Numerical Simulation of CO₂-ECBM Based on Multi-Physical Field Coupling Model

Abstract

In this paper, heat injection and CO₂ injection are combined, and the influence of coal seam parameters on CO₂-ECBM is analyzed to improve the production of CH₄ and CO₂ reserves and the effective control of both greenhouse gases. A multi-physical field coupling model of CO₂-ECBM was established based on Darcy’s law, Fick’s law of diffusion, the extended Langmuir model for adsorption, and the equation of state. Numerical simulation of CO₂-ECBM under different coal seam parameters was carried out by COMSOL Multiphysics. The results show that increasing the injection pressure of the CO₂ injection well and the initial pressure of the coal seam can effectively increase the gas pressure and concentration gradient, which has a positive effect on improving the extraction concentration of CH₄ and the sequestration concentration of CO₂ in the coal seam. The increase of the initial temperature of the coal seam will promote the desorption and diffusion of the binary elemental gas, resulting in a decrease in the concentration of coalbed methane and a decrease in the displacement effect. In the process of displacement, the greater the initial permeability, the greater the fracture opening of the coal seam, which is more conducive to the seepage transport of the gas. The closer to the position of the injection well, the better the displacement effect and the lower the permeability rate ratio.

1. Introduction

With the development of modern industrial technology, humans use a large amount of fossil energy, and CO₂ emissions have increased significantly. Therefore, the “greenhouse effect” has become a globally significant issue. In the process of coal mining, coalbed methane (CBM), a highly efficient, non-polluting flammable gas, is released from coal seams. Meanwhile, CBM is the greenhouse gas second only to CO₂, and its direct emission into the atmosphere will not only cause air pollution but also cause a huge waste of resources [1,2]. Due to the high gas storage capacity of coal, CH₄; recovery and CO₂ storage have received attention in many countries [3,4]. The technology of injecting CO₂ into coal seams to improve the CH₄ extraction rate (hereinafter referred to as CO₂-ECBM) can not only reduce greenhouse gas emission but also develop new energy, which has attracted widespread attention [5,6]. CO₂-ECBM not only addresses safety issues, increasing environmental requirements, but also extracts methane from coal for additional energy use [7]. CO₂-ECBM is mainly based on competitive adsorption between CH₄ and CO₂. With the injection of CO₂, the affinity of CO₂ on coal is greater than that of CH₄; for every CH₄ molecule released, at least two CO₂ molecules can be absorbed [8,9]. Therefore, CO₂ begins to occupy the adsorption sites of CH₄ [10], and this will decrease the harmful influences of carbon dioxide gas on the existing climate by providing safe storage locations. Moreover, the method of ECBM recovery by injecting flue gas into the coal seams may be a striking alternative way of increasing the production of gas considerably [11]. Therefore, it is of great significance to improve CO₂-ECBM by establishing a reasonable and accurate mathematical model to simulate CBM exploitation and compare different coal seam parameters.

For the CO₂-ECBM, many countries have carried out pilot experimental research and proved the feasibility, economic and environmental benefits of this project. Among them, numerical simulation research is one of the main research directions of gas injection displacement. It can quantitatively analyze the potential of CO₂-ECBM, and the research investment is small and the time involved is short [12]. Multiphysics coupling numerical simulation research has been widely used in the field of CBM development [13], and some experimental studies have been carried out at home and abroad to prove the feasibility of this project. Fang et al. [14] established a fluid-solid coupling model of CO₂-ECBM to study the distribution of gas pressure and concentration, and analyzed the CH₄ production and CO₂ storage, but ignored the effect of thermal field on displacement, and only the coupling of force field and mechanical field is carried out. Qu et al. [15] established a permeability evolution model in CO₂-ECBM which only considered a single gas and ignored the effect of competitive adsorption between multiple gases. Perera [16] used COMET3 to establish a three-dimensional numerical model for the numerical simulation of CO₂-ECBM, only considering the effect of temperature changes on the coal skeleton strain. Yang et al. [17] established a multi-physics coupled mathematical model to simulate the variation of borehole gas discharge flow and drain flow when N₂ and CO₂ were injected into the coal seam, but ignored the influence of thermal fields on multi-physics fields. Rutqvist et al. [18] proposed a thermal-water-mechanical coupling model to analyze the multiphase fluid flow, heat transfer and deformation in porous and fractured rocks, although the disadvantage is that the influence of gas adsorption and the Klinkenberg effect on the whole is not considered. Sun [19] established multi-component gas flow models for coalbed CO₂ injection and CH₄ exploitation, but these models did not consider the fluid-solid coupling effect of coal seams.

From the above analysis it can be seen that the injection of heat into the coal seam and the injection of CO₂ into the coal seam can both affect the effect of CBM extraction. However, few studies have been published on combining heat injection and CO₂ injection to reduce CH₄ concentration in coal seams. In order to be closer to the actual geological conditions, the typical three-wells layout of the CO₂-ECBM project in the Qinshui basin is selected as the research object. The depth of coal seam is 1200–2000 m; the No. 3 coal seam is mainly the primary structure coal, the macro coal and rock composition are mainly bright coal, with mirror coal strip, and the micro coal and rock composition is mainly vitrinite, The content ranged from 74.9% to 77.9%, with an average of 76.4%. The inertinite content was 22.4–25.1%, with an average of 23.18%. The mineral content ranged from 16.0% to 22.5%, with an average of 19.2%. The maximum reflectance of vitrinite is 2.2–3.0%, which is mainly anthracite. The ash content of the coal seam is 8–15%, which is from the low ash coal [20].

In this work, the fluid-solid-thermal coupling model of CO₂-ECBM was established, consider the permeation, diffusion and competitive adsorption of binary gas in the coal seam, the influence of coal seam initial temperature on CO₂-ECBM is studied, permeability evolution and displacement effect in the reservoir under different CO₂ injection pressures and initial coal seam pressures were analyzed. The influence of the different initial permeability of the coal seam on the displacement effect was also discussed. Based on the COMSOL Multiphysics numerical simulation software, the influence of different characteristic parameters on the displacement effect was analyzed by comparing the displacement effect under different coal seam parameters; the CO₂ extraction and CH₄ storage can be improved, the greenhouse gas content can be effectively reduced and more clean energy can be obtained. This provided the basis for the prediction of the CO₂-ECBM and the engineering site selection.

2. Materials and Methods

2.1. Model Assumptions

The injection of CO₂ to displace CH₄ in coal seams is a complex multiphase flow coupled process. The displacement process is often accompanied by multi-physical field coupling effects such as gas adsorption and desorption, coal seam deformation, and the heat exchange of the gas and coal skeleton. In order to explore the mechanism of multi-physical field coupling in the process of CO₂-ECBM, the following assumptions need to be made [21,22,23]: ➀ The coal seam is a homogeneous isotropic body, and the gas is evenly distributed in the coal seam; ➁ The deformation of the coal seam is an infinitesimal deformation; ➂ The gas in the coal seam is an ideal gas, and the influence of temperature change on the gas dynamic viscosity is not considered; ➃ The seepage and diffusion of CH₄ and CO₂ conform to Darcy’s law and Fick’s law, respectively; and ➄ The influence of water and vapor on gas transport is not considered [24].

2.2. Gas Transport Equation

According to the assumption, CBM is first in a dynamic equilibrium state of adsorption and desorption. When the equilibrium state is broken due to the injection of CO₂, the CH₄ in the adsorbed state is desorbed and diffused into the fracture system under the action of the concentration gradient. The equation describing this phenomenon can be expressed as [13,25,26]:

$$\frac{\partial m_n}{\partial t}+\nabla ·(\overrightarrow{v}·{\rho }_{gn})+\nabla ·(-\overrightarrow{D_n}·\nabla m_{fn})=Q_{sn}.$$

(1)

In the formula, $m_n$ is the gas content, including free phase gas and absorbed gas, kg/m³; $n$ is the gas code, $n$ is 1 for CH₄, $n$ is 2 for CO₂; t is time, s; $\nabla$ is the Laplace calculation; $m_{fn}$ is the mass of the free phase gas, kg/m³; $m_{sn}$ is the mass of the adsorbed gas, kg/m³; $\overrightarrow{v}$ is the convection velocity vector; ${\rho }_{gn}$ is the gas density, kg/m³; $Q_{sn}$ is the source term W/m³.

$$Q_{sn}=-(1-{\varphi }_0)·{\rho }_c·{\rho }_{sg}·DD·\frac{\partial C_n}{\partial t}.$$

(2)

where:

$$DD=\frac{V_{lj0}\exp \left[-\frac{d_2(T-T_0)}{1+d_1{C}_{n}RT}\right]·C_n·b_1·b_2·{(R·T)}^2}{{(1+C_1·b_{1}RT+C_2·b_{2}RT)}^2}.$$

The mass of gas contained in a unit volume of coal can be defined as [27]:

$$m_n=m_{fn}+m_{sn}=\varphi ·C_n·M_n+(1-\varphi )·{\rho }_c{\rho }_{sg}\frac{V_{\infty n}{b}_n{C}_n}{1+C_1{b}_1+C_2{b}_2}.$$

(3)

In the formula: $\varphi$ is the porosity of coal seam; ${\rho }_c$ is the coal density, kg/m³; $V_{\infty n}$ is the corrected Langmuir volume constant, m³/kg; ${\rho }_{sg}$ is the gas density at standard conditions, kg/m³; $M_n$ is the molar mass of the component, k; $C_n$ is the gas concentration, mol/m³; $b_n$ is the Langmuir pressure constant, ${\mathrm{Pa}}^{-1}$.

Where: $\overrightarrow{v}$ is the convective velocity vector, which is determined by the injection gas concentration gradient and can be expressed as [27]:

$$\overrightarrow{v}=-\frac{kRT}{\mu }\nabla C_n.$$

(4)

Substitute Equations(2), (3) and (4) into Equation (1) to obtain the gas migration formula in the coal seam:

$$\left[\varphi ·M_n+(1-\varphi )·{\rho }_c·P_{sg}·AA\right]·\frac{\partial C_n}{\partial t}+\nabla \left(-C_n·\frac{k·R·T}{{\mu }_n}\nabla C_n\right)+\nabla (-D_n·\varphi \nabla C_n)=Q_{sn}.$$

(5)

where:

$$AA=\frac{V_{\infty n}·b_n·R·T(1+C_n·b_n·R·T)}{{(1+C_1·b_{1}RT+C_2·b_{2}RT)}^2}.$$

where: $k$ is the permeability of the coal seam, m²; $R$ is the gas molar constant, $\frac{\mathrm{J}}{\mathrm{mol}·\mathrm{K}}$; $T$ is the coal seam temperature, $K$; ${\mu }_n$ is the dynamic viscosity coefficient of the gas, $\mathrm{Pa}·\mathrm{s}$; $M_n$ is the mole of the gas mass, $\frac{\mathrm{kg}}{\mathrm{mol}}$; $D_n$ is the vector of hydrodynamic dispersion coefficient.

2.3. Governing Equation of Coal Seam Stress Field

Gas transport and exchange typically causes significant changes in effective stress, so that influences coal seam deformation and the evolution of transport parameters.

The Navier equation of the force balance of the CH₄-containing coal seam is [28,29]:

$${\sigma }_{ij,i}+f_i=0.$$

(6)

In the formula, ${\sigma }_{ij,i}$ is the stress tensor; $f_i$ is the body force component, and this study only considers the vertical gravity.

Considering that the elastic deformation of coal seam is small deformation, the strain-displacement relation is defined as [28,30]:

$${\epsilon }_{i,j}=\frac{1}{2}(u_{i,j}+u_{j,i}).$$

(7)

The constitutive equation for the deformed coal seam becomes [28,30]:

$${\epsilon }_{ij}=\frac{1}{2G}{\sigma }_{ij}-\left(\frac{1}{6G}-\frac{1}{9K}\right){\sigma }_{KK}{\delta }_{ij}+\frac{\alpha }{3k}p{\delta }_{ij}+\frac{{\epsilon }_s}{3}{\delta }_{ij}.$$

(8)

In the formula: $G=\frac{E}{2(1+v)}$, $K=\frac{E}{3(1-2v)}$; $K, K_s$ are the bulk modulus of coal and coal grains respectively, Pa; $G$ is the shear modulus of coal, Pa; $E$ is the Young’s modulus of the coal; $v$ is the Poisson’s ratio of the coal; ${\delta }_{ij}$ is the Kronecker delta.

$$G{u}_{i,jj}+\frac{G}{1-2v}{u}_{j,\mathrm{ji}}=(\alpha ·RT+K·BB)C_{1,i}+(\alpha ·RT+K·CC)C_{2,i}-K·{\alpha }_T{T}_{,i}-f_i.$$

(9)

where: $BB=\frac{{\epsilon }_{\infty 1}{b}_1(1+b_2{C}_2)}{{(1+b_1{C}_1+b_2{C}_2)}^2}-\frac{{\epsilon }_{\infty 2}{b}_1{b}_2{C}_2}{{(1+b_1{C}_1+b_2{C}_2)}^2}$; $CC=\frac{{\epsilon }_{\infty 2}{b}_2(1+b_1{C}_1)}{{(1+b_1{C}_1+b_2{C}_2)}^2}-\frac{{\epsilon }_{\infty 1}{b}_1{b}_2{C}_1}{{(1+b_1{C}_1+b_2{C}_2)}^2}$; ${\epsilon }_{\infty \mathrm{n}}$ is the gas swelling strain constant.

2.4. Control Equation of Coal Seam Temperature Field

In the entire fluid-solid-thermal coupled model, the coal seam temperature changes are mainly caused by the exothermic or endothermic reactions induced by CO₂ injection and adsorption-desorption during the displacement process. Based on the energy conservation law and the Fourier law, the control equation of the coal seam temperature field can be obtained [31,32,33]:

$$\frac{\partial \left({(\rho C_p)}_{c}T\right)}{\partial t}+\eta \nabla T-\nabla ·({\lambda }_c\nabla T)+q_{st1}\frac{{\rho }_C{\rho }_{sg1}}{M_1}\frac{\partial V_{c1}}{\partial t}+q_{st2}\frac{{\rho }_C{\rho }_{sg2}}{M_2}\frac{\partial V_{c2}}{\partial t}+K{\alpha }_{T}T\frac{\partial ({\epsilon }_{s1}+{\epsilon }_{s2})}{\partial t}=0.$$

(10)

In the formula: ${(\rho C_p)}_c$ is the effective heat capacity, $\frac{\mathrm{J}}{{\mathrm{m}}^3·\mathrm{K}}$; $\eta$ is the convection coefficient, $\frac{\mathrm{J}}{{\mathrm{m}}^2·\mathrm{s}}$; ${\lambda }_c$ is the effective coefficient of the isotropic thermal conductivity, $\frac{\mathrm{W}}{\mathrm{m}·\mathrm{K}}$; $q_{st1}$ is the isosteric heat of adsorption of CH₄, $\frac{\mathrm{J}}{\mathrm{mol}}$; ${\rho }_{sg1}$ is the gas density of CH₄ under standard conditions, $\frac{\mathrm{kg}}{{\mathrm{m}}^3}$; $V_{c1}$ is the mass of CH₄ adsorbed by coal, $\frac{{\mathrm{m}}^3}{\mathrm{kg}}$; $q_{st2}$ is CO₂ isosteric heat of adsorption, $\frac{\mathrm{J}}{\mathrm{mol}}$; ${\rho }_{sg2}$ is CO₂ gas density under standard conditions,$\frac{\mathrm{kg}}{{\mathrm{m}}^3}$;$V_{c2}$ is the mass of CO₂ adsorbed by the expansion and shrinkage of the matrix, $\frac{{\mathrm{m}}^3}{\mathrm{kg}}$; ${\epsilon }_{s1}$ is the total volume strain generated by the adsorption or desorption of CH₄ by the coal; ${\epsilon }_{s2}$ is the total volume strain generated by the adsorption or desorption of CO₂ by the coal;

$${(\rho C_p)}_c=(1-\phi ){\rho }_c{C}_s+\phi (M_1{C}_{\mathrm{v}1}{C}_{L1}+M_2{C}_{\mathrm{v}2}{C}_{L1}).$$

(11)

$$\eta =-\frac{k}{{\mu }_1}\nabla C_{1}RT{\rho }_{ga1}{C}_{L1}-\frac{k}{{\mu }_2}\nabla C_{2}RT{\rho }_{ga2}{C}_{L2}.$$

(12)

$${\lambda }_c=(1-\varphi ){\lambda }_s+\varphi ({\lambda }_{g1}+{\lambda }_{g2}).$$

(13)

where: $\varphi$ is the porosity; $C_{\mathrm{v}1}$ is the volume fraction of CH₄ in coal seam; $C_{L1}$ is the constant volume specific heat capacity of CH₄, $\frac{\mathrm{J}}{{\mathrm{m}}^3·\mathrm{K}}$; $C_{\mathrm{v}2}$ is the volume fraction of CO₂ s in the coal seam; $C_{L2}$ is the constant volume specific heat capacity of CO₂, $\frac{\mathrm{J}}{{\mathrm{m}}^3·\mathrm{K}}$; ${\lambda }_{g1}$ is the heat conductivity coefficient of the coal skeleton of CH₄, $\frac{\mathrm{W}}{\mathrm{m}·\mathrm{K}}$; ${\lambda }_{g2}$ is the heat conductivity coefficient of the coal skeleton of CO₂, $\frac{\mathrm{W}}{\mathrm{m}·\mathrm{K}}$.

2.5. Coupling Terms

After gas injection, there are only CO₂ and CH₄ in the coal seam. The calculation formula of the total gas adsorption is as follows [34,35]:

$$V=V_{{\mathrm{CO}}_2}+V_{{\mathrm{CH}}_4}=\frac{V_{L1}{b}_1{P}_1+V_{L2}{b}_2{P}_2}{1+b_1{P}_1+b_2{P}_2}.$$

(14)

where: $V_{L1}$ and $V_{L2}$ are the Langmuir volume constants of CH₄ and CO₂, respectively, $\frac{m^3}{kg}$; $P_1$ and $P_2$ are the partial pressures of CH₄ and CO₂, respectively, $\mathrm{MPa}$.

Binary gas adsorption and desorption can cause stress deformation of the coal seam, and the calculation formula of the total volume strain is [36]:

$${\epsilon }_s={\epsilon }_{{\mathrm{CO}}_2}+{\epsilon }_{{\mathrm{CH}}_4}=\frac{{\epsilon }_{L1}{b}_1{P}_1+{\epsilon }_{L2}{b}_2{P}_2}{1+b_1{P}_1+b_2{P}_2}.$$

(15)

where ${\epsilon }_{L1}$ and ${\epsilon }_{L2}$ are the Langmuir volume strain constants of CH₄ and CO₂, respectively.

By analyzing the coupled model, the porosity model is obtained [34]:

$$\varphi =\frac{V_P}{V}=1-\frac{1-{\varphi }_0}{1+{\epsilon }_V}\left(1+\frac{\Delta V_s}{V_{s0}}\right).$$

(16)

where: $V_P$ is the pore volume of coal, m³; $V$ is the total volume of coal, m³; ${\varphi }_0$ is the initial porosity; ${\epsilon }_V$ is the volumetric strain of coal seam; $\Delta V_s$ is the change of skeleton volume, m³; $V_{s0}$ is the initial skeleton volume, m³.

$$\frac{\nabla V_s}{V_{s0}}=-\frac{\alpha }{K_s}(\Delta P_1+\Delta P_2)+\Delta {\epsilon }_s+{\alpha }_s·\Delta T.$$

(17)

$\alpha$ is the Biot effective stress coefficient; $K_s$ is the volume modulus of the skeleton, $\mathrm{MPa}$; ${\alpha }_s$ is the thermal expansion coefficient, ${\mathrm{K}}^{-1}$; $T$ is the temperature, $\mathrm{K}$.

Which brings (17) into (16):

$$\varphi =\frac{V_P}{V}=1-\frac{1-{\varphi }_0}{1+{\epsilon }_V}\left[1-\frac{\mathsf{\alpha }}{K_s}(\Delta P_1+\Delta P_2)+\Delta {\epsilon }_s+{\alpha }_s·\Delta T\right].$$

(18)

The model is [37,38]:

$$k=k_0{[\frac{1}{{\varphi }_0}-\frac{1-{\varphi }_0}{{\varphi }_0(1+{\epsilon }_V)}\left(1-\frac{\mathsf{\alpha }}{K_s}(\Delta P_1+\Delta P_2)+\Delta {\epsilon }_s+{\alpha }_s·\Delta T\right)]}^3.$$

(19)

In the formula: $k_0$ is the initial permeability, m².

2.6. Fluid-Solid-Thermal Field Cross-Coupling

Governing equations and coupling terms are nonlinear second-order partial differential equations (PDEs) in space and time domains. Therefore, we introduced these equations into the solid mechanics and PDE module of COMSOL Multiphysics (COMSOL Multiphysics 5.6) to obtain numerical solutions through discrete and finite element methods. The coupling effect of CBM mining can be obtained by combining Equations (18) and (19), combining Equations (5), (9) and (10) the THM coupled mathematical model can be achieved, see the following equation.

It can be seen from the above formula that each physical field is coupled and related to each other, and the relationship between them is shown in Figure 1. The temperature stress caused by the change of temperature has an impact on the mechanic model; the strain energy generated by energy dissipation within the skeleton has an impact on the coal seam temperature; the change of temperature causes the change of gas adsorption and desorption, which has an impact on the gas transport model; the heat transfer and the seepage of gas has an impact on the temperature model; the change of porosity and permeability caused by coal deformation has an impact on the gas transport model; and the change of gas pressure can result in coal deformation.

2.7. Geometric Model Description

Qinshui Basin is located in the south-central Shanxi province; it is one of the most active and promising areas for CBM exploration and development in China. The No. 3 coal seam in the Qinshui basin is the main target area because of its unique characteristics, such as stable tectonic environment, weak hydrodynamic condition and good regional cap [32].

The CO₂-ECBM is actually a 3D model, but compared with the parallel bedding direction, the coal seam perpendicular to the bedding direction can be ignored. It can be approximated as a 2D model. The model diagram is shown in Figure 2. The model selects a square area of 150 m × 150 m as the research domain, with a radius of 0.1 m. The W_in, CO₂ injection well is located at the lower left corner of the geological model, and the W_out, CH₄ production well is located at the upper right corner of the model. Observation point A is selected to observe the simulation effect, and points B and C are the comparison points.

3. Results and Discussion

3.1. Boundary Conditions

Except for the boundary of the injection well and the production well, the other boundaries have zero flow boundary conditions with no outflow and no heat conduction. The average thickness of the coal seam is 5 m, the initial gas pressure is 5 MPa, the CO₂ injection well pressure is set to 8 MPa, the initial permeability is $5.14\times {10}^{-16}{\mathrm{m}}^2$, the injection wellbore are constant temperature boundary conditions of 300 K, and the initial coal seam temperature is 300 K. Other parameters used in the numerical simulations are taken from the literature and are listed in

Table 1. Numerical simulation parameters.

Parameter	Numerical Value	Parameter	Numerical Value
Young’s modulus of coal $\mathrm{E}/\mathrm{MPa}$	2710	Coal skeleton expansion coefficient ${\alpha }_T/{\mathrm{K}}^{-1}$	2.4−5
Poisson’s ratio of coal $v$	0.35	CO2 specific heat capacity $C_s/\left[\mathrm{J}/(\mathrm{kg}\ast \mathrm{K})\right]$	1250
Density of coal ${\rho }_s/(\mathrm{kg}/{\mathrm{m}}^3$)	1370	CO2 thermal conductivity ${\mathsf{\lambda }}_{ge}/\left[\mathrm{W}/(\mathrm{m}\ast \mathrm{K})\right]$	0.015
Initial porosity of coal ${\varphi }_0$	0.037	CO2 constant pressure heat capacity $C_{pe}/\left[\mathrm{J}/(\mathrm{mol}\ast \mathrm{K})\right]$	37.18
Dynamic viscosity coefficient of CH4 ${\mu }_1/(\mathrm{Pa}·\mathrm{s})$	1.84 × 10−5	Dynamic viscosity coefficient of CO2 ${\mu }_2/(\mathrm{Pa}·\mathrm{s})$	1.84 × 10−5
Skeletal Young’s Modulus $E_s/\mathrm{MPa}$	8469	CH4 thermal conductivity ${\mathsf{\lambda }}_{gj}/\left[\mathrm{W}/(\mathrm{m}\ast \mathrm{K})\right]$	0.031
CH4 heat capacity at constant pressure $C_{pj}/\left[\mathrm{J}/(\mathrm{mol}\ast \mathrm{K})\right]$	34.4	Thermal conductivity of coal skeleton ${\mathsf{\lambda }}_s/\left[\mathrm{W}/(\mathrm{m}\ast \mathrm{K})\right]$	0.191
CH4 Langmuir pressure $P_{lj0}/\mathrm{MPa}$	2.07	CO2 Langmuir pressure $P_{le0}/\mathrm{MPa}$	1.38
CH4 Langmuir volume $V_{lj0}/({\mathrm{m}}^3/\mathrm{kg})$	0.0256	CO2 Langmuir volume $V_{le0}/({\mathrm{m}}^3/\mathrm{kg})$	0.0477
CH4 dynamic dispersion coefficient $D_1/({\mathrm{m}}^2/\mathrm{s})$	3.6 × 10−12	CO2 dynamic dispersion coefficient $D_2/({\mathrm{m}}^2/\mathrm{s})$	5.8 × 10−12
Coal skeleton density ${\rho }_s/(g/{\mathrm{m}}^3)$	1470	CO2 isosteric heat of adsorption $q_{st2}/(\mathrm{J}/\mathrm{mol})$	33.4
CH4 isosteric heat of adsorption $q_{st1}/(\mathrm{J}/\mathrm{mol})$	35	Temperature correction coefficient $d_2/{\mathrm{K}}^{-1}$	0.021
Pressure correction coefficient $d_1/{\mathrm{K}}^{-1}$	0.071

. [25,30,31,32].

3.2. CBM Extraction Law

3.2.1. Pressure Cloud Map Distribution

In the process of CO₂-ECBM, with the continuous injection of CO₂ and the continuous extraction of CH₄, the concentrations of CO₂ and CH₄ and pore pressure of the coal seam will also change continuously. Figure 3 shows the cloud map distribution.

It can be seen from Figure 2a,b that with the continuous injection of CO₂, CO₂ enters the coal seam from the injection well in the lower left corner and diffuses throughout the coal seam. When the gas injection time is 100 days, the influence radius is only 50 m. By 3650 days, the influence radius has reached about 170 m. Figure 3c,d show the CH₄ concentration distribution as CH₄ is pumped out from the upper right production well. It can be seen from the figures that the CH₄ concentration has been effectively reduced. At 100 days, the CH₄ concentration was 1971.916 mol/m³, and at 3650 days, the CH₄ concentration was 1102.834 mol/m³, which is a decrease of 44%.

3.2.2. Displacement Effect at Different Positions of Coal Seam

The displacement effect at different positions of the coal seam is shown in Figure 4, where the positions of point A, B and C are (50, 50), (75, 75), (100, 100) respectively. It can be seen from the figure that the closer to the injection well, the better the displacement effect. The change of coal seam permeability is the result of the combined action of the multi-physical field. When these three points are not affected by CO₂, the permeability ratio is a process of slightly decreasing and then increasing. The larger initial permeability corresponds to higher gas velocity [22]. This is because CH₄ flows out of the CH₄ production well, causing the pressure to decrease. The CH₄ pressure decreases over time, and the increase in effective stress reduces the pore size of the fracture and its space, resulting in a decrease in permeability. When CH₄ is desorbed from the coal seam, the coal seam shrinks, which leads to an increase in the fracture space, and the increase of the fracture caused by desorption is much greater than the decrease of the fracture space caused by the increase of effective stress, so the permeability gradually increases with time [14,29].

Point A, B and C have different distances from the CO₂ injection well. The farther the distance is, the longer the CO₂ injection was unaffected. As time increases, CO₂ injection affects points A, B and C, while CO₂ injection causes matrix shrinkage [14], and the permeability ratio decreases. This is because the closer to the injection well, the higher the CO₂ concentration, which leads to an increase in the amount of CO₂ adsorption under the competitive adsorption, the greater the space expansion of the coal seam, and lower permeability. The farther the distance from the CO₂ injection well, the lower the CO₂ concentration at this point, the smaller the pressure gradient formed, and the slower the seepage velocity, the less chance for CO₂ to contact CH₄, and the worse the displacement effect [34]. Therefore, the displacement effect of point A is greater than that of point B, and the displacement effect of point B is greater than that of point C.

3.3. Influence of Coal Seam Characteristic Parameters on CO₂-ECBM

3.3.1. Displacement Effect under Different Initial Temperatures

Figure 5 shows the displacement effect of different initial temperatures at point A within 3650 d. With the injection of CO₂, the permeability decreases gradually. The lower the initial coal seam temperature, the more obvious the decrease in permeability. When the extraction time was 3650 days, the permeability ratio with an initial temperature of 300 K decreased by 5.7% compared with the initial coal seam temperature of 340 K. The lower the initial temperature, the smaller the permeability ratio change. This is because as the temperature decreases, the coal seam will have a shrinking effect, and the gas pressure will also decrease, so the permeability rate decline will be slower.

Both CH₄ and CO₂ concentrations decreased with increasing initial coal seam temperature. When the initial coal seam temperature was 300 K, the CO₂ concentration was 966.046 mol/m³ at 3650 days, and the total output of CH₄ was 901.817 mol/m³. When the initial coal seam temperature was 320 K, the CO₂ decreased by 14.6% at 3650 days, and the total output of CH₄ was 822.555 mol/m³, a decrease of 8.8%. When the initial coal seam temperature was 340 K, the CO₂ decreased by 32% in 3650 days, and the total output of CH₄ was 754.145 mol/m³, a decrease of 16.4%. The higher the coal seam temperature, the kinetic energy of injected CO₂ molecules increases, which reduces the adsorption rate of CO₂ to coal [15], the less the gas content in the adsorbed state per unit volume of the coal seam. Therefore, the less total concentration of CH₄ produced. The increase of temperature promotes the desorption and diffusion of binary gas [8]. As the temperature of coal seam increases, the content of adsorbed gas in the coal seam will decrease [1], so the content of CO₂ stored in the coal seam will also decrease.

3.3.2. Displacement Effect under Different Coal Seam Pressures

The displacement effect under different initial coal seam pressures is shown in Figure 6. The concentrations of CH₄ and CO₂ increase with the increase of the initial pressure of the coal seam. When the initial coal seam pressure was 4 MPa, the CO₂ concentration was 929.215 mol/m³ at 3650 days. When the initial coal seam pressure increased to 5 MPa, the CO₂ concentration was 966.046 mol/m³ at 3650 days, an increase of 4%. When the initial coal seam pressure was 6 MPa, the CO₂ concentration was 991.276 mol/m³ at 3650 days, an increase of 6.7%. When the initial pressure was 4 MPa, the total output of CH₄ was 592.085 mol/m³. When the initial coal seam pressure was 5 MPa, the total output of CH₄ was 901.817 mol/m³, an increase of 34.4%. When the initial coal seam pressure was 6 MPa, the total output of CH₄ was 1232.880 mol/m³, an increase of 108.2%. The higher the initial pressure of the coal seam, the higher the initial CH₄ content in the coal seam, and the higher the concentration of CH₄ production [34]. At the same time, as the initial coal seam pressure increases, the pressure gradient between the coal seam and the CH₄ production well also increases, the seepage velocity increases, and the CH₄ production rate increases. Due to the faster migration of CH₄ in the coal seam, the faster the migration of CO₂ is, and the amount of CO₂ sequestered also increases.

The permeability ratio decreases as the initial pressure of the coal seam increases. The increase of the initial pressure of the coal seam will increase the pressure gradient between the CO₂ injection well and the coal seam, promote the acceleration of seepage, reduce the effective stress, reduce the matrix pore radius, and reduce the matrix porosity, so the permeability is also smaller.

3.3.3. Displacement Effect under Different Initial Permeability

The displacement effect under different initial permeability is shown in Figure 7. The greater the initial permeability of the coal seam, the faster the seepage velocity of the binary gas to the production well, the greater the desorption of CH₄ and the adsorption of CO₂, the faster the permeability ratio decreases, and the faster the change [39]. At 3650 days, when the initial coal seam permeability was $5.14\times {10}^{-16}$ m², the permeability ratio increased by 2.5% compared with the condition that the initial coal seam permeability was $6.14\times {10}^{-16}$ m². When the initial coal seam permeability was $7.14\times {10}^{-16}$ m², the permeability ratio is reduced by 4.8% compared with the condition that the initial coal seam permeability was $5.14\times {10}^{-16}$ m².

It can also be seen from Figure 7 that the displacement effect is better with the increase of the initial permeability. At 3650 days, when the initial coal seam permeability was $5.14\times {10}^{-16}$ m², the CH₄ storage concentration was 1102.834 mol/m³, and the CO₂ storage concentration was 966.046 mol/m³. When the initial coal seam permeability increased to $6.14\times {10}^{-16}$ m², the CH₄ storage concentration was 1030.514 mol/m³, a decrease of 6.7%, and the CO₂ storage concentration was 1036.94296 mol/m³, an increase of 7.4%. When the permeability was $7.14\times {10}^{-16}$ m², the CH₄ storage concentration was 971.274 mol/m³, a decrease of 11.9%, and the CO₂ storage concentration was 1117.2951 mol/m³, an increase of 15.7%. In the process of displacement, the greater the initial permeability, the greater the fracture opening of the coal seam, which is more conducive to the seepage and migration of gas [11]. The porosity determines the change of permeability. The larger the initial permeability, the higher the porosity of the coal seam, the more desorption and diffusion paths of CBM. When the initial permeability is relatively small, the matrix gas pressure decreases slowly and the matrix shrinkage effect is not significant [31]. Therefore, a larger initial permeability has a positive effect on increasing the CH₄ output concentration and CO₂ storage concentration.

3.4. Displacement Effect under Different Gas Injection Pressures

The changes of permeability ratio, CH₄ and CO₂ concentrations at point A under different CO₂ injection pressures are shown in Figure 8. The higher the injection pressure, the better the displacement effect at each stage, and the faster the permeability ratio decreases. When the CO₂ injection pressure increased from 8 MPa to 12 MPa, the CH₄ concentration in the coal seam decreased from 831.806 mol/m³ to 522.494 mol/m³ at 2800 days, and the CO₂ concentration increased from 914.003 mol/m³ to 1918.241 mol/m³ at 2800 days. When the CO₂ injection pressure increased from 8 MPa to 10 MPa, the CH₄ concentration in the coal seam decreased by 149.7933 mol/m³ at 2800 days, meanwhile the CO₂ concentration increased by 404.260 mol/m³ at 2800 days. This shows that the increase of CO₂ injection pressure can effectively promote the displacement of CH₄. The gas pressure gradient will have a great impact on the gas seepage velocity in the coal seam. The larger the CO₂ migration area, the greater the pressure gradient, which effectively increases the CO₂ seepage velocity [40], and this shows that increasing the injection pressure of the injection well can effectively remove the CH₄ in the coal from the original position and improve the effect of displacement [32]. At the same time, increasing the injection pressure will also increase the surface activation energy of the coal, so that the contact and collision opportunities of the binary gas are greater [13], and the adsorption and desorption effect is strengthened, which is conducive to the displacement effect.

In the process of CO₂-ECBM, with the increase of production time, the overall trend showed a decreasing trend, as shown in Figure 8b. The increase of CO₂ injection pressure promotes the larger pressure gradient formed at point A, resulting in a faster decrease in the permeability ratio. Since the CO₂ injection pressure is greater than the initial coal seam pressure, the gas pressure in the coal seam increases, the effective stress decreases, the matrix pore radius decreases, the matrix porosity decreases, and the permeability decreases [11]. In addition, since the coal seam has a preferential adsorption capacity for CO₂ and the molar amount of adsorbed CO₂ is twice that of CH₄, the injection of CO₂ will cause the coal seam to continuously desorb and adsorb, resulting in the expansion of the coal seam, which further reduces the matrix porosity and permeability. Therefore, under the combined action of injection pressure and competitive adsorption of CO₂ and CH₄, the permeability gradually decreased.

4. Conclusions

A fully coupled coal deformation, binary gas flow and diffusion and gas absorption/desorption finite element model is developed to achieve a better understanding of the CO₂-ECBM recovery mechanisms, and COMSOL Multiphysics was used for numerical simulation. The influence of parameters such as gas pressure, coal seam temperature and permeability on the displacement effect were analyzed. The main conclusions are as follows:

(1)

Under the same working conditions, the increase of the gas injection pressure or the initial coal seam pressure has a positive effect on increasing the cumulative production concentration of CH₄ and the cumulative storage concentration of CO₂.

(2)

With the increase of the coal seam temperature, the CH₄ production concentration and CO₂ storage concentration in the coal seam will decrease, and the permeability ratio will decrease faster.

(3)

In the process of displacement, the greater the initial permeability, the greater the fracture opening of the coal seam, which is more conducive to the seepage migration of gas, and the displacement effect is also better.

(4)

The closer to the injection well, the better the displacement effect and the lower the permeability ratio.