until recently, coal fines of the 1–0 mm and 0.5–0 mm size classes were not subjected to fractional analysis in production. Earlier, 10–15 years ago, when the yield of fines in coal sent for beneficiation was comparatively small, and the imbalance of coking coals was not felt as strongly as it is now, the fines did not receive proper attention, and they most often went as an admixture to the concentrate or to the middlings product in an unbeneficiated form [1]. In subsequent years, owing to the enormous growth in the mechanization of coal mining and transportation, the yield of small size classes increased sharply and, at individual mines supplying coals for coking, exceeds 25–30% [2]. The ever-increasing requirements of the metallurgical industry for coal quality lead to the necessity of beneficiating coal fines. It is known that only knowledge of the theoretically possible beneficiation indices makes it possible to judge the correctness of the choice of beneficiation method, the efficiency of operation of the beneficiation equipment, etc. Therefore, the investigation of coal fines with respect to washability is becoming an urgent necessity.

Fractional analysis of coal powders may be carried out by separating free coal grains in heavy liquids in high-speed centrifuges. A number of works by various researchers have been devoted to the development of this question [2, 3, 4]. GOST 4790-58 provides for the stratification of coal fines in a laboratory-type centrifuge TsE-3. However, investigations of the stratification process carried out by the Laboratory of Centrifugal Methods of Beneficiation of the NIIUgleobogashchenie showed that stratification in a test-tube centrifuge makes it possible to draw the most accurate conclusions regarding the washability of coal fines only after three stratifications. A single stratification leads to significant errors [5].

Thus, the existing methods are complex, require special installations, and take much time. Therefore, they cannot be widely used in beneficiation practice and, in essence, still remain the province of scientific-research laboratories.

K. K. Dell [6] proposed a method of graphically representing the washability of coal as a function of the size of its particles by means of the Mayer curve and its use for determining the fractional

of the composition of samples, including the fine classes. Dell’s method consists in finding an extrapolated curve of the fractional composition of the sample from the fractional composition of the coarse classes. This method does indeed make it possible to obtain an extrapolated curve that, to one degree or another, corresponds to the fractional composition of the entire sample. However, such a curve reflects the dependence of ash content on the yield of any part of the sample and is in no way connected with the specific gravities of the fractions. It follows from this that neither the fractional composition of the entire sample nor the fractional composition of the coal fines can be determined from the extrapolated curve.

Below, the method developed by the author of the article for determining the fractional composition of coal fines is considered.

Hard coal is not a monomineral substance and, in its composition, may rather be assigned to polymineral than to monomineral substances. Consequently, if coal is divided into a number of parts (for example, according to specific gravity), then each of the parts may be regarded as an independent, simplest, as it were monomineral, product distinct from all the other parts, with its own characteristic properties. With such a conception, each separate fraction of hard coal must be a carrier of certain properties and regularities.

If the distribution of coal particles by size classes obeys a definite regularity [7, 8], then the granulometric characteristic of a separate coal fraction must also obey a quite definite regularity, which may be expressed in the form of an analytical dependence.

Fig. 1. Determination of the yield of the 0.63–0 mm class of the light fraction. Hard coal from the “Krasnogorskaya” mine (Kuzbass).

1) Size characteristic of the light fraction (cl. 60–0 mm); 2) yield of the 0.63–0 mm class is equal to zero; 3) yield of the 0.63–1 mm class is equal to 5%; 4) yield of the 0.53–0 mm class is equal to 15%.

In Fig. 1, curve 1 shows the granulometric composition of the light fraction of hard coal from the “Krasnogorskaya” mine of Kuzbass. The data for constructing curve 1 are given in Table 1 [9].

Table 1

Screen composition of the light fraction of hard coal from the “Krasnogorskaya” mine of Kuzbass [9].

The size characteristics of individual specific-gravity fractions of hard coal in logarithmic coordinates are represented in the form of straight lines, the equation of which, analogous to the equation for the size characteristic of hard coals [8], for the present case may be written as follows:

\[ Y=\frac{CX^n}{1+qCX^n}, \tag{1} \]

where \(X\) is the particle size of the given fraction, to which their cumulative undersize yield \(Y\) corresponds; \(C\), \(q\), and \(n\) are constants determined experimentally.

The parameter \(C\) characterizes the yield of particles of the fraction smaller than the unit used to measure the diameter of its grains. Taking the logarithm of equation (1) gives the equation of a straight line

\[ \lg(Y^{-1}-q)=-n\lg X-\lg C, \tag{2} \]

from which it follows that \(\lg C\) is the initial ordinate of the size-characteristic curve of the fraction in the coordinates \(\lg(Y^{-1}-q)\), \(\lg X\). The value of the coefficient \(C\) can be determined from the equation

\[ C=\frac{1}{(1-q)M^n}, \tag{3} \]

where \(M\) is the diameter of the largest particles of the fraction.

The parameter \(q\) characterizes the granulometric composition of the fraction. Under the condition of selecting values of the cumulative yields of fractions corresponding to the ratio \(X_1:X_2=X_2:X_3\), the parameter \(q\) can be calculated from equation (4) [10].

\[ q=\frac{Y_2^2-Y_1\cdot Y_3}{Y_2\left(Y_1\cdot Y_2-2Y_1\cdot Y_3+Y_2\cdot Y_3\right)} . \tag{4} \]

The parameter \(n\) reflects the character of the distribution of the particles of the given fraction by size classes. It is characterized by the degree of curvature of the size-characteristic curve of the fraction in the coordinates \(Y, X\), and in logarithmic coordinates \(\lg X, \lg (Y^{-1}-q)\) is equal to the tangent of the angle of inclination of the straight size-characteristic line to the abscissa axis \((\lg X)\).

\[ n=\frac{\lg (Y_1^{-1}-q)-\lg (Y_2^{-1}-q)}{\lg X_2-\lg X_1}. \tag{5} \]

If, from the composition of the given fraction, represented by curve 1, the class \((0.63\text{–}0\ \mathrm{mm})\) is removed, then the remaining part of the fraction will be represented on the same graph by curve 2. If the yield of the light fraction into this class is set equal to 5%, curve 3 is obtained. If the yield of this fraction is taken as 15%, curve 4 is obtained. The best straightening of the size characteristic of the light fraction in this example occurs when its yield into the class \((0.63\text{–}0\ \mathrm{mm})\) is equal to 9%. In this case the absolute error in determining the yield of the light fraction into the class being determined was \(\Delta=0.2\%\), and the relative error was \(\Delta'=3.0\%\). The calculated straight line of the size characteristic of the light fraction practically coincided with curve 1. An analogous picture is observed for all fractions of hard coal.

Thus, an excess or deficiency of fines in the granulometric composition of a fraction, as was observed earlier also for the whole coal [11], leads to a deviation of the end points of the size characteristic in logarithmic coordinates from the straight line drawn through the remaining experimental points. Moreover, when the yield of fines of the given fraction is insufficient, the end points of the characteristic deviate upward, and when it is excessive, downward. Consequently, from the deviation of the end points of the curves of the sieve composition of a fraction in the region of the fine classes, one can judge the granulometric composition of the given fraction and the correctness of determining the fractional composition of the fines.

The method for determining the yield of fines of any fraction is reduced to establishing the yield of the class being determined in the given fraction at which the end point of the curve of the size characteristic of the fraction will lie on the straight line drawn through the remaining experimental points. In practice this amounts to the following: after specifying the yield of fines of the given fraction, one should calculate the cumulative yield of particles of various size classes of the fraction by minus \(Y^{-1}\) and the function \(\lg (Y^{-1}-q)\), and then, from the data obtained, construct the size-characteristic curve of the fraction in the coordinates \(\lg (Y^{-1}-q);\ \lg X\). If the end point of the size characteristic lies on the extension of the straight line drawn through the remaining experimental points, then the adopted yield is the true yield of the given class of the fraction.

In an analogous way, the yield of hard-coal fines of all separately taken fractions can be established, or, in other words, the fractional composition of the fines.

In Fig. 2 are given curves of the size characteristics of fractions of hard coal from the “Vladimir” seam (the calculation data are given in Table 2).

As is evident from the graph, the size characteristics of the light and heavy fractions without the class \((0.5\text{–}0\ \mathrm{mm})\) have a characteristic upward deviation of the end points (curves 1; 4). Straightening of the characteristics

Fig. 2. Curves of size characteristics of specific-weight fractions. Coal of the “Vladimir” seam (Donbass):
1) light fraction without the 0.5–0 mm size class; 2) light fraction, 50–0 mm size class; 3) heavy fraction, 50–0 mm size class; 4) heavy fraction without the 0.5–0 mm size class.

Table 2

Determination of the yield of the 0.5–0 mm size class of the light and heavy fractions of coal from the “Vladimir” seam

size fractions was obtained with a yield of the light fraction of the \((0.5—0\ \mathrm{mm})\) class equal to 7%, and of the heavy fraction of the same class equal to 0.5% (curves 2; 3).

A check on the correctness of the determination carried out may be provided by adding the yields of fines of all fractions of the given class. Their sum must be equal to the yield of fines of this class according to the sieve analysis. In the example considered, the yield of the sum of the light and heavy fractions was found to be 7.5%. The discrepancy between the calculated yield of the sum of fractions of the \((0.5—0\ \mathrm{mm})\) class and the actual yield of this class was \(\Delta = 0.14\%\), and the relative error \(\Delta' = 2.0\%\).

The recovery of combustible matter and of rock in a fraction may be regarded as their distribution by size classes. Consequently, by the method described above it is possible to determine the recovery of combustible matter and rock into the fine classes of a sample.

The method of representing the fractional composition of coal in the form of the granulometric composition of individual fractions makes it possible, with its aid, to solve a whole series of problems connected with coal cleaning.

The method set forth acquires special value in cases where, for some reason, the finest classes are absent from the sample. Thus, for example, in mines with hydraulic extraction, coal is transported by a stream of water, sampling from which presents considerable difficulties. In such cases, samples are taken either in a vessel with a mesh bottom, through which fine coal particles pass together with the water, or in a settling tank, into which return water, contaminated with fine particles of coal and rock that have no direct relation to the given sample, enters together with the coal. As a result, in both cases the sample, as a rule, is not representative with respect to the composition of the fine classes. The method considered makes it possible in this case as well to determine the fractional composition of the fines of the seam being worked.

Conclusions

1. The distribution of particles of individual fractions of hard coal by size classes obeys a quite definite regularity, which can be expressed by equation (1).

2. Equation (1) makes it possible, from the fractional composition of the coarse classes of a sample, to determine the fractional composition of the fines without separating them in heavy liquids, which is of special value in cases where fine classes are absent from the sample.

Literature

1. Proceedings of the Conference on Dewatering the Products of Cleaning at the Coal-Preparation Plants of the Donbass. Moscow–Kharkov, 1952.

2. Davydkov N. I. Fractional analysis of coal fines. Problems of Coal Cleaning and Briquetting. Collection of VUGI, 9, 1953.

3. Zarubin S. L. Laboratory centrifuge for fractional analysis of coal fines. Information Collection on Coal Cleaning and Briquetting, 4, Ugletekhizdat, 1957.

4. Korshunov V. I., Demidov L. G. Methods for investigating the washability of small-grained and fine-grained coal classes. Transactions of the Institute of Fossil Fuels, Academy of Sciences of the USSR, vol. 6, Moscow, 1955.

5. Borts M. A., Skvortsov M. N. Method for separating coal fines in heavy liquids. Collection of NIIUgleobogashchenie, 15, Moscow, 1960.

6. Dell C. C. The effect of size on Coal-cleaning results. Collery Eng. 395, 396, 1957.

7. Verkhovsky I. M. Fundamentals of Designing and Evaluating Processes for the Cleaning of Mineral Resources. Ugletekhizdat, Moscow–Leningrad, 1949.

1. B. A. Zemlyakov. Equation of the granulometric characteristic of hard coals. Izv. vuzov, Mining Journal, 8, 1959.

2. A. A. Popov. New equipment for coal-preparation plants. Collection of the Institute NIUIugleobogashchenie, Moscow, 1960.

3. B. A. Zemlyakov, N. K. Beloglazov. Distribution of combustible matter and rock in hard coals by size classes. Izv. SO AN SSSR, 9, Novosibirsk, 1961.

4. B. A. Zemlyakov. Determination of the yield of fine size classes of material when they are absent from the sample subjected to investigation. Mining Industry of Kazakhstan, 6, Alma-Ata, 1960.

5. Geological-chemical map of the Donets Basin. Issue 1, GNTI. 1936.