# Numerical Assessment on Unloading Disturbance and Gas Extraction in Remote Distance Protective Layer Mining

Authors: Zhigang Yuan; Zehua Jiang; Shuqing Li; Jintao Zhao; Fei Huang
Journal: Geofluids
 (2022)

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## Abstract

Protective layer mining could not only significantly alter geostress but also increase the permeability of protected layer, which is beneficial for the coal gas extraction rate and ensures coal mining safety. However, due to unique geologic conditions, remote distance protective layer mining has its own characteristics. To investigate characteristic changes caused by remote distance protective layer mining, a suitable mathematical model that considered disturbance of unloading mining and solid-gas coupling effects during gas extraction was developed. The established mathematical model was implemented by combining FLAC3D and COMSOL programs to study characteristic changes during remote distance protective layer mining of Chajiaotan coal mine. Numerical simulation results of unloading disturbance mining indicated that the protected layer would experience a process of stress loading, stress unloading, stress recovery, and stress stability as the working face of protective layer advanced; unloading disturbance has a greater influence on coal permeability than gas pressure; gas extraction measure should be further adopted to decrease gas pressure. Numerical comparisons of gas pressure distribution in the original protected layer and unloading protected layer revealed that gas extraction after unloading disturbance can reduce gas pressure more effectively, and appropriate borehole spacings in the fully pressure-relief and nonfully pressure-relief zones are 30 m and 5 m, respectively. The layout of field boreholes for gas extraction was designed according to numerical results. The results of site investigation showed that numerical simulation results of relative expansion deformation and gas extraction radii agree well with the results of site observation, demonstrating reliability of the mathematical model and its implementation. The proposed mathematical model is promising for assessing unloading disturbance and gas extraction in remote distance protective layer mining.


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## Body

## 1. Introduction

Coal is of significance for the development of China’s society and economy [1]. However, with coal mining intensity increasing, hazard of coal and gas outburst would also be increased, which severely influences the efficiency and safety of coal mine production. Hence, disaster control of gas outburst is urgent for coal mining. As is well-known, gas extraction measures have been extensively employed to reduce gas content, and the extraction rate is primarily determined by the coal permeability [2, 3]. Nevertheless, permeability of coal seams in China is relatively lower, which means they are not suitable for gas extraction in their natural state [4]. At present, many artificial permeability enhancement measures have been adopted to improve the coal permeability, such as hydraulic flushing, hydraulic fracturing, and liquid CO2 phase change fracturing [5, 6]. However, these measures have specific application conditions and shortcomings [7]. When there are several minable coal seams existing in a coal mine, protective layer mining has been regarded as an effective and economic measure to eliminate outburst risk [8], as it leads to geostress relief of protected layer and then significantly enhances the permeability of protected layer, providing a favorable gas extraction condition for protected layer [9, 10]. Recently, many advances have been achieved on protection effect of protected layer based on numerical modelling, theoretical study, and site investigation. Wang and Zhou [11] proposed a mining stress disturbance factor and obtained the evolution law of mining-induced stress in deep coal bodies during protective layer mining based on numerical simulation. Cai et al. [12] investigated stress distribution law of close distance protected layer using the FLAC3D software and stated that lower protected layer would experience a process of stress loading, stress unloading, and stress recovery with stresses presenting an “O” shape distribution. Pang et al. [13] used a stress disturbance coefficient to characterize mining disturbance intensity and determined disturbance intensity zoning and mining stress evolution law employing discrete element method. Xue et al. [14] established a relationship between volumetric strain and coal permeability and studied permeability evolution law of protected layer as working face of protective layer advanced, revealing that distribution characteristics of coal volume strain and permeability in protected layer were similar. Xie et al. [15] raised a permeability enhancement rate, based on which distributions of permeability enhancement rate of overlying strata during mining were quantitatively analyzed. Yang et al. [16] investigated deformation and fracture characteristics of overlying close distance strata based on a proposed permeability function with damage considered, and laws of coal permeability and gas flow of target strata were obtained. Using the regression analysis method and considering the fracture constitutive relationship, Zhang et al. [17] proposed a permeability function in form of stress. Liu et al. [18] studied the gas extraction processes in coal seams under original and unloading states using COMSOL and indicated that gas extraction in coal seam with remote unloading disturbance has a better effect than that of original coal seam without disturbance. Liu et al. [19] put forward an index called equivalent relative interval to subdivide protective layer mining into three types, and engineering practices of protective layer mining in China were systematically summarized. In conclusion, existing literature primarily focused on close distance protective layer mining, in which either stress evolution laws or gas extraction processes were studied independently; moreover, the permeability evolution models for coal seam adopted in numerical simulation were mostly derived from the coalbed methane exploitation field. However, for protective layer mining, the effect of unloading disturbance and gas extraction should be considered as a unified process, because the stress and pressure states of the protected layer after unloading disturbance would differ significantly from the original state; i.e., initial conditions for gas extraction should be taken from the obtained results resulting from unloading disturbance. Nonetheless, to the best of our knowledge, a unified study in combination with characteristic changes caused by unloading disturbance of protective mining and gas extraction has received little attention. Furthermore, as the gas migration environment would differ in coal mines with varying interlayer distances, remote distance protective layer mining has its own characteristics due to specific geologic conditions [8]. In short, the unloading disturbance and gas extraction in remote distance protective layer mining are not fully understood, so an in-depth investigation is required. In the remainder of this paper, the engineering background is introduced in Section 2; a suitable mathematical model that considers unloading disturbance of remote distance protective layer mining and solid-gas coupling effects during gas extraction is developed in Section 3; the characteristic changes during remote distance protective layer mining and gas extraction are investigated in Section 4; field application and validation are carried out in Section 5; relevant conclusions are drawn in Section 6.


## 2. Engineering Background

This research is focused on the engineering background of Chajiaotan coal mine, which is located at Guxu mining area of Luzhou City, Sichuan province. Two coal seams called C19 and C25 coal seams are minable. The C19 coal seam is overlying the C25 coal seam with interlayer distance being 26.6 m. The average thickness of C19 and C25 coal seams is 2.0 m and 1.0 m, respectively, with average dip angle being 20°. The original gas pressures of C25 and C19 coal seams are 0.95 MPa and 2.06 MPa, respectively. The geographical position and lithology columnar of Chajiaotan coal mine are illustrated in Figure 1. According to the literature [20], C25 coal seam (referred to as protective layer) with lower outburst risk is first mined, as it would improve the permeability and reduce gas pressure of C19 coal seam (referred to as protected layer) in combination with subsequent gas extraction, leading to decrease of gas outburst risks in C19 coal seam.Figure 1
Geographical position and lithology columnar of Chajiaotan mine.According to relevant studies [8], the unloading effect induced by protective layer mining varies with interlayer distance, resulting in different gas migration environments in the protected layer. Lower protective layer mining is subdivided into three types, as shown in Table 1 [19].Table 1
Classification method.
Classification typeEquivalent relative intervalLocation of protected layerSuper-remote protective layer40<R≤RmaxBending zoneRemote distance protective layer20<R≤40Edge of bending zone and fractured zoneClose distance protective layerRmin<R≤20Lower and middle location of fractured zoneThe equivalent relative intervalR is calculated by [19]:
(1)R=SM1Kβ1β2βα,where S represents the interlayer distance, m; M represents the protective layer thickness, m; K represents the coefficient of roof management; β1 represents the influence coefficient of mining height; β2 is the content coefficient of hard rock between the protected layer and protective layer; and βα represents the coefficient of dip angle; i.e., when dip angle of protective layer α<60°, βα=cosα; otherwise, βα=sinα/2.Based on protective layer mining condition of Chajiaotan coal mine, whereS=26.6 m, M=1.0 m, K=1 m, β1=1, β2=1, and βα=0.94, then the calculated equivalent relative interval R is 28.3. It indicates that the classification type of Chajiaotan coal mine is a remote distance protective layer, which also implies that C19 coal seam is near edge of fractured zone and bending zone.


## 3. Description of Mathematical Model

### 3.1. Mathematical Model for Unloading Disturbance of Remote Distance Protective Mining

Coal permeability is a significant factor that affects gas extraction effect [4, 5]. In general, a measure of gas extraction should be used prior to decrease the gas content before coal mining. Nonetheless, only a small percentage of adsorption gas could desorb because gas pressure changes little during gas extraction of low permeability coal seams before unloading. Lower protective mining, on the other hand, would effectively cause stress variation of overlying strata, resulting in strata expansion, development, and coalescence of mining-induced fissures. Figure 2 depicts a typical diagram of lower protective layer mining, based on which characteristic changes during unloading disturbance of protective layer mining are explained.Figure 2
Illustration diagram for lower protective layer mining.


#### 3.1.1. Evolution Model for Permeability

According to ground control theory [19, 21], the surrounding rock of protective layer after coal mining can be subdivided into three different zones, as shown in Figure 2. When protected layer is near or above the boundary of bending zone and fractured zone, as in the case of C19 protected layer, whose roof and floor are still relatively complete, original gas can be assumed to be still stored in protected layer. During remote distance protective layer mining, permeability evolution of protected layer involves two stages. The first stage is the unloading disturbance caused by protective layer mining, and the second stage is the effects of gas-solid coupling during gas extraction after unloading disturbance. The influence of gas-solid coupling on permeability at the first stage is minor and ignored. The permeability evolution of protected layer because of unloading disturbance is given by [22]:
(2)k=k0bσ∆Θ,Θ>Θ0,1+Θ0−ΘΘξk0,Θ≤Θ0,where k0 and k represent the coal permeability before and after unloading disturbance, mD; Θ0 and Θ represent volumetric stress of coal seam before and after unloading disturbance, Pa; ξ is the permeability jump coefficient; and bσ represents the influencing coefficient of volumetric stress, Pa−1.


#### 3.1.2. Evolution Model for Gas Pressure

As previously stated, the geostress state of the protected layer changes during protective layer mining, resulting in the deformation of protected layer. Due to deformation of protected layer, there is an imbalance of gas pressure in the fissures of coal body. In other words, the balance between gas desorption and adsorption is broken, and a small amount of adsorbed gas is transformed into its free state. Taking into characteristics of the remote distance protective layer mining into account, evolution model for gas pressure is built according to assumptions: (A1) coal is a dual-porosity medium saturated with coal gas; (A2) gas content within the protected layer is kept constant prior to gas extraction; and (A3) variation of macroscopic volume of the coal seam at stage one is dominated by fracture expansion, with variation of coal matrix porosity ignored. The fracture porosity is given by assumptions (A1) and (A3):(3)ϕf=ϕf0+∆εv,where ϕf0 denotes original coal fracture porosity before unloading, ϕf denotes coal fracture porosity after unloading, and ∆εv denotes increment of coal volumetric strain.With the expansion of fractures in protected layer, gas adsorbed in coal matrix pores is desorbed and then diffuses to coal fracture due to gas concentration difference, causing fracture gas pressure to vary. As coal gas pressure is affected by both unloading disturbance and gas extraction, fracture gas pressure after the unloading protected layer is reckoned as a transition variable to connect them. According to assumption (A2), the transition gas pressure can be obtained after an unloading disturbance:(4)VLpp+PLρsρa+ϕmMcRTp+ϕfMcRTp=VLp0p0+PLρsρa+ϕmMcRTp0+ϕf0McRTp011+ϕf−ϕf0,where PL and VL denote Langmuir pressure and volume, respectively, ρa denotes coal density, ρs denotes coal gas density in the standard state, Mc denotes gas molecule mass, T denotes coal body temperature, R denotes ideal gas constant, p denotes transition gas pressure after unloading disturbance, and p0 denotes original gas pressure.Since Equation (4) only contains unknown variables of gas pressure p and fracture porosity ϕf, it establishes the relationship between gas pressure and fracture porosity after unloading disturbance.


### 3.2. Mathematical Model for Gas Extraction

The preceding sections have described characteristic changes caused by mining disturbance prior to gas extraction for remote distance protective layer mining. After unloading disturbance, gas extraction is implemented under the unloading state of protected layer. As mentioned before, the transition gas pressure is a parameter that represents an initial condition of gas pressure during gas extraction. Meanwhile, unloading disturbance causes variation of coal permeability and porosity; thus, initial values for coal permeability and porosity during gas extraction are the corresponding coal permeability and porosity after unloading disturbance. In short, the preceding sections provide initial conditions for subsequent gas extraction simulation.


#### 3.2.1. Controlling Equation of Coal Deformation

The controlling equation could be derived in combination with the constitutive relationship, strain-displacement equation, and stress equilibrium equation of coal body. Based on assumption (A1), the principle of effective stress, and strain induced by gas sorption [22], the controlling equation of coal deformation is given as
(5)G1−2vuj,ji+Gui,jj−Kεs,i−βmpm,i−βfpf,i+fi=0,where K and G represent coal bulk and shear moduli, ui represents displacement in ith direction, v represents Poisson’s ratio of coal, βf and βm represent corresponding coefficients for fracture and matrix pore, pm and pf represent matrix and fracture gas pressure, εs represents strain induced by gas sorption, and fi represents the ith component of coal body force.


#### 3.2.2. Controlling Equation of Gas Migration

The adsorption-desorption equilibrium of coal seam would be broken during gas drainage. Matrix gas would diffuse into coal fracture obeying Fick’s law. Governing equation for matrix gas pressure evolution can be derived based on continuity equation [22]:
(6)∂pm∂t=VMpm−pfpm+PL2τVLRTPLρa+τϕmVMpm+PL2,where τ represents the adsorption time, d, and VM represents the gas molar volume in standard state, L/mol.The gas seepage in coal fracture also satisfies continuity equation, and then, the governing equation for fracture gas pressure evolution is obtained [22]:
(7)pf∂ϕf∂t+ϕf∂pf∂t+1τpf−pm1−ϕf=∇∙kμpf∇pf,where μ represents gas dynamic viscosity.Assuming the coal body as a dual-porosity media with single permeability and ignoring variation of matrix porosity [22], the coal fracture porosity with sorption-induced strain considered is given by
(8)ϕfϕf0=1+βfMpf−p0+βmMpm−p0+KM−1εlpmpm+PL−εlp0p0+PL,where εl denotes the ultimate adsorption expansion deformation of coal body.In accordance with the cubic relation between porosity and coal fracture permeability [22], fracture permeability is expressed as
(9)kk0=1+βfMpf−p0+βmMpm−p0+KM−1εlpmpm+PL−εlp0p0+PL3.Equations (5)–(9) are coupled governing equations for gas extraction, in which coal deformation, gas diffusion, gas seepage, and fracture permeability evolution are all considered.


## 3.1. Mathematical Model for Unloading Disturbance of Remote Distance Protective Mining

Coal permeability is a significant factor that affects gas extraction effect [4, 5]. In general, a measure of gas extraction should be used prior to decrease the gas content before coal mining. Nonetheless, only a small percentage of adsorption gas could desorb because gas pressure changes little during gas extraction of low permeability coal seams before unloading. Lower protective mining, on the other hand, would effectively cause stress variation of overlying strata, resulting in strata expansion, development, and coalescence of mining-induced fissures. Figure 2 depicts a typical diagram of lower protective layer mining, based on which characteristic changes during unloading disturbance of protective layer mining are explained.Figure 2
Illustration diagram for lower protective layer mining.


### 3.1.1. Evolution Model for Permeability

According to ground control theory [19, 21], the surrounding rock of protective layer after coal mining can be subdivided into three different zones, as shown in Figure 2. When protected layer is near or above the boundary of bending zone and fractured zone, as in the case of C19 protected layer, whose roof and floor are still relatively complete, original gas can be assumed to be still stored in protected layer. During remote distance protective layer mining, permeability evolution of protected layer involves two stages. The first stage is the unloading disturbance caused by protective layer mining, and the second stage is the effects of gas-solid coupling during gas extraction after unloading disturbance. The influence of gas-solid coupling on permeability at the first stage is minor and ignored. The permeability evolution of protected layer because of unloading disturbance is given by [22]:
(2)k=k0bσ∆Θ,Θ>Θ0,1+Θ0−ΘΘξk0,Θ≤Θ0,where k0 and k represent the coal permeability before and after unloading disturbance, mD; Θ0 and Θ represent volumetric stress of coal seam before and after unloading disturbance, Pa; ξ is the permeability jump coefficient; and bσ represents the influencing coefficient of volumetric stress, Pa−1.


### 3.1.2. Evolution Model for Gas Pressure

As previously stated, the geostress state of the protected layer changes during protective layer mining, resulting in the deformation of protected layer. Due to deformation of protected layer, there is an imbalance of gas pressure in the fissures of coal body. In other words, the balance between gas desorption and adsorption is broken, and a small amount of adsorbed gas is transformed into its free state. Taking into characteristics of the remote distance protective layer mining into account, evolution model for gas pressure is built according to assumptions: (A1) coal is a dual-porosity medium saturated with coal gas; (A2) gas content within the protected layer is kept constant prior to gas extraction; and (A3) variation of macroscopic volume of the coal seam at stage one is dominated by fracture expansion, with variation of coal matrix porosity ignored. The fracture porosity is given by assumptions (A1) and (A3):(3)ϕf=ϕf0+∆εv,where ϕf0 denotes original coal fracture porosity before unloading, ϕf denotes coal fracture porosity after unloading, and ∆εv denotes increment of coal volumetric strain.With the expansion of fractures in protected layer, gas adsorbed in coal matrix pores is desorbed and then diffuses to coal fracture due to gas concentration difference, causing fracture gas pressure to vary. As coal gas pressure is affected by both unloading disturbance and gas extraction, fracture gas pressure after the unloading protected layer is reckoned as a transition variable to connect them. According to assumption (A2), the transition gas pressure can be obtained after an unloading disturbance:(4)VLpp+PLρsρa+ϕmMcRTp+ϕfMcRTp=VLp0p0+PLρsρa+ϕmMcRTp0+ϕf0McRTp011+ϕf−ϕf0,where PL and VL denote Langmuir pressure and volume, respectively, ρa denotes coal density, ρs denotes coal gas density in the standard state, Mc denotes gas molecule mass, T denotes coal body temperature, R denotes ideal gas constant, p denotes transition gas pressure after unloading disturbance, and p0 denotes original gas pressure.Since Equation (4) only contains unknown variables of gas pressure p and fracture porosity ϕf, it establishes the relationship between gas pressure and fracture porosity after unloading disturbance.


## 3.1.1. Evolution Model for Permeability

According to ground control theory [19, 21], the surrounding rock of protective layer after coal mining can be subdivided into three different zones, as shown in Figure 2. When protected layer is near or above the boundary of bending zone and fractured zone, as in the case of C19 protected layer, whose roof and floor are still relatively complete, original gas can be assumed to be still stored in protected layer. During remote distance protective layer mining, permeability evolution of protected layer involves two stages. The first stage is the unloading disturbance caused by protective layer mining, and the second stage is the effects of gas-solid coupling during gas extraction after unloading disturbance. The influence of gas-solid coupling on permeability at the first stage is minor and ignored. The permeability evolution of protected layer because of unloading disturbance is given by [22]:
(2)k=k0bσ∆Θ,Θ>Θ0,1+Θ0−ΘΘξk0,Θ≤Θ0,where k0 and k represent the coal permeability before and after unloading disturbance, mD; Θ0 and Θ represent volumetric stress of coal seam before and after unloading disturbance, Pa; ξ is the permeability jump coefficient; and bσ represents the influencing coefficient of volumetric stress, Pa−1.


## 3.1.2. Evolution Model for Gas Pressure

As previously stated, the geostress state of the protected layer changes during protective layer mining, resulting in the deformation of protected layer. Due to deformation of protected layer, there is an imbalance of gas pressure in the fissures of coal body. In other words, the balance between gas desorption and adsorption is broken, and a small amount of adsorbed gas is transformed into its free state. Taking into characteristics of the remote distance protective layer mining into account, evolution model for gas pressure is built according to assumptions: (A1) coal is a dual-porosity medium saturated with coal gas; (A2) gas content within the protected layer is kept constant prior to gas extraction; and (A3) variation of macroscopic volume of the coal seam at stage one is dominated by fracture expansion, with variation of coal matrix porosity ignored. The fracture porosity is given by assumptions (A1) and (A3):(3)ϕf=ϕf0+∆εv,where ϕf0 denotes original coal fracture porosity before unloading, ϕf denotes coal fracture porosity after unloading, and ∆εv denotes increment of coal volumetric strain.With the expansion of fractures in protected layer, gas adsorbed in coal matrix pores is desorbed and then diffuses to coal fracture due to gas concentration difference, causing fracture gas pressure to vary. As coal gas pressure is affected by both unloading disturbance and gas extraction, fracture gas pressure after the unloading protected layer is reckoned as a transition variable to connect them. According to assumption (A2), the transition gas pressure can be obtained after an unloading disturbance:(4)VLpp+PLρsρa+ϕmMcRTp+ϕfMcRTp=VLp0p0+PLρsρa+ϕmMcRTp0+ϕf0McRTp011+ϕf−ϕf0,where PL and VL denote Langmuir pressure and volume, respectively, ρa denotes coal density, ρs denotes coal gas density in the standard state, Mc denotes gas molecule mass, T denotes coal body temperature, R denotes ideal gas constant, p denotes transition gas pressure after unloading disturbance, and p0 denotes original gas pressure.Since Equation (4) only contains unknown variables of gas pressure p and fracture porosity ϕf, it establishes the relationship between gas pressure and fracture porosity after unloading disturbance.


## 3.2. Mathematical Model for Gas Extraction

The preceding sections have described characteristic changes caused by mining disturbance prior to gas extraction for remote distance protective layer mining. After unloading disturbance, gas extraction is implemented under the unloading state of protected layer. As mentioned before, the transition gas pressure is a parameter that represents an initial condition of gas pressure during gas extraction. Meanwhile, unloading disturbance causes variation of coal permeability and porosity; thus, initial values for coal permeability and porosity during gas extraction are the corresponding coal permeability and porosity after unloading disturbance. In short, the preceding sections provide initial conditions for subsequent gas extraction simulation.


### 3.2.1. Controlling Equation of Coal Deformation

The controlling equation could be derived in combination with the constitutive relationship, strain-displacement equation, and stress equilibrium equation of coal body. Based on assumption (A1), the principle of effective stress, and strain induced by gas sorption [22], the controlling equation of coal deformation is given as
(5)G1−2vuj,ji+Gui,jj−Kεs,i−βmpm,i−βfpf,i+fi=0,where K and G represent coal bulk and shear moduli, ui represents displacement in ith direction, v represents Poisson’s ratio of coal, βf and βm represent corresponding coefficients for fracture and matrix pore, pm and pf represent matrix and fracture gas pressure, εs represents strain induced by gas sorption, and fi represents the ith component of coal body force.


### 3.2.2. Controlling Equation of Gas Migration

The adsorption-desorption equilibrium of coal seam would be broken during gas drainage. Matrix gas would diffuse into coal fracture obeying Fick’s law. Governing equation for matrix gas pressure evolution can be derived based on continuity equation [22]:
(6)∂pm∂t=VMpm−pfpm+PL2τVLRTPLρa+τϕmVMpm+PL2,where τ represents the adsorption time, d, and VM represents the gas molar volume in standard state, L/mol.The gas seepage in coal fracture also satisfies continuity equation, and then, the governing equation for fracture gas pressure evolution is obtained [22]:
(7)pf∂ϕf∂t+ϕf∂pf∂t+1τpf−pm1−ϕf=∇∙kμpf∇pf,where μ represents gas dynamic viscosity.Assuming the coal body as a dual-porosity media with single permeability and ignoring variation of matrix porosity [22], the coal fracture porosity with sorption-induced strain considered is given by
(8)ϕfϕf0=1+βfMpf−p0+βmMpm−p0+KM−1εlpmpm+PL−εlp0p0+PL,where εl denotes the ultimate adsorption expansion deformation of coal body.In accordance with the cubic relation between porosity and coal fracture permeability [22], fracture permeability is expressed as
(9)kk0=1+βfMpf−p0+βmMpm−p0+KM−1εlpmpm+PL−εlp0p0+PL3.Equations (5)–(9) are coupled governing equations for gas extraction, in which coal deformation, gas diffusion, gas seepage, and fracture permeability evolution are all considered.


## 3.2.1. Controlling Equation of Coal Deformation

The controlling equation could be derived in combination with the constitutive relationship, strain-displacement equation, and stress equilibrium equation of coal body. Based on assumption (A1), the principle of effective stress, and strain induced by gas sorption [22], the controlling equation of coal deformation is given as
(5)G1−2vuj,ji+Gui,jj−Kεs,i−βmpm,i−βfpf,i+fi=0,where K and G represent coal bulk and shear moduli, ui represents displacement in ith direction, v represents Poisson’s ratio of coal, βf and βm represent corresponding coefficients for fracture and matrix pore, pm and pf represent matrix and fracture gas pressure, εs represents strain induced by gas sorption, and fi represents the ith component of coal body force.


## 3.2.2. Controlling Equation of Gas Migration

The adsorption-desorption equilibrium of coal seam would be broken during gas drainage. Matrix gas would diffuse into coal fracture obeying Fick’s law. Governing equation for matrix gas pressure evolution can be derived based on continuity equation [22]:
(6)∂pm∂t=VMpm−pfpm+PL2τVLRTPLρa+τϕmVMpm+PL2,where τ represents the adsorption time, d, and VM represents the gas molar volume in standard state, L/mol.The gas seepage in coal fracture also satisfies continuity equation, and then, the governing equation for fracture gas pressure evolution is obtained [22]:
(7)pf∂ϕf∂t+ϕf∂pf∂t+1τpf−pm1−ϕf=∇∙kμpf∇pf,where μ represents gas dynamic viscosity.Assuming the coal body as a dual-porosity media with single permeability and ignoring variation of matrix porosity [22], the coal fracture porosity with sorption-induced strain considered is given by
(8)ϕfϕf0=1+βfMpf−p0+βmMpm−p0+KM−1εlpmpm+PL−εlp0p0+PL,where εl denotes the ultimate adsorption expansion deformation of coal body.In accordance with the cubic relation between porosity and coal fracture permeability [22], fracture permeability is expressed as
(9)kk0=1+βfMpf−p0+βmMpm−p0+KM−1εlpmpm+PL−εlp0p0+PL3.Equations (5)–(9) are coupled governing equations for gas extraction, in which coal deformation, gas diffusion, gas seepage, and fracture permeability evolution are all considered.


## 4. Numerical Simulation of Unloading Disturbance and Gas Extraction

### 4.1. Numerical Simulation Workflow

Currently, COMSOL Multiphysics program has been extensively adopted to analyze multiphysics coupled problems [23]. Nonetheless, when it is adopted in solving large deformation occurred by mining engineering, its convergence becomes relatively poor, especially in three-dimensional problems. The FLAC3D program, a finite difference code with high accuracy for large deformation problems, is adopted instead to solve the deformation field before gas extraction. Hence, in this work, numerical simulation is conducted by combining the COMSOL Multiphysics and FLAC3D programs. The detailed simulation flowchart is illustrated in Figure 3. Firstly, the FLAC3D program is utilized to obtain deformation and stress of C19 protected layer due to unloading mining of C25 protective layer. Secondly, Fish language (secondary development language embedded in FLAC3D) is used in accordance with Equations (2)–(4) to obtain permeability, fracture porosity, and gas pressure in C19 protected coal seam. Thirdly, the geometric model for C19 protected layer is reconstructed in COMSOL Multiphysics program, and then, permeability, fracture porosity, and gas pressure data obtained in the FLAC3D program, which are used as an initial condition, are input to COMSOL to study gas migration during gas extraction. The following results indicate that unidirectional sequential coupling of FLAC3D and COMSOL Multiphysics programs can simulate characteristic changes of remote distance protective layer mining accurately.Figure 3
Numerical simulation flowchart.


### 4.2. Characteristic Changes during Unloading Disturbance of Remote Distance Protective Mining

According to mining conditions of C25 protective layer in Chajiaotan mine, a FLAC3D numerical model is built based on the lithology columnar as illustrated in Figure 1. Table 2 gives the corresponding parameters adopted in numerical simulation. During numerical simulation, the C25 protective layer is mined with a step length of 10 m, and distributions of stress, displacement, and strain are stored and analyzed after each step.Table 2
Physicomechanical parameters for each rock layer.
Rock formationElasticity moduli (GPa)Tensile strength (MPa)Cohesion (MPa)Friction angle (°)Poisson’s ratioDensity (kg/m3)Overlying strata2.22.76.6370.201900Siltstone5.05.46.2400.252500Sandy mudstone3.03.53.7320.232530Claystone1.81.13.0320.201900Mudstone2.02.52.7300.182430Coal seam1.01.02.0280.211300Kaolinite rock1.82.54.0350.242400Lower strata3.02.04.6400.252500


#### 4.2.1. Results of Vertical Stress and Analysis

With the excavation of C25 protective layer, stresses within surrounding rock would be redistributed. Vertical stress distributions in surrounding rock along the strike direction at different advancing distances (i.e., 40 m, 80 m, 120 m, and 160 m) are depicted in Figure 4. As can be seen, stress concentration zones with vertical stress greater than its original value occur on both sides of the working face, while pressure-relief zones are located at the floor and roof of working face; morphology of vertical stress distribution in the surrounding rock is nearly symmetrical. With the working face of C25 protective layer advancing forward, zones of stress concentration and pressure relief increase continuously. The peak vertical stress on both sides of working face increases from 19.1 MPa to 25.6 MPa with the working face of C25 protective layer advancing from 40 m to 80 m. However, when the advancing distance is changed from 120 m to 160 m, the variation of vertical peak stress is relatively minor, and vertical stress remains basically stable.Figure 4
Distributions of vertical stress along strike direction at different advancing distances.
(a)
40 m(b)
80 m(c)
120 m(d)
160 mWith the advancement of lower C25 protective layer, vertical stress curves for the upper C19 protected layer at varying advancing distances are obtained and illustrated in Figure 5.Figure 5
Vertical stress curves for upper C19 protected layer at varying advancing distances.As seen in Figure5, vertical stress in C19 protected layer is less affected by protective layer mining with advancing distance of C25 protective layer being less than 20 m. When advancing distance is 40 m, maximum and minimum vertical stresses within the protected layer are -9.0 MPa and -7.6 MPa (negative denotes compression stress), respectively, which indicates that the coefficient of vertical stress concentration reaches 1.03 and maximum pressure-relief stress is 12.9% lower than its original vertical stress. With the continuous increase of advancing distance (e.g., 60 m ~ 80 m), mining influence of C25 protective layer on protected layer would gradually increase, which are represented by the increase of stress concentration coefficient, pressure-relief, and stress concentration zones and decrease of vertical stress within the pressure relief zone. When advancing distance is 120 m, the maximum vertical stress is -12.1 MPa (i.e., with concentration coefficient of stress being 1.39), and minimum vertical stress is -2.2 MPa, which is 74.8% lower than its original vertical stress. When the advancing distance reaches to an extent (e.g., 140 m), the vertical stress in the pressure relief zone begins to recover resulting from the roof compaction effect of protected layer, and the vertical stress in this zone presents a saddle-shaped distribution.Figure6 presents distributions of vertical stress along the bedding plane of protected layer at varying advancing distances.Figure 6
Distributions of vertical stress along bedding plane of protected layer at varying advancing distances.
(a)
80 m(b)
160 mAs shown in Figure6, the vertical stress along bedding plane of protected layer varies in different zones. At the advancing distance of 80 m, the zone with increased vertical stress is from 44 m ahead to 3 m in the rear of the open-off cut, the zone with decreased vertical stress is from 3 m to 80 m in the rear of open-off cut, and other zone with vertical stress kept unchanged is from 44 m to 80 m ahead of open-off cut. Therefore, according to distribution characteristics of vertical stress, the protected layer with advancing distance being 80 m could be subdivided into three different zones as illustrated in Figure 6(a). Furthermore, when the advancing distance reaches to an extent (e.g., 140 m), the zone whose vertical stress had been significantly released starts to recover again. Therefore, after the protective layer mining ended (i.e., an advance distance of 140 m), the protected layer could be subdivided into four different zones as illustrated in Figure 6(b).The vertical stress variation of a measuring point, located at the corresponding center of working face of C25 protective layer, was also monitored. Figure 7 gives the vertical stress variation of a central measuring point in protected layer.Figure 7
Vertical stress variation of a central measuring point in protected layer.As shown in Figure7, when the measuring point is located ahead of C25 working face, vertical stress would be increased. However, when C25 working face has passed the measuring point (e.g., 5 m), the vertical stress of measuring point decreases due to the unloading mining affect. If C25 working face continues advancing to an extent, vertical stress of measuring point would tend to be stable. The results are consistent with the previous analysis. From the perspective of stress evolutions, the C19 protected layer experienced a process of stress loading, stress unloading, stress recovery, and stress stability.


#### 4.2.2. Results and Analysis of Relative Expansion Deformation

Figure8 presents the roof and floor displacement curves for C19 protected layer at different advancing distances, based on which the relative expansion deformation of C19 protected layer is calculated:
(10)ς=df−drm×1000,where ς is the relative expansive deformation of protected layer, ‰; df and dr are the roof and floor displacements of protected layer, respectively, m; and m is the thickness of protected layer, m.Figure 8
Displacement curves of C19 protected layer at different advancing distances.
(a)
Roof displacement(b)
Floor displacementThrough calculation, the relative expansion deformation curves of protective layer at different advancing distances are shown in Figure9. If the relative expansion deformation of protected layer has a magnitude greater than 3‰, it could be considered that the coal permeability has increased significantly and the outburst risk of protected layer would be eliminated [20]. Hence, taking the relative expansion deformation of 3‰ as the discrimination value, effective pressure-relief angle in strike direction for C19 protected layer obtained is 59°.Figure 9
Deformation curves for C19 protected layer at different advancing distances.Based on the pressure-relief angle, the corresponding zone of C19 protected layer can be subdivided into the fully pressure-relief zone and nonfully pressure-relief zone as illustrated in Figure 10.Figure 10
Pressure-relief angle and corresponding zones of protected layer.


#### 4.2.3. Results and Analysis of Permeability, Fracture Porosity, and Gas Pressure

As mentioned in Section3.1, the permeability, fracture porosity, and gas pressure would change due to the unloading disturbance of protective layer. The permeability, fracture porosity, and gas pressure are calculated using the Fish language according to Equations (2)–(4). Table 3 lists calculation parameters used in numerical simulation.Table 3
Calculation parameters used in study.
ParameterValuesInitial matrix porosity,ϕm00.06Initial permeability,k02.8×10−4 mDInitial fracture porosity,ϕf00.012Initial gas pressure,p02.06 MPaThrough calculation, evolutions of permeability, fracture porosity, and gas pressure of protected layer during C25 protective layer mining are illustrated in Figures 11–13, respectively.Figure 11
Permeability evolutions of protected layer at different advancing distances.
(a)
40 m(b)
80 m(c)
120 m(d)
160 mFigure 12
Fracture porosity evolutions of protected layer at varying advancing distances.Figure 13
Gas pressure evolutions of protected layer at different advancing distances.
(a)
40 m(b)
80 m(c)
120 m(d)
160 mThe permeability variation of C19 protected layer is on contrary to stress (see Figure 11). In other words, the permeability in the protected layer would be decreased in stress-concentration zone, while it is increased in the pressure-relief zone, which are consistent with the theoretical analysis. With working face continuously advancing, the permeability of protected layer can be increased by 1429 times after the stress decreases significantly. The permeability increase resulting from remote protective layer mining is beneficial for subsequent gas drainage. Moreover, the distributions of gas pressure and vertical stress in protected layer are similar (see Figures 6 and 13). The gas pressure of protected layer is reduced in pressure-relief zone, while it is increased slightly in stress-concentration zone. For an advancing distance of 160 m, the minimum gas pressure in pressure-relief zone is 1.92 MPa, which is 6% lower than the original pressure of 2.06 MPa. The results indicate that although geostress in protected layer is decreased significantly (see Section 4.2.1) due to unloading disturbance, the reduction of gas pressure in protected layer is still relatively minor. Hence, when the remote distance protective layer mining is ended, a measure of gas extraction must be further adopted to decrease gas pressure and thus reducing risks of gas outbursts.


### 4.3. Characteristic Changes during Gas Extraction Process

To effectively extract coal gas in protected layer, crossing borehole is widely adopted [22]. Gas flow around the crossing borehole of a protected layer is approximate to radial flow. Therefore, a plane strain model is employed to study the gas flow during gas extraction of protected layer after unloading disturbance. The geometric model of C19 coal seam is reconstructed in COMSOL Multiphysics program, and permeability, fracture porosity, and gas pressure data obtained in FLAC3D program after unloading disturbance, which are used as initial condition of gas extraction simulation, are input in the form of COMSOL functions [23]. The schematic diagram for gas extraction simulation is illustrated in Figure 14.Figure 14
Schematic diagram for gas extraction simulation.The geometric size is20m×20m (length×width) with the gas extraction borehole diameter being 0.1 m located in model center. To solve the coupled problem, two built-in modules are utilized: one is the “PDE Module” for the gas migration field, and the other is the “Solid Mechanics Module” for coal deformation [23]. The initial and boundary conditions are illustrated in Figure 14. Normal stresses of 10 MPa are applied in inward directions of left and top boundaries, while roller supports are set on bottom and right boundaries. Four outer edges are all set to be zero flux boundaries, and a negative drainage pressure of 25 kPa is set on the borehole wall boundary. Table 4 lists the related calculation parameters for gas extraction simulation.Table 4
Calculation parameters for gas extraction simulation.
ParametersValuesParametersValuesLangmuir constant,PL1.41 MPaLangmuir constant,VL0.0228 m3/kgPoisson’s ratio,v0.21Coal elastic moduli,E1×109 PaElastic moduli for coal matrix,Em3×109 PaAdsorption time,τ1 dMethane molar mass,Mc0.016 kg/molCoal density,ρa1300 kg/m3Ambient temperature,T293 KIdeal gas constant,R8.314 J/(mol·K)Langmuir strain constant,εL0.004Dynamic viscosity of gas,μ1.081 × 10-5 Pa·s


#### 4.3.1. Results and Analysis of Borehole Gas Extraction before and after Unloading Disturbance

To investigate the unloading disturbance effect on gas extraction, numerical simulation of gas extraction in protected layer with unloading disturbance considered is compared to that with unloading disturbance not considered. The gas pressure distributions with varying gas drainage periods before and after unloading disturbance of protective layer mining are shown in Figures15 and 16, respectively.Figure 15
Distributions of gas pressure at varying gas extraction times before unloading disturbance.Figure 16
Distributions of gas pressure at varying gas extraction times after unloading disturbance.As seen from Figures15 and 16, cloud distributions of gas pressure can be regarded as concentric circles; the gas pressure on the borehole wall, a negative drainage pressure of 25 kPa, is the smallest; the greater the distance from borehole center, the greater the gas pressure. Gas pressure at a permanent position around the borehole would gradually decrease with gas drainage time, but its decreased amount is not significant. For instance, when the drainage time changes from 30 d to 180 d, the influence range is relatively constant. The reason is that the original coal permeability before unloading disturbance is low, resulting in the low flow velocity of gas (see Figure 15). Compared to the gas extraction before unloading disturbance, the effect of gas extraction on gas pressure after unloading disturbance has changed significantly as illustrated in Figure 16, from which gas pressure within simulation domain has been changed. For instance, gas pressure in the simulation domain could be decreased to an extent even with a short gas extraction time of 30 days, as illustrated in Figure 16(a).Figure17 shows variation curves for fracture porosity and gas pressure of a monitoring point with radial distance being 0.5 m from the center of gas extraction borehole.Figure 17
Variation curves for fracture porosity and gas pressure of monitoring point.As described in Figure17, gas pressure is reduced sharply at the initial phase of gas extraction. However, its decline rate would gradually reduce and gas pressure tends to reach a stable state. In other words, the velocity of gas flow would decrease with gas extraction time increasing. The reason is that, according to the principle of effective stress and Equation (9), the effective coal stress would increase with gas pressure decreasing, resulting in a compression state for coal skeleton and decreases of fracture porosity and permeability. It should be also noted that although the gas desorption will lead to coal matrix shrink (see Equation (5)) followed by expansion of coal fracture and increase of fracture porosity, the final variation of fracture porosity is attributed to the two competition effects between effective stress and gas sorption. As illustrated in Figure 17, the porosity of coal fracture has gradually been decreased, demonstrating that the increase of effective stress caused by gas pressure reduction plays a greater role in the compression of fractures than the volume expansion of fractures caused by gas desorption.To further describe the gas pressure evolution in the protected layer before and after the unloading disturbance, a measuring line (i.e., “A-A” line in Figure 14) is arranged along radial direction of the borehole. Variation curves for gas pressure on the measuring line before and after unloading disturbance are obtained as shown in Figures 18 and 19, respectively. As seen from Figure 18, the influence radius before unloading disturbance is only 3 m with a gas drainage time of 180 d due to low coal permeability. Therefore, for low permeability coal seam without unloading disturbance, the gas extraction measure is not efficient for gas outburst elimination. Nonetheless, if the unloading disturbance of protective layer mining is considered, gas pressure on the measuring line (see Figure 19) is reduced significantly with gas drainage time increasing, and gas pressure within the whole simulation domain has been influenced; the greatest gas pressure is 1.58 MPa (0.90 MPa) with gas drainage time of 30 d (180 d). In comparison with the two numerical results, it demonstrates that gas extraction combined with remote protective layer mining can reduce gas pressure effectively, which is beneficial for eliminating the outburst risk of protected layer.Figure 18
Variation curves for gas pressure before unloading disturbance.Figure 19
Variation curves for gas pressure after unloading disturbance.


#### 4.3.2. Reasonable Borehole Spacing in Different Pressure Relief Zones

(1) Reasonable Borehole Spacing in a Fully Pressure-Relief Zone. To determine reasonable borehole spacing in the fully pressure-relief zone (see Figure 10), according to the literature [24], five cases of gas extraction with borehole spacing being 20 m, 25 m, 30 m, 35 m, and 40 m are simulated, respectively. The gas pressure-time curves for monitoring point under varying borehole spacings are given in Figure 20. On basis of the “provisions” of China [20], if the magnitude of residual gas pressure was smaller than 0.74 MPa, it could be regarded that risk of outburst is already eliminated. Thus, we adopt the magnitude of 0.74 MPa as the discrimination criterion to determine reasonable borehole spacing. As seen from Figure 20, when borehole spacing of gas extraction is increased to 35 m, residual gas pressure with gas extraction time of 360 d will become greater than discrimination criterion value, which indicates that the reasonable borehole spacing in the fully pressure-relief zone is 30 m with gas extraction time being 360 d. In other words, the effective gas extraction radius in fully pressure-relief zone of protected layer in Chajiaotan coal mine is about 15 m.Figure 20
Gas pressure evolutions of monitoring point in fully pressure-relief zone.(2) Reasonable Borehole Spacing in the Nonfully Pressure-Relief Zone. Similarly, five cases of gas extraction with borehole spacing being 1 m, 3 m, 5 m, 7 m, and 9 m are simulated to determine the reasonable borehole spacing in the nonfully pressure-relief zone (see Figure 10). Numerical results of gas pressure-time curves for monitoring point under varying borehole spacings are illustrated in Figure 21. When borehole spacing is increased to 7 m, residual gas pressure at gas extraction time of 360 d will become greater than the discrimination criterion value, implying that the effective gas extraction radius for the fully pressure-relief zone is 2.5 m with gas extraction time being 360 d. Therefore, the reasonable borehole spacing of gas extraction for Chajiaotan coal mine in the nonfully pressure-relief zone is about 5 m.Figure 21
Gas pressure evolutions of monitoring point in nonfully pressure-relief area.


## 4.1. Numerical Simulation Workflow

Currently, COMSOL Multiphysics program has been extensively adopted to analyze multiphysics coupled problems [23]. Nonetheless, when it is adopted in solving large deformation occurred by mining engineering, its convergence becomes relatively poor, especially in three-dimensional problems. The FLAC3D program, a finite difference code with high accuracy for large deformation problems, is adopted instead to solve the deformation field before gas extraction. Hence, in this work, numerical simulation is conducted by combining the COMSOL Multiphysics and FLAC3D programs. The detailed simulation flowchart is illustrated in Figure 3. Firstly, the FLAC3D program is utilized to obtain deformation and stress of C19 protected layer due to unloading mining of C25 protective layer. Secondly, Fish language (secondary development language embedded in FLAC3D) is used in accordance with Equations (2)–(4) to obtain permeability, fracture porosity, and gas pressure in C19 protected coal seam. Thirdly, the geometric model for C19 protected layer is reconstructed in COMSOL Multiphysics program, and then, permeability, fracture porosity, and gas pressure data obtained in the FLAC3D program, which are used as an initial condition, are input to COMSOL to study gas migration during gas extraction. The following results indicate that unidirectional sequential coupling of FLAC3D and COMSOL Multiphysics programs can simulate characteristic changes of remote distance protective layer mining accurately.Figure 3
Numerical simulation flowchart.


## 4.2. Characteristic Changes during Unloading Disturbance of Remote Distance Protective Mining

According to mining conditions of C25 protective layer in Chajiaotan mine, a FLAC3D numerical model is built based on the lithology columnar as illustrated in Figure 1. Table 2 gives the corresponding parameters adopted in numerical simulation. During numerical simulation, the C25 protective layer is mined with a step length of 10 m, and distributions of stress, displacement, and strain are stored and analyzed after each step.Table 2
Physicomechanical parameters for each rock layer.
Rock formationElasticity moduli (GPa)Tensile strength (MPa)Cohesion (MPa)Friction angle (°)Poisson’s ratioDensity (kg/m3)Overlying strata2.22.76.6370.201900Siltstone5.05.46.2400.252500Sandy mudstone3.03.53.7320.232530Claystone1.81.13.0320.201900Mudstone2.02.52.7300.182430Coal seam1.01.02.0280.211300Kaolinite rock1.82.54.0350.242400Lower strata3.02.04.6400.252500


### 4.2.1. Results of Vertical Stress and Analysis

With the excavation of C25 protective layer, stresses within surrounding rock would be redistributed. Vertical stress distributions in surrounding rock along the strike direction at different advancing distances (i.e., 40 m, 80 m, 120 m, and 160 m) are depicted in Figure 4. As can be seen, stress concentration zones with vertical stress greater than its original value occur on both sides of the working face, while pressure-relief zones are located at the floor and roof of working face; morphology of vertical stress distribution in the surrounding rock is nearly symmetrical. With the working face of C25 protective layer advancing forward, zones of stress concentration and pressure relief increase continuously. The peak vertical stress on both sides of working face increases from 19.1 MPa to 25.6 MPa with the working face of C25 protective layer advancing from 40 m to 80 m. However, when the advancing distance is changed from 120 m to 160 m, the variation of vertical peak stress is relatively minor, and vertical stress remains basically stable.Figure 4
Distributions of vertical stress along strike direction at different advancing distances.
(a)
40 m(b)
80 m(c)
120 m(d)
160 mWith the advancement of lower C25 protective layer, vertical stress curves for the upper C19 protected layer at varying advancing distances are obtained and illustrated in Figure 5.Figure 5
Vertical stress curves for upper C19 protected layer at varying advancing distances.As seen in Figure5, vertical stress in C19 protected layer is less affected by protective layer mining with advancing distance of C25 protective layer being less than 20 m. When advancing distance is 40 m, maximum and minimum vertical stresses within the protected layer are -9.0 MPa and -7.6 MPa (negative denotes compression stress), respectively, which indicates that the coefficient of vertical stress concentration reaches 1.03 and maximum pressure-relief stress is 12.9% lower than its original vertical stress. With the continuous increase of advancing distance (e.g., 60 m ~ 80 m), mining influence of C25 protective layer on protected layer would gradually increase, which are represented by the increase of stress concentration coefficient, pressure-relief, and stress concentration zones and decrease of vertical stress within the pressure relief zone. When advancing distance is 120 m, the maximum vertical stress is -12.1 MPa (i.e., with concentration coefficient of stress being 1.39), and minimum vertical stress is -2.2 MPa, which is 74.8% lower than its original vertical stress. When the advancing distance reaches to an extent (e.g., 140 m), the vertical stress in the pressure relief zone begins to recover resulting from the roof compaction effect of protected layer, and the vertical stress in this zone presents a saddle-shaped distribution.Figure6 presents distributions of vertical stress along the bedding plane of protected layer at varying advancing distances.Figure 6
Distributions of vertical stress along bedding plane of protected layer at varying advancing distances.
(a)
80 m(b)
160 mAs shown in Figure6, the vertical stress along bedding plane of protected layer varies in different zones. At the advancing distance of 80 m, the zone with increased vertical stress is from 44 m ahead to 3 m in the rear of the open-off cut, the zone with decreased vertical stress is from 3 m to 80 m in the rear of open-off cut, and other zone with vertical stress kept unchanged is from 44 m to 80 m ahead of open-off cut. Therefore, according to distribution characteristics of vertical stress, the protected layer with advancing distance being 80 m could be subdivided into three different zones as illustrated in Figure 6(a). Furthermore, when the advancing distance reaches to an extent (e.g., 140 m), the zone whose vertical stress had been significantly released starts to recover again. Therefore, after the protective layer mining ended (i.e., an advance distance of 140 m), the protected layer could be subdivided into four different zones as illustrated in Figure 6(b).The vertical stress variation of a measuring point, located at the corresponding center of working face of C25 protective layer, was also monitored. Figure 7 gives the vertical stress variation of a central measuring point in protected layer.Figure 7
Vertical stress variation of a central measuring point in protected layer.As shown in Figure7, when the measuring point is located ahead of C25 working face, vertical stress would be increased. However, when C25 working face has passed the measuring point (e.g., 5 m), the vertical stress of measuring point decreases due to the unloading mining affect. If C25 working face continues advancing to an extent, vertical stress of measuring point would tend to be stable. The results are consistent with the previous analysis. From the perspective of stress evolutions, the C19 protected layer experienced a process of stress loading, stress unloading, stress recovery, and stress stability.


### 4.2.2. Results and Analysis of Relative Expansion Deformation

Figure8 presents the roof and floor displacement curves for C19 protected layer at different advancing distances, based on which the relative expansion deformation of C19 protected layer is calculated:
(10)ς=df−drm×1000,where ς is the relative expansive deformation of protected layer, ‰; df and dr are the roof and floor displacements of protected layer, respectively, m; and m is the thickness of protected layer, m.Figure 8
Displacement curves of C19 protected layer at different advancing distances.
(a)
Roof displacement(b)
Floor displacementThrough calculation, the relative expansion deformation curves of protective layer at different advancing distances are shown in Figure9. If the relative expansion deformation of protected layer has a magnitude greater than 3‰, it could be considered that the coal permeability has increased significantly and the outburst risk of protected layer would be eliminated [20]. Hence, taking the relative expansion deformation of 3‰ as the discrimination value, effective pressure-relief angle in strike direction for C19 protected layer obtained is 59°.Figure 9
Deformation curves for C19 protected layer at different advancing distances.Based on the pressure-relief angle, the corresponding zone of C19 protected layer can be subdivided into the fully pressure-relief zone and nonfully pressure-relief zone as illustrated in Figure 10.Figure 10
Pressure-relief angle and corresponding zones of protected layer.


### 4.2.3. Results and Analysis of Permeability, Fracture Porosity, and Gas Pressure

As mentioned in Section3.1, the permeability, fracture porosity, and gas pressure would change due to the unloading disturbance of protective layer. The permeability, fracture porosity, and gas pressure are calculated using the Fish language according to Equations (2)–(4). Table 3 lists calculation parameters used in numerical simulation.Table 3
Calculation parameters used in study.
ParameterValuesInitial matrix porosity,ϕm00.06Initial permeability,k02.8×10−4 mDInitial fracture porosity,ϕf00.012Initial gas pressure,p02.06 MPaThrough calculation, evolutions of permeability, fracture porosity, and gas pressure of protected layer during C25 protective layer mining are illustrated in Figures 11–13, respectively.Figure 11
Permeability evolutions of protected layer at different advancing distances.
(a)
40 m(b)
80 m(c)
120 m(d)
160 mFigure 12
Fracture porosity evolutions of protected layer at varying advancing distances.Figure 13
Gas pressure evolutions of protected layer at different advancing distances.
(a)
40 m(b)
80 m(c)
120 m(d)
160 mThe permeability variation of C19 protected layer is on contrary to stress (see Figure 11). In other words, the permeability in the protected layer would be decreased in stress-concentration zone, while it is increased in the pressure-relief zone, which are consistent with the theoretical analysis. With working face continuously advancing, the permeability of protected layer can be increased by 1429 times after the stress decreases significantly. The permeability increase resulting from remote protective layer mining is beneficial for subsequent gas drainage. Moreover, the distributions of gas pressure and vertical stress in protected layer are similar (see Figures 6 and 13). The gas pressure of protected layer is reduced in pressure-relief zone, while it is increased slightly in stress-concentration zone. For an advancing distance of 160 m, the minimum gas pressure in pressure-relief zone is 1.92 MPa, which is 6% lower than the original pressure of 2.06 MPa. The results indicate that although geostress in protected layer is decreased significantly (see Section 4.2.1) due to unloading disturbance, the reduction of gas pressure in protected layer is still relatively minor. Hence, when the remote distance protective layer mining is ended, a measure of gas extraction must be further adopted to decrease gas pressure and thus reducing risks of gas outbursts.


## 4.2.1. Results of Vertical Stress and Analysis

With the excavation of C25 protective layer, stresses within surrounding rock would be redistributed. Vertical stress distributions in surrounding rock along the strike direction at different advancing distances (i.e., 40 m, 80 m, 120 m, and 160 m) are depicted in Figure 4. As can be seen, stress concentration zones with vertical stress greater than its original value occur on both sides of the working face, while pressure-relief zones are located at the floor and roof of working face; morphology of vertical stress distribution in the surrounding rock is nearly symmetrical. With the working face of C25 protective layer advancing forward, zones of stress concentration and pressure relief increase continuously. The peak vertical stress on both sides of working face increases from 19.1 MPa to 25.6 MPa with the working face of C25 protective layer advancing from 40 m to 80 m. However, when the advancing distance is changed from 120 m to 160 m, the variation of vertical peak stress is relatively minor, and vertical stress remains basically stable.Figure 4
Distributions of vertical stress along strike direction at different advancing distances.
(a)
40 m(b)
80 m(c)
120 m(d)
160 mWith the advancement of lower C25 protective layer, vertical stress curves for the upper C19 protected layer at varying advancing distances are obtained and illustrated in Figure 5.Figure 5
Vertical stress curves for upper C19 protected layer at varying advancing distances.As seen in Figure5, vertical stress in C19 protected layer is less affected by protective layer mining with advancing distance of C25 protective layer being less than 20 m. When advancing distance is 40 m, maximum and minimum vertical stresses within the protected layer are -9.0 MPa and -7.6 MPa (negative denotes compression stress), respectively, which indicates that the coefficient of vertical stress concentration reaches 1.03 and maximum pressure-relief stress is 12.9% lower than its original vertical stress. With the continuous increase of advancing distance (e.g., 60 m ~ 80 m), mining influence of C25 protective layer on protected layer would gradually increase, which are represented by the increase of stress concentration coefficient, pressure-relief, and stress concentration zones and decrease of vertical stress within the pressure relief zone. When advancing distance is 120 m, the maximum vertical stress is -12.1 MPa (i.e., with concentration coefficient of stress being 1.39), and minimum vertical stress is -2.2 MPa, which is 74.8% lower than its original vertical stress. When the advancing distance reaches to an extent (e.g., 140 m), the vertical stress in the pressure relief zone begins to recover resulting from the roof compaction effect of protected layer, and the vertical stress in this zone presents a saddle-shaped distribution.Figure6 presents distributions of vertical stress along the bedding plane of protected layer at varying advancing distances.Figure 6
Distributions of vertical stress along bedding plane of protected layer at varying advancing distances.
(a)
80 m(b)
160 mAs shown in Figure6, the vertical stress along bedding plane of protected layer varies in different zones. At the advancing distance of 80 m, the zone with increased vertical stress is from 44 m ahead to 3 m in the rear of the open-off cut, the zone with decreased vertical stress is from 3 m to 80 m in the rear of open-off cut, and other zone with vertical stress kept unchanged is from 44 m to 80 m ahead of open-off cut. Therefore, according to distribution characteristics of vertical stress, the protected layer with advancing distance being 80 m could be subdivided into three different zones as illustrated in Figure 6(a). Furthermore, when the advancing distance reaches to an extent (e.g., 140 m), the zone whose vertical stress had been significantly released starts to recover again. Therefore, after the protective layer mining ended (i.e., an advance distance of 140 m), the protected layer could be subdivided into four different zones as illustrated in Figure 6(b).The vertical stress variation of a measuring point, located at the corresponding center of working face of C25 protective layer, was also monitored. Figure 7 gives the vertical stress variation of a central measuring point in protected layer.Figure 7
Vertical stress variation of a central measuring point in protected layer.As shown in Figure7, when the measuring point is located ahead of C25 working face, vertical stress would be increased. However, when C25 working face has passed the measuring point (e.g., 5 m), the vertical stress of measuring point decreases due to the unloading mining affect. If C25 working face continues advancing to an extent, vertical stress of measuring point would tend to be stable. The results are consistent with the previous analysis. From the perspective of stress evolutions, the C19 protected layer experienced a process of stress loading, stress unloading, stress recovery, and stress stability.


## 4.2.2. Results and Analysis of Relative Expansion Deformation

Figure8 presents the roof and floor displacement curves for C19 protected layer at different advancing distances, based on which the relative expansion deformation of C19 protected layer is calculated:
(10)ς=df−drm×1000,where ς is the relative expansive deformation of protected layer, ‰; df and dr are the roof and floor displacements of protected layer, respectively, m; and m is the thickness of protected layer, m.Figure 8
Displacement curves of C19 protected layer at different advancing distances.
(a)
Roof displacement(b)
Floor displacementThrough calculation, the relative expansion deformation curves of protective layer at different advancing distances are shown in Figure9. If the relative expansion deformation of protected layer has a magnitude greater than 3‰, it could be considered that the coal permeability has increased significantly and the outburst risk of protected layer would be eliminated [20]. Hence, taking the relative expansion deformation of 3‰ as the discrimination value, effective pressure-relief angle in strike direction for C19 protected layer obtained is 59°.Figure 9
Deformation curves for C19 protected layer at different advancing distances.Based on the pressure-relief angle, the corresponding zone of C19 protected layer can be subdivided into the fully pressure-relief zone and nonfully pressure-relief zone as illustrated in Figure 10.Figure 10
Pressure-relief angle and corresponding zones of protected layer.


## 4.2.3. Results and Analysis of Permeability, Fracture Porosity, and Gas Pressure

As mentioned in Section3.1, the permeability, fracture porosity, and gas pressure would change due to the unloading disturbance of protective layer. The permeability, fracture porosity, and gas pressure are calculated using the Fish language according to Equations (2)–(4). Table 3 lists calculation parameters used in numerical simulation.Table 3
Calculation parameters used in study.
ParameterValuesInitial matrix porosity,ϕm00.06Initial permeability,k02.8×10−4 mDInitial fracture porosity,ϕf00.012Initial gas pressure,p02.06 MPaThrough calculation, evolutions of permeability, fracture porosity, and gas pressure of protected layer during C25 protective layer mining are illustrated in Figures 11–13, respectively.Figure 11
Permeability evolutions of protected layer at different advancing distances.
(a)
40 m(b)
80 m(c)
120 m(d)
160 mFigure 12
Fracture porosity evolutions of protected layer at varying advancing distances.Figure 13
Gas pressure evolutions of protected layer at different advancing distances.
(a)
40 m(b)
80 m(c)
120 m(d)
160 mThe permeability variation of C19 protected layer is on contrary to stress (see Figure 11). In other words, the permeability in the protected layer would be decreased in stress-concentration zone, while it is increased in the pressure-relief zone, which are consistent with the theoretical analysis. With working face continuously advancing, the permeability of protected layer can be increased by 1429 times after the stress decreases significantly. The permeability increase resulting from remote protective layer mining is beneficial for subsequent gas drainage. Moreover, the distributions of gas pressure and vertical stress in protected layer are similar (see Figures 6 and 13). The gas pressure of protected layer is reduced in pressure-relief zone, while it is increased slightly in stress-concentration zone. For an advancing distance of 160 m, the minimum gas pressure in pressure-relief zone is 1.92 MPa, which is 6% lower than the original pressure of 2.06 MPa. The results indicate that although geostress in protected layer is decreased significantly (see Section 4.2.1) due to unloading disturbance, the reduction of gas pressure in protected layer is still relatively minor. Hence, when the remote distance protective layer mining is ended, a measure of gas extraction must be further adopted to decrease gas pressure and thus reducing risks of gas outbursts.


## 4.3. Characteristic Changes during Gas Extraction Process

To effectively extract coal gas in protected layer, crossing borehole is widely adopted [22]. Gas flow around the crossing borehole of a protected layer is approximate to radial flow. Therefore, a plane strain model is employed to study the gas flow during gas extraction of protected layer after unloading disturbance. The geometric model of C19 coal seam is reconstructed in COMSOL Multiphysics program, and permeability, fracture porosity, and gas pressure data obtained in FLAC3D program after unloading disturbance, which are used as initial condition of gas extraction simulation, are input in the form of COMSOL functions [23]. The schematic diagram for gas extraction simulation is illustrated in Figure 14.Figure 14
Schematic diagram for gas extraction simulation.The geometric size is20m×20m (length×width) with the gas extraction borehole diameter being 0.1 m located in model center. To solve the coupled problem, two built-in modules are utilized: one is the “PDE Module” for the gas migration field, and the other is the “Solid Mechanics Module” for coal deformation [23]. The initial and boundary conditions are illustrated in Figure 14. Normal stresses of 10 MPa are applied in inward directions of left and top boundaries, while roller supports are set on bottom and right boundaries. Four outer edges are all set to be zero flux boundaries, and a negative drainage pressure of 25 kPa is set on the borehole wall boundary. Table 4 lists the related calculation parameters for gas extraction simulation.Table 4
Calculation parameters for gas extraction simulation.
ParametersValuesParametersValuesLangmuir constant,PL1.41 MPaLangmuir constant,VL0.0228 m3/kgPoisson’s ratio,v0.21Coal elastic moduli,E1×109 PaElastic moduli for coal matrix,Em3×109 PaAdsorption time,τ1 dMethane molar mass,Mc0.016 kg/molCoal density,ρa1300 kg/m3Ambient temperature,T293 KIdeal gas constant,R8.314 J/(mol·K)Langmuir strain constant,εL0.004Dynamic viscosity of gas,μ1.081 × 10-5 Pa·s


### 4.3.1. Results and Analysis of Borehole Gas Extraction before and after Unloading Disturbance

To investigate the unloading disturbance effect on gas extraction, numerical simulation of gas extraction in protected layer with unloading disturbance considered is compared to that with unloading disturbance not considered. The gas pressure distributions with varying gas drainage periods before and after unloading disturbance of protective layer mining are shown in Figures15 and 16, respectively.Figure 15
Distributions of gas pressure at varying gas extraction times before unloading disturbance.Figure 16
Distributions of gas pressure at varying gas extraction times after unloading disturbance.As seen from Figures15 and 16, cloud distributions of gas pressure can be regarded as concentric circles; the gas pressure on the borehole wall, a negative drainage pressure of 25 kPa, is the smallest; the greater the distance from borehole center, the greater the gas pressure. Gas pressure at a permanent position around the borehole would gradually decrease with gas drainage time, but its decreased amount is not significant. For instance, when the drainage time changes from 30 d to 180 d, the influence range is relatively constant. The reason is that the original coal permeability before unloading disturbance is low, resulting in the low flow velocity of gas (see Figure 15). Compared to the gas extraction before unloading disturbance, the effect of gas extraction on gas pressure after unloading disturbance has changed significantly as illustrated in Figure 16, from which gas pressure within simulation domain has been changed. For instance, gas pressure in the simulation domain could be decreased to an extent even with a short gas extraction time of 30 days, as illustrated in Figure 16(a).Figure17 shows variation curves for fracture porosity and gas pressure of a monitoring point with radial distance being 0.5 m from the center of gas extraction borehole.Figure 17
Variation curves for fracture porosity and gas pressure of monitoring point.As described in Figure17, gas pressure is reduced sharply at the initial phase of gas extraction. However, its decline rate would gradually reduce and gas pressure tends to reach a stable state. In other words, the velocity of gas flow would decrease with gas extraction time increasing. The reason is that, according to the principle of effective stress and Equation (9), the effective coal stress would increase with gas pressure decreasing, resulting in a compression state for coal skeleton and decreases of fracture porosity and permeability. It should be also noted that although the gas desorption will lead to coal matrix shrink (see Equation (5)) followed by expansion of coal fracture and increase of fracture porosity, the final variation of fracture porosity is attributed to the two competition effects between effective stress and gas sorption. As illustrated in Figure 17, the porosity of coal fracture has gradually been decreased, demonstrating that the increase of effective stress caused by gas pressure reduction plays a greater role in the compression of fractures than the volume expansion of fractures caused by gas desorption.To further describe the gas pressure evolution in the protected layer before and after the unloading disturbance, a measuring line (i.e., “A-A” line in Figure 14) is arranged along radial direction of the borehole. Variation curves for gas pressure on the measuring line before and after unloading disturbance are obtained as shown in Figures 18 and 19, respectively. As seen from Figure 18, the influence radius before unloading disturbance is only 3 m with a gas drainage time of 180 d due to low coal permeability. Therefore, for low permeability coal seam without unloading disturbance, the gas extraction measure is not efficient for gas outburst elimination. Nonetheless, if the unloading disturbance of protective layer mining is considered, gas pressure on the measuring line (see Figure 19) is reduced significantly with gas drainage time increasing, and gas pressure within the whole simulation domain has been influenced; the greatest gas pressure is 1.58 MPa (0.90 MPa) with gas drainage time of 30 d (180 d). In comparison with the two numerical results, it demonstrates that gas extraction combined with remote protective layer mining can reduce gas pressure effectively, which is beneficial for eliminating the outburst risk of protected layer.Figure 18
Variation curves for gas pressure before unloading disturbance.Figure 19
Variation curves for gas pressure after unloading disturbance.


### 4.3.2. Reasonable Borehole Spacing in Different Pressure Relief Zones

(1) Reasonable Borehole Spacing in a Fully Pressure-Relief Zone. To determine reasonable borehole spacing in the fully pressure-relief zone (see Figure 10), according to the literature [24], five cases of gas extraction with borehole spacing being 20 m, 25 m, 30 m, 35 m, and 40 m are simulated, respectively. The gas pressure-time curves for monitoring point under varying borehole spacings are given in Figure 20. On basis of the “provisions” of China [20], if the magnitude of residual gas pressure was smaller than 0.74 MPa, it could be regarded that risk of outburst is already eliminated. Thus, we adopt the magnitude of 0.74 MPa as the discrimination criterion to determine reasonable borehole spacing. As seen from Figure 20, when borehole spacing of gas extraction is increased to 35 m, residual gas pressure with gas extraction time of 360 d will become greater than discrimination criterion value, which indicates that the reasonable borehole spacing in the fully pressure-relief zone is 30 m with gas extraction time being 360 d. In other words, the effective gas extraction radius in fully pressure-relief zone of protected layer in Chajiaotan coal mine is about 15 m.Figure 20
Gas pressure evolutions of monitoring point in fully pressure-relief zone.(2) Reasonable Borehole Spacing in the Nonfully Pressure-Relief Zone. Similarly, five cases of gas extraction with borehole spacing being 1 m, 3 m, 5 m, 7 m, and 9 m are simulated to determine the reasonable borehole spacing in the nonfully pressure-relief zone (see Figure 10). Numerical results of gas pressure-time curves for monitoring point under varying borehole spacings are illustrated in Figure 21. When borehole spacing is increased to 7 m, residual gas pressure at gas extraction time of 360 d will become greater than the discrimination criterion value, implying that the effective gas extraction radius for the fully pressure-relief zone is 2.5 m with gas extraction time being 360 d. Therefore, the reasonable borehole spacing of gas extraction for Chajiaotan coal mine in the nonfully pressure-relief zone is about 5 m.Figure 21
Gas pressure evolutions of monitoring point in nonfully pressure-relief area.


## 4.3.1. Results and Analysis of Borehole Gas Extraction before and after Unloading Disturbance

To investigate the unloading disturbance effect on gas extraction, numerical simulation of gas extraction in protected layer with unloading disturbance considered is compared to that with unloading disturbance not considered. The gas pressure distributions with varying gas drainage periods before and after unloading disturbance of protective layer mining are shown in Figures15 and 16, respectively.Figure 15
Distributions of gas pressure at varying gas extraction times before unloading disturbance.Figure 16
Distributions of gas pressure at varying gas extraction times after unloading disturbance.As seen from Figures15 and 16, cloud distributions of gas pressure can be regarded as concentric circles; the gas pressure on the borehole wall, a negative drainage pressure of 25 kPa, is the smallest; the greater the distance from borehole center, the greater the gas pressure. Gas pressure at a permanent position around the borehole would gradually decrease with gas drainage time, but its decreased amount is not significant. For instance, when the drainage time changes from 30 d to 180 d, the influence range is relatively constant. The reason is that the original coal permeability before unloading disturbance is low, resulting in the low flow velocity of gas (see Figure 15). Compared to the gas extraction before unloading disturbance, the effect of gas extraction on gas pressure after unloading disturbance has changed significantly as illustrated in Figure 16, from which gas pressure within simulation domain has been changed. For instance, gas pressure in the simulation domain could be decreased to an extent even with a short gas extraction time of 30 days, as illustrated in Figure 16(a).Figure17 shows variation curves for fracture porosity and gas pressure of a monitoring point with radial distance being 0.5 m from the center of gas extraction borehole.Figure 17
Variation curves for fracture porosity and gas pressure of monitoring point.As described in Figure17, gas pressure is reduced sharply at the initial phase of gas extraction. However, its decline rate would gradually reduce and gas pressure tends to reach a stable state. In other words, the velocity of gas flow would decrease with gas extraction time increasing. The reason is that, according to the principle of effective stress and Equation (9), the effective coal stress would increase with gas pressure decreasing, resulting in a compression state for coal skeleton and decreases of fracture porosity and permeability. It should be also noted that although the gas desorption will lead to coal matrix shrink (see Equation (5)) followed by expansion of coal fracture and increase of fracture porosity, the final variation of fracture porosity is attributed to the two competition effects between effective stress and gas sorption. As illustrated in Figure 17, the porosity of coal fracture has gradually been decreased, demonstrating that the increase of effective stress caused by gas pressure reduction plays a greater role in the compression of fractures than the volume expansion of fractures caused by gas desorption.To further describe the gas pressure evolution in the protected layer before and after the unloading disturbance, a measuring line (i.e., “A-A” line in Figure 14) is arranged along radial direction of the borehole. Variation curves for gas pressure on the measuring line before and after unloading disturbance are obtained as shown in Figures 18 and 19, respectively. As seen from Figure 18, the influence radius before unloading disturbance is only 3 m with a gas drainage time of 180 d due to low coal permeability. Therefore, for low permeability coal seam without unloading disturbance, the gas extraction measure is not efficient for gas outburst elimination. Nonetheless, if the unloading disturbance of protective layer mining is considered, gas pressure on the measuring line (see Figure 19) is reduced significantly with gas drainage time increasing, and gas pressure within the whole simulation domain has been influenced; the greatest gas pressure is 1.58 MPa (0.90 MPa) with gas drainage time of 30 d (180 d). In comparison with the two numerical results, it demonstrates that gas extraction combined with remote protective layer mining can reduce gas pressure effectively, which is beneficial for eliminating the outburst risk of protected layer.Figure 18
Variation curves for gas pressure before unloading disturbance.Figure 19
Variation curves for gas pressure after unloading disturbance.


## 4.3.2. Reasonable Borehole Spacing in Different Pressure Relief Zones

(1) Reasonable Borehole Spacing in a Fully Pressure-Relief Zone. To determine reasonable borehole spacing in the fully pressure-relief zone (see Figure 10), according to the literature [24], five cases of gas extraction with borehole spacing being 20 m, 25 m, 30 m, 35 m, and 40 m are simulated, respectively. The gas pressure-time curves for monitoring point under varying borehole spacings are given in Figure 20. On basis of the “provisions” of China [20], if the magnitude of residual gas pressure was smaller than 0.74 MPa, it could be regarded that risk of outburst is already eliminated. Thus, we adopt the magnitude of 0.74 MPa as the discrimination criterion to determine reasonable borehole spacing. As seen from Figure 20, when borehole spacing of gas extraction is increased to 35 m, residual gas pressure with gas extraction time of 360 d will become greater than discrimination criterion value, which indicates that the reasonable borehole spacing in the fully pressure-relief zone is 30 m with gas extraction time being 360 d. In other words, the effective gas extraction radius in fully pressure-relief zone of protected layer in Chajiaotan coal mine is about 15 m.Figure 20
Gas pressure evolutions of monitoring point in fully pressure-relief zone.(2) Reasonable Borehole Spacing in the Nonfully Pressure-Relief Zone. Similarly, five cases of gas extraction with borehole spacing being 1 m, 3 m, 5 m, 7 m, and 9 m are simulated to determine the reasonable borehole spacing in the nonfully pressure-relief zone (see Figure 10). Numerical results of gas pressure-time curves for monitoring point under varying borehole spacings are illustrated in Figure 21. When borehole spacing is increased to 7 m, residual gas pressure at gas extraction time of 360 d will become greater than the discrimination criterion value, implying that the effective gas extraction radius for the fully pressure-relief zone is 2.5 m with gas extraction time being 360 d. Therefore, the reasonable borehole spacing of gas extraction for Chajiaotan coal mine in the nonfully pressure-relief zone is about 5 m.Figure 21
Gas pressure evolutions of monitoring point in nonfully pressure-relief area.


## 5. Field Application and Validation

### 5.1. Borehole Layout for Gas Extraction

To intercept and extract the pressure-relief gas of C19 protected layer after unloading disturbance of protective layer mining, crossing boreholes are arranged in the roadway of C25 protective layer. On one hand, such layout of crossing boreholes can effectively save the construction cost of roadway or boreholes and shorten the preparation period. On the other hand, crossing boreholes would effectively cover the corresponding C19 protected layer, which ensures that all free gas would be efficiently intercepted and drained by the gas extraction boreholes, thus decreasing gas pressure or content of C19 protected layer to reduce its outburst risk.As mentioned in Section4.2.2, the corresponding C19 protected layer can be subdivided into the fully pressure-relief zone and nonfully pressure-relief zone. Moreover, numerical simulations of gas drainage after unloading disturbance indicated that the effective gas drainage radii are 15 m and 2.5 m in the fully pressure-relief zone and nonfully pressure-relief zone, respectively. Therefore, according to the engineering mining plan of Chajiaotan coal mine, borehole spacings of gas extraction in the fully and nonfully pressure-relief zones are set to be 30 m and 5 m, respectively.


### 5.2. Investigation on Residual Gas Pressure

According to “provisions” of China [20], if residual gas pressure was below 0.74 MPa, then it could be regarded that the outburst risk was already eliminated. Hence, the outburst elimination effect of C19 protected layer is further investigated by analyzing residual gas pressure in C19 protected layer after gas extraction. Eleven gas pressure inspection boreholes are designed, among which five inspection boreholes (i.e., boreholes Pz1 ~ Pz5) and six inspection boreholes (i.e., boreholes Pq1 ~ Pq5) are located along the strike and dip direction of coal seam, respectively, as illustrated in Figure 22.Figure 22
Layout of crossing boreholes.
(a)
Plane view(b)
Cross-sectional viewAfter C25 protective layer mining was ended, the residual gas pressures in inspection boreholes were gathered. Table 5 lists the observed residual gas pressures in these inspection boreholes.Table 5
Residual gas pressure in inspection boreholes.
BoreholeResidual gas pressure (MPa)BoreholeResidual gas pressure (MPa)Pq10.45Pz10.31Pq20.39Pz20.29Pq30.34Pz30.22Pq40.29Pz40.26Pq50.30Pz50.20Pq60.36As seen from Table5, residual gas pressure values in eleven investigated boreholes are all less than discrimination value, which indicate that outburst risk in C19 protected layer is effectively decreased by remote protective layer mining in combination with gas extraction, which also verifies the rationality of borehole layout proposed for gas extraction in remote protected layer and reliability of mathematical model and its implementation.


### 5.3. Investigation on Relative Expansion Deformation in Protected Layer

To further investigate and validate the unloading disturbance of remote protective layer mining, an inspection point (theD point as shown in Figure 22(a)) in C19 protected layer was designed to investigate the relative expansion deformation with working face of protective layer advancing. The inspection point is situated along dip direction of C25 protected layer, 70 m away from the opening cut of protective layer. The variation curve for relative expansion deformation for C19 protected layer during C25 protective layer mining is given in Figure 23.Figure 23
The variation curve for the relative expansion deformation.As shown in Figure23, when the inspection point is located ahead of working face, the relative expansion deformation is negative, and its minimum value is -3.8‰, which means that the inspection point is in the compression state affected by stress concentration. When the working face of C25 protective layer has passed the inspection point, the relative expansion deformation at the inspection point turns from a negative value to a positive value. The relative expansion deformation has reached a maximum value of 14.2‰ when it passes 50 m away from the inspection point. With the working face continuously advancing, relative expansion deformation of the protected layer would tend to be stable. From the perspective of stress evolution, it can be inferred that the C19 protected layer experienced processes of stress loading, stress unloading, stress recovery, and stress stability. The field result of the relative expansion deformation of inspection point agrees well with numerical simulation (see Section 4.2.2). According to “provisions” of China, if relative expansion deformation for coal seam is more than a magnitude of 3‰, it is deemed that protected coal seam is effectively protected. Thus, it can be inferred that C19 protected coal seam has achieved a reasonable unloading effect after remote distance protective layer mining.In brief, the results demonstrated that the outburst risk of C19 protected layer could be reduced due to the unloading disturbance of C25 coal seam mining in combination with gas extraction of C19 protected layer, which also validates the reliability of the mathematical model and corresponding implementation proposed.


## 5.1. Borehole Layout for Gas Extraction

To intercept and extract the pressure-relief gas of C19 protected layer after unloading disturbance of protective layer mining, crossing boreholes are arranged in the roadway of C25 protective layer. On one hand, such layout of crossing boreholes can effectively save the construction cost of roadway or boreholes and shorten the preparation period. On the other hand, crossing boreholes would effectively cover the corresponding C19 protected layer, which ensures that all free gas would be efficiently intercepted and drained by the gas extraction boreholes, thus decreasing gas pressure or content of C19 protected layer to reduce its outburst risk.As mentioned in Section4.2.2, the corresponding C19 protected layer can be subdivided into the fully pressure-relief zone and nonfully pressure-relief zone. Moreover, numerical simulations of gas drainage after unloading disturbance indicated that the effective gas drainage radii are 15 m and 2.5 m in the fully pressure-relief zone and nonfully pressure-relief zone, respectively. Therefore, according to the engineering mining plan of Chajiaotan coal mine, borehole spacings of gas extraction in the fully and nonfully pressure-relief zones are set to be 30 m and 5 m, respectively.


## 5.2. Investigation on Residual Gas Pressure

According to “provisions” of China [20], if residual gas pressure was below 0.74 MPa, then it could be regarded that the outburst risk was already eliminated. Hence, the outburst elimination effect of C19 protected layer is further investigated by analyzing residual gas pressure in C19 protected layer after gas extraction. Eleven gas pressure inspection boreholes are designed, among which five inspection boreholes (i.e., boreholes Pz1 ~ Pz5) and six inspection boreholes (i.e., boreholes Pq1 ~ Pq5) are located along the strike and dip direction of coal seam, respectively, as illustrated in Figure 22.Figure 22
Layout of crossing boreholes.
(a)
Plane view(b)
Cross-sectional viewAfter C25 protective layer mining was ended, the residual gas pressures in inspection boreholes were gathered. Table 5 lists the observed residual gas pressures in these inspection boreholes.Table 5
Residual gas pressure in inspection boreholes.
BoreholeResidual gas pressure (MPa)BoreholeResidual gas pressure (MPa)Pq10.45Pz10.31Pq20.39Pz20.29Pq30.34Pz30.22Pq40.29Pz40.26Pq50.30Pz50.20Pq60.36As seen from Table5, residual gas pressure values in eleven investigated boreholes are all less than discrimination value, which indicate that outburst risk in C19 protected layer is effectively decreased by remote protective layer mining in combination with gas extraction, which also verifies the rationality of borehole layout proposed for gas extraction in remote protected layer and reliability of mathematical model and its implementation.


## 5.3. Investigation on Relative Expansion Deformation in Protected Layer

To further investigate and validate the unloading disturbance of remote protective layer mining, an inspection point (theD point as shown in Figure 22(a)) in C19 protected layer was designed to investigate the relative expansion deformation with working face of protective layer advancing. The inspection point is situated along dip direction of C25 protected layer, 70 m away from the opening cut of protective layer. The variation curve for relative expansion deformation for C19 protected layer during C25 protective layer mining is given in Figure 23.Figure 23
The variation curve for the relative expansion deformation.As shown in Figure23, when the inspection point is located ahead of working face, the relative expansion deformation is negative, and its minimum value is -3.8‰, which means that the inspection point is in the compression state affected by stress concentration. When the working face of C25 protective layer has passed the inspection point, the relative expansion deformation at the inspection point turns from a negative value to a positive value. The relative expansion deformation has reached a maximum value of 14.2‰ when it passes 50 m away from the inspection point. With the working face continuously advancing, relative expansion deformation of the protected layer would tend to be stable. From the perspective of stress evolution, it can be inferred that the C19 protected layer experienced processes of stress loading, stress unloading, stress recovery, and stress stability. The field result of the relative expansion deformation of inspection point agrees well with numerical simulation (see Section 4.2.2). According to “provisions” of China, if relative expansion deformation for coal seam is more than a magnitude of 3‰, it is deemed that protected coal seam is effectively protected. Thus, it can be inferred that C19 protected coal seam has achieved a reasonable unloading effect after remote distance protective layer mining.In brief, the results demonstrated that the outburst risk of C19 protected layer could be reduced due to the unloading disturbance of C25 coal seam mining in combination with gas extraction of C19 protected layer, which also validates the reliability of the mathematical model and corresponding implementation proposed.


## 6. Conclusions

A new mathematical model considering unloading disturbance and solid-gas coupling effect during gas extraction was developed for remote distance protective layer mining. The proposed model was implemented by combining the FLAC3D and COMSOL programs to study characteristic changes during remote distance protective layer mining of Chajiaotan mine. The obtained conclusions are as follows:
(1)
Numerical results of unloading disturbance indicated that the protected layer would gradually experience stress loading, unloading, stress recovery, and stability as the protective layer’s working face advances; the protected layer could be subdivided into concentration zone, pressure-relief zone, compaction zone, and original zone; the effective pressure-relief angle in strike direction of C19 protected layer is 59°, and the C19 protected layer can be subdivided into the fully pressure-relief zone and nonfully pressure-relief zone(2)
When the stress in protected layer is reduced by 74.8%, the gas pressure in protected layer is only reduced by 6%, but the permeability of protected layer could be increased by 1429 times. Numerical results of unloading disturbance demonstrated that unloading disturbance plays a greater role on coal permeability than gas pressure, so gas drainage measure must be further adopted to reduce gas pressure(3)
Numerical comparisons of gas pressure distributions in the unloading and original protected layer showed that gas extraction of protected layer after unloading disturbance can reduce gas pressure more effectively. Numerical results of gas extraction under varying borehole spacings showed that appropriate borehole spacings are 30 m and 5 m in the fully and nonfully pressure-relief zones(4)
Numerical results are applied in the design of borehole layout for gas extraction, and residual gas pressure in investigated boreholes is all smaller than the discrimination value of 0.74 MPa; the outburst risk of protected layer has been reduced. The numerical simulation results of relative expansion deformation and gas extraction radii agree well with the results of site observation, which demonstrated the reliability of the mathematical model and its realization. The approach is promising for assessing unloading disturbance and gas drainage in the engineering practice of remote protective layer mining



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*Source: 3679384-2022-08-16.xml*