# A Static Fracturing Technology to Enhance the Permeability of Coalbed: Mechanical Study

Authors: Long Wang; Baohua Guo; Zhaofeng Wang
Journal: Advances in Civil Engineering
 (2019)

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## Abstract

Low permeability of coalbed has always been a main bottleneck impeding the safety production of coal mines and the high-efficient gas recovery. A static fracturing technology, relied on hydraulic-driving modules to expand outwards for producing artificial fissures in coalbed, is proposed here for coalbed reservoir stimulation. The mechanical model of borehole fracturing is established to clarify the associated mechanisms for fracturing stimulation based on the elastic-plastic mechanics. The numerical results indicate when the fracturing load is over twice as much as in situ stress, the concentration of hoop stress around borehole would be released and the range of fracturing-induced fissures gradually extends with the rising load. While the lateral stress coefficient of strata rising from 1 to 3, the stress distribution around borehole evolves from a ring to a saddle shape, resulting in the horizontal extension of fissures in the early stage. According to underground monitoring, a significant improvement of coalbed permeability up to 5 times has been achieved in 16031 tailgate, in Guhanshan coalmine, China.


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## Body

## 1. Introduction

On account of a specific energy structure and a gigantic consumption, China has already been the world’s largest coal producer with the output of 3.41 billion tons in 2016, meanwhile suffering serious gas disasters [1, 2]. State Work Safety Administration of China reported that there were totally 164 gas accidents, killing about 955 people from 2013 to 2016 [3]. Insisting on gas recovery before mining can not only eliminate the danger of coal and gas outbursts during coal production but also offer clean energy and reduce greenhouse gas emissions [4–6]. Gas drainage from deep underground coal mine seems a promising solution for the energy crisis.However, most of the coalfields in China were formed in Permo-Carboniferous system, experiencing several large-scale tectogenesises, which brought about fragmented coal and mylonitic coal [7, 8]. Thus, these coalfields are characterized by low permeability (K ≤ 0.005 mD), small firmness (f ≤ 1), strong adsorption, and high gas pressure (P ≥ 0.74 MPa) [9]. Up to date, many analytical models [10–14] were proposed to describe the dynamic changes in coalbed permeability during gas drainage period under uniaxial compression conditions. These models show coal permeability reduces with the increase of in situ stress, representing a negative exponential function as the coalbed buried depth. On the other hand, coal permeability is also dominated by matrix porosity and fractures with a unique cleat system, including size, spacing, connectivity, orientation, and the aperture of mineral infill [15]. Under the increased effective stress action, gas flow channels within these cleats become narrower, even close completely. Thus, the permeability decreases dramatically. However, the existing permeability models, on the assumptions of uniaxial strain and constant vertical stress, have not taken into account the original stress state and the varying of cleat compressibility and thus are unsuitable in the field application.On the other hand, conventional methods of gas drainage face difficulties: long preextraction time, quick reduction in gas flowrate, and huge drilling project. The reservoir stimulation techniques are needed to enhance coalbed permeability, mainly including hydraulic fracturing [16–19], hydraulic flushing [20, 21], presplitting blasting [22–25], liquid CO2 phase-transition fracturing [26–29], and CO2 injection [30–32]. These measures were implemented in coal mines and achieved fine effects. However, there is still a lack of general applicability owing to various hosting characteristics of coalbed occurrence. For example, hydraulic fracturing with complicated equipment is not applicable for soft coalbeds with the firmness below 0.8. However, hydraulic flushing easily causes borehole collapse to bury drilling tools and even triggers the coal and gas outburst with an inappropriate pressure of flushing. Moreover, all of hydraulic operations usually make a muddy and rugged working place. As for presplitting blasting in deep hole, it has a strong explosive force, but the charge quantity of explosives is hard to control and there is a hidden danger when detonator once misses fire. The greater adsorption potential of carbon dioxide (CO2) in coal is an appealing fact in relation to enhanced coalbed methane recovery (ECBM) and the long-term CO2 storage. However, the associated coal structure modification, particularly by coal matrix swelling, and the CO2 flow ability through the coalbed bring many uncertainties to the injection operation [33–35]. Further, many factors directly affect the production of CO2-ECBM in respect to its capacity, injectivity, plume movement, saturation period, and leakage assessment.A static fracturing technology, relied on hydraulic-driving modules to expand outwards for producing a large amount of artificial fissures in coalbed, was proposed here. Firstly, the fracturing model was established based on the elastic-plastic mechanics. Then, the effect of fracturing load on stress distribution and the initial fissure position were discussed by using FLAC3D software. Eventually, three groups of fracturing tests were conducted in 16031 tailgate tunnel, Guhanshan coalmine, to verify the permeability improvement of No. 2-1 coalbed.


## 2. Engineering Background

### 2.1. Test Site

The field trials of the static fracturing technology have been conducted in Guhanshan coalmine, located in the northeast of Jiaozuo coalfield. Nowadays, the coalmine is mainly recovering No. 2-1 coalbed, and the design production capacity is about 1.2 million tons of anthracite annually. The average thickness of No. 2-1 coalbed is approximately 2.8 m, with the dip angle of 12°∼17°. According to identification results over the years, the maximum of relative gas emission quantity reaches 33.32 m3/t and the absolute gas emission quantity is 75.59 m3/min. Undoubtedly, Guhanshan coalmine faces a high risk of coal and gas outburst both in driving and mining periods.In order to extract gas gushed from No. 16031 working face, a single row of drainage boreholes was arranged in the range of 10∼680 m of the lower rib of No. 16031 tailgate. The aperture of borehole is perpendicular to the middle line of the tunnel. The depth of borehole is 70 m, and the initial drilling height is 1.2 m away from the floor within the deviation of ±10 cm. The angles of odd and even borehole are −2° and −3°, respectively. The borehole spaces are, respectively, 0.8 m and 1.6 m in the range of 10–74 m and of 74–680 m away from the open-off cut. Three groups of the static fracturing tests were implemented as shown in Figure1.Figure 1
Location of 16031 tailgate and drilling layout.


### 2.2. Underground Trial Setup

A static fracturing equipment (Figure2) is mainly composed of a fracturing bit, an outburst preventer, a driller, and a hydraulic pump. The planform of the fracturing bit includes a high pressure wire-rope capsule, inner and outer fracturing modules, and antifriction cushions. Firstly, the fracturing bit was placed in the preset site of borehole after drilling up to the coalbed. When adjusting the pressure of hydraulic pump to 25 MPa, the wire-rope capsule immediately swelled up and pushed both inner and outer fracturing modules to gradually expand outwards the hole wall, thus fissures generating around borehole. The wire-rope capsule can automatically reset by shutting off the hydraulic pump after completing the fracturing operation, and then, it was handily removed from the borehole. Unlike most traditional blasting techniques, the fracturing equipment exerts static loads on coalbed by virtue of the incompressibility and fluidity of hydraulic oil, thus realizing the safe and controllable work.Figure 2
Operation chart of static fracturing technology.


## 2.1. Test Site

The field trials of the static fracturing technology have been conducted in Guhanshan coalmine, located in the northeast of Jiaozuo coalfield. Nowadays, the coalmine is mainly recovering No. 2-1 coalbed, and the design production capacity is about 1.2 million tons of anthracite annually. The average thickness of No. 2-1 coalbed is approximately 2.8 m, with the dip angle of 12°∼17°. According to identification results over the years, the maximum of relative gas emission quantity reaches 33.32 m3/t and the absolute gas emission quantity is 75.59 m3/min. Undoubtedly, Guhanshan coalmine faces a high risk of coal and gas outburst both in driving and mining periods.In order to extract gas gushed from No. 16031 working face, a single row of drainage boreholes was arranged in the range of 10∼680 m of the lower rib of No. 16031 tailgate. The aperture of borehole is perpendicular to the middle line of the tunnel. The depth of borehole is 70 m, and the initial drilling height is 1.2 m away from the floor within the deviation of ±10 cm. The angles of odd and even borehole are −2° and −3°, respectively. The borehole spaces are, respectively, 0.8 m and 1.6 m in the range of 10–74 m and of 74–680 m away from the open-off cut. Three groups of the static fracturing tests were implemented as shown in Figure1.Figure 1
Location of 16031 tailgate and drilling layout.


## 2.2. Underground Trial Setup

A static fracturing equipment (Figure2) is mainly composed of a fracturing bit, an outburst preventer, a driller, and a hydraulic pump. The planform of the fracturing bit includes a high pressure wire-rope capsule, inner and outer fracturing modules, and antifriction cushions. Firstly, the fracturing bit was placed in the preset site of borehole after drilling up to the coalbed. When adjusting the pressure of hydraulic pump to 25 MPa, the wire-rope capsule immediately swelled up and pushed both inner and outer fracturing modules to gradually expand outwards the hole wall, thus fissures generating around borehole. The wire-rope capsule can automatically reset by shutting off the hydraulic pump after completing the fracturing operation, and then, it was handily removed from the borehole. Unlike most traditional blasting techniques, the fracturing equipment exerts static loads on coalbed by virtue of the incompressibility and fluidity of hydraulic oil, thus realizing the safe and controllable work.Figure 2
Operation chart of static fracturing technology.


## 3. Methodology

### 3.1. Mechanical Model of Borehole Fracturing

The static fracturing technology aims to relieve or even eliminate the hoop stress concentration around borehole to produce more gas flow channels by exerting a high-pressure load on the hole wall. Providing the surrounding coal around borehole is submitted to the homogenous elastic-plastic material, the borehole model should be regarded as a microcircular tunnel complied with the Mohr–Coulomb criterion. Since the axial length and the buried depth of borehole are much more than 20 times its diameter, the model is simplified as the plane strain model as shown in Figure3 [36].Figure 3
Mechanical model of borehole fracturing.


#### 3.1.1. Elastic-Plastic Solutions of the Fracturing Model

Providing the cohesion and the friction angle of coal are always constant and the lateral coefficientλ = 1, the elastic-plastic solutions of resultant stress should be discussed on the two conditions.Ifσθ<σr, Mohr–Coulomb criterion is described as follows:(1)σθ=ξσr+σc,where σr is the radial stress of a point around borehole; σθ is the hoop stress of a point around borehole; P is the fracturing load exerting on hole wall; P0 is the in situ stress; r is the distance of a point to the hole wall; ra is the borehole radius; ξ=1+sinφ/1−sinφ; and σc=2ccosφ/1−sinφ. Putting Mohr–Coulomb criterion into the equation of static equilibrium (σθp=rdσr/dr+σrp), the solutions can be written as(2)σθp=σc1−ξ+Crξ−1,σrp=1ξξσc1−ξ+Crξ−1.The integration constantC can be determined by inputting the boundary condition (when r = ra, σrp = P).(3)C=pξ+ξσcξ−1⋅1raξ−1.Thus, the elastic-plastic solutions of stress can be expressed as follows:(4)σθp=σcξ−1ξrraξ−1−1+prraξ−1,σrp=σcξ−1rraξ−1−1+prraξ−1,where σrp is the radial stress of a point on the plastic zone; σθp is the hoop stress of a point on the plastic zone; and σc is the compressive stress. Since the radial and the hoop stresses on the plastic boundary well meet the elastic stress condition (σθp+σrp=2p0), the radius of the plastic zone Rp is expressed as follows:(5)Rp=ra2p0−pξ+1ξ−1+2σcσcξ+11/ξ−1.Whenσθ<σr, Mohr–Coulomb criterion is represented as follows:(6)σr=ξσθ+σc.Putting Mohr–Coulomb criterion into the equation of static equilibrium, we can also get the differential equation:(7)∂σrp∂r+ξ−1σrp+σcrξ=0.The solution of differential equation is expressed as follows:(8)σrp=σcr1−ξ+Cr1−ξ/ξ.The integration constantC can be determined by inputting the boundary condition (when r = ra, σrp = p):(9)C=p+σcξ−1⋅raξ−1/ξ.Thus, the radial stress on the plastic zone can be written as(10)σrp=prarξ−1/ξ+σc1−ξ1−rarξ−1/ξ.The hoop stress is expressed as follows:(11)σθp=pξrarξ−1/ξ+σc1−ξ1−1ξrarξ−1/ξ.The hoop stress on the plastic boundary can be determined with inputting condition:(12)σθp=σc1−ξ+1ξp+σcξ−1=1ξp−σc.Therefore, the radius of plastic zone is represented as follows:(13)Rp=ra1−ξp−σcξ+12ξ1−ξp0−σcξ/ξ−1.WhenP > 2P0, σθp < 0, which demonstrates the tensile stress generated on the hoop direction of surrounding coal. Therefore, the tensile fissure radius Rt can be determined by inputting the condition (σθp = −σt)(14)−σt=p0+p0−prar2,(15)Rt=rap−p0p0+σt1/2.


#### 3.1.2. Initial Position of Radial Fissures

When the stresses distribute nonuniformly (λ ≠ 1), the hoop stress on hole wall σθ is determined based on elastic mechanics as follows:(16)σθr=r0=1+λp0+21−λp0cos2θ−p.Two cases (the azimuthθ = 0°/90°) are also discussed here.Firstly, providingθ = 0°, the hoop stress on hole wall is shown as follows:(17)σθr=r0,θ=0=3−λp0−p.To satisfy the generation condition of tensile fissures around borehole, the hoop stressσθ must meet σθ < 0; σθ>Rt. Thus, the fracturing load P should meet the condition as follows:(18)p≥3−λp0+Rt.While providingθ = 90°, the hoop stress on hole wall is represented as follows:(19)σθr=r0,θ=90=3λ−1P0−P.The fracturing loadP should meet the following condition to produce tensile fissures:(20)p≥3λ−1p0+Rt.Accordingly, providingλ > 1, it is easier for the fracturing load P to meet equation (18). Thus, the tensile fissures initially occur in the horizontal direction of borehole. While λ < 1, it is easier for the fracturing load P to meet equation (20); thus, tensile fissures are generated in the vertical direction of the borehole. It should be noted that both the coalbed occurrence and the mining disturbance have great impacts on the positions of radial fissures in the field.


### 3.2. Numerical Simulation

The numerical model was established based on the geological and mining conditions of Guhanshan coalmine. According to the borehole histogram, rock strata were regarded as isotropic material without considering the influences of structural plane, interlayer, and groundwater. In the model, a borehole (Φ = 90 mm) was drilled in the middle of the tunnel right side. Owing to the buried depth of tunnel of 400 m, the stress of 10 MPa was applied on the top boundary to simulate the gravity of the overburden strata. Besides, the bottom boundary of the model was fixed, and the roller boundary was adopted on the lateral of the model (Figure 4).Figure 4
Numerical model.


## 3.1. Mechanical Model of Borehole Fracturing

The static fracturing technology aims to relieve or even eliminate the hoop stress concentration around borehole to produce more gas flow channels by exerting a high-pressure load on the hole wall. Providing the surrounding coal around borehole is submitted to the homogenous elastic-plastic material, the borehole model should be regarded as a microcircular tunnel complied with the Mohr–Coulomb criterion. Since the axial length and the buried depth of borehole are much more than 20 times its diameter, the model is simplified as the plane strain model as shown in Figure3 [36].Figure 3
Mechanical model of borehole fracturing.


### 3.1.1. Elastic-Plastic Solutions of the Fracturing Model

Providing the cohesion and the friction angle of coal are always constant and the lateral coefficientλ = 1, the elastic-plastic solutions of resultant stress should be discussed on the two conditions.Ifσθ<σr, Mohr–Coulomb criterion is described as follows:(1)σθ=ξσr+σc,where σr is the radial stress of a point around borehole; σθ is the hoop stress of a point around borehole; P is the fracturing load exerting on hole wall; P0 is the in situ stress; r is the distance of a point to the hole wall; ra is the borehole radius; ξ=1+sinφ/1−sinφ; and σc=2ccosφ/1−sinφ. Putting Mohr–Coulomb criterion into the equation of static equilibrium (σθp=rdσr/dr+σrp), the solutions can be written as(2)σθp=σc1−ξ+Crξ−1,σrp=1ξξσc1−ξ+Crξ−1.The integration constantC can be determined by inputting the boundary condition (when r = ra, σrp = P).(3)C=pξ+ξσcξ−1⋅1raξ−1.Thus, the elastic-plastic solutions of stress can be expressed as follows:(4)σθp=σcξ−1ξrraξ−1−1+prraξ−1,σrp=σcξ−1rraξ−1−1+prraξ−1,where σrp is the radial stress of a point on the plastic zone; σθp is the hoop stress of a point on the plastic zone; and σc is the compressive stress. Since the radial and the hoop stresses on the plastic boundary well meet the elastic stress condition (σθp+σrp=2p0), the radius of the plastic zone Rp is expressed as follows:(5)Rp=ra2p0−pξ+1ξ−1+2σcσcξ+11/ξ−1.Whenσθ<σr, Mohr–Coulomb criterion is represented as follows:(6)σr=ξσθ+σc.Putting Mohr–Coulomb criterion into the equation of static equilibrium, we can also get the differential equation:(7)∂σrp∂r+ξ−1σrp+σcrξ=0.The solution of differential equation is expressed as follows:(8)σrp=σcr1−ξ+Cr1−ξ/ξ.The integration constantC can be determined by inputting the boundary condition (when r = ra, σrp = p):(9)C=p+σcξ−1⋅raξ−1/ξ.Thus, the radial stress on the plastic zone can be written as(10)σrp=prarξ−1/ξ+σc1−ξ1−rarξ−1/ξ.The hoop stress is expressed as follows:(11)σθp=pξrarξ−1/ξ+σc1−ξ1−1ξrarξ−1/ξ.The hoop stress on the plastic boundary can be determined with inputting condition:(12)σθp=σc1−ξ+1ξp+σcξ−1=1ξp−σc.Therefore, the radius of plastic zone is represented as follows:(13)Rp=ra1−ξp−σcξ+12ξ1−ξp0−σcξ/ξ−1.WhenP > 2P0, σθp < 0, which demonstrates the tensile stress generated on the hoop direction of surrounding coal. Therefore, the tensile fissure radius Rt can be determined by inputting the condition (σθp = −σt)(14)−σt=p0+p0−prar2,(15)Rt=rap−p0p0+σt1/2.


### 3.1.2. Initial Position of Radial Fissures

When the stresses distribute nonuniformly (λ ≠ 1), the hoop stress on hole wall σθ is determined based on elastic mechanics as follows:(16)σθr=r0=1+λp0+21−λp0cos2θ−p.Two cases (the azimuthθ = 0°/90°) are also discussed here.Firstly, providingθ = 0°, the hoop stress on hole wall is shown as follows:(17)σθr=r0,θ=0=3−λp0−p.To satisfy the generation condition of tensile fissures around borehole, the hoop stressσθ must meet σθ < 0; σθ>Rt. Thus, the fracturing load P should meet the condition as follows:(18)p≥3−λp0+Rt.While providingθ = 90°, the hoop stress on hole wall is represented as follows:(19)σθr=r0,θ=90=3λ−1P0−P.The fracturing loadP should meet the following condition to produce tensile fissures:(20)p≥3λ−1p0+Rt.Accordingly, providingλ > 1, it is easier for the fracturing load P to meet equation (18). Thus, the tensile fissures initially occur in the horizontal direction of borehole. While λ < 1, it is easier for the fracturing load P to meet equation (20); thus, tensile fissures are generated in the vertical direction of the borehole. It should be noted that both the coalbed occurrence and the mining disturbance have great impacts on the positions of radial fissures in the field.


## 3.1.1. Elastic-Plastic Solutions of the Fracturing Model

Providing the cohesion and the friction angle of coal are always constant and the lateral coefficientλ = 1, the elastic-plastic solutions of resultant stress should be discussed on the two conditions.Ifσθ<σr, Mohr–Coulomb criterion is described as follows:(1)σθ=ξσr+σc,where σr is the radial stress of a point around borehole; σθ is the hoop stress of a point around borehole; P is the fracturing load exerting on hole wall; P0 is the in situ stress; r is the distance of a point to the hole wall; ra is the borehole radius; ξ=1+sinφ/1−sinφ; and σc=2ccosφ/1−sinφ. Putting Mohr–Coulomb criterion into the equation of static equilibrium (σθp=rdσr/dr+σrp), the solutions can be written as(2)σθp=σc1−ξ+Crξ−1,σrp=1ξξσc1−ξ+Crξ−1.The integration constantC can be determined by inputting the boundary condition (when r = ra, σrp = P).(3)C=pξ+ξσcξ−1⋅1raξ−1.Thus, the elastic-plastic solutions of stress can be expressed as follows:(4)σθp=σcξ−1ξrraξ−1−1+prraξ−1,σrp=σcξ−1rraξ−1−1+prraξ−1,where σrp is the radial stress of a point on the plastic zone; σθp is the hoop stress of a point on the plastic zone; and σc is the compressive stress. Since the radial and the hoop stresses on the plastic boundary well meet the elastic stress condition (σθp+σrp=2p0), the radius of the plastic zone Rp is expressed as follows:(5)Rp=ra2p0−pξ+1ξ−1+2σcσcξ+11/ξ−1.Whenσθ<σr, Mohr–Coulomb criterion is represented as follows:(6)σr=ξσθ+σc.Putting Mohr–Coulomb criterion into the equation of static equilibrium, we can also get the differential equation:(7)∂σrp∂r+ξ−1σrp+σcrξ=0.The solution of differential equation is expressed as follows:(8)σrp=σcr1−ξ+Cr1−ξ/ξ.The integration constantC can be determined by inputting the boundary condition (when r = ra, σrp = p):(9)C=p+σcξ−1⋅raξ−1/ξ.Thus, the radial stress on the plastic zone can be written as(10)σrp=prarξ−1/ξ+σc1−ξ1−rarξ−1/ξ.The hoop stress is expressed as follows:(11)σθp=pξrarξ−1/ξ+σc1−ξ1−1ξrarξ−1/ξ.The hoop stress on the plastic boundary can be determined with inputting condition:(12)σθp=σc1−ξ+1ξp+σcξ−1=1ξp−σc.Therefore, the radius of plastic zone is represented as follows:(13)Rp=ra1−ξp−σcξ+12ξ1−ξp0−σcξ/ξ−1.WhenP > 2P0, σθp < 0, which demonstrates the tensile stress generated on the hoop direction of surrounding coal. Therefore, the tensile fissure radius Rt can be determined by inputting the condition (σθp = −σt)(14)−σt=p0+p0−prar2,(15)Rt=rap−p0p0+σt1/2.


## 3.1.2. Initial Position of Radial Fissures

When the stresses distribute nonuniformly (λ ≠ 1), the hoop stress on hole wall σθ is determined based on elastic mechanics as follows:(16)σθr=r0=1+λp0+21−λp0cos2θ−p.Two cases (the azimuthθ = 0°/90°) are also discussed here.Firstly, providingθ = 0°, the hoop stress on hole wall is shown as follows:(17)σθr=r0,θ=0=3−λp0−p.To satisfy the generation condition of tensile fissures around borehole, the hoop stressσθ must meet σθ < 0; σθ>Rt. Thus, the fracturing load P should meet the condition as follows:(18)p≥3−λp0+Rt.While providingθ = 90°, the hoop stress on hole wall is represented as follows:(19)σθr=r0,θ=90=3λ−1P0−P.The fracturing loadP should meet the following condition to produce tensile fissures:(20)p≥3λ−1p0+Rt.Accordingly, providingλ > 1, it is easier for the fracturing load P to meet equation (18). Thus, the tensile fissures initially occur in the horizontal direction of borehole. While λ < 1, it is easier for the fracturing load P to meet equation (20); thus, tensile fissures are generated in the vertical direction of the borehole. It should be noted that both the coalbed occurrence and the mining disturbance have great impacts on the positions of radial fissures in the field.


## 3.2. Numerical Simulation

The numerical model was established based on the geological and mining conditions of Guhanshan coalmine. According to the borehole histogram, rock strata were regarded as isotropic material without considering the influences of structural plane, interlayer, and groundwater. In the model, a borehole (Φ = 90 mm) was drilled in the middle of the tunnel right side. Owing to the buried depth of tunnel of 400 m, the stress of 10 MPa was applied on the top boundary to simulate the gravity of the overburden strata. Besides, the bottom boundary of the model was fixed, and the roller boundary was adopted on the lateral of the model (Figure 4).Figure 4
Numerical model.


## 4. Results and Discussion

### 4.1. Effect of the Fracturing Load on Stress Distribution around Borehole

To investigate the effects of fracturing load on stress distribution around borehole, the loads of 15∼30 MPa were, respectively, exerted on hole wall. The stress and plastic zone distribution under different loads are shown in Figures5 and 6.Figure 5
Stress contour under fracturing loads of 15∼30 MPa.Figure 6
Plastic zone distribution under the load of 15∼30 MPa.Figure5 indicates with the fracturing load rising from 15 MPa to 30 MPa, the radial compressive stresses on hole wall gradually increase, which are 13.73 MPa, 17.46 MPa, 20.44 MPa, and 24.91 MPa, respectively. On the other hand, the hoop stress on hole wall decreases from 6.09 MPa to 2.12 MPa when the fracturing load rises up to 20 MPa. After the load reaches 24 MPa, the hoop compressive stresses gradually turn to become the tensile stresses and constantly increase with the load rising from 24 MPa∼30 MPa, which are 1.06 MPa and 5.81 MPa, respectively. In this case, the hoop stress concentration around borehole is absolutely eliminated when the fracturing load is over twice of in situ stress.Figure6 indicates compression-shear fissures mainly arise around borehole when the fracturing load is less than 20 MPa and the plastic-damage zone extends with a rising load. When the load is over 24 MPa, tensile fissures start to occur around borehole and the damage range would significantly extend with the rising load. Under the combined effects of tensile fissures and compression-shear fissures, the fissure range around borehole is considerably larger than the original one.


### 4.2. Effect of the Lateral Coefficient on Fracturing

In the field, the horizontal stress in strata is always larger than the vertical stress under the action of tectonic movement. Thus, the characteristics of stress distribution around borehole were discussed under different lateral coefficients as shown in Figure7. The fracturing load of 30 MPa was equally applied in each model.Figure 7
Stress contour around borehole under different lateral coefficients.Figure7 depicts the stress distribution around borehole gradually evolves from a ring to the saddle shape when the lateral coefficient of coalbed rises from 1 to 3. The tensile stresses in horizontal direction increase with a rising lateral coefficient, which are 5.81, 7.92, 10.21, and 14.87 MPa, respectively. When the lateral coefficients are 2 and 3, the hoop compressive stress mainly concentrates in the vertical direction and the peak compressive stresses are 16.84 and 29.47 MPa, respectively, thus generating more fracturing-induced damage in the horizontal direction. At this time, the occurrence of fissures is no longer randomly distributed. Besides, the peak radial stresses in the vertical direction gradually increase with the rising lateral coefficient, which are 24.91, 26.21, 26.75, and 39.99 MPa, respectively. It would cause larger horizontal displacements owing to Poisson’s effect.


### 4.3. Verification of Fracturing Effect

In order to determine the difference of permeability coefficient of coalbed before and after fracturing, a cross-borehole was firstly drilled and sealed to measure the residual gas pressure of No. 2-1 coalbed. Then, an orifice flowrate was installed one day after the gas pressure gauge removed to measure the daily gas flowrate, and the measurement duration was recorded. The permeability coefficient can be evaluated based on the theory of unstable radial gas flow in coalbed as follows [37]:(21)λ=A1.39B1/2.56,where λ is the permeability coefficient; A=qr/P02−P12; B=4P01.5/α⋅r2; P0 is the gas pressure of coalbed; P1 is the atmospheric pressure; q is the gas flowrate through unit area; r is the borehole radius; and α is the gas content coefficient.Figure8 indicates the number of radial fissures around borehole increases and the coal mass becomes loose after fracturing, resulting in the permeability of coalbed significantly improved. Then, with the increase of drainage time, the shrinkage deformation inevitably happens in coal mass and the fissures would be gradually closed. The permeability coefficient tends to be stable after one month, which is increased by 4.7∼5.8 times.Figure 8
Changes of permeability coefficient of coalbed.Drainage parameters (gas concentration, drainage pressure of the system, the diameter of drainage pipe, and the flow velocity of gas) of the three groups of measurement; boreholes were totally monitored for 84 days so as to determine the variation of gas flowrate before and after fracturing. Figure9 gives the changes of flowrate and concentration of gas of 1# drilling group before and after the fracturing operation.Figure 9
Curves of gas flowrate and gas concentration.
(a)
(b)For the traditional drainage method, the gas flow started at the formation of borehole and the results indicate clearly that the gas flowrate gradually reduced in a short period of 26 days after the beginning of gas drainage. However, by fracturing operation, a large amount of absorbed gas would be desorbed into free state with the improvement of the permeability of coalbed, resulting in a sharp increase in gas drainage concentration. The flowrate of mixed gas also increased owing to the fissure formation caused by fracturing, which demonstrates the significant improvement in efficiency of gas drainage by using the fracturing technology. According to the statistical analysis of each measurement borehole, after fracturing, the gas drainage concentration increased by 2.16 times on average, and the pure flowrate of gas recovery flow increased by 2.05 times.


## 4.1. Effect of the Fracturing Load on Stress Distribution around Borehole

To investigate the effects of fracturing load on stress distribution around borehole, the loads of 15∼30 MPa were, respectively, exerted on hole wall. The stress and plastic zone distribution under different loads are shown in Figures5 and 6.Figure 5
Stress contour under fracturing loads of 15∼30 MPa.Figure 6
Plastic zone distribution under the load of 15∼30 MPa.Figure5 indicates with the fracturing load rising from 15 MPa to 30 MPa, the radial compressive stresses on hole wall gradually increase, which are 13.73 MPa, 17.46 MPa, 20.44 MPa, and 24.91 MPa, respectively. On the other hand, the hoop stress on hole wall decreases from 6.09 MPa to 2.12 MPa when the fracturing load rises up to 20 MPa. After the load reaches 24 MPa, the hoop compressive stresses gradually turn to become the tensile stresses and constantly increase with the load rising from 24 MPa∼30 MPa, which are 1.06 MPa and 5.81 MPa, respectively. In this case, the hoop stress concentration around borehole is absolutely eliminated when the fracturing load is over twice of in situ stress.Figure6 indicates compression-shear fissures mainly arise around borehole when the fracturing load is less than 20 MPa and the plastic-damage zone extends with a rising load. When the load is over 24 MPa, tensile fissures start to occur around borehole and the damage range would significantly extend with the rising load. Under the combined effects of tensile fissures and compression-shear fissures, the fissure range around borehole is considerably larger than the original one.


## 4.2. Effect of the Lateral Coefficient on Fracturing

In the field, the horizontal stress in strata is always larger than the vertical stress under the action of tectonic movement. Thus, the characteristics of stress distribution around borehole were discussed under different lateral coefficients as shown in Figure7. The fracturing load of 30 MPa was equally applied in each model.Figure 7
Stress contour around borehole under different lateral coefficients.Figure7 depicts the stress distribution around borehole gradually evolves from a ring to the saddle shape when the lateral coefficient of coalbed rises from 1 to 3. The tensile stresses in horizontal direction increase with a rising lateral coefficient, which are 5.81, 7.92, 10.21, and 14.87 MPa, respectively. When the lateral coefficients are 2 and 3, the hoop compressive stress mainly concentrates in the vertical direction and the peak compressive stresses are 16.84 and 29.47 MPa, respectively, thus generating more fracturing-induced damage in the horizontal direction. At this time, the occurrence of fissures is no longer randomly distributed. Besides, the peak radial stresses in the vertical direction gradually increase with the rising lateral coefficient, which are 24.91, 26.21, 26.75, and 39.99 MPa, respectively. It would cause larger horizontal displacements owing to Poisson’s effect.


## 4.3. Verification of Fracturing Effect

In order to determine the difference of permeability coefficient of coalbed before and after fracturing, a cross-borehole was firstly drilled and sealed to measure the residual gas pressure of No. 2-1 coalbed. Then, an orifice flowrate was installed one day after the gas pressure gauge removed to measure the daily gas flowrate, and the measurement duration was recorded. The permeability coefficient can be evaluated based on the theory of unstable radial gas flow in coalbed as follows [37]:(21)λ=A1.39B1/2.56,where λ is the permeability coefficient; A=qr/P02−P12; B=4P01.5/α⋅r2; P0 is the gas pressure of coalbed; P1 is the atmospheric pressure; q is the gas flowrate through unit area; r is the borehole radius; and α is the gas content coefficient.Figure8 indicates the number of radial fissures around borehole increases and the coal mass becomes loose after fracturing, resulting in the permeability of coalbed significantly improved. Then, with the increase of drainage time, the shrinkage deformation inevitably happens in coal mass and the fissures would be gradually closed. The permeability coefficient tends to be stable after one month, which is increased by 4.7∼5.8 times.Figure 8
Changes of permeability coefficient of coalbed.Drainage parameters (gas concentration, drainage pressure of the system, the diameter of drainage pipe, and the flow velocity of gas) of the three groups of measurement; boreholes were totally monitored for 84 days so as to determine the variation of gas flowrate before and after fracturing. Figure9 gives the changes of flowrate and concentration of gas of 1# drilling group before and after the fracturing operation.Figure 9
Curves of gas flowrate and gas concentration.
(a)
(b)For the traditional drainage method, the gas flow started at the formation of borehole and the results indicate clearly that the gas flowrate gradually reduced in a short period of 26 days after the beginning of gas drainage. However, by fracturing operation, a large amount of absorbed gas would be desorbed into free state with the improvement of the permeability of coalbed, resulting in a sharp increase in gas drainage concentration. The flowrate of mixed gas also increased owing to the fissure formation caused by fracturing, which demonstrates the significant improvement in efficiency of gas drainage by using the fracturing technology. According to the statistical analysis of each measurement borehole, after fracturing, the gas drainage concentration increased by 2.16 times on average, and the pure flowrate of gas recovery flow increased by 2.05 times.


## 5. Conclusions

A static fracturing technology to enhance the permeability of coalbed is proposed here for the high efficiency of gas recovery. The mechanism of borehole fracturing is clarified based on the mechanical analysis and numerical modeling. The results demonstrate the following (1) When the fracturing load is over twice as much as in situ stress, the concentration of hoop stress around borehole is released and there are more tensile fissures generated with a rising load, which results in the promotion in coal permeability. (2) When the lateral coefficient >1, tensile fissures are generated in the horizontal direction of borehole and vice versa. The stress distribution around borehole gradually evolves from a ring to the saddle shape with the lateral coefficient rising from 1∼3. (3) After the fracturing operation, the gas drainage concentration increased by 2.16 times on average, and the pure flowrate of gas recovery flow increased by 2.05 times.In the future, more experimental effects and field applications are needed in order to understand the evolvement of fracturing-induced fissures and the characteristics of gas flow in coalbed, associated with different drainage periods by the static fracturing stimulation.



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*Source: 9207145-2019-06-09.xml*