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ACS Omega
ACS Omega
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acsodf
ACS Omega
2470-1343
American Chemical Society

10.1021/acsomega.4c05820
Article
Modeling Study of Enhanced Coal Seam Gas Extraction via N2 Injection Under Thermal–Hydraulic–Mechanical Interactions
https://orcid.org/0000-0001-9126-886X
Zuo Weiqin *†‡
Li Liwen †
Liu Yanwei †
https://orcid.org/0000-0003-0042-6223
Han Hongkai †
Cui Peiwen †
† School of Safety Science and Engineering, Henan Polytechnic University, Jiaozuo 454000, China
‡ State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing University, Chongqing 400044, China
* Email: zuoweiqin@163.com.
30 08 2024
17 09 2024
9 37 3905139064
22 06 2024
14 08 2024
18 07 2024
© 2024 The Authors. Published by American Chemical Society
2024
The Authors
https://creativecommons.org/licenses/by-nc-nd/4.0/ Permits non-commercial access and re-use, provided that author attribution and integrity are maintained; but does not permit creation of adaptations or other derivative works (https://creativecommons.org/licenses/by-nc-nd/4.0/).

N2 injection into coal seams can effectively enhance the gas flow capacity in the late stage of pumping, thereby improving the recovery rate and recovery efficiency of low coalbed methane (CBM). To reveal the thermodynamic flow coupling relationship between the reservoir and the gas phase and its transportation mechanism in the process of thermal N2 injection, a mathematical coupling model of N2 injection that considers the deformation of the coal seam, fluid transportation, and temperature change was established. The influence of the seepage heat transfer effect of the coal seam under the effect of N2 injection on the CH4 extraction rate was investigated using this model. Results indicate that the action mechanism of N2 injection in coal seams includes increasing seepage, promoting flow, and displacing gases. A higher initial coal seam temperature results in a smaller thermal expansion and deformation of the coal skeleton during thermal N2 injection and less pronounced coal permeability increase. A larger initial coal seam permeability results in more favorable N2 diffusion, which strengthens the flow-promoting effect on CH4. The effect of gas injection pressure on CH4 recovery is greater than that of the gas injection temperature: High pressure promotes N2 seepage, carries CH4 flow, and increases the CH4 diffusion effect, whereas higher temperature promotes the desorption of adsorbed gas in the coal seam and improves the recovery rate.

National Natural Science Foundation of China 10.13039/501100001809 52274188 State Key Laboratory of Coal Mine Disaster Dynamics and Control 10.13039/501100011200 2011DA105827-FW202201 document-id-old-9ao4c05820
document-id-new-14ao4c05820
ccc-price
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pmc1 Introduction

Coalbed methane (CBM) is a clean and efficient energy source.1,2 As an important unconventional natural gas resource, CBM is conducive to safe coal mine production, gas explosion risk reduction, energy structure optimization, energy succession support, and ultimately to realization of the “dual carbon” goal, energy conservation, and carbon reduction.3,4 However, CBM reservoirs in China generally have low permeability; with increasing depletion of shallow CBM resources, CBM development has shifted to deeper coal seams, and the issue of low permeability has become more prominent. In recent years, a number of measures have been implemented to increase the coal bed permeability, such as protective layer mining, loose blasting, and other measures for gas extraction strengthening. Practice shows that although these initiatives improve coal bed permeability, in the late stage of mining, gas saturation in the reservoir is reduced, reservoir pressure drops, and gas flow power is insufficient, leading to a drastic mining rate decrease. The above issues can be effectively addressed by finding a way to improve reservoir permeability and intensify gas desorption to realize the transformation of the target reservoir.5

In the field of CBM extraction, several laboratory studies, field tests, and numerical simulations have shown that gas injection is an effective measure for increasing CBM production.6 The gas injection medium is usually CO2 or N2. Field tests of CO2 injection in coal seams have been conducted in San Juan Basin, United States, and Qinshui Basin, China,7 and the results showed that the permeability has been reduced to varying degrees.8 N2 injection in coal seams has been conducted in Anhui Province, China, and Sydney Basin, Australia,9 and results showed that N2 injection into coal seams can effectively increase the CH4 volume under the action of pressure. Zhou et al. experimentally verified that the reservoir permeability decreases significantly by injecting CO2 into the coal seam and increases moderately by injecting N2.10 Wang et al. verified through field tests that pressurizing N2 into low-permeability coal seams increases the pressure gradient and promotes the directional flow of free gas through the cracks of the coal seams toward the gas-producing wells, with the mixing flow rate and CH4 flow rate increasing significantly.11 During a mixed N2 and CO2 injection process, N2 can effectively slow down the CO2 adsorption expansion and deformation, which improves the CBM production.12 After N2 injection, the cumulative contraction rate of the sample is higher than the expansion rate in the adsorption process, and the CH4 content of the free phase in the reactor increases by 12%.13 Talapatra et al. found that N2 injection can increase the extraction rate and revealed through a numerical simulation that the N2 breakthrough in the reservoir occurs at an early stage.14 A higher N2 injection pressure results in a higher temperature and increased methane desorption. The mechanism of N2 injection and CH4 desorption in coal seams primarily includes gas displacement and dilution diffusion.15

In the field of CBM extraction, scholars have proposed several mathematical coupling models.16,17 Chen et al. developed a fluid–solid coupling model for CO2-ECBM, though it overlooked the impact of temperature fields on permeability and adsorption–desorption effects.18 Ren et al. established a binary gas transport model to investigate the impact of N2 injection on gas emission efficiency.19 Connell and Detournay developed a gas–solid coupling model to simulate coalbed methane migration and explored the coupling relationship between coal adsorption strain and pressure, but did not verify the model’s temperature effects.20 Previous studies have significantly advanced our foundational theory and understanding of enhanced gas injection and extraction. Nonetheless, two critical challenges persist in the study of the N2 reservoir reconstruction and enhanced gas extraction. First, the current modeling approaches often overlook the nonisothermal competitive adsorption effect, which is profoundly influenced by temperature variations. Second, while existing research predominantly examines gas pressure and concentration distribution, there remains a notable decline in conducting comparative analyses of reservoir permeability under diverse influencing factors.

To study the evolutionary influence of the N2 seepage heat transfer process on permeability and the gas extraction promotion mechanism, this study establishes a thermal–hydraulic–mechanical coupling model of reservoir heat injection of N2, while simultaneously considering the nonisothermal adsorption of binary gases. Simulations are based on the COMSOL partial differential equation interface. The gas transportation law under the discharge and extraction processes, different reservoir properties, and different injection parameters are examined, which are important for understanding the thermal–hydraulic–mechanical coupling relationship of heat injection of N2.

2 Modeling of Coupled Thermal–Hydraulic–Mechanical Transport in Coal Seams Under the Action of Heat Injection N2

Natural systems typically maintain an energy equilibrium state when external disturbances are absent and change only when the original energy balance is disturbed. For example, methane desorption within a coal seam is triggered when the seam is disturbed. Therefore, to improve the CBM recovery rate, breaking the energy equilibrium state of the coal seam structure is necessary. The reservoir, CBM, and injection medium as a system should conform to the energy conservation equation.211

where Epr is the energy flowing out of the system, i.e., the effective energy, including the kinetic and internal energies of the gas extracted from the system; Ein is the energy injected into the system, including the total energy injected into the system from outside through the medium (e.g., hot N2); Eor is the original energy of the system, including the internal, kinetic, and other intrinsic energies of the coal and CBM; and Eco is the energy consumed by the coal and CBM, including the energy consumed by CBM desorption and transportation, heat exchange between the injection medium and coalbed, and deformation of the coal skeleton.

2.1 Modeling Assumptions

When injecting N2 gas into a coal seam, increasing the energy of the target reservoir and promoting the process of methane desorption and diffusion from the matrix into the cracks of the coal seam are necessary for improving the CBM recovery rate. The process of injecting N2 gas to extract coal seam gas is illustrated in Figure 1.22 The following hypotheses are proposed in combination with the characteristics of gas storage in coal seams:12,23

Figure 1 N2 injection and gas mixture transportation processes.

(1) The coal seam is an elastic continuous porous medium consisting of a matrix and fractures, and CH4 is uniformly distributed in the reservoir.

(2) The gas in the coal seam is an ideal gas with a constant dynamic viscosity coefficient.

(3) The adsorption process of CH4 and N2 in the coal seam conforms to the Langmuir equation, migrates through the matrix, and fractures by Fick’s diffusion.

(4) The seepage of CH4 and N2 in the fractures follows Darcy’s law.

(5) The coal seam is saturated with CH4 and N2 and water is not considered.

2.2 Governing Equations

2.2.1 Porosity and Permeability Models

Porosity and permeability are key factors affecting the binary gas flow in coal seams. By considering the matrix contraction and expansion caused by the competitive gas adsorption, the thermal deformation of coal seams during the heat transfer process, and the role of effective stresses in coal seams, the dynamic change law of the elastic pore medium porosity can be expressed as follows:24,252

where φ0 is the initial porosity, %; e is the body strain; α is the Biot coefficient, ; K is the bulk modulus of the coal, MPa; Km is the bulk modulus of the coal matrix, MPa; ΔPx is the amount of pressure change, x = 1 corresponds to CH4, x = 2 corresponds to N2; εs is the adsorptive strain, kg/m3; αT is the thermal expansion coefficient of the coal skeleton, K–1; and ΔT is the temperature variation, K.

According the cubic law, the relationship between the permeability and porosity can be expressed as follows:263

where k0 is the initial permeability, m2.

2.2.2 Model of Gas Adsorption in Coal Matrix

The total gas adsorption in the coal seam after N2 injection into the seam can be expressed as274

Where and are the Langmuir volume constant and Langmuir pressure constant of CH4 in m3/kg and MPa–1, respectively, with and ; and are according to and; dT is the temperature correction coefficient, K–1; dP is the pressure correction coefficient, Pa–1; CPx is the heat capacity at constant pressure, J/(kg·K); p1 is the CH4 pressure, MPa; and p2 is N2 pressure, MPa.

The volumetric strain due to the nonisothermal adsorption of the binary gas on the coal matrix is the sum of the strains due to each component and can be expressed as follows:285

where αsg is the adsorption strain coefficient; ε1 and ε2 are Langmuir volume strain constant of CH4 and N2, respectively.

2.2.3 Governing Equation of the Coal Seam Deformation Stress Field

The total deformation of the coal seam comprises skeleton deformation under effective stress, expansion/contraction deformation of the coal seam during adsorption/desorption, coal seam deformation caused by fluid pressure, and reservoir deformation caused by coal seam temperature changes.296

where εij is the strain tensor component, m; G is the shear modulus, MPa, G = E/(2 + 2v); σij the stress tensor component; δij the stress tensor component; K is the bulk modulus of coal, MPa, K = E/(1 – 2v); v is the Poisson ratio of coal seam.

The stress balance equation of coal seam is shown in eq 7,30 and the relationship between strain and displacement of elastic homogeneous coal seam is shown in eq 8.307

8

Where fi is the volume force component, and uij is the displacement of the coal seam, m.

Based on the elastic mechanics theory and the constitutive relationship of the coal, the mechanical derivation of the Navier-type deformation equation, which considers the shrinkage and expansion of the coal matrix caused by the coal seam fluid pressure, heat injection, and gas adsorption and desorption, is as follows:319

where αTKΔTi reflects the influence of coal seam temperature change on coal matrix deformation; αp,i reflects the effect of pore pressure change caused by fluid flow on coal deformation; KΔεs reflects the influence of CBM adsorption/desorption on coal matrix deformation.

2.2.4 CH4–N2 Convective Dispersion Control Equation of the Coal Seam

N2 injection into the coal seam disrupts the equilibrium state of the coal seam system. During this process, CH4 changes from adsorbed to free state. Based on the conservation of mass principle, dynamic dispersion law of fluid in porous media, and fluid continuity equation, the convective dispersion equation in porous media during N2 injection containing CH4 is as follows:3210

where mx is the mass of the combined free and adsorbed gas per unit volume, kg, with x = 1 representing the mass of CH4 and x = 2 representing the mass of N2; vgx is the gas flow velocity vector; ρgx is the gas density, kg·m–3, where ; Mx is the molar mass of gas, kg·mol–1; Dx is the gas dynamic dispersion coefficient, m2·s–1; and Qsx is the gas source term, kg·m–3·s–1.

Considering the gas slippage effect combined with Darcy’s seepage law, the gas seepage velocity can be expressed as follows:3211

where k is the absolute permeability of coal, m2; krx is the relative permeability of the gas phase; μx is the aerodynamic viscosity, Pa·s; b is the slip factor, MPa; and px is the gas pressure, MPa.

The gas component x mass per unit volume can be expressed as follows:12

where R is the gas molar constant, J/(mol·K); T is the temperature of coal seam, K; ρc is the density of coal, kg/m3; and Pa is the standard atmospheric pressure, 101.325 kPa. eqs 11,12 are substituted into eq 10, and the seepage equations for CH4 and N2 are given by eqs 13,14, respectively:13

14

2.2.5 Temperature Field Governing Equation

During high-temperature N2 injection into the coal seam, heat exchange between the high-temperature N2 and coal seam increases the coal seam temperature. The heat exchange in the coal seam is mainly caused by the endothermic/exothermic reactions of heat conduction, heat convection, and gas adsorption/desorption. The solid skeleton of the coal seam conducts heat transfer through heat conduction, whereas the fluid between adjacent coal seams conducts heat transfer through heat convection. According to the energy conservation and heat conduction equations,23,3215

16

17

18

where is the effective heat capacity, J/(kg·K); neff is the effective convective heat transfer coefficient, J/(m2·s); λeff is the effective heat transfer coefficient, W/(m·K); and qst is the heat removed by gas adsorption, kJ/mol. These terms represent the temperature changes caused by the inherent energy, heat convection, heat conduction, strain energy, and gas adsorption, respectively. Cc and Cgx are the specific heat capacities of coal and gas (CH4 and N2), respectively, J/(kg·K); λc and λgx are the heat transfer coefficients of coal and gas (CH4 and N2), respectively, W/(m·K).

Eq 9 is the governing equation of the coal stress field, and eqs 13,14 are the convective dispersion equations of the binary gas, and eq 15 is the evolution equation of the coal temperature field. eqs 9, 13–15 constitute a thermal–hydraulic–mechanical coupling model under the action of hot N2 injection, and the coupling relationship between various physical fields is shown in Figure 2.

Figure 2 THM field coupling relationship during N2 injection in a reservoir.

2.3 Model Validation

A high-temperature gas thermal extraction seepage experiment system is used to inject 338 K N2 into a 50 × 100 mm2 coal pillar at 1 and 2 MPa pressure, measure the volume proportion of gas components at the air outlet within 3000 s, establish a similar 2D model for simulation, and compare and analyze the simulation results with the experimental results. Figure 3 shows the matching results between the experimental and simulated data. With N2 injection, the CH4 volume fraction continues to decline, whereas the N2 volume fraction continues to rise. Under 1 and 2 MPa gas injection pressure, the variation trend of the CH4 volume fraction measured in the experiment is similar to that of the simulation results, with relative errors of 6.20% and 7.93%, respectively. During the experiment, the gas injection pressure continues to decrease because it could not maintain the stability of the gas injection pressure with the gas injection equipment in the experimental device; therefore, the experimental data are theoretically smaller than the simulated data, as shown in the experimental device, and the mathematical model can describe the heat transfer process of the coal seam during N2 injection.

Figure 3 Comparison between simulated and experimental gas components at different injection pressures: (a) 1 and (b) 2 MPa.

3 Numerical Simulation Results and Discussion

3.1 Modeling and Model Parameters

3.1.1 Geometric Model and Boundary Conditions

Coal seam 3# in the Zhangcun Coal Mine area has a coal thickness of 6 m.29 The hole distribution model of the N2 injection mining of the CBM is shown in Figure 4. A 2D geometric model was established according to the 3D hole distribution. An 8-m long and 4-m wide rectangle was selected as the coal seam. An injection hole is arranged in the middle of two extraction holes with diameters of 75 mm. Monitoring line ON and monitoring points E (1,0), F (2,0), and G (3,0) were set. The boundary conditions for the deformation, temperature, and flow fields of the geometric model are listed in Table 1.33 A load weight of 10 MPa was set at the top, and the bottom boundary was fixed. Gas with an injection pressure of 4 MPa was injected through injection hole O, the extraction pressure of extraction holes M and N was 0.02 MPa, and the gas injection duration was 100 d.

Figure 4 Model diagram of N2 injection mining in a coal seam.

Table 1 Boundary Conditions for Numerical Simulation

condition	coal deformation	fluid flow	heat transfer	
Boundary A–B	Loading (10 MPa)	Nonpermeable	Insulated	
Boundary C–D	Fixed	Nonpermeable	Insulated	
Boundary A–C	Symmetrical	Symmetrical	Symmetrical	
Boundary B–D	Symmetrical	Symmetrical	Symmetrical	
Borehole O	Free boundary	Dirichlet (4 MPa)	Dirichlet (348.15 K)	
Borehole M	Free boundary	Dirichlet (20 kPa)	Dirichlet (295 K)	
Borehole N	Free boundary	Dirichlet (20 kPa)	Dirichlet (295 K)	

3.1.2 Simulation Parameters and Scheme Selection

The calculation parameters set by the model are given in Table 2. Part of the data was obtained from the field or experiment, and the rest was obtained from the literature.34 To study the influence of the N2 injection process on the coal seam, four groups of variables were set according to the two influencing factors of coal seam properties and gas injection mode, as listed in Table 3.35

Table 2 Model Parameter Table

parameter	value	unit	
Young’s modulus of coal seam, E	2710	MPa	
Young’s modulus of coal skeleton, Es	8143	MPa	
Poisson’s ratio of coal, υ	0.345	-	
Coal density, ρc	1300	kg·m3	
Initial permeability, k0	1.5 × 10–17	m2	
Initial porosity, φ0	0.043	-	
Initial CH4 pressure, P0	1.8	MPa	
Initial temperature in coal seam, T0	300	K	
Thermal expansion coefficient, αT	2.4 × 10–5	K–1	
Langmuir volume constant of CH4, VL1	0.0196	m3/kg	
Langmuir volume constant of N2, VL2	0.0146	m3/kg	
Langmuir pressure constant of CH4, PL1	1.32	MPa	
Langmuir pressure constant of N2, PL2	2.61	MPa	
Thermal conductivity for coal, λc	0.1913	W/(m·K)	
Thermal conductivity for CH4, λg1	0.0371	W/(m·K)	
Thermal conductivity for N2, λg2	0.0262	W/(m·K)	
Dynamic viscosity of CH4, μ1	1.03 × 10–5	Pa·s	
Dynamic viscosity of N2, μ2	1.69 × 10–5	Pa·s	
Specific heat capacity of coal, Cc	1255	J/(kg·K)	
Specific heat capacity of CH4, Cg1	2227	J/(kg·K)	
Specific heat capacity of N2, Cg2	1040	J/(kg·K)	
Isosteric heat of CH4 adsorption, qst1	15.3	kJ/mol	
Isosteric heat of N2 adsorption, qst2	12.8	kJ/mol	
Hydrodynamic dispersion coefficient of CH4, D1	3.6 × 10–12	m2/s	
Hydrodynamic dispersion coefficient of N2, D2	5.8 × 10–12	m2/s	
Klinkenberg factor, b	0.360	MPa	
Temperature correction factor, d1	0.023	1/K	
Pressure correction factor, d2	0.072	1/MPa	

Table 3 Different Numerical Simulation Research Schemes

schemes	program	model	
Impact of coal seam properties	Case 1: Temperature of coal seam	Model 1: T0 = 300 K	
Model 2: T0 = 320 K	
Model 3: T0 = 340 K	
Case 2: Initial permeability of coal seam	Model 4: k0 = 1.5 × 10–17 m2	
Model 5: k0 = 3.5 × 10–17 m2	
Model 6: k0 = 5.5 × 10–17 m2	
Impact of injection method	Case 3: Injection temperature	Model 7: Tin = 323.15 K	
Model 8: Tin = 348.15 K	
Model 9: Tin = 373.15 K	
Case 4: Injection pressure	Model 10: Pin = 2 MPa	
Model 11: Pin = 4 MPa	
Model 12: Pin = 6 MPa	

3.2 High-Temperature N2 Injection Discharge and Mining Laws

3.2.1 Reservoir Temperature Evolution

Figures 5, 6 show the temperature evolutions of the coal seams, monitoring line ON, and monitoring points E, F, and G during N2 injection.

Figure 5 Coal seam temperature evolution at 373.15 K.

Figure 6 Coal reservoir temperature evolution at 373.15 K. Temperatures of the (a) monitoring line ON, and (b) monitoring points E, F, and G.

Figure 5 shows the coal seam temperature evolution at 20, 40, 60, 80, and 100 days for an injected N2 temperature of 373.15 K and pressure of 2 MPa. With continuous gas injection, the coal seam temperature increases significantly, and its distribution at different time points differs. With an N2 injection time increase, heat is transferred from the gas injection hole to the surrounding low-temperature region via heat convection and conduction. This leads to temperature fluctuation range expansion and formation of a temperature gradient field distribution with the gas injection hole as the center and several approximately concentric circles with an increasing radius and decreasing temperature. In the vicinity of the gas injection hole, the N2 concentration is higher, and the heat carried by N2 increases the temperature of the reservoir, whereas in the vicinity of the extraction hole, the temperature decreases slightly; the closer to the extraction hole, the larger the temperature decrease.

In Figure 6a, the temperature curve of monitoring line ON shows an obvious “C”-shaped bending angle, indicating that heat exchange has occurred inside the reservoir after N2 injection, and with an injection time increase, N2 can more fully interact with the reservoir and cause temperature changes. Reservoir temperature decreases slowly from the gas injection hole to the production hole; the temperature curve moves to the right with a gas injection time increase; and the N2 heat exchange effect gradually affects the entire coal seam. After 20 days of gas injection, the influence radius of N2 injected at a temperature of 373.15 K on the CBM reservoir is only 1 m. After 100 days of gas injection, the influence radius gap increases to 3 m, indicating that with an injection time increase, the total heat carried increases, the effective heat injection area of the coal seam expands, and heat transfer between N2 and the coal seams becomes more significant.

Figure 6b shows the temperature evolutions of monitoring points E, F, and G on monitoring line ON during 100 days of gas injection and extraction. Overall, reservoir temperature increases continuously with injection time. Specifically, points E, F, and G are affected by the N2 temperature breakthrough around the fifth, 30th, and 60th days, respectively; the temperature of point E increases sharply after the fifth day, and the temperature of point F increases slowly on the 30th day. At point G, due to the effect of CH4 desorption induced by the pumping pressure, reservoir temperature tends to decrease; however, it slightly recovers on the 60th day, at which point the heat carried by N2 and temperature reduction due to gas desorption start to offset each other, with the N2 temperature influence eventually dominating.

3.2.2 Gas Pressure Distribution

Figures 7–89 show the CH4 and N2 pressure changes in the coal seam, monitoring line ON, and monitoring points E, F, and G during gas injection.

Figure 7 Simulation of the CH4/N2 pressure change in high-temperature N2-injected reservoirs. (a) CH4 and (b) N2 pressures at the coal seam.

Figure 8 Simulation of CH4/N2 pressure change in high-temperature N2-injected reservoirs. (a) CH4 and (b) N2 pressures at the monitoring line ON.

Figure 9 Simulation of CH4 and N2 pressures change at monitoring points E, F, and G in high-temperature N2-injected reservoirs.

The coal seam pressure gradient is the driving force of CH4 seepage, and the pressure change within the coal seam affects the CH4 seepage rate in the coal seam. Figures 7a,b show the simulated cloud diagrams of the CH4 and N2 pressure changes within the coal seam under a gas injection temperature of 373.15 K, a gas injection pressure of 2 MPa, and a negative pumping pressure of 20 kPa. With a gas injection time increase, N2 spreads from the injection hole to the surroundings, the N2 influence radius gradually increases, and the CH4 pressure in the influence area gradually decreases. With continuous extraction at the extraction wells, the CH4 pressure of the coal seam around the extraction wells exhibits an obvious pressure gradient under the influence of the negative pressure at the extraction hole, which accelerates the gas seepage speed around the extraction hole and forms a pressure difference from the other areas. Pressure increase and decrease areas appear near the gas injection and extraction wells, respectively, which increases the pressure difference of the gas in the pores of the coal seam interior and increases the gas seepage speed.

To study the dynamic change law of gas pressure inside of the coal, we examine the gas pressure changes on the ON monitoring line. The CH4 and N2 pressure changes at the coal seam at 5, 10, 20, 30, 40, 50, 60, 70, 80, 90, and 100 d were plotted to quantitatively examine pressure change trend. The CH4 and N2 pressures at the monitoring line ON at different moments are shown in Figures 8a,b, respectively. The initial CH4 pressure at the coal bed is 1.8 MPa, and the gas injection pressure is 2.0 MPa. With a gas injection time increase, the N2 pressure gradually rises, pushing CH4 to flow toward the extraction wells, forming a CH4 agglomeration area, which increases the CH4 pressure at the coal bed in this range. With an extraction time increase, the extraction hole range gradually increases and the CH4 agglomeration area gradually disappears. In addition, the CH4 pressure at the coal seam closer to the extraction hole decreases significantly as the vicinity of the extraction hole is affected by the negative extraction pressure. The CH4 seepage speed there is increased compared with those in other areas, and the CH4 content of the coal seam around the extraction hole decreases by a larger amount during the same period of time, which leads to a significant CH4 pressure decrease at the coal seam closer to the extraction hole. With continuous extraction, the CH4 pressure of the coal seam farther away from the extraction hole also decreases gradually. With a CH4 pressure decrease at the coal seam, a low-pressure zone first forms around the extraction hole and subsequently gradually expands. Finally, a certain low-pressure area range forms in the coal seam.

Figure 9 shows the CH4 and N2 pressure change curves at points E, F, and G during 100 days of gas injection. CH4 pressure at point E decreases sharply in the first 5 days of gas injection and follows a more gradual decrease thereafter. This is caused by an obvious pressure gradient between N2 and CH4 in the preinjection period, which drives the CH4 pressure down. The CH4 pressure at point F remains unchanged in the first 2 days of gas injection because the injection pressure in the preinjection period has not yet arrived at a distance that can affect point F. Hence, CH4 pressure maintains a short-term equilibrium and CH4 changes from the adsorbed to the free state in the coal seam due to the temperature effect in the middle and late stages of gas injection. In the middle and late stages of gas injection, owing to the temperature effect, the coal-bed CH4 changes from the adsorbed to the free state, which slows the CH4 pressure decline rate at the coal bed. CH4 pressure at point G shows a decreasing trend due to the effect of the most pronounced pumping pressure decrease and the N2 diffusion range not having reached point G in the early stage of gas injection. N2 pressure remains unchanged. However, with a longer gas injection time, the N2 pressure gradually diffuses across the entire coal bed, and the difference in the N2 pressure of the coal bed gradually decreases.

3.2.3 Reservoir Permeability Evolution

Figure 10 shows the adsorbed CH4 content change and volumetric strain of the coal seam at the monitoring points and the permeability ratio change at the monitoring line and the monitoring points during the gas injection process.

Figure 10 Coal seam permeability variation and evolution. (a) Adsorbed CH4 content, (b) reservoir volume strain, and permeability ratio at (c) monitoring line ON and (d) monitoring points E, F, and G.

Figure 10a shows the change in the CH4 content adsorbed on the coal at the monitoring points. The adsorbed CH4 content at each monitoring point gradually decreases throughout the pumping process. Specifically, the adsorbed CH4 content decreases at points E and G because of thermal expansion and desorption, respectively. Two days before gas injection and extraction, the CH4 content adsorbed on the coal at point F is in a short-lived equilibrium; then, it begins to decrease because of the combined effect of gas injection and extraction, especially on the 10th day, when N2 breaks through point F, increasing the rate of decrease of the adsorbed CH4 content. Figure 10b shows the volumetric strain changes at each monitoring point. Expansion and deformation increase with increasing distance from the gas injection hole. Because the effect of the gas injection temperature on the coal seam lags behind that of the gas injection pressure, the coal seam volume at point E contracts sharply in the preinjection period. Then, it rebounds under the effect of thermal expansion due to the temperature and causes a contraction trend due to CH4 desorption in the late stage of gas injection. In general, thermal expansion is dominant in the coal seam volumetric strain at point E. Simultaneously, the volumetric strain at point F is dominated by the effects of temperature, while that at point F is basically balanced by temperature and extraction desorption. Point G is mainly subject to the contraction of the coal caused by extraction, because it is the closest to the extraction hole, and the overall volumetric strain is negative.

Figures 10c,d show the permeability changes at the monitoring line and the monitoring points. Permeability is the result of a combination of factors, including strains due to pressure, gas adsorption/desorption, and thermal expansion. Figure 10c shows the coal seam permeability along the ON monitoring line during the gas injection and extraction processes, which are influenced by the combination of thermal N2 injection and CH4 extraction. Because the gas injection pressure during N2 injection supports the seepage cracks, promotes pore development and induces CH4 desorption, and the strain of coal adsorption of N2 is smaller than that of CH4. Thus, the permeability of N2-injected coal shows an overall increasing trend, and the permeability near the extraction hole is affected by the desorption-induced contraction of the coal, resulting in a rapid increase in permeability increase. Permeability at the monitoring points follows an upward trend. In the preinjection period, point E is subject to the action of gas injection pressure, CH4 is transported to the direction of the extraction hole, and permeability at point E is the largest. With the gas injection, the temperature of the coal increases, and the permeability increase rate decreases. In the late stage of the injection period, point G is the closest to the extraction hole, and due to coal contraction during gas extraction, the pore structure becomes more connected, resulting in the highest permeability increase rate.

3.3 Influence of Coal Seam Parameters

3.3.1 Initial Seam Temperature

The N2 concentration for different coal seam temperatures in Figure 11a indicates that when the coal seam temperature is higher, the diffusion rate of N2 injected at the same temperature and pressure in the coal is significantly affected. Owing to the higher coal seam temperature, the thermal movement of some molecules in coal is more intense, which hampers the diffusion and uniform distribution of N2 molecules to the coal pores, leading to an N2 concentration decrease in the coal seam and breakthrough time prolongation. In addition, owing to the decreased temperature difference between the injected gas and coal seam, the role of heat conduction due to gas injection is weakened, and the internal temperature distribution of the coal is not uniform, forming a local temperature gradient, which further affects the coal permeability performance, resulting in a deceleration of the penetration rate growth, thereby lowering the overall increase in penetration rate.

Figure 11 Concentration and permeability at the monitoring points under different initial coal seam temperature. (a) N2 concentration and (b) permeability ratio.

Figures 12a,b show CH4 yield variation with different initial coal seam temperatures. The CH4 yield decreases with increasing initial coal seam temperature, because higher coal seam temperature provides greater thermal energy to the fractions within the coal, hindering the diffusion of CH4 molecules into the coal pores, which in turn restricts the CH4 release and yield.

Figure 12 CH4 cumulative production and extraction rates under different initial coal seam temperature. (a) CH4 cumulative production and (b) CH4 recovery ratio.

3.3.2 Initial Penetration Rate

Figures 13a,b show the N2 concentration and permeability changes, respectively, with injection time at points E, F, and G under different initial permeabilities. A larger initial coal seam permeability means that the pore channels inside the coal seam are more abundant; hence, the N2 flow ability in the coal is stronger, and the diffusion rate in the coal seam is increased, leading to a shorter breakthrough time in the coal seam. Simultaneously, the N2 concentration increase rate is higher, and the combined effect of these factors ultimately leads to a faster arrival of the coal seam at the pressure equilibrium state. Figure 13b shows that an initial coal seam permeability increase results in a more pronounced increasing permeability due to gas injection. In particular, under high initial permeability, more N2 enters into the coal seam, thereby opening the pore channels in the coal seam and promoting gas diffusion and transportation in the coal.

Figure 13 Concentration and permeability at the monitoring points under different initial permeabilities. (a) N2 concentration and (b) permeability ratio.

Figures 14a,b show the cumulative CH4 production and extraction rates under different initial permeabilities during gas injection. The cumulative CH4 productions are 2906.201, 3389.291, and 3553.111 m3, and the CH4 extraction rates are 61.81%, 72.08%, and 75.57% after 100 d of gas injection under initial coal seam permeabilities of 1.5 × 10–17, 3.5 × 10–17, and 5.5 × 10–17 m2, respectively. Therefore, the higher the initial permeability, the greater the amount of injected gas in the coal seam, which further strengthens the flow-promoting effect of N2 on CH4 and effectively improves the extraction rate.

Figure 14 CH4 cumulative production and extraction rates under different initial permeabilities. (a) CH4 cumulative production and (b) CH4 recovery ratio.

3.4 Influence of Injected Gas Parameters

3.4.1 Injection Pressure

Figures 15a,b show the changes in N2 concentration and permeability at monitoring points E–G for injection pressures of 2, 4, and 6 MPa. N2 concentration increases significantly with increasing injection pressure, and the higher the injection pressure, the shorter the N2 breakthrough time. With continuous pumping, the N2 concentration tends to equilibrate at the late stage of gas injection. A gas injection pressure increase causes first a permeability increase and then a decrease until stabilization. Continuous gas injection pressure increases form a more obvious gas accumulation effect between the injection and extraction holes; hence, the pore gas pressure in the coal seam rises sharply and plays an expansion role in the coal skeleton. To a certain extent, this causes the coal seam deformation to undergo a compaction effect, at which point the coal permeability begins to decrease. However, owing to the continuous injection and extraction, the partial pressure of the gas component drops, and the N2 concentration trends toward equilibrium. Eventually, the partial pressure of the gas components reaches a balanced state and maintains a stable permeability. The closer the production well is, the more easily the coal matrix is affected by the extraction and desorption process to shrink, thereby reducing the permeability reduction caused by pore pressure.

Figure 15 Concentration and permeability at the monitoring points for different injection pressures. (a) N2 concentration and (b) permeability ratio.

Figures 16a,b show that the cumulative CH4 production and gas extraction rates increase with increasing injection pressure. Taking 100 d of driving as a reference, when the injection pressure is 2 MPa, the CH4 production is 2905.754 m3, and when the driving pressure is 4 and 6 MPa, the CH4 production is 3631.809 and 3901.538 m3, corresponding to increases by approximately 15.44% and 21.18%, respectively, indicating that the N2 injection pressure change is significant. Increasing the gas injection pressure to 6 MPa results in the CH4 production and recovery rate maintaining slight changes after the 22nd day, which indicates that increasing the gas injection pressure not only improves the production but also reduces the extraction time. N2 drives out CH4 in the free state, breaking the gas adsorption balance. CH4 concentration in the fracture is reduced, and gas adsorption on the pore matrix absorbs the necessary energy to begin desorption and diffusion to the fracture under the action of the concentration gradient. The pore pressure of the coal seam increases with an increasing gas injection pressure, resulting in increased seepage and gas extraction from the coal seam.

Figure 16 CH4 cumulative production and extraction rate under different pressures. (a) CH4 cumulative production and (b) CH4 recovery ratio.

3.4.2 Injection Temperature

To study the effect of the injection temperature on N2 driving CH4, the general laws under different injection temperatures were investigated by studying the changes in N2 concentration, permeability, CH4 production, and pumping rate at the monitoring points during the gas injection process. As shown in Figures 17a,b and Figures 18a,b, the increase in permeability decreases with an increasing gas injection temperature, and the N2 concentration decreases at each monitoring point. The reason is that the temperature increase promotes heat transfer between the coal seams. On the one hand, thermal stresses lead to coal expansion and deformation and reduced porosity and permeability; on the other hand, there is CH4 desorption on the coal seam as well as adsorption expansion reduction and increased permeability, both of which determine the rule of coal seam permeability change. The figure shows that coal expansion and deformation caused by thermal stress play a dominant role in the permeability change rule.

Figure 17 Concentration and permeability at the monitoring points for different injection temperatures. (a) N2 concentration and (b) permeability ratio.

Figure 18 CH4 cumulative production and extraction rate at different temperatures. (a) CH4 cumulative production and (b) CH4 recovery ratio.

Figures 18a,b show the effects of different injection temperatures on the cumulative pumping production and extraction rate. For injection temperatures of 323.15, 348.15, and 373.15 K, the yields at 100 d of gas injection are 2796.892, 2855.296, and 2905.754 m3, and the CH4 extraction rates are 59.483%, 60.730%, and 61.800%, respectively. Increasing the N2 injection temperature increases the kinetic energy of N2 molecules, improves the adsorption competition between N2 and CH4, generates more heat, and the CH4 molecules are more active, leading to a higher extraction rate. This indicates that the temperature increase enhances the activity of the CH4 molecules. The internal and kinetic energy increase, promoting the movement of gas molecules and accelerating the transition of CBM from the adsorbed to the free state, which in turn strengthens the coal desorption ability, resulting in an increase in free gas and gas extraction rate.

4 Conclusions

By coupling coal deformation, convective diffusion of binary gases, and heat transfer, and considering the nonisothermal competitive adsorption, the coupled THM migration equation of N2 injection in the coal seam is established. The discharge and mining laws of the N2 injection process were simulated, and the following conclusions were drawn:

(1) In the early stage of N2 injection and CH4 extraction, N2 mainly increases the CH4 extraction rate by promoting flow; in the later stage, the heat carried by N2 gradually increases the coal seam temperature and further promotes CH4 desorption. The two synergies increase coal permeability, and the influence of the injection temperature on CH4 lags behind that of the gas injection pressure.

(2) During pumping without gas injection, the permeability is mainly determined by the coal matrix shrinkage caused by the temperature change and the expansion deformation caused by the CH4 pressure reduction, which shows a trend of decreasing first and then increasing. The N2 injection process maintains the pore pressure and supports the pore structure; the pressure difference promotes CH4 desorption, and the overall effect increases the coal permeability.

(3) Higher initial coal seam temperatures inhibit N2-ECBM to some extent. Greater initial permeability in coal seams promotes the N2-ECBM more effectively. The N2 injection pressure changes the gas pressure gradient in the coal seam and increases the gas seepage rate. The injection temperature promotes the desorption of adsorbed gas on the coal seam and increases its recovery rate.

(4) The effect of N2 injection on CH4 extraction is reflected in three aspects: increasing seepage, promoting flow, and displacing gases. The N2 injection process supports the pore structure of the coal seam, enhancing the reservoir permeability. It generates a pressure gradient that accelerates CH4 flow and promotes CH4 desorption, thereby improving the extraction efficiency. The combined action mechanism of these three aspects renders N2 injection into coal seams significant for promoting CH4 extraction.

The authors declare no competing financial interest.

Acknowledgments

This work was partially supported by the National Natural Science Foundation of China (Grant No, 52274188) and the State Key Laboratory of Coal Mine Disaster Dynamics and Control (Grant No, 2011DA105827-FW202201).
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