Model development and analysis of coal permeability based on the equivalent characteristics of dual-porosity structure

Mining is a dynamic fracture process of coal and/or rock. The structural failure of coal bodies will change the coal matrix-fracture characteristics and then affect the distribution characteristics of the coalbed methane (CBM). Because of the structural complexity of coal, the coal matrices and fractures will be assumed to the geometries with rule shapes when the gas seepage characteristics in coals are analyzed. The size of the simplified geometries is the equivalent scale of dual-porosity coal structures (i.e. the equivalent fracture width and equivalent matrix scale). In this paper, according to the reasonable assumptions with regarding to dual-porosity coal structures, a new coal permeability evolution model based on the equivalent characteristics of dual-porosity structure (ECDP model) was built and the effect of the equivalent characteristics of dual-porosity structure on the coal permeability evolution law was analyzed. It is observed that if the initial fracture porosity is constant and the equivalent matrix scale increases, the range in which the permeability of coal rises with rising gas pressure increases; if the equivalent fracture width decreases and the equivalent matrix scale is constant, the range in which the permeability of coal rises with rising gas pressure decreases. The ECDP model is more suitable for revealing the evolution law of the coal permeability when large deformations occur in the coal bodies and/or the coal structure is damaged irreversibly, especially during enhancing CBM recovery.

. Simplified models of the dual-porosity coal structure. the coal structure, can be considered a dynamic fracture process of coal (Klepaczko et al. 1984). The structural failure of coal bodies will change the coal matrix-fracture characteristics and then affect the distribution law of the permeability in coal seams, which is closely related to the coalbed methane (CBM) development Wang 2012;Lu et al. 2017;Zhang et al. 2019). In China, the permeability of coal is generally poor but the gas content is relatively abundant, which results in a high risk of coal and gas outburst (Xue et al. 2014;He et al. 2018;Li et al. 2018;Liu et al. 2019). To ensure the safety mining of coal resources and make effective use of the CBM, which is widely considered to be a clean energy resource, Chinese scholars mostly focused on studying the enhanced coalbed methane (ECBM) technique by methods of increasing the permeability of coal seams (e.g. the hydraulic fracturing technique and the relief of ground stress) (Lu et al. 2016;Wang et al. 2017;Zhang et al. 2018;Lin et al. 2019). In the process of improving coal permeability, ground stress is released dramatically, coal matrices are damaged severely and large numbers of new fractures appear (Lu et al. 2017;Chen et al. 2018;Zhang et al. 2018). Therefore, it is extremely significant for the prediction of CBM capacity to scientifically evaluate the impact of coal matrix-fracture characteristics on the permeability evolution law in coal seams.
Generally, when the seepage characteristics of coal is studied, the units that constitute the dual-porosity coal structure (i.e. coal matrices and fractures) are assumed to be the geometries with rule shapes to quantitatively analyze the impact of effective stresses and the sorption deformation of coal matrices on coal permeability (Palmer & Mansoori 1998;Shi & Durucan 2004). The three main simplified structure models of coal are sheet models, matchstick models and cube models (Reiss 1980), which are shown in figure 1.
In the past few decades, large numbers of models characterizing the permeability of coals have been established. In the light of the assumptions of matchstick models and uniaxial strain, Gray (1987) first built a coal permeability model, which involved both effective stresses and the sorption deformation of coal matrices. Then, Palmer & Mansoori (1998) developed an extensively used model using the same assumptions, then the P-M model was amended by adding an additional parameter (Palmer et al. 2007). However, some scholars (Liu & Harpalani 2013) found that the P-M model cannot match some field data well, due to overestimated coal matrix compressibility. Afterwards, using matchstick models, some scholars (Shi & Durucan 2004;Cui & Bustin 2005) also developed their permeability evolution models (i.e. S-D and C-B models) for coal according to the uniaxial strain assumption. According to the constant volume assumption, Ma et al. (2011) built a model for the seepage properties of CBM reservoirs on the basis of the balance of volumes between the bulk coal, and coal pores and solid grains. Considering the influence of the Klinkenberg effect and gas diffusion on coal permeability evolution laws, Liu et al. (2015) proposed a common porosity and permeability evolution model on the basis of the P-M model. According to the assumption of the cube model and triaxial stress, many scholars (Robertson & Christiansen 2008;Guo et al. 2014) also proposed lots of coal permeability evolution models. Liu et al. (2011) studied the relationship of the boundary conditions using a simple 'free expansion + push back' method. Liu et al. (2017) and Lu et al. (2016) developed their coal permeability evolution models according to the different boundary conditions and showed the transformation forms of the coal permeability evolution models under different boundary conditions, respectively.
In the process of low permeability reservoir reconstruction, the change of the coal matrix-fracture structure is a direct factor affecting the permeability of coal seams. However, a few studies have been now carried out regarding the quantitative characterization of coal matrices and fractures on the basis of the dual-porosity coal structure theory. Moreover, many permeability evolution models have been established on the basis of the dual-porosity coal structure theory. However, these models are all relative permeability models, which can describe the impact of effective stresses and the sorption deformation of coal matrices on the permeability evolution law in coal, but the influence of the dual-porosity structural change on the permeability of coal is ignored. Therefore, it is distinctly important to establish a general model that comprehensively includes the impact of the dual-porosity coal structures, effective stresses and the sorption deformation of coal matrices on the permeability of CBM reservoirs.
In this paper, the complex coal structure was simplified in an equivalent way and the equivalent characteristics of the dualporosity coal structure were studied. Based on the assumption of cube models, the coal permeability evolution model based on the equivalent characteristics of dual-porosity structure (ECDP model) was built and validated. Then, the effect of the ECDP structure on the permeability evolution characteristics of coals was analyzed. The ECDP model can be used to reveal the permeability evolution law of coals when the large deformations occur in the coal bodies and/or the coal structure is damaged irreversibly.

Development of the model
The permeability evolution model is a basic mathematic model used to analyze and resolve the gas migration law in coal (Pan & Connell 2011;Lu et al. 2016;Xue et al. 2018). However, the permeability evolution model that can describe the gas migration law in coals under all conditions is extremely complex due to the variation of coal structure (Salmachi & Karacan 2017). Generally, when the coal permeability evolution model is established, the relation between the main control factors and the coal deformation should be studied first, then the mathematic relation between the coal porosity and deformation subsequently analyzed. Finally, the relation between the coal permeability and the main control factors is established based on the quantitative characterization of the relationship between coal permeability and porosity. However, above all, it is necessary to scientifically evaluate the equivalent characteristics of the dual-porosity coal structure.

Equivalent characteristics of the dual-porosity coal structure
Both the equivalent fracture width and equivalent matrix scale are the microscopic characteristic parameters of coal, which are extremely difficult to measure by means of laboratory experiments because of the complicated nature of coal structures. However, based on the simplified structure models of coal, they can be calculated by the inverse analysis method using macroscopic property parameters (i.e. permeability and porosity) of the coal.
Evaluation of permeability based on the equivalent characteristics of the dual-porosity coal structure. The fractures are the main channels for the gas flow in coal. The permeability depends on the direction of gas seepage, which is assumed to be parallel to the fracture planes, as shown in figure 2 (Reiss 1980). In figure 2, the arrowhead represents the direction of gas seepage.
Actually, the fractures between two matrices are very small in coal seams, especially in the coal seams that have coal and gas outburst risk or tectonic coals where the low permeability results in a low gas seepage rate in fractures and gas migration is limited to laminar flow. In light of Darcy's law, gas seepage velocity has a positive correlation with the gas pressure gradient in fractures and the mathematical expression is shown as follows (Reiss 1980;Zhou 1990): where Gas is the gas seepage rate (m s −1 ), k is the permeability of coals (mD), is the kinetic viscosity of gases (Pa⋅s) and ∇ is the Hamilton operator. Combined with figure 2, equation (1) is converted as follows: where H is the depth of the fracture (m). Assumed that a coal body includes many fractures with the same length and width, and their total cross-sectional area is A. Thus, the total quantity of the gas seepage through the coal body is where q n is the total quantity of the gas seepage through the coal body (m 3 s −1 ). The gas flow in coal seams mainly occurs in the fracture system, and the key factor affecting the gas seepage is fracture width. In the 1950s, an experimental study on gas flow in a single fracture was carried out in the laboratory (Zhou et al. 2007;An 2014). According to the experimental results, gas flow in a fracture has a positive correlation with the cube of the fracture width. The results are known as the famous cubic law. The mathematical expression of the cubic law is shown as follows (Reiss 1980): where q 1 is the quantity of the gas seepage through a fracture (m 3 s −1 ), l is the length of fractures in coals (m) and b is the equivalent fracture width in coals (m). Similarly, with regard to the coal body including many fractures with the same length and width, the total gas flow is Combining the equations (3) and (5), coal permeability depending on the scale characteristics of the fracture, can be obtained as follows.
where f s = nl∕A represents the total fracture length per unit cross-sectional area (m m −2 ). For the cube model (Reiss 1980): where a is the equivalent matrix scale in coal (m). Thus, combining the equations (6) and (7), the relational expression between the permeability of coal and the equivalent scale of the dual-porosity coal structure is obtained as follows.
Evaluation of the fracture porosity based on the equivalent characteristics of the dual-porosity coal structure. The equivalent model of the coal fracture porosity is shown in figure 3 (Reiss 1980). In figure 3, the dark part enclosed by the solid lines indicates the coal matrix with sides a 1 , a 2 and a 3 , and the light-colored part outside of the solid lines and surrounded by the dotted lines represents a fracture of the width b. If the volumes of the coal matrices and fractures in figure 3 are V m and V f , respectively, then the fracture porosity f can be defined as Thus, substituting equation (10) into equation (9), we can obtain In general, the fracture dimensions are considerably less than the coal matrix dimensions (i.e. b ≤ a 1 , a 2 , a 3 ) (Reiss 1980). Therefore, equation (11) can be simplified and converted to equation (12) as follows.
For the cube model, a 1 = a 2 = a 3 = a, the relationship between the fracture porosity and the equivalent scale of the dualporosity coal structure can be expressed as follows.
Evaluation of equivalent characteristics of the dual-porosity coal structures. The study on the equivalent properties of dualporosity coal structures is highly significant for the understanding of the gas migration law in coal. If ECDP structures are determined, structure properties of coal matrices and fractures can be introduced when the coal permeability evolution model is established. Furthermore, the initial fracture porosity and initial structure permeability of coal can be more accurately introduced into the coal permeability evolution model when it is used to characterize variation of permeability in coal seams. Combining equations (8) and (13), the equivalent fracture width and the equivalent matrix scale can be calculated as follows.
5 Thus, given the initial fracture porosity and the initial structure permeability of coals, the equivalent fracture width and equivalent matrix scale can be obtained using equation (14).

Mathematical model of the coal permeability evolution law
Influence of the effective stress on the deformation of coals. Based on the principle of effective stresses, total coal strains consist of coal bulk strains and strains of fractures in coal. The increment of coal bulk strains and strains of fractures in coal for effective stress can be expressed, respectively, as (positive in compression) (Detournay & Cheng 1993) where e c is the bulk strains of coals induced by effective stresses, e f is the strain of fractures in coal induced by effective stresses, V e c is the variation of coal volume induced by effective stresses (ml), V e f is the variation of the fracture volume in coal induced by effective stresses (ml), V c is the original volume of coals (ml),̄is the average stress (MPa), is the Biot coefficient of coals K and K f are the bulk moduli of coals and coal fractures, respectively (MPa) and K m is the bulk modulus of coal matrices (MPa). Combining equations (15) and (16), the following relationship expression can be obtained: According to the Betti-Maxwell reciprocal theory (Lu et al. 2016;Li et al. 2017), we can obtain Moreover, the coal bulk modulus is generally much bigger than the bulk modulus of fractures in coal (Guo et al. 2014;Lu et al. 2016); thus, equation (17) can be simplified as follows.
Gas sorption-induced swelling deformation. There are large numbers of pores in the coal matrices, which provide an enormous space for coal to adsorb gas. It is believed that the coal matrices are concatenated with each other by 'coal matrix bridges' (Lu et al. 2016;Liu et al. 2017). Some scholars (Lu et al. 2016;Liu et al. 2017;Zhang et al. 2018) have observed that coal matrix deformation would change the space of fractures. Coal matrices will expand after absorbing gas, which is shown in figure 4. Coal matrix sorption deformation affects not only the volume of fractures in coal but also the coal volume. Therefore, some scholars (Lu et al. 2016;Liu et al. 2017) introduced a parameter f m (i.e. the internal deformation coefficient of the coal), which represents the ratio of the deformation of coal matrices that affects the volume of fractures in coal and changes from 0 to 1. Generally, f m is affected by the coal structural characteristics (Guo et al. 2014). If the deformation of coal matrices is completely used to affect the volume of fracture in coal, f m is equal to 1. If the deformation of coal matrices is completely used to affect the volume of coal, f m is equal to 0. The parameter f m can be obtained by contrasting the sorption deformation of coal matrices and the swelling deformation of coals under the same conditions, or it can be obtained by fitting data using coal permeability evolution models (Lu et al. 2016). According to previous studies (Guo et al. 2014;Lu et al. 2016;Li et al. 2017;Liu et al. 2017), the increments of coal bulk strains and fracture strains in coal for the sorption deformation of coal matrices can be expressed as follows (positive in compression): where a f is the strain of fractures in coals induced by the sorption deformation of coal matrices, a c is the strain of coal bulk induced by the sorption deformation of coal matrices, a m is the strain of coal matrices after absorbing the gas, V a f is the variation of coal volume induced by the sorption deformation of coal matrices (ml), V a f is the variation of fracture volumes in coals induced by the sorption deformation of coal matrices (ml) and f is the fracture porosity of coals.
Combining equations (20) and (21), we can obtain Considering that f is much smaller than 1 (Guo et al. 2014;Lu et al. 2016), the relationships between d a c and d a f can be derived as follows.
Coal permeability model development. According to the definition of the fracture porosity, we can obtain Take a derivative with respect to the above equation, and then we obtain Substituting equation (24) into equation (25), we can obtain where c is the bulk strain of coals and f is the fracture strain in coals. 7 With respect to coal, the increments of bulk strains and strains of fractures in coal for effective stress and matrix sorption deformation can be expressed, respectively, as (Connell et al. 2010;Li et al. 2017) Thus, Substituting equations (19) and (23) into equation (29), we can obtain Then, substitute equation (30) into equation (26), and the following equation can be obtained.
Integrating the equation (31) yields where f0 is the initial fracture porosity of coal. According to the previous study (Cui & Bustin 2005;Zhang et al. 2008;Connell 2009;Hu et al. 2015), coal matrices expand after adsorbing gas, and strain can be characterized using the formula a m = a max p p + p , where a max is the maximum sorption strain of coal matrices and p is the Langmuir pressure of the sorption deformation of coal matrices, which represents the pressure that the matrix sorption strain is half of the maximum matrix sorption strain of coal (MPa). Thus, where a m0 is the coal matrix strain when it absorbs gas at the adsorption equilibrium pressure of p 0 . Substituting equation (34) into equation (32), we can obtain .
Fracture porosity and permeability are parameters widely used to characterize coal permeability evolution model. From equation (14), the quantitative relation between coal permeability and equivalent scale characteristics can be expressed as follows.  Substituting equation (35) into equation (36), we can obtain Above are the mathematical expressions of the ECDP model. In the ECDP model, the effect of equivalent characteristics of dual-porosity structure on coal permeability is considered. Moreover, the internal deformation coefficient of coal is introduced, and the Biot coefficient of coals, which is equal to 1 in some coal permeability evolution models (Palmer & Mansoori 1998;Shi & Durucan 2004;Robertson & Christiansen 2008;Liu et al. 2015;Lu et al. 2016), varies between 0 and 1.

Model validation and assessment
Model validation. Pini et al. (2009) carried out experiments testing fracture porosity, mechanical characteristics, sorption deformation properties and permeability of coals from the Monte Sinni coal mine in Italy. These data are so sufficiently detailed and comprehensive that they have been used by many scholars (Chen et al. 2012;Guo et al. 2014;Lu et al. 2016) to validate their permeability models. The experiments were carried out using N 2 and CO 2 , respectively. The basic characteristics of coals were shown in Table 1. According to the measured permeability and fracture porosity of coals, the equivalent fracture width and equivalent matrix scale were calculated (Table 2).
During the coal permeability experiment conducted by Pini et al. (2009), the confining stress is constant. Therefore, equation (37) can be simplified as follows.
The testing data are used to validate the ECDP model based on the characteristic parameters of coals in Tables 1 and 2. The results of validation are shown in figures 5 and 6. When the ECDP model was validated, the Biot coefficient ( ) and the internal deformation coefficient (f m ) of coal were considered to be constants changing from 0 to 1, and the results that were calculated with f m = 0 and f m = 1 are also shown in figure 5. The correlation coefficient R 2 for different methods, which is a numerical measure of a type of correlation that means a statistical relationship between two variables (Taylor 1982), is used to represent the accuracy of fitting experimental data.
As shown in figure 5, the ECDP model fits the testing data well. The result obtained is that the Biot coefficient of coal samples used by Pini et al. is 0.8779; thus, the bulk modulus of coal matrices is 6364.29 MPa. Moreover, this validation   10 reveals that the internal deformation coefficient of the coal sample varies with the type of the gas used in the coal permeability experiment, which is consistent with the results reported by some previous studies (Liu et al. 2017). For the coal samples used by Pini et al., if the gas used in the coal permeability experiment is carbon dioxide, the internal deformation coefficient of the coal sample is 0.17; but if the gas used in the coal permeability experiment is nitrogen, the internal deformation coefficient of the coal sample is 0.25. This finding may be observed due to the difference in the adsorption capacity in coal for the different gases. Moreover, when carbon dioxide molecules were adsorbed on the internal surface of pores in coal matrices, a small thimbleful of gas molecules will enter the internal skeleton structure of the coal matrix and also have a slight effect on the coal matrix sorption deformation (Yu & Cheng 2012). As shown in figure 5, when f m = 0, there is no sorption deformation of coal matrices contributing to changing the coal permeability, and when f m = 1, the total sorption deformation of coal matrices will be used to affect the permeability of coals. Therefore, the variation of coal permeability when f m = 1 is considerably bigger than that when f m = 0 in the later period of CBM production. In addition, figure 5 shows that a number of permeability values were negative when the gas used in the coal permeability experiment was carbon dioxide and f m = 1, which illustrates that not all of the sorption deformation of coal matrices is used to change the volume of fractures in coals.
Model assessment. In recent decades, many coal permeability evolution models have been developed, such as the P-M, S-D and R-C models, which are shown as follows.
The P-M model (Palmer & Mansoori 1998): The S-D model (Shi & Durucan 2004): The R-C model (Robertson & Christiansen 2008): In the above models, the Biot coefficients are all considered to be 1. Furthermore, the sorption deformation of coal matrices is assumed to entirely contribute to the change of coal fractures in these models. We matched these three widely used models to the testing data of coal samples used by Pini et al. For P-M model, the empirical coefficient f p is acquired by fitting and the compressibility of coal matrices is equal to the reciprocal of the bulk modulus of coal matrices. For the S-D model, the compression coefficient of fractures in coal is obtained by matching. For R-C model, the decline ratio of coal fracture compressibility as effective stresses rise is obtained by also fitting the initial compressibility of fractures in coal. The characteristic parameters of coals are presented in Table 1 and fitting results are displayed in figure 6.
Compared figure 6 with figure 5, it is found that the ECDP model can fit testing data well but the P-M and S-D models poorly match the testing data according to the correlation coefficients of the fitted curves. In addition, the R-C model can only fit the experimental data measured by the N 2 well, which reveals that the ECDP model is superior to the R-C model for a wide range of applications. This is because the Biot coefficient is not equal to 1 due to compressibility of coal matrices, for example, the Biot coefficient of coal samples used by Pini et al. is 0.8779 in this paper. In addition, the factor f m , which ranges from 0 to 1, is introduced in the ECDP model, which indicates that only part of the strain of coal matrices after absorbing the gas contributes to the change of fracture volume in coals. Therefore, the ECDP model can more accurately reveal the coal permeability evolution law.

Analysis on the ECDP model
Coal is a complex porous medium with dual-porosity structure. Based on certain geometric assumptions, the ECDP model was established. Now, the influence of equivalent fracture width and equivalent matrix scale on the coal permeability evolution law will be discussed, respectively. Assume that coal is under constant confined stress of 10 MPa and gas pressures vary from 11   Table 3.
Effect of the equivalent matrix scale on the coal permeability evolution law. Coal matrices are highly important in the dual-porosity coal structure theory because their size and number directly affect the gas flow path and communication among pores in coal that, in turn, affect the coal permeability. The effect of the equivalent matrix scale on the coal permeability evolution law is shown in figure 7. From the ECDP model, it can be observed that, if the other influencing factors are constant, the larger the equivalent matrix scale is, the greater the coal permeability is. Equation (13) indicates that the equivalent fracture width increases with the increasing equivalent matrix scale when the initial fracture porosity of coals is constant. Moreover, when the equivalent matrix scale increases, the increase of internal consumption of the coal matrix adsorption deformation will reduce the compression effect on the fracture space in coal, which results in the range of coal permeability rising with an increase in gas pressure.
Effect of the equivalent fracture width on the coal permeability evolution law. When the coal matrix-fracture system is simplified as the dual-porosity structural model, the gas migration in coal can be considered to be two steps in series with each other. After the gas desorption in coal matrix pores is undertaken, gas molecules diffuse from pores in coal matrices to fractures, and then the gas in fractures migrates into the borehole or roadway by means of seepage. When gas flows in the coal fractures, the equivalent fracture width has a strong effect on the coal permeability if the external environment remains unchanged, which is shown in figure 8. When the equivalent matrix scale is constant, if the equivalent fracture width decreases and the volume of coal remains unchanged, the number of the coal matrix will increase, which results in the cumulative impact of deformation of matrices in coal increasing. Although the impact of effective stresses on the permeability of coal is still at an advantage, the increasing impact of the deformation of matrices in coals results in the range of coal permeability rising as rising gas pressure decreases.

Discussion
According to the aforementioned analyses, we found that the ECDP model not only takes the influence of the effective stresses and deformation of coal matrices on the coal permeability evolution law into account, but it also introduces the effect of the ECDP structure on the coal permeability evolution law. Moreover, the ECDP model is an absolute permeability model rather than a relative permeability model, which can not only describe the distribution characteristics of the coal permeability, but also can provide an actual meaning for specific coal permeability and has a great advantage in the prediction of the permeability in coal seams.
In the past, when the ECBM technique was carried out the coal permeability evolution law in the plastic deformation phase was mostly characterized by introducing the equivalent plastic shear strain of coal and the blast coefficient of coal permeability (Hajiabdolmajid & Kaiser 2003;An et al. 2013), which can describe the coal permeability evolution law in the plastic deformation phase to a certain extent but cannot reveal the essential reasons why coal permeability jumps after entering the plastic deformation phase. Now, the ECDP model can be used to explain the phenomenon by studying the variation of the equivalent fracture width and the equivalent matrix scale in the plastic deformation phase.
The original coal structure is damaged irreversibly in the plastic deformation phase and, essentially, it is irreversible deformation occurring in coal matrices and fractures. This irreversible deformation will result in a dramatic increase of the equivalent fracture width in coal. Also, the equivalent matrix scale of the coal decreases and the number of coal matrices increases, which is shown in figure 9. Under the influence of the irreversible deformation of coal matrices and fractures, coal permeability will significantly increase by as much as a thousand-fold in the plastic deformation phase . Therefore, characterizing quantitatively the equivalent characteristics of dual-porosity coal structure in the plastic deformation phase by means of some scientific measures and introducing the values into the ECDP model is of far-reaching practical significance for the comprehensive understanding of the coal permeability evolution law, especially during enhancing CBM recovery.

Conclusions
The objective of this work was to analyze the impact of the structural change of coals on gas flow characteristics during the coal mining process. The main conclusions are shown as follows: (1) Because of the structural complexity of coal, the coal matrices and fractures are simplified to the geometries with rule shapes when the relevant theoretical research is conducted. Specifically, the scale characteristics of the simplified geometries are considered as the equivalent fracture width and the equivalent matrix scale.
(2) Based on the reasonable assumption of the dual-porosity coal structure, a new permeability evolution model (ECDP model) based on the equivalent characteristic of dual-porosity coal structures is constructed. For ECDP model, the effect of dual-porosity coal structures, effective stresses and the sorption deformation of coal matrices on the coal permeability is considered comprehensively. (3) It is observed that if the initial fracture porosity is constant and the equivalent matrix scale increases, the range in which coal permeability rises with rising gas pressure increases; if the equivalent fracture width decreases and the equivalent matrix scale is constant, the range in which coal permeability rises with rising gas pressure decreases. (4) The equivalent fracture width and the equivalent matrix scale were introduced in the ECDP model, which means it can be used to reveal the evolution law of coal permeability when large deformations occur in the coal bodies and/or coal structure is damaged irreversibly, especially during enhancing CBM recovery.