Fractal dimension of the morphology on differently oriented surfaces of coal preparations

Choosing the surface of a lump section was justified to determine the degree of metamorphism by the index of gray shade intensity. The main method is optical spectroscopy using a video-optical complex MBI-11, NB 200 with subsequent digital computer processing and calculation of the fractal dimension (Scope photo software) of microphoto images of coal matter preparations by lump sections. The values for the index of gray shade intensity of photographic images of surfaces (section, bedding, cut) for lump sections based on samples of coals of various grades were analyzed. It has been established that the average values of the degree of metamorphism indices for different surfaces of the preparation differ, which is confirmed by low correlation coefficients: 0.585 (section-bedding), 0.666 (section-cut), 0.462 (cut-bedding). It has been found that the fractal dimension, which characterizes the complexity of the morphology of the surfaces under study, reflects an increase in the amount and orderliness of hydrocarbons associated with a change in the degree of metamorphism. It was proven that its most natural decrease related to an increase in the degree of metamorphism, is observed on surfaces perpendicular to the bedding (section).


Introduction
In the process of ensuring one's life activity, humanity is increasingly using both natural and artificially created materials.Their usefulness is determined by their properties, which depend not only on the composition but also on the structure of the materials.It is very problematic to describe the structure of such complex polymers as, for example, coal using Euclidean characteristics (length, width, square, volume).Therefore, "fractal geometry" [1] proposed at the end of the 20th century by B. Mandelbrot aroused great interest among researchers.To date, numerous works have confirmed the fractal nature of the structure of metals [2,3], rubber [4], wood [5], and rocks [6].
We noted some aspects of the fractality of the coal structure in the work [7].
Coal metamorphism is one of the main factors that determine the possibility of its practical industrial use.Indicators of metamorphism serve as the basis for most existing classifications.However, due to the complexity of the research object, the variety of optical characteristics of instruments and measurement methods, the range of changes for each grade is quite large, which leads to overlapping values and, ultimately, ambiguity in determining the degree of metamorphism [8].Therefore, increasing the accuracy of determining the degree of metamorphism is relevant and has practical and scientific significance.
The work [9] proposes a new method for determining the degree of metamorphism based on the index of gray shade intensity (GI) for microphoto images of lump sections in coal preparations with subsequent digital computer processing.Subsequently, the spectral characteristics of this method were refined [10].In these works, the choice of maceral for research (vitrinitis) and the orientation of the observation plane in the preparation (cross-section) were justified, which does not contradict existing standards [11].There was also a significant discrepancy in the values of the "GI" index depending on the orientation of the observation plane.To confirm and explain this fact, it is advisable to carry out a fractal analysis of multidirectional planes of coal preparations.
The purpose of the work is to substantiate choosing the surface of lump sections to determine the degree of metamorphism based on the index of GI using the method of fractal analysis.

Methods
To calculate the fractal dimension in the Scope Photo Image Software [12], microphotographs obtained from each surface are converted to the ImageJ program [13] in binary mode (figure 1).Using the built-in platinum in the same software, we calculate the fractal dimension (figure 2).

Results and discussion
A fractal analysis of multidirectional planes of coal preparations was carried out.Samples were taken from coal beds of various grades: LF ("Blahodatna" mine, bed c1), F-K (Mine named after O.F. Zasyadko, bed l3), and L ("Ilovaiska" mine, bed h10).For each grade, particulate blocks with three polished surfaces were made: along the layering, transverse to the strike, and at an angle of 45°.
On each surface, the values of the "GI" index are determined at ten points.The values of gray shade intensity by vitrinite for all preparations are summarized in table 1.It is obvious that the average values of the degree of metamorphism for different surfaces of the preparation differ, which is confirmed by low correlation coefficients: 0.585 (section-bedding), 0.666 (section-cut), 0.462 (cut-bedding).With the growth of metamorphism, the "GI" index naturally increases in all three directions, but with a different gradient.For one degree of metamorphism, its values in the section can be either greater or less compared to bedding.
The coal preparation lump section, the studied surface of which is parallel to the bedding is a set of macerals formed from plant material and accumulated at the same time (it is a season of the year or period of subsidence of the earth's surface with stable conditions).
If the surface of the preparation is perpendicular to the layering (section), then the visible laminas differ in the time of accumulation of the material by tens and hundreds of years and only subsequently, under the impact of metamorphism, they acquired properties characteristic of the entire coal bed.
A preparation whose surface is made at any angle to the layering (mainly 45°, tangential cut) is, as it were, averaging (figure 3).Since the structures of the preparation surfaces differ, the question arose about using a fractal approach to their characterization for the comparability of measurements of metamorphism degree indices on three planes and choosing the most reliable one.
The values of the fractal dimension of the studied preparations are given in table 2. Macerals on the surfaces of the preparations are located randomly.Therefore, fractal dimension can be used for analysis.The value of the fractal dimension is a measure of complexity and has direct information about the spatial structure of the object.In a section, the fractal dimension decreases linearly with increasing metamorphism and thus can serve as an additional index of the degree of metamorphism.In a tangential cut, it is similar but gentler.On the bedding surface, on medium grades, its value is even less than for the "L" grade.
The formation of the maceral composition of the studied coal beds occurred in the Lower and Middle Carbonic period (C1 -C2).The reconstructed stress field of this period in almost all studies for the Donbas is the same: the maximum stress values (1) are horizontal and directed across the strike of the basin, the average 2 are caused by gravitational forces and are directed vertically downward, the minimum 2 are directed horizontally along the strike of the basin.Under the impact of this field, coalbearing strata accumulated.The stressed state of the massif persisted for a long time.Periodic changes in the magnitude (but not direction) of stress contributed to the formation of layering in coals and rocks.At the same time, the vertical thickness of the coal bed from grade LF to L one decreased by approximately ten times (in the section, the morphology of the surface of the preparation became more uniform and ordered); horizontallythe surface morphology of individual laminas remains virtually unchanged.With the exception of areas damaged by folding and rupturing deformations (longitudinal folds, flexures, etc.).Perhaps this explains the reduced value of the fractal dimension on the "F-K" grades, which are the most fractured in the series of metamorphism [14].
It is obvious that the calculated values of the fractal dimension reflect the impact of the stress state on the morphology of the preparation's surface.This makes it possible to use a vertical surface (section) to assess the degree of metamorphism, and a horizontal one to characterize the stress state.
A comparison of changes in fractal dimension with parameters characterizing the physical and mechanical properties of coals (table 3) shows that during metamorphism only the carbon content unidirectionally changes (increases) (decreasing aliphatics and increasing the number of aromatic rings).It is known that during the process of metamorphism, the proportion of aromatic hydrocarbons and the degree of condensation of aromatic rings increases, which leads to the ordering of the coal structure and an increase in the reflectivity of vitrinite.Fractal dimension decreases with increasing metamorphism and the amount of carbon (aromatic rings) increases.Consequently, in this case, the fractal dimension reflects an increase in the number and the ordering of aromatic rings associated with a change in the degree of metamorphism.However, on bedding surfaces and tangential cuts, the fractal dimension values on coals of the F-K and L grades are close.An analysis of the geological conditions at the mines showed that the coals at the "Ilovaiska: mine (grade L) contain sapropelite small layers, and the transformation of coal containing sapropelites (bed h10) differs from humus.At the final stages of metamorphism, in contrast to humus, the sapropelic substance remains uncrystallized (the number of carbon rings does not increase) [15].That is why only on these surfaces, formed from plant material and accumulated at the same time, the influence of sedimentation features manifested itself.
The most natural decrease in fractal dimension is observed on surfaces perpendicular to bedding (section), so using them to determine the degree of metamorphism based on index of GI is more appropriate.

Conclusions
1. Based on the results of the analysis of statistical characteristics, it was established that the average values of the degree of metamorphism for differently oriented surfaces of the preparation differ, which is confirmed by low correlation coefficients: 0.585 (cut-bedding), 0.666 (section-cut), 0.462 (cutbedding).In general, statistical characteristics reflect the heterogeneity of the data, both depending on the degree of metamorphism and the orientation of the studied surfaces.
2. The fractal dimension, which characterizes the complexity of the morphology of the surfaces under study, reflects the increase in the number and ordering of aromatic rings associated with a change in the degree of metamorphism.Its decrease is most naturally associated with an increase in the degree of metamorphism and is noted on surfaces perpendicular to bedding (section).

Figure 1 .
Figure 1.Conversion of a real microimage (on the left) of the preparation surface to binary mode (on the right).

Figure 2 .
Figure 2. Calculation of fractal dimension in the ImageJ program.

Table 1 .
Indices of gray shade intensity by vitrinite for coals of various grades.
*The average values of the "GI" index are highlighted in bold

Table 2 .
Fractal dimension of differently oriented surfaces of coal preparations.
* The average values of the fractal dimension are highlighted in bold

Table 3 .
Generalized data of elemental composition, physical mechanical properties of coals on the Donbas.