Effect of damage zone around borehole on carbon dioxide injection promoted gas extraction in soft and low-permeability coal seam

Abstract

Injecting external CO₂ into soft and low-permeability coal seams can improve CH₄ extraction efficiency, and also benefit in CO₂ sequestration. However, the distribution law of damage zone around borehole in soft coal seam and its effect on the efficiency of CO₂ injection promoted CH₄ extraction are not clear. In this paper, a multi-physics coupling mathematical model considering damage effect is established for simulating the process of CO₂ injection promoted CH₄ extraction in soft and low-permeability coal seam. The distribution of damage zone and permeability around boreholes under different diameters and coal strengths are analyzed. The gas pressure and gas content in coal seam during CO₂ injection promoted CH₄ extraction when the model considered damage effect are compared with that of ignored. The results show that small borehole diameter corresponds to narrow damage zone around the borehole in coal seam. The damage zone expands with the increase of the borehole diameter. The damage zone increases exponentially with the borehole diameter, while decreases exponentially with the compressive strength of coal seam. The highest permeability in the damage zone has increased by nearly 300 times under the condition of simulated case. CH₄ pressure around the extraction borehole reduces, and the reduction area expands with the increase of time. Compared with the result of considering the damage effect, the reduction area of ignoring it is smaller, and the reducing speed is slower. The integrated effect of CO₂ injection and CH₄ extraction leads to rapid decrease of CH₄ content in coal seam near the boreholes. The CO₂ pressure and content increase around the injection borehole, and the increasing area gradually extends to the whole coal seam. In soft coal seams, failure to consider the damage effect will underestimate the efficiency of CH₄ extraction and CO₂ sequestration, resulting conservative layout of boreholes.

Graphical abstract

Keywords

soft and low-permeability coal seam / carbon dioxide injection / gas extraction / damage effect / permeability evolution

1 Introduction

Gas disaster is the primary killer in underground coal mining, which seriously threatens the safety of miners and equipment (Yuan, 2015; Liu et al., 2021a). Gas extraction is the basic measurement to prevent gas disasters (Fan et al., 2017; Fan et al., 2020; Zhao et al., 2022a). However, the efficiency of gas extraction in soft coal seam is poor due to its extremely low permeability and prone to borehole collapse (Yao et al., 2011; Zhao et al., 2020; Zhao et al., 2022b). Scholars have been exploring a series of technologies for enhancing permeability in coal seam to obtain greater gas production, such as deep hole blasting, carbon dioxide pre-splitting, hydraulic punching, hydraulic fracturing, and hydraulic slotting (Liu et al., 2021; Wang et al., 2022; Zhang et al., 2023). These have promoted and improved the gas extraction efficiency to a certain extent (Liu et al., 2021b; Zhang et al., 2021; Fan et al., 2022; Zhu et al., 2022). However, the above technologies are complex, and are prone to collapse the boreholes. Gas extraction in soft and low-permeability coal seams faced with poor investment and high efficiency is still a technical difficulty (Yi et al., 2021).

Injecting carbon dioxide into soft and low-permeability coal seams can improve gas extraction efficiency through competitive adsorption and displacement effects (Mukherjee and Misra, 2018; Yang et al., 2023). Scholars have carried out a lot of beneficial explorations on gas injection to displace gas. The permeability model for studying the process of gas extraction and injection in coal seam was proposed and the simulations of carbon dioxide injection to displace gas in coal seam were carried out (Durucan and Shi, 2009; Wu et al., 2011). Meanwhile, the coupling effect of fluid and geological body in the process of carbon dioxide injection to strengthen gas drainage and carbon dioxide geological storage in coal seams was analyzed (Connell and Detournay, 2009; Vishal et al., 2018). The deformation of coal or shale skeleton during CO₂ injection was studied (Liu et al., 2017; Liu et al., 2019; Fan et al., 2021; Bai et al., 2022a). The thermal-fluid-solid coupling models were built to extensively investigate the process of carbon dioxide injection enhanced coalbed methane extraction, and the change law of coal permeability was analyzed (Fan et al., 2018; Fan et al., 2019a; Fang et al., 2019; Bai et al., 2022b; Zhou et al., 2022). However, the above studies were based on the assumption that the coal seam is an elastic and atraumatic material. Generally speaking, under the action of in situ stress, there will be a fractured damage zone around the drilling borehole in the soft coal seam (Li, 2016). Several investigations were carried out on the gas drainage in soft coal seam considered the damage zone around boreholes. The damage zone produced by large-diameter boreholes (200 mm, 300 mm) in soft coal would increase the coal permeability and improve the gas extraction efficiency (Wei et al., 2019; Wang et al., 2020). The change law of damage and permeability of coal samples during unloading was studied, and the damage triggered permeability evolution of coal samples during cyclic loading was obtained (Chen et al., 2013; Fan and Liu, 2019). The damage effect on coal permeability and gas extraction is significant, and will largely affect the extraction efficiency (Liu et al., 2014; Zheng et al., 2017; Lu et al., 2019). However, there is lack of report on the damage zone around the drilling borehole with different diameters or strengths of coal seam, as well as the influence of damage zone on the CO₂ promoted CH₄ extraction.

In this paper, a multi-physics coupling model considering damage effect will be established to simulate the process of CO₂ injection promoted CH₄ extraction in soft and low-permeability coal seam. Taking No. 3 coal seam in Zhangcun Coal Mine as the background, the distribution of damage zone and coal permeability in coal seam with different borehole diameters and coal strengths will be analyzed. The evolution laws of gas (CH₄, CO₂) pressure and content in the process of CO₂ injection promoted CH₄ extraction using the model that considered the damage effect will be compared with those ignored it. The influence mechanism of drilling damage zone in soft coal seam on CO₂ injection promoted CH₄ extraction will be revealed. The results may provide a theoretical basis for the design of CO₂ injection promoted CH₄ extraction under similar conditions.

2 Mathematical model for multi-physics couplings during CO₂ injection in coal seam

2.1 Equations for gas mixture migration in coal

Coal seam is a dual-porosity and single-permeability medium, containing matrix pores and coal fractures (Song et al., 2020). The free gas of CO₂/CH₄ exists and migrates in fractures and pores, while adsorbed gas adsorbs on the surface of matrix pores. The thermal effect and water migration are ignored. The gas content in coal matrix consists of both free and absorbed gases (CH₄ and CO₂), which is defined as (Cheng et al., 2021; Zhou et al., 2022)

(1)m_{\mathrm{m}\mathrm{g}i}={\varphi }_{\mathrm{m}}{\rho }_{\mathrm{g}i}+V_{\mathrm{s}\mathrm{g}i}{\rho }_{\mathrm{c}}{\rho }_{\mathrm{g}\mathrm{s}i},

where the subscript i stands the gas component in gas mixture, i = 1 for CH₄ and i = 2 for CO₂; m_mg is the gas content in coal matrix per unit volume, kg/m³; φ_m is the porosity in matrix; ρ_g is the gas density, kg/m³; V_sg is the absorbed gas content, m³/kg; ρ_c is the coal skeleton density, kg/m³; ρ_gs is the gas density under standard condition, kg/m³.

The free gas of CO₂/CH₄ in the volume of fracture and pore satisfies the ideal gas law, and the gas sorption on coal satisfies the modified Langmuir law. The absorbed gas content and the gas density can be expressed as (Fan et al., 2021)

(2)\{\begin{array}{c}{V}_{\mathrm{s}\mathrm{g}i}=\frac{V_{\mathrm{L}i}{b}_i{p}_{\mathrm{m}\mathrm{g}i}}{1+{\displaystyle {\sum }_{i=1}^2{b}_i{p}_{\mathrm{m}\mathrm{g}i}}}\\ {\rho }_{\mathrm{g}i}=\frac{M_{\mathrm{g}i}}{RT}{p}_{\mathrm{g}i},\end{array},

where V_L is the Langmuir volume constant, m³/kg; p_L is the Langmuir pressure constant, Pa; b_i = 1/p_L; p_mg is the gas pressure in the matrix, Pa; M_g is the gas molar mass, g/mol; p_g is the gas pressure, Pa; R is gas molar constant, J/(mol·K); and T is the temperature of gas, K.

Gas migration from pores to fractures is dominated by gas diffusion satisfying the Fick’s Law. The sorption/desorption equilibrium of CH₄ and CO₂ is disturbed by the operation of extraction or injection. On the one hand, the adsorbed CH₄ desorbs and diffuses from pores to fractures, on the other hand, the injected CO₂ migrates in the opposite pathway－from fractures to pores. Based on the Fick᾽s law, mass transport in coal matrix is defined as (Wu et al., 2011; Fang et al., 2019)

(3)\frac{\mathrm{\partial }{m}_{\mathrm{m}\mathrm{g}i}}{\mathrm{\partial }t}=-\frac{1}{{\tau }_i}\frac{M_{\mathrm{g}i}}{RT}\left(p_{\mathrm{m}\mathrm{g}i}-p_{\mathrm{f}\mathrm{g}i}\right),

where p_fg is the gas pressure in fractures, Pa; τ is the desorption time, s; and t is time, s.

Substituting Eqs. (1) and (2) into Eq. (3), the equation for CH₄ and CO₂ transport in coal matrix system is obtained as

(4)\begin{array}{rl}& \frac{\mathrm{\partial }}{\mathrm{\partial }t}\left(\frac{V_{\mathrm{L}i}{b}_i{p}_{\mathrm{m}\mathrm{g}i}}{1+{\displaystyle {\sum }_{i=1}^2{b}_i{p}_{\mathrm{m}\mathrm{g}i}}}{\rho }_{\mathrm{c}}\frac{M_{\mathrm{g}i}}{R{T}_{\mathrm{s}}}{p}_{\mathrm{g}\mathrm{s}i}+{\varphi }_{\mathrm{m}}\frac{M_{\mathrm{g}i}}{RT}{p}_{\mathrm{m}\mathrm{g}i}\right)\\ & =-\frac{1}{{\tau }_i}\frac{M_{\mathrm{g}i}}{RT}\left(p_{\mathrm{m}\mathrm{g}i}-p_{\mathrm{f}\mathrm{g}i}\right).\end{array}

During CO₂ injection promoted CH₄ extraction, the free gases of CH₄ and CO₂ exist in the fractures. The Darcy’s law is applied to indicate the velocity of gas flow in fractures. The equation of mass conservation in the fracture system is defined as (Fan et al., 2018)

(5)\begin{array}{rl}& \frac{\mathrm{\partial }\left({\varphi }_{\mathrm{f}}{\rho }_{\mathrm{f}\mathrm{g}i}\right)}{\mathrm{\partial }t}+\mathrm{\nabla }\cdot \left(-\frac{{\rho }_{\mathrm{f}\mathrm{g}i}{k}_{\mathrm{f}}}{{\mu }_{\mathrm{g}i}}\left(1+\frac{b_{\mathrm{k}}}{p_{\mathrm{f}\mathrm{g}i}}\right)\mathrm{\nabla }{p}_{\mathrm{f}\mathrm{g}i}\right)\\ & =\frac{1}{{\tau }_i}\frac{M_{\mathrm{g}i}}{RT}\left(p_{\mathrm{m}\mathrm{g}i}-p_{\mathrm{f}\mathrm{g}i}\right),\end{array}

where φ_f is the porosity of fracture; k_f is the permeability of fracture, m²; μ_g is the gas dynamic viscosity, Pa·s; and b_k is the Klinkenberg factor, Pa.

2.2 Equations for stress field in coal seam

Accommodating the stress induced by thermal expansion, the effective stress by fluid pressure of gas mixture, and the stress by gas sorption induced shrinkage/swelling, the Navier-type equation is defined to express the stress field in coal seam (Fan et al., 2018):

(6)\begin{array}{rl}& G{u}_{\mathrm{k},\mathrm{l}\mathrm{l}}+\frac{G}{1-2v}{u}_{\mathrm{l},\mathrm{l}\mathrm{k}}-\left({\alpha }_{\mathrm{m}}{p}_{\mathrm{m}\mathrm{g},\mathrm{k}}\text{+}{\alpha }_{\mathrm{f}}{p}_{\mathrm{f}\mathrm{g},\mathrm{k}}\right)\\ & -K{\left({\epsilon }_{\mathrm{s}1}+{\epsilon }_{\mathrm{s}2}\right)}_{,\mathrm{k}}+f_{\mathrm{k}}=0,\end{array}

where G = D/2(1 + ν) is the shear modulus, Pa; ν is Poisson᾽s ratio; D = 1/[1/E + 1/(a∙K_n)] is effective elastic modulus, Pa; K_n is the normal stiffness of the fracture, Pa/m; a is the fracture aperture, m; E is the elastic modulus of coal, Pa; K = D/3(1−2ν) is the bulk modulus, Pa; K_s = E_s/3(1−2ν) is the skeletal bulk modulus, Pa; E_s is the skeletal elastic modulus, Pa; α_m = 1−K/K_s is the Biot effective stress coefficient for coal matrix, and α_f = 1−K/(a∙K_n) is the Biot effective stress coefficient for fractures; ε_s is the gas sorption caused volumetric strain.

Experimental evidence supports that the extended Langmuir equation can be used to represent the gas mixture sorption caused volumetric strain. Thus, the sorption induced volume strain may be expressed as (Fang et al., 2019; Fan et al., 2023)

(7){\epsilon }_{\mathrm{s}i}=\frac{{\epsilon }_{\mathrm{L}i}{b}_i{p}_{\mathrm{m}\mathrm{g}i}}{\left(1+{\displaystyle {\sum }_{j=1}^2{b}_j{p}_{\mathrm{m}\mathrm{g}j}}\right)},

where ε_L is the Langmuir-type strain coefficient.

2.3 Equations for coal damage field

The deformation and failure behavior of coal and rock can be described by elastic-damage model. The strain equivalence principle defines that the strain of damaged coal induced by the real stress is equal to that of undamaged coal induced by the effective stress (Fan et al., 2017):

(8)\sigma =E\epsilon =E_0\left(1-D\right)\cdot \epsilon ,

where E₀ and E are undamaged elastic modulus and damaged elastic modulus respectively, Pa; D is the damage variable, 0 ≤ D ≤ 1, in which D = 0 expresses that the coal is undamaged, and D = 1 is completely damaged.

We use the maximum tensile stress criterion and Mohr-Coulomb criterion to judge whether coal is damaged or failed, as shown in Fig.1. Therefore, the strength criterion of coal mass can be expressed as (Fan et al., 2017)

(9)\{\begin{array}{c}{F}_1={\sigma }_1-{\sigma }_t=0\\ F_2=-{\sigma }_3+{\sigma }_1\frac{1+\sin \theta }{1-\sin \theta }-{\sigma }_c=0\end{array},

where σ₁ is the maximum principal stress, MPa; σ₃ is the minimum principal stress, MPa; σ_t and σ_c are the uniaxial tensile strength and uniaxial compressive strength of coal respectively, MPa; θ is the internal friction angle of coal, °; F₁ and F₂ are the threshold functions of tensile and shear damage, respectively. In the process of damage calculation, the maximum tensile stress criterion first is used to judge whether the coal is damaged under the tensile stress. If it is not damaged, then the Mohr-Coulomb criterion is used to judge whether the coal is damaged under the shear stress.

The damage variable of coal mass is expressed as

(10)

where ε_t is the maximum principal strain of coal; ε_c is the minimum principal strain of coal; ε_t0 represents the ultimate tensile strain when coal mass is damaged by tension stress; ε_c0 represents the ultimate compressive strain when the coal mass is damaged by shear stress.

Coal seam permeability is the key factor to determine the migration speed of CH₄ and CO₂ in coal seams (Liu et al., 2018). It is closely related to the elastic and damage state of coal seam. Here, we assume that the overall change of permeability in coal seam is a linear combination of changes caused by elastic deformation and damage of coal. In the elastic stage, the permeability changes slightly and is dominated by the elastic deformation caused by the change in pore pressure, stress and gas adsorption. However, in the damage stage, the permeability rises sharply and is controlled by the damage variable of coal

(11)k_{\mathrm{f}}=k_{\mathrm{e}\mathrm{f}}+k_{\mathrm{d}\mathrm{f}}.

According to the literature (Fan et al., 2019b), the permeability in elastic state can be expressed as

(12)\begin{array}{rl}{k}_{\mathrm{e}\mathrm{f}}=& k_{\mathrm{f}0}(\text{1 +}\frac{K_{\mathrm{m}}}{3\left(K_{\mathrm{f}}{r}_{as}^3\text{+}{K}_{\mathrm{m}}-K_{\mathrm{m}}{r}_{\mathrm{a}\mathrm{s}}^3\right)}\\ & \cdot {\left(r_{as}^3\mathrm{\Delta }\left({\epsilon }_{s1}+{\epsilon }_{s2}\right)\text{+}\mathrm{\Delta }{\epsilon }_v\text{+}\frac{r_{as}^3}{K_{\mathrm{m}}}{\alpha }_{\mathrm{m}}\mathrm{\Delta }{p}_{\mathrm{m}\mathrm{g}}\right))}^3,\end{array}

where k_f0 is the initial fracture permeability, m²; K_m is the buck modulus of coal matrix, Pa; r_as = a/s as the ratio of matrix width to the REV length; s = a + b is the length of the REV, m; a is the spacing between parallel fracture sets, m; and b is the facture aperture, m.

The damage permeability of coal is controlled by the sudden increase coefficient and damage variable, which can be expressed as (Zhu et al., 2018)

(13)k_{\mathrm{d}\mathrm{f}}=k_{\mathrm{f}0}\left(e^{{\alpha }_{D}D}-1\right),

where α_D is the sudden increase coefficient; D is the damage variable.

Submitting Eqs. (12) and (13) into Eq. (11), the coal permeability can be obtained

(14)\begin{array}{rl}{k}_{\mathrm{f}}=& k_{\mathrm{f}0}(\text{1 +}\frac{K_{\mathrm{m}}}{3\left(K_{\mathrm{f}}{r}_{as}^3\text{+}{K}_{\mathrm{m}}-K_{\mathrm{m}}{r}_{as}^3\right)}\\ & \cdot (r_{as}^3\mathrm{\Delta }\left({\epsilon }_{s1}+{\epsilon }_{s2}\right)\text{+}\mathrm{\Delta }{\epsilon }_v\text{+}\frac{r_{as}^3}{K_{\mathrm{m}}}{\alpha }_{\mathrm{m}}\mathrm{\Delta }{p}_{\mathrm{m}}){)}^3+k_{\mathrm{f}0}\left(e^{{\alpha }_{D}D}-1\right).\end{array}

We assemble the Eqs. (4)−(6), (10), and (14) to establish the mathematical model for multi-physics couplings during CO₂ injection into coal seam. These complex nonlinear partial differential equations (PDEs) are difficult to obtain analytic solution. We apply the COMSOL with MATLAB code to calculate the numerical solution.

3 Influence of coal strength and borehole diameter on damage zone around boreholes

3.1 Geometer model and solving conditions

Zhangcun Coal Mine is located in the north-east of Changzhi City, Shanxi Province, China. The No. 3 coal seam is the main minable seam with stable occurrence, small variation in thickness and simple geology structure. The thickness of the coal seam is 5.33−6.19 m, with an average of 5.86 m. The buried depth of the coal seam is about 537 m. The immediate roof is sandy mudstone with an average thickness of 3.33 m. The basic roof is fine-grained sandstone with an average thickness of 3.64 m. The immediate floor is sandy mudstone with an average thickness of 3.9 m. The main floor is fine-grained sandstone with an average thickness of 3.9 m. The gas pressure in the coal seam is 0.76−1.46 MPa, and the gas content is 5.71−15.5 m³/t, with an average of 10.63 m³/t. Gas extraction is the main measurement to prevent gas disasters. The layout of extraction boreholes directly affects the economic benefits of the coal mine. Therefore, the No. 3 coal seam in Zhangcun coal mine is taken as the research object to simulate the influence of the damage zone around the boreholes on the gas injection and extraction.

As shown in Fig.2, the rectangular geometric model of coal seam with size of 26 m × 6 m (length × width) is constructed, and three boreholes are arranged in the coal seam, including one gas injection borehole and two extraction boreholes. The spacing between boreholes is 8 m. The triangular mesh method is used to divide the geometry with 35806 meshes. In this simulation, the initial gas pressure in coal seam is 1.24 MPa, and the initial permeability is 4.7 × 10⁻¹⁷ m². The coal seam is heterogeneous. It is assumed that the uniaxial compressive strength, tensile strength and elastic modulus obey the random Weibull distribution. The uniformity degree of coal seam is taken as 5, and the elastic modulus distribution is shown in Fig.3. For solving the solid mechanics equation, the left and bottom boundaries of the coal seam are rolling support boundaries. The gravity loading of overlying strata - 15 MPa is applied to the top boundary. The horizontal stress of the right boundary is set as 18 MPa. For solving the gas migration equation, the surrounding boundaries of the geometry are impermeable. The sucking pressure of the extraction borehole is 0.08 MPa, and the injection pressure of the gas injection borehole is 4 MPa. The sudden increase coefficient of coal seam is set as 8. The operation of CH₄ extraction and CO₂ injection are carried out at the same time. The parameters used in the following are listed in Tab.1. Relevant parameters are obtained through literature, experimental tests and field measurements. The finite element method, COMSOL with MATLAB code, was used to calculate the numerical solution and discrete mesh. The methods of linear interpolation and free tetrahedral mesh are adopted. The meshed elements are used for both hydraulic and structural calculation.

3.2 Damage zone and permeability change around boreholes with different diameters

According to the proposed mathematical model, the numerical simulations on CO₂ injection promoted CH₄ extraction were carried out to explore the evolution of damage zone and permeability around the boreholes with different diameters, 100, 150, 200, and 250 mm. Fig.4 shows the distribution of elastic modulus in the coal seam under different borehole diameters. It can be implied that small borehole diameter corresponds to narrow damage zone around the borehole in coal seam. As the diameter increases, the damage zone expands, especially when the borehole diameter is 250 mm, the damage zone goes deep into the coal wall about 180 mm.

By integrating the damage zone, the areas of damaged coal in the coal seam under different borehole diameters are obtained, as shown in Fig.5. When the borehole diameter is 100, 150, 200, and 250 mm, the area of damage zone is 0.147, 0.345, 0.614, and 0.962 m², respectively. The damage zone in coal seam increases exponentially with the increase of diameter.

With the developing and extending of fractures in coal seam around the borehole, and the permeability in this area increases sharply. The distribution of permeability in the coal seam is numerically obtained is shown in Fig.6. The initial coal permeability is 4.7 × 10⁻¹⁷ m², while the coal permeability in damage zone around the borehole reaches 1.4 × 10⁻¹⁴ m², increased by nearly 300 times. This indicates that the damage zone around the borehole acts significant role in the gas migration during CO₂ injection promoted CH₄ extraction.

3.3 Damage zone and permeability change around boreholes with different coal strengths

We fix the borehole diameter as 150 mm, and discuss the influence of coal compressive strength on the evolution of damage zone and permeability, as illustrated in Fig.7. The studied coal compressive strength is 2.5, 4.5, 6.5, and 8.5 MPa. When the compressive strength equals to 2.5 MPa, the damage zone around the borehole is the largest, about 230 mm deep into the borehole wall. The greater the compressive strength, the smaller the damage zone. When the compressive strength is 8.5 MPa, the damage area is the smallest, about 50 mm into the wall. The softer the coal seam (lower strength), the larger the damage zone around the borehole, and the greater the impact on CH₄ extraction and CO₂ injection.

We extract the area of damage zone in the coal seam with different compressive strengths, the result is shown in Fig.8. It can be found that when the compressive strength is 2.5, 4.5, 6.5, and 8.5 MPa, the area of damage zone is 6.312, 1.567, 0.345, and 0.163 m², respectively. The damage zone in coal seam decreases exponentially with the increase of coal compressive strength. When the compressive strength is small, large-scale damage occurs around the borehole. Meanwhile, the damage and failure also occur at the low compressive strength position in the heterogeneous coal seam under the action of in situ stress. This is the main reason for the large area of damage usually appears in the soft coal seam.

Fig.9 shows the permeability distribution in the coal seam near the borehole under different compressive strengths. When the compressive strength is 2.5 MPa, the damage zone in the coal seam is largest. The coal permeability around the borehole increases, meanwhile the increasing permeability in the other region of coal seam has a scattered distribution. With the increase of compressive strength, both area and value of rising permeability in coal seam gradually decrease.

4 Damage effect on CO₂ injection promoted CH₄ extraction

Taking the borehole diameter of 150 mm and coal compressive strength of 6.5 MPa as constant value, we comparatively studied the change of gas pressure and content of CH₄ and CO₂ in the process of promoted extraction with both considering and ignoring the damage effect.

4.1 CH₄ pressure and content

Fig.10 shows the CH₄ pressure contour in the coal seam after different durations of extraction. CH₄ pressure around the extraction borehole reduces, and the reducing area expands with time. Affected by the displacement effect of injected high-pressure gas, the CH₄ pressure around the injection borehole increases transiently in the early stage, but it gradually decreases with the progress of operation. Compared with considering the damage effect, CH₄ pressure reducing area in the coal seam of ignoring the damage effect is smaller and the reducing speed is slower. Taking the CH₄ pressure of 0.6 MPa as a reference, after 60 days of gas extraction, the area where the CH₄ pressure is less than 0.6 MPa of considering the damage effect is about 2.5 times that of ignoring it.

Fig.11 illustrates the change curves of CH₄ pressure on reference line AB and point C in coal seam. In Fig.11(a), the CH₄ pressure generally decreases with the time, and there is a significant difference of CH₄ pressure between with considering and ignoring the damage effect. It can be found that CH₄ pressure considering the damage effect drops faster, especially near the extraction borehole. Taking the distance of 2 m from the extraction borehole as a reference, CH₄ pressure ignoring damage is 0.917, 0.765, 0.647, and 0.552 MPa when the operation time is 30, 60, 90, and 120 days, respectively. The CH₄ pressure with considering damage is 0.857, 0.697, 0.575, and 0.479 MPa, with an error of 6.54%, 8.89%, 11.13%, and 13.22%, respectively. In Fig.11(b), CH₄ pressure at reference point C decreases with the time. The longer the operation time, the greater the error caused by ignoring the damage effect.

Fig.12 shows the CH₄ content distribution in the coal seam after different duration of extraction and injection. Consistent with the change of CH₄ pressure, the CH₄ content in coal seam decreases rapidly near the extraction borehole. The CH₄ content around the injection hole also decreases sharply due to the displacement effect of CO₂, and the displaced CH₄ is driven to migrate toward the extraction borehole. Taking the CH₄ content of 5 m³/t as a reference, it can be decided that the damage effect will lead to faster decline of CH₄ content. At 120 days, the CH₄ content of the whole coal seam is lower than 5 m³/t for considering the damage effect, but there is still a large area where the gas content is higher than 5 m³/t for ignoring the damage effect.

Fig.13 compares the change curves of CH₄ content on line A-B and point C between considering and ignoring the damage effect. In Fig.13(a), the CH₄ content generally decreases with the time. The CH₄ content considering the damage effect decreases faster, especially in the area near the boreholes. In Fig.13(b), the CH₄ content on point C decreases with the time, which is consistent with the result in Fig.13(a). The longer the operation time, the greater the difference between considering and ignoring the damage effect. When operation time is 30, 60, 90, and 120 days, the CH₄ content ignoring the damage is 8.312, 7.129, 6.078, and 5.196 m³/t, and the CH₄ content considering the damage is 8.157, 6.746, 5.559, and 4.613 m³/t, with the error of 1.86%, 5.37%, 8.54%, and 11.22%, respectively. Therefore, if the damage effect is not considered, the CH₄ extraction efficiency will be underestimated, causing conservative layout of boreholes in soft coal seams.

4.2 CO₂ pressure and content

Fig.14 shows the pressure distribution of CO₂ in coal seam after different durations of CO₂ injection. CO₂ pressure around the injection borehole increases. As time prolongs, the CO₂ reaching area in coal seam gradually extends to the inner of the coal seam until to the extraction borehole. Compared with considering the damage effect, the area of CO₂ reaching in the coal seam of ignoring the damage effect is smaller. Taking CO₂ pressure of 0.6 MPa as a reference, for considering the damage effect, the area where the CO₂ pressure around the borehole is higher than 0.6 MPa is 14.2, 28.2, and 43.3 m² when the CO₂ is injected for 30, 60, and 90 days respectively, which is 1.72, 1.55, and 1.29 times that of ignoring the damage effect.

Fig.15 presents the change curves of CO₂ pressure at reference line A-B and point C in coal seam. In Fig.15(a), the CO₂ pressure generally increases with the time. For considering the damage effect, the CO₂ pressure of increases faster, especially near the injection borehole. In Fig.15(b), the CO₂ pressure of ignoring damage is 0.121, 0.208, 0.300, and 0.388 MPa at 30, 60, 90, and 120 days, and that of considering damage is 0.146, 0.275, 0.404, and 0.523 MPa, with the error of 20.66%, 32.21%, 34.67%, and 34.79% respectively. Longer injection time corresponds to slower increase of CO₂ pressure at point C if the damage effect is ignored.

Fig.16 shows the distribution contour of CO₂ content in coal seam after different durations of gas injection. Consistent with the variation of CO₂ pressure, the CO₂ content in coal seam increases rapidly near the injection borehole. Taking 5 m³/t as a reference, the damage effect makes the CO₂ content rise faster. At 120 days, for considering the damage effect, the area of the CO₂ content higher than 5 m³/t is 71.9 m², while for ignoring the damage effect, this area is 63.1 m², with an error of 12.24%.

In Fig.17, the CO₂ content increases with time, and the CO₂ content considering the damage effect increases faster. The difference of the CO₂ content on point C between considering and ignoring damage effects differs with time. At 120 days, the CO₂ content of ignoring damage is 10.02 m³/t, and the CO₂ content of considering the damage is 7.77 m³/t. Therefore, the CO₂ injection efficiency will be underestimated if the damage effect is ignored, especially in the soft coal seam.

5 Conclusions

1) The multi-physics coupling model considering the damage effect is established to numerically simulate the process of CO₂ injection promoted CH₄ extraction in soft and low-permeability coal seam, including equations of gas mixture migration, coal deformation and damage. The influence of effective stress, adsorption strain and damage on coal permeability has been considered in this model.

2) The variations of damage zone and permeability around the boreholes under different borehole diameters and coal strengths are comprehensively analyzed. The small borehole diameter corresponds small range of damage zone around the borehole. The damage zone increases exponentially with the borehole diameter, while decreases exponentially with the compressive strength. The permeability of the damaged coal seam has increased by nearly 300 times, which significantly impacts the migration rate of CO₂ and CH₄ in the coal seam.

3) Compared with considering the damage effect, the CH₄ pressure reducing area in coal seam of ignoring the damage effect is smaller and the reducing speed is slower. Under the operation of injection and extraction, CH₄ content decreases rapidly near all boreholes. The pressure and content of CO₂ increase around the injection borehole. In soft and low-permeability coal seam, ignoring the damage effect will underestimate the efficiency of gas extraction and injection.

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