Target Area Selection for Residual Coalbed Methane Drainage in Abandoned Multi-Seam Mines

Abstract

To optimize the location optimization of the coalbed methane (CBM) extraction target area in abandoned mines, based on the background of the Songzao mining area in Chongqing, theoretical analysis and numerical simulation research methods were comprehensively used to systematically evaluate the potential of residual CBM resources in the goaf of the Songzao mining area. The stress-fracture evolution law and permeability enhancement characteristics of overlying strata under repeated mining of inclined multi-coal seams were deeply revealed, and the location optimization of the residual CBM extraction borehole target area was carried out. The results show that the amount of CBM resources in Songzao Coal Mine is 5.248 × 10⁷ m³, accounting for 26.57% of the total resources, which is suitable for the extraction of CBM left in goaf. The maximum height of the overburden fracture zone caused by repeated mining of K2b, K1, and K3b coal seams in Songzao Coal Mine is 72.3 m, which is basically consistent with the results of the numerical simulation (69.76 m). The fracture development of overlying strata is in the distribution form of a symmetrical trapezoid and inclined asymmetrical trapezoid, and its development height increases with an increase in coal seam mining times, and finally forms a three-dimensional ‘O’-ring fracture area, which provides a channel and enrichment area for the effective migration of CBM. The significant permeability-increasing zone of overburden rock is stable in the range of 10~40 m above the roof of the K3b coal seam and is nearly trapezoidal. According to the calculation of the height prediction model of the fracture zone in the abandoned goaf, the fracture height of the long-term compaction of the Songzao Coal Mine is reduced to 63.74 m. Based on the stress-fracture evolution characteristics of the overburden rock, combined with the permeability-increasing characteristics of the overburden rock and the migration law of the remaining CBM, it is determined that the preferred position of the remaining CBM extraction target area of the Songzao Coal Mine should be in the upper corner of the fracture development area within the range of 10~32.47 m above the K36 coal seam.

1. Introduction

China has an energy structure characterized by abundant coal reserves, limited oil, and scarce natural gas resources. Coal will remain a dominant energy source in the country’s energy mix for the foreseeable future [1,2]. Continuous coal mining activities, coupled with energy restructuring and the implementation of carbon peak/neutrality targets, have led to a continuous increase in abandoned mine shafts in China [3,4,5]. Projections indicate that this number will reach 15,000 by 2030 [6]. Upon mine closure, significant CBM resources remain trapped in underground goafs, resulting in energy waste. In shallow abandoned mines, residual gas can escape to the surface through mining-induced fracture zones, posing severe climate and ecological risks [7,8,9,10]. The exploitation of these residual CBM resources has become an urgent priority.

The stress redistribution of overlying strata caused by coal seam mining forms a complex mining fracture network, which is the key area for CBM migration and enrichment. Therefore, identifying the stable fracture zone in abandoned mines is the basis for evaluating and developing the remaining CBM resources [11,12,13]. However, the stress of overlying strata and the law of crack propagation in coal seam group mining are different from those in single coal seam mining [14], which restricts the enrichment and migration of CBM, and then affects the precise layout of the location of the extraction target area. Scholars at home and abroad have performed a lot of research on the fracture development characteristics of mining rock mass and the migration law of CBM, and put forward stress and fracture development characteristic models such as ‘O’ ring [15], roof annular fracture ring [16], and ‘∩’ type high cap fracture [17]. With the deepening of the research on the mining-induced fracture zone of overlying strata, Guo et al. [18] carried out research on the poor theory of the development characteristics of the fracture zone in high-intensity mining, and proposed a new theoretical method for predicting the fracture height by using model analysis and other methods. To better determine the CBM enrichment area, He et al. [19] used physical experiments to explore the relationship between fracture development and fractal dimension. An area with a larger fractal dimension is more conducive to the desorption and migration of CBM. Zhang et al. [20,21] analyzed the damage and fracture of coal caused by repeated mining in detail through experiments. The results showed that the plastic strain failure increased significantly with an increase in loading–unloading cycles. Ma et al. [22] analyzed the failure and fracture development characteristics of mining overburden rock through a 3DEC numerical simulation experiment, and divided the mining overburden rock fracture into four areas, which can provide a basis for the layout of drainage drilling. Xie et al. [23] studied the fracture evolution related to the mining of the upper protective layer and its influence on the pressure relief gas drainage in the protected coal seam. It is considered that the stress change during the mining process affects the development of the fracture and changes the permeability value of the coal. In order to improve the efficiency of CBM extraction in thin to medium-thick coal seam group mining areas, Xu et al. [24] used a numerical simulation method to analyze the stress–strain relationship of mining overburden and the increase in fracture permeability, and optimized the structure of the CBM extraction well. Zhao et al. [25] analyzed the development range, connectivity, and fractal dimension of pressure relief gas transportation and storage channels under different mining conditions by carrying out multiple sets of two-dimensional physical similarity simulation tests, so as to make up for the shortcomings of existing research on structural characterization and parameter coupling. Wu et al. [26,27] explored the influence of working face width and key strata of overlying strata on gas migration range by means of similar simulation, numerical simulation, and theoretical analysis. Xie [28,29] explored the change law of surrounding rock migration and asymmetric stress in multi-section mining with a large dip angle. The results showed that the asymmetric load on the upper and lower sides of the coal pillar led to the failure of coal and rock mass again. Meng et al. [30] took the high gassy coal seam with a large dip angle as the research object, analyzed the fracture development morphological characteristics and evolution trend of the overlying strata, and clarified the development height of the fracture zone. Yang and Wang et al. [6,31] studied the distribution law of the stress field and fracture field in the process of mining and the stability of goaf after this process by means of a numerical simulation and physical experiment, which provided the basis for the evaluation and utilization of CBM resources in abandoned mines.

Current research primarily focuses on the disturbance characteristics of single-seam mining and CBM migration patterns during active extraction. Limited attention has been paid to the coupling relationship between stress-fracture field evolution in inclined multi-seam groups and CBM migration behavior. Studies optimizing drainage target zones for residual CBM in abandoned multi-seam mines remain particularly scarce. This study investigates optimal drainage target zones for residual multi-seam CBM in abandoned goafs of the closed Songzao Mining Area in Chongqing. This research evaluates residual CBM resources, clarifies the stress-fracture field distribution and overburden permeability zones under multi-seam mining conditions, analyzes CBM migration mechanisms, and optimizes drainage target zone locations. The findings provide theoretical guidance for residual CBM extraction in this mine and similar geological conditions.

2. Evaluation of CBM Resources in Songzao Mining Area

2.1. Overview of Geological and Hydrological Conditions in Mining Area

The coal seam groups in the Songzao mining area of Chongqing contain 6 to 14 layers of coal. The coal quality category of each coal seam belongs to anthracite No. 3, featuring low permeability and abundant CBM reserves. Currently, the main closed mines include the Songzao Mine, Yuyang Mine, Fengchun Mine, Datong Yi Mine, and Shihao Mine, all of which are coal and gas outburst mines. The specific geological and hydrogeological conditions are presented in

Table 1. Geological and hydrological conditions of mining area.

Name of Indicator	Songzao	Fengchun	Datong Yi	Shihao	Yuyang
Geological structure complexity	Medium	Complex	Medium	Medium	Medium
Average buried depth (m)	298	302	466	485	351
Inclination degree of coal seam	Inclined	Steep inclined	Gentle inclined	Gentle inclined	Gentle inclined
Height of water outlet point (m)	+333	+523	+460	+480	+470
Water accumulation in the goaf (104 m3)	981	127	3384	2510	2000
Goaf area (km2)	12.55	3.36	18.36	3.84	6.31
Water-free space in the goaf (104 m3)	1426	333.5	0	132	0
CBM emission (m3/min)	114.37	54.02	267.27	202.18	137.4
Maximum CBM content (m3/t)	28.51	26.87	24.03	29.45	29.44
Remaining coal resources (104 t)	4786.6	4484.8	8418.2	7860.6	3391.9

.

In 2015 and 2016, two CBM exploration wells (Qimei #1 and Qimei #2) were implemented in the Songzao Mining Area and the fracturing, drainage and production, gas testing, and other work were carried out. One CBM well group was deployed, and the construction and cementing of eight directional wells were completed. Among them, Well #1 was drilled starting on 30 September 2016 and was completed on 31 October. After entering the pressure-controlled and stable production stage, it maintained a stable gas production of 1500–2000 m³/d for 196 days, with a cumulative gas production of 691,000 cubic meters. Well #2 was drilled starting on 11 March 2015 and was completed on 9 April. After entering the pressure-controlled and stable production stage, the stable gas production was 1000~1537 m³/d. The stable production lasted for 453 days, with a cumulative gas production of 692,300 cubic meters, indicating that the Songzao mining area has good potential for CBM exploration and development.

2.2. Evaluation of CBM Resources in Mining Area

Due to the lack of fundamental data in the Songzao mining area, this study uses the volume method to preliminarily estimate the amount of CBM resources left in the goaf by taking the remaining coal reserves and residual gas content as the key parameters (Equation (1)). The coal extraction volumes and recovery rates of Datong Yi, Shihao, Yuyang, Fengchun, and Songzao Mines are presented in

Table 2. Evaluation data of CBM resources in mining area.

Name of Indicator	Songzao	Fengchun	Datong Yi	Shihao	Yuyang
Coal consumption (104 t)	5242.1	1940.27	4392.91	2752.7	3303.6
Rate of recovery	80%	80%	80%	78.69%	68.40%

Note: The recovery rate data for Songzao and Fengchun Mine are unavailable and thus assumed to be 80%.

. The average volatile matter yield (V_daf) of the main coal seams in the Songzao mining area is 9.38%. The residual gas content was predicted according to AQ/T 1018-2006 Methods for Predicting Mine Gas Emission [32] and was determined to be 5 m³/t.

$$Q=B·q$$

(1)

where $Q$ is the coalbed gas resources (m³); $B$ is the coal reserves (t); $q$ is the coal seam average gas content (m³/t).

Based on this estimation, the CBM resources in the goaf are 1.975 × 10⁸ m³, among which the adsorbed CBM resources are 1.385 × 10⁸ m³, accounting for 70.13%, and the free CBM resources are 5.899 × 10⁷ m³, accounting for 29.87%. Among the coal seam distributions, the remaining CBM resources in the K1, K2b, and K3b coal seams account for 24.97%, 22.94%, and 52.09%, respectively, and are mainly stored in the K3 coal seam. In terms of horizontal distribution, the first, second, and third levels account for 47.82%, 44.48%, and 14.62%, respectively. The proportions of the Datong Yi, Shihao, Yuyang, Fengchun, and Songzao coal mines are 22.27%, 14.87%, 26.46%, 9.84%, and 26.57%, respectively. The CBM resources are shown in Figure 1. It can be seen that the potential of the remaining CBM resources in the closed mining areas is as follows: Songzao > Yuyang > Datong Yi > Shihao > Fengchun.

Based on a comprehensive analysis of the geological structures, goaf areas, and water-accumulated areas of the five closed mines, the following conclusions were drawn: Datong Yi Coal Mine, Shihao Coal Mine, and Yuyang Coal Mine are gently inclined coal seams, located on the western limb of the study area. There is relatively little remaining space in the goaf areas, making them unsuitable for goaf gas extraction. Fengchun Coal Mine is a steeply inclined coal seam, located on the southeastern limb. The geological structure in this area is complex, and there is a remaining goaf area of 3.335 × 10⁶ m³ above the +523 m adit. Songzao Coal Mine is an inclined coal seam, located on the northeastern limb. The geological structure in this area is of moderate complexity, and there is a remaining space of 1.426 × 10⁷ m³ above the No.2 adit at 333 m. Moreover, the amount of CBM resources in Songzao Coal Mine is 5.248 × 10⁷ m³, which is the most abundant in the five coal mines. Therefore, the mine mainly suitable for goaf gas extraction is Songzao Coal Mine.

3. Theoretical Calculation of ‘Two Zones’ Height in Songzao Coal Mine

3.1. Project Profile

The strike length of Songzao Coal Mine is 9 km, the inclined width is 1.5–2.5 km, and the area is 14.8612 km². It is a monoclinic structure, and the mine adopts the strike longwall mining method. The coal-bearing strata are the Longtan Formation (P3l) of the upper Permian system. The mineable coal seams are mainly K2b, K1, and K3b coal seams, and the average dip angle of the coal seam is 30°. Among them, the K3b coal seam is a strong outburst coal seam, followed by the K1 coal seam, and the K2b coal seam is a weak outburst coal seam. The specific mining sequence is the K2b, K1, and K3b coal seams. The mine field was divided into three levels, but because the second and third levels have been flooded, the first level was selected as the research object. The water accumulation and geological topographic map of Songzao Coal Mine are shown in Figure 2a.

A comprehensive histogram of the coal-bearing strata is shown in Figure 2b. There is a significant main key stratum in the overlying rock, that is, a medium-hard sandstone layer with a thickness of 5.32 m at about 5.68 m above the K3b coal seam, which plays a decisive role in controlling the overall movement and rupture height of the overlying rock mass. The K3b, K2b, and K1 coal seams are distributed from top to bottom. The distance between the K3b and K2b coal seams is 20.37 m, and the distance between the K2b and K1 coal seams is 10.90 m. The average thickness of the K3b coal seam is 2.5 m. The coal seam structure is simple, occasionally containing gangue, and the horizon is stable. It belongs to the recoverable stable coal seam in the whole area. The average thickness of the K2b coal seam is 0.56 m, the horizon is relatively stable, the coal seam structure is relatively simple, and there is a layer of gangue locally. It is an unstable thin coal seam and locally recoverable. The average thickness of the K1 coal seam is 0.97 m. The coal seam structure is simple, without gangue, and the horizon is relatively stable. It is a relatively stable coal seam that can be basically mined in the whole area.

3.2. Theoretical Calculation of ‘Two-Band’ Height

During multi-seam mining, repeated mining activities can induce the secondary development of mining-induced fractures, thereby expanding the scope of roof fractures. Based on the comprehensive geological and coal-bearing stratum columnar diagram of Songzao Coal Mine and in accordance with the Regulations for Coal Pillar Retention and Mining under Buildings, Water Bodies, Railways, and Major Shafts, the development height of the fracture zone after mining the main coal seams in Songzao Coal Mine was calculated. The overlying strata of the main coal seams in Songzao Coal Mine are primarily composed of alternating layers of mudstone, sandy mudstone, and sandstone. According to previous rock mechanics test results, the average saturated ultimate compressive strength is below 40 MPa, with most values ranging from 20 to 30 MPa, indicating that the rocks belong to the medium-hard category. Therefore, an empirical formula is selected to calculate the height of the caving zone and the fracture zone.

The calculation formula for the caving zone was as follows:

$$H_k={\displaystyle \frac{100\sum M}{4.7\sum M+19}}\pm 2.2$$

(2)

The calculation formula for the fracture zone was as follows:

$$H_{li}={\displaystyle \frac{100M}{1.6M+3.6}}\pm 5.6$$

(3)

where H_k is the height of the caving zone (m); M is the thickness of the mined coal seam (m); H_li is the height of the fracture zone (m).

To be safe, in the actual calculation, ±2.2 and ±5.6 were taken as +2.2 and +5.6, respectively. When repeated mining of multiple coal seams was carried out, the mining of the lower coal seam was affected by the upper goaf, resulting in a further expansion of the fracture range. Therefore, for the calculation of the height of the caving zone and the fracture zone of multiple coal seams, when the minimum vertical distance h of the upper and lower coal seams is greater than the height H of the caving zone of the lower coal seam, the maximum height of the fracture zone of the upper and lower coal seams can be calculated according to Equation (3), and the highest elevation was taken as the maximum height of the fracture zone of the two coal seams. When the caving zone of the lower coal seam contacts or completely enters the upper coal seam, the maximum height of the fracture zone of the upper coal seam was calculated by Equation (3), and the maximum height of the fracture zone of the lower coal seam should be calculated by Equation (4). The highest elevation is the maximum height of the fracture zone of the two coal seams:

$$M_Z=M_2+(M_1-{\displaystyle \frac{H_{1-2}}{Y}})$$

(4)

where $M_Z$ is the comprehensive mining thickness of the upper and lower coal seams, m; $M_1$ is the thickness of the upper coal seam mining, m; $M_2$ is the thickness of the lower coal seam mining, m; $H_{1-2}$ is the normal distance between the upper and lower coal seams, m; $Y$ is the caving ratio of the lower coal seam.

Based on the calculations using Equations (2)–(4), the heights of the caving zone and the fracture zone for coal seams K2b, K1, and K3b are shown in

Table 3. Maximum height of single coal seam mining ‘two-zones‘.

Coal Seam	Mining Thickness/m	Caving Zone/m
K2b	0.56	0.58–4.98
K1	0.97	2.41–6.81
K3b	2.50	8.11–12.51

.

From Table 3, it can be seen that, after the mining of the K1 coal seam is completed, the maximum height of the caving zone is 6.81 m, and the maximum height of the fracture zone is 29.70 m. The average spacing between the K2b and K1 coal seams is 10.90 m, which is greater than the height of the caving zone in the overlying strata of the K1 coal seam but less than the height of its fracture zone. Therefore, it is considered that fractures have penetrated between the K1 and K2b coal seams after the mining of the K1 coal seam is completed. For the K2b coal seam, after its mining is completed, the maximum height of the caving zone is 4.98 m, and the maximum height of the fracture zone is 18.06 m. The spacing between the K3b and K2b coal seams is 20.37 m, which is greater than the heights of both the caving and fracture zones in the overlying strata of the K2b coal seam. Therefore, the mining of the K2b coal seam has no significant impact on the heights of the fracture and caving zones of the K3b coal seam. At this point, the fracture development height of the K1 coal seam represents the overall fracture zone height of the K2b and K1 coal seams. Thus, the maximum height of the fracture zone after the repeated mining of the K2b and K1 coal seams is 29.70 m. After the mining of the K3b coal seam, the maximum height of the fracture zone is 38.49 m. Therefore, for the K2b, K1, and K3b coal seams, the maximum height of the fracture zone after repeated mining of the three coal seams reaches 69.76 m, as shown in Figure 3.

4. Numerical Investigation of Mining-Induced Stress-Fracture Field Evolution in Songzao Coal Mine

4.1. Model Development

According to the occurrence and mining situation of the main coal seam in the first level and first mining area of Songzao Coal Mine, combined with the geological histogram of the working face shown in Figure 2a, a three-dimensional numerical calculation model considering multiple goafs was established by FLAC^3D7.0. The model takes the coal seam strike as the x direction and the tendency as the y direction. To model and facilitate excavation, the numerical simulation model was appropriately simplified, and the coal seam dip angle is 30°. The model size is 600 m (length) × 600 m (width) × 600 m (height), the construction range is horizontal ground elevation −675~−75 m, and the simulated goaf size is 400 m (trend) × 100 m (dip). The model was discretized by hexahedral mesh, which was divided into 554,700 units and 575,244 nodes. To improve the calculation accuracy, the mesh of the excavation area (near the coal seam and the roof and floor) was encrypted. The model size and mining method are shown in Figure 4.

The boundary conditions of the model were set to apply horizontal displacement boundary constraints in the horizontal direction, fixed boundary constraints at the bottom, and gravity load conditions at the top of the free end. The coal and rock mass in the model adopts the Mohr–Coulomb constitutive model. To effectively reduce the boundary interference, 150 m and 100 m of protective coal pillars were set up in the X direction and Y direction, respectively. The physical and mechanical parameters of the related rock strata are shown in

Table 4. Physical and mechanical parameters of rock strata.

Lithologic Characteristics	Density (kg·m−3)	Bulk Modulus (GPa)	Shear Modulus (GPa)	Angle of Internal Friction (°)	Cohesion (MPa)	Tensile Strength (MPa)
Sandy mudstone	2558	2.69	2.15	33	4.43	1.68
Limestone	2600	9.32	6.54	31	6.67	4.57
Coal	1400	2.31	1.63	18	1.88	0.52
Mudstone	2330	3.12	2.56	23	3.89	1.17
Sandstone	2752	8.86	5.26	33	5.72	3.53
Argillaceous limestone	2559	5.85	2.40	42	3.51	1.65
Siliceous limestone	2320	4.38	3.32	30	3.32	2.45
Calcareous mudstone	2550	2.45	1.86	33	2.15	1.53
Bauxite mudstone	2620	2.33	1.54	35	2.07	1.12

.

According to the actual engineering situation, the simulation software-FLAC^3D7.0 developed by ITASCA company in the Minneapolis, MN, United States is used for numerical calculation. The specific simulation process was as follows: According to the actual engineering situation, the numerical model was constructed, the material parameters were assigned, the boundary constraints of the model were set, and the calculation balance of the original rock stress environment was completed. The mining process of the working face was simulated by gradual excavation. The mining step distance is 10 m, and the mining of the working face is simulated from left to right. The mining process is strictly simulated according to the actual coal seam mining sequence, followed by K2b, K1, and K3b.

4.2. Stress Evolution Characteristics of Overburden Strata During Multi-Seam Mining

Figure 5 and Figure 6 present the vertical stress distribution contours in the strike and dip directions after the sequential extraction of K2b, K1, and K3b coal seams. The left panels show dip-direction sections, while the right panels display strike-direction sections. Each mining stage significantly alters the stress distribution in the coal measure strata, with characteristic stress-release zones developing in the goaf roof (often accompanied by tensile failure) and compressive stress concentrations near the coal pillars.

It can be seen from Figure 5 and Figure 6 that, after the end of multi-coal seam mining, the stress of rock strata is redistributed, and the stress release area and stress concentration area in the dip and strike direction of the coal seam show obvious zoning distribution characteristics. As shown in Figure 5a and Figure 6a, after the mining of the K2b coal seam, stress concentration areas are formed at both sides of the coal wall in the goaf, and the vertical stress of both sides of the coal wall is about 53.65 MPa. The vertical stress of the overlying strata in the middle of the goaf shows an arched stress relief area with a high middle and low sides. The stress relief area is basically symmetrically distributed with the goaf as the central axis. Stress concentration also occurs at the upper and lower ends of the goaf. The stress concentration at the upper left end is lower than that at the lower right end. The vertical stress at the upper left end reaches 47.28 MPa, and the vertical stress at the lower right end reaches 53.95 MPa. The pressure relief range of the goaf shows that the roof rock layer at the upper end is higher, the stress release is more sufficient, the regional damage is greater, and the whole is obviously asymmetric.

As shown in Figure 5b and Figure 6b, during the mining process of the K1 coal seam below the K2b coal seam, the characteristics of the stress field after mining are similar to those of single coal seam mining in the K2b coal seam. Because the K1 coal seam is in the pressure relief zone of the K2b coal seam floor, with the advancement of the K1 coal seam, the pressure relief range of the strike goaf increases obviously, and the vertical stress of the coal wall on both sides reaches 52.45 MPa, which is still symmetrically distributed as a whole. Its dip is still asymmetric, the vertical stress at the upper left reaches 50.36 MPa, the vertical stress at the lower right reaches 53.14 MPa, and the arched pressure relief area further expands to the upper left. As shown in Figure 5c and Figure 6c, during the mining process of the K3b coal seam, the arched stress reduction area in the middle of the goaf is further increased, and the stress-release area at the roof and floor continues to expand, which provides a good condition for the gas desorption of the coal seam. At the same time, the asymmetric characteristics of the inclined overburden stress are more significant. A wide range and high degree of stress concentration area is formed at the lower right coal wall, and the vertical stress reaches 53.23 MPa, while the stress peak at the upper left is reduced to about 42.57 MPa. The arched pressure relief area not only expands further in the vertical direction but also obviously shifts to the upper left, which is in stark contrast to the state of the lower right rock mass subjected to higher pressure shear stress, and ultimately leads to the asymmetric development of the fracture ranges.

In summary, in the process of multi-coal seam mining, the overburden stress field shows the evolution characteristics of strike symmetry and dip asymmetry, which is manifested in the basic symmetrical distribution of the goaf as the central axis in the strike, and the arch pressure relief zone and stress concentration on both sides are formed in the middle of the goaf. The vault of the pressure relief arch in the inclined goaf is obviously shifted to the upper left end, and the height and range of the pressure relief area in the upper left end are larger than those in the lower right end [33].

4.3. Fracture Development Characteristics of Overburden Strata During Multi-Seam Mining

After the coal seam mining, the non-coordinated deformation of the overlying rock results in the longitudinal fracture and the transverse separation fracture of the coal seam. In the process of multi-coal seam mining, the overlying rock fracture is constantly experiencing the evolution process of ‘opening–closing–opening’. The plastic zone of the coal and rock mass in the strike and dip of K2b, K1, and K3b coal seams after mining in turn is shown in Figure 7 and Figure 8. According to the distribution characteristics of the plastic zone, the stress difference between the coal and rock strata causes the shear failure of the coal and rock strata, and the plastic deformation of the tensile fracture of the coal and rock mass in the strike direction is fully developed. The development zone gradually increases in tendency and direction with the advancement of the working face, showing a symmetrical shape as a whole, and the plastic deformation of the tensile fracture of the coal and rock mass in the dip direction shows an asymmetrical shape as a whole. At the same time, the shear failure area mainly located in the upper part of the tensile failure area is also expanding. With an increase in the number of coal seam mining, the plastic area of coal and rock above the goaf gradually increases.

It can be seen from Figure 7 and Figure 8 that, when the K2b coal seam is mined, the coal and rock masses of the upper and lower adjacent layers have shear and tensile failure, and are mainly dominated by shear failure. Among them, the underlying coal and rock mass is less damaged by mining, and the upper coal and rock strata in the goaf are more damaged. In the strike direction, the cracks on both sides of the goaf are more densely developed, and the fracture development height of the upper rock strata is up to 20.46 m. The fracture development in the dip direction is mainly concentrated on both sides of the goaf, and the maximum height of fracture development in the upper rock stratum reaches 22.6 m. At the same time, the coal wall floors on both sides of the goaf are damaged due to the influence of mining. When the K1 coal seam is mined, the cracks between it and the K2b coal seam gradually penetrate, and the fracture zone develops above the K3b coal seam. The maximum height of fracture development in the final direction reaches 31.4 m, and the maximum height of fracture development in the dip direction reaches 32.6 m. When the K3b coal seam is mined, the development of overburden fractures is further increased, and the plastic failure area in the strike direction shows typical trapezoidal characteristics. The fracture-intensive areas are mainly concentrated on both sides of the failure area, and the overall rock fracture development height reaches 72.3 m. In the dip direction, the failure height of the plastic zone shows obvious asymmetric characteristics, and the overall rock fracture development height reaches 74.5 m.

Based on the development and failure of the strike and dip plastic zones of the coal seam, it can be clearly observed that the tensile failure points (shear-n and shear-p in the figure) are fully developed due to the plastic deformation of the tensile fracture of the horizontal coal and rock mass, and the tensile failure does not form a continuous path. Different from the tensile failure, the stress difference caused by the difference in the mechanical properties of the coal and rock strata above and below the lithology contact surface causes the shear failure of the coal and rock strata. The shear failure points (tension-n and tension-p in the figure) are densely connected into one, which constitutes the network skeleton of the transportation path. The development area gradually increases in direction and tendency with the advance of the working face, and the shear failure area mainly located in the upper part of the tensile failure area also expands. From the perspective of three-dimensional space, the ‘O’-ring area with sufficient fracture development is formed around the goaf, which establishes the dominant channel for the migration of the remaining CBM.

As shown in

Table 5. Comparison of simulated values and empirical predicted values of ‘fracture zone’ height in different mining stages.

Mining Stage	Fracture Zone Development Height/m
	Empirical Formula Prediction	Numerical Simulation Results
		Toward	Dip
K2b coal seam	18.06 m	20.46 m	22.60
K1 coal seam	29.70 m	31.40 m	32.60
K3b coal seam	69.76 m	72.30 m	74.50 m

, the development height of the ‘fracture zone’ after mining K2b, K1, and K3b coal seams in turn is extracted, and the height of the ‘fracture zone‘ calculated by a numerical simulation and empirical formula is further compared in each mining stage, as shown in Figure 9. Therefore, it can be seen that, in the process of single coal seam mining and subsequent multi-coal seam repeated mining, the numerical simulation results are different from the predicted values of the empirical formula, but the overall trend is consistent, indicating that the model can well reflect the overburden failure fracture development law under repeated multi-coal seam mining.

4.4. The Characteristics of Increasing Permeability of Overlying Strata in Multi-Coal Seam Mining

To determine the migration characteristics and enrichment areas of CBM, it is necessary to quantify the effect of the mining-induced permeability increase. The stress-induced permeability evolution model can be used to quantitatively describe the permeability variation coefficients of different layers. For three groups of orthogonal fractured rock masses, the change in fracture aperture caused by the change in three-dimensional stress and the change in permeability in the k direction are mainly caused by two groups of fractures perpendicular to the i direction and the j direction (where i, j, and k are three orthogonal directions, such as x, y, and z). Therefore, the permeability in the x, y, and z directions can be summarized as follows [34]:

$${\displaystyle \frac{K_k}{K_{k0}}}={\displaystyle \frac{1}{2}}\left\{{\left[1-{\displaystyle \frac{1}{K_{ni}{b}_i}}\left(\Delta {\sigma }_i-\nu \left(\Delta {\sigma }_j+\Delta {\sigma }_k\right)\right)\right]}^3+\right.\left.{\left[1-{\displaystyle \frac{1}{K_{nj}{b}_j}}\left(\Delta {\sigma }_j-\nu \left(\Delta {\sigma }_i+\Delta {\sigma }_k\right)\right)\right]}^3\right\}$$

(5)

where K_k is the permeability in the k direction (m²); K_k0 is the permeability in the k direction in the initial state (m²); K_ni and K_nj are the stiffness of cracks in i and j directions (Pa/m); v is the Poisson’s ratio of coal; ∆σ_i, ∆σ_j, and ∆σ_k are the stress variation in the i, j, and k directions (Pa); b_i and b_j are the crack openings in the i and j directions (m).

The model can reflect the increment of fracture aperture according to the state of effective stress, so as to obtain the evolution law of effective stress-induced permeability. Due to the complex distribution of cracks, new cracks will appear in the deformation process. Therefore, as a mathematical model, the model can reflect the influence mechanism of effective stress on the permeability of coal and rock mass to a certain extent. It should be noted that the normal stiffness (K_n) of the crack is a key parameter for characterizing the mechanical properties of the crack, which needs to be obtained by an indoor compression test of the fractured rock mass. The selection of fracture aperture (b) is not a direct measurement value but an equivalent value obtained by inverse calculation of the ‘cubic law‘ based on the initial permeability K₀ of the rock mass. In this model, the normal stiffness and initial permeability of each rock layer were determined using geological data and laboratory tests, and then the equivalent initial fracture opening was calculated.

According to the stress-induced seepage evolution model, the seepage evolution of rock mass can be calculated from the stress in the x, y, and z directions. In this section, the evolution of vertical permeability is taken as an example to discuss. It is assumed that the fracture parameters are uniform in the X, Y, and Z directions of coal rock, that is, that the rock is uniform, so as to simplify the calculation of permeability, such that K_n = 6800 MPa/m, b = 0.001 m, and v = 0.23. The variation characteristics of the vertical stress of overlying strata in the process of multi-coal seam mining are obtained by numerical simulation. According to the above stress-induced permeability evolution model, the vertical stress data of overlying strata at different heights above the working face are substituted into the formula to obtain the plane characteristics of the vertical permeability variation coefficient (K_z/K_kz0), as shown in Figure 10. The rock permeability variation coefficient at 10 m above the K3b coal seam is only significantly increased in the stress concentration areas on the left and right sides of the goaf, and the permeability variation coefficient in most areas does not exceed 30. The permeability variation coefficient on the upper left side of the K3b coal seam is the most obvious, and the maximum is close to 80. The effect of increasing permeability in the middle of the goaf is not significant due to the compaction of the overlying rock mass. The distribution range and value of the permeability variation coefficient at 20 m above the K3b coal seam have increased. Among them, the permeability variation coefficient on the upper left side of the rock K3b coal seam is close to 120, making it the largest area of permeability variation. The distribution of the permeability variation coefficient at 30 m and 40 m above the K3b coal seam is similar to that at 20 m above the K3b coal seam, Among them, the permeability variation coefficient of the upper left side of the 30 m above the K3b coal seam is reduced, and the maximum is close to 100, but it is still the largest area of permeability change, and the permeability variation coefficient of the upper and lower sides of the goaf is increased. The permeability variation coefficient of the upper left side at 40 m above the K3b coal seam is reduced to a maximum of no more than 80, and the permeability variation coefficient of the upper and lower sides of the goaf is significantly increased, with a value of about 20.

In summary, with the mining of K2b, K1, and K3b coal seams in turn, the permeability-increase area is mainly distributed directly above the roof of the K3b coal seam, and its range is roughly located in the height range of 10~40 m from the roof. The overall spatial form is a significant increase permeability zone with an approximate trapezoid.

5. Optimization of CBM Extraction Target Area in Fracture Zone

5.1. Height Prediction of Fracture Zone in Abandoned Goaf

From the initiation of mining at the working face to a period after the goaf area is sealed, the development of the fracture zone is a dynamic evolutionary process. The evolutionary characteristics of the fracture zone height are inseparable from the movement of overlying strata and the settlement of the unconsolidated layer. After the goaf area is sealed, it undergoes long-term compaction, resulting in a reduction in the height of the fracture zone compared to that during the mining period. In response to the height evolution of the fracture zone under compaction, a prediction model for the height of the fracture zone in abandoned goaf areas was proposed. The dynamic evolutionary process of the fracture zone height was divided into two stages [13]: The first stage involves the progressive upward propagation of rock stratum fractures, corresponding to the development of the fracture zone. The second stage involves a reduction in the height of the fracture zone, corresponding to the closure of bedding separations and fractures, the deformation and rebound of fractured strata under pressure, and the natural compaction of broken rock masses.

The predictive formula for the height of the caving zone is

$$H_k^{\prime }=H_k{\displaystyle \frac{K_2}{K_1}}$$

(6)

where $H_k^{\prime }$ represents the height of the caving zone at the end of the first stage (m); $K_1$ is the bulking coefficient of the caved rock in the caving zone at the end of the first stage; $K_2$ is the bulking coefficient of the caved rock in the caving zone at the end of the second stage.

The predictive formula for the height of the fracture zone is

$$\Delta h_1=(K_1-1)\left[{\displaystyle \frac{H_1-H_k}{\ln (H_1-H_k+1)}}-1\right]-(K_2-1)\left[{\displaystyle \frac{H_1^{\prime }-H_k^{\prime }}{\ln (H_1^{\prime }-H_k^{\prime }+1)}}-1\right]$$

(7)

where $∆h_1$ is the reduction in the unloading height of the fracture zone in the second stage (m); $H_1$ is the height of the fracture zone at the end of the first stage (m); $H_1^{\prime }$ is the height of the fracture zone at the end of the second stage (m).

On the basis of the height $H_k^{\prime }$ of the second-stage caving zone obtained by the prediction solution, the height $H_1^{\prime }$ of the fracture zone at the end of the second stage can be predicted. The development height of the caving zone and fractured zone in the first stage of coal seam stopping in Songzao Coal Mine was obtained by the previous theoretical calculation. Because Songzao Coal Mine is an abandoned mine, according to the closed pit data, the average final surface subsidence is 1778 mm, and the expansion coefficient of the first-stage caving zone is 1.40. According to the lithology description in the geological data, it can be seen that the rock stratum of the caving zone belongs to medium-hard rock. Taking the average value of 30 MPa as the calculation basis, combined with the literature [13], it is substituted into Equations (6) and (7) to solve, and the height of the fracture zone after the compaction is 63.74 m.

5.2. Determination of CBM Extraction Target Area

After coal seam mining, the longitudinal fracture cracks and transverse separation cracks formed provide channels and spaces for the migration and storage of CBM. When the overlying strata are fully mined, the separation cracks in the middle of the goaf are re-compacted, while the separation cracks around the goaf can still be maintained; that is, a certain size of ‘O’-ring fracture area is formed around the goaf [35]. Based on the numerical simulation results, it can be inferred that the remaining protective coal pillars of Songzao Mine are affected by mining, the stress of coal pillars changes, and some coal pillars are broken to produce cracks. The horizontal level is a well-developed fracture penetration area, and the gas migration channel is generated inside, which can make the CBM migrate horizontally. The adjacent stopes are connected as a whole to form different sizes of mining-induced fracture ‘O’ rings, as shown in Figure 11. After the K3b coal seam is mined, the height of the strike and dip plastic failure zone reaches 72.3 m and 74.5 m, respectively. The rock mass at this height is destroyed, which is enough to form an area connected to the fracture network and form a fracture ‘O’ ring.

Driven by the floating effect, the CBM left in the abandoned goaf [36] first diffuses and migrates to the upper space of the goaf. Relying on the fracture network of the overburden rock, the CBM continues to diffuse to the top area of the fracture zone. In view of the multi-coal seam mining conditions, if the fracture zone in the lower goaf is connected with the upper goaf, the CBM in the lower goaf will continue to migrate upward until the key strata above are intact, and finally converge to the top goaf that is interconnected. For inclined coal seams, CBM enrichment areas will also be formed in the top area of the fracture zone. Under the action of buoyancy, CBM migrates upward along the transverse fracture, resulting in a higher concentration of CBM at the upper end than in other areas, as shown in Figure 12.

Based on the ‘O’-ring theory of mining fracture development and the development characteristics of the overburden stress-fracture field in the mining process, the fracture development in the upper corner area is more sufficient and dense, which is the remaining CBM enrichment area. The permeability-increasing area of Songzao Coal Mine is stable in the fracture zone development area within 10–40 m above the K3b coal seam, and the height of the fracture zone after long-term compaction is 63.74 m above the K1 coal seam. Therefore, the preferred location of the remaining CBM drilling and drainage target area in Songzao Coal Mine should be arranged in the upper corner of the fracture development area within the range of 10~32.47 m above the K3b coal seam.

6. Conclusions

(1) The amount of CBM resources left in abandoned goaf of the Songzao mining area was evaluated. Based on the analysis of the geological and hydrological conditions of the Songzao mining area, the remaining coal reserves and residual gas content were used to estimate the potential of the remaining CBM resources in Songzao Coal Mine, and the volume method was used to calculate the amount of CBM resources in Songzao Coal Mine, which is 5.248 × 10⁷ m³, accounting for 26.57% of the total resources, and which is suitable for the extraction of residual CBM.

(2) The distribution of the stress-fracture field and overburden permeability zone under the multiple mining of an inclined coal seam group is clarified. Under the multiple mining of an inclined coal seam group, the stress distribution of overlying strata is obviously asymmetric. The stress concentration on the low side (downdip end) is significant, and the pressure relief effect on the high side (updip end) is more obvious. With an increase in mining layers, an arch-shaped pressure relief zone is formed in the middle of the goaf, the stress concentration degree of coal pillars on both sides decreases, and the pressure relief range expands to the deep part. The fracture development of overlying rock is distributed in the form of a symmetrical trapezoid and asymmetrical oblique trapezoid. The fracture height increases with an increase in mining times and finally forms a three-dimensional ‘O’-ring fracture corridor. The significant permeability-increasing area of overlying strata is stable in the trapezoid body within 10~40 m above the K3b coal seam, and the permeability variation coefficient is up to 120.

(3) The migration law of CBM and the optimization of the extraction target area were comprehensively analyzed. The fracture zone area formed after coal seam mining provides the main channel for CBM migration and enrichment. In the horizontal coal seam, CBM is enriched on both sides of the fracture zone in the upper part of the goaf. In the inclined coal seam, CBM migrates and enriches along the fracture upward tip. The height of the fracture zone in the abandoned goaf of Songzao Coal Mine decreased to 63.74 m after long-term compaction. Combined with the migration law of CBM and the permeability enhancement characteristics of overlying strata, the preferred position of the remaining CBM drilling and extraction target area in Songzao Coal Mine should be arranged in the upper corner of the fracture development area in the range of 10~32.47 m above the K3b coal seam.