## 3 Materials and Methods
### Microstructural Analysis of Coal Cleats  
The properties of coal cleats were determined by the results of coal microstructural analysis, which included the determination of the cleat width, coal matrix block sizes, and angle between fracture systems. X-ray microcomputed tomography (micro-CT) is a common method to analyze rock fractures [13; 28; 29]. It is a nondestructive technique that produces rock three-dimensional images on the basis of the variation of X-ray attenuation in an object. This technique provides a high-resolution study of the coal microstructure, which is important to model filtration processes and numerical estimates of permeability [29]. In [PERSON] et al. (2016), a structural model was made on the basis of micro-CT in situ imaging, and the expected effect of coal compression on its porosity and permeability was estimated [13]. It was found that with an increase in the effective stress from 0 to 10 MPa, the width of the cleats decreased from 0.52% to 0.22%. The established morphological features of fractures were consistent with the results of filtration tests [13]. The averaged features of the coal microstructure were of interest in regional studies. Primarily, the fracture parameters (length, width, interval between cleats, etc. ), characteristic of the region as a whole, can be studied using less detailed and expensive methods of optical and electron microscopy. The standard method was to measure the required parameters along 1D scanlines or line profiles. This method has several excellences: (1) it is a relatively easy and quick method; (2) several related characteristics are measured together, such as fracture width and fracture spacing; and (3) the application of the technique does not depend on the lithological composition of the rock samples and the scale of observations [30]. To perform the experiments, we used cylindrical samples drilled perpendicular to the butt cleat direction, i.e., in the direction of the maximum coal permeability. The analysis of the coal microstructure was carried out along the core longitudinal section and perpendicular to the face and butt cleat directions (plane \(\alpha\)) and in the plane \(\beta\) (core end surface) (Figure 3). The sample surfaces were finally treated using a thin diamond paste with abrasive granules less than 0.05 micrometers (\(\upmu\)m). Samples were subjected to additional treatment to identify structural defects with internal volume. Before the experiments, the prepared polished sections were saturated by luminophore under a low vacuum to help identify defects with internal volume. With the luminophore, EpOye powder dissolved in alcohol at a 1:40 volume ratio was utilized. Furthermore, we dried the samples for 24 h before starting the experimental studies. A detailed description of the sample preparation is given in an earlier paper [31]. The polished rock sections were studied by reflected light using a Mineral C7 analyzer designed to measure the linear dimensions of the microstructure of solids. The analyzer included an optical microscope OLYMPUS BX51; a digital video camera SIMAGIS 2P-3C; a camera-to-PC interface module with SIAMS Photolab software installed to control sample scanning, image treatment, and analysis; and determination of the microstructure parameters. The main technical characteristics of the analyzer are shown in Table 3[32]. Structural analysis of the tested coal included a measurement of the linear dimensions of the coal matrix block, the cleat width, and the angle between the face and butt cleats. A treatment of images was performed in the \"Measurement of angles and lengths\" module of SIAMS Photolab software and included preliminary treatment with stitching of images, threshold filtering and noise removal, and measurement of the linear dimensions of structural elements (Figure 4). The cleat width is taken as the distance between its two opposite walls along the scanning line. In the samples treated by luminophore, the cleat width was determined by the characteristic glow in ultraviolet light.