Investigation on Coal Skeleton Deformation in CO2 Injection Enhanced CH4 Drainage From Underground Coal Seam

To reveal the evolution law of coal skeleton deformation during the process of CO2 flooding and displacing CH4 in coal seam, a fluid-solid coupling mathematical model of CO2 injection enhanced CH4 drainage was established based on Fick’s law, Darcy’s law, ideal gas state equation, and Langmuir equation. Meanwhile, numerical simulations were carried out by implementing the mathematical model in the COMSOL Multiphysics. Results show that the CH4 content of both regular gas drainage and CO2 enhanced gas drainage gradually decreases with time, and the decreasing rate is high between 10 and 60 days. Compared with regular gas drainage, the efficiency of CO2 enhanced gas drainage is more obvious with greater amount of CH4 extracted out. When coal seam gas is extracted for 10, 60, 120, and 180 days, CH4 content in coal seam is reduced by 5.2, 17.2, 23.6, and 26.7%, respectively. For regular gas drainage, the deformation of coal skeleton is dominated by the shrink of coal matrix induced by gas desorption, and the strain curve shows a continuous downward trend. For CO2 enhanced gas drainage, the strain curve of coal skeleton showed a decrease—rapid increase—slow increase trend. The evolution of permeability is opposite to the evolution of coal skeleton strain. Higher gas injection pressure will lead to a greater coal skeleton strain. The pumping pressure affects the deformation of coal skeleton slightly compared with that of initial water saturation and initial temperature. Greater initial water saturation leads to larger deformation of coal skeleton in the early stage. The strain value of coal skeleton gradually tends to be consistent as gas injection prolongs. Higher initial temperature leads to greater reduction in coal skeleton strain when the gas injection continues. Research achievements provide a basis for the field application of CO2 injection enhanced CH4 drainage in underground coal mines.


INTRODUCTION
Coal seam gas is a by-product of coal mining, mainly composed of CH 4 (Fan et al., 2017). Coal seam gas is a clean energy source. However, coal and gas outbursts and gas explosions often occur with coal mining, which severely restricts the safe and efficient production of coal mines (Huo et al., 2019). With the increase of mining depth, the permeability of coal seam gradually decreases, resulting in the increase of difficulty of gas drainage. Therefore, improving the efficiency of coal seam gas drainage is a key technology for preventing and controlling mine gas disasters, as well as the development and utilization of gas resources (Guo et al., 2020).
Scholars have explored the method of replacing CH 4 by injecting waste gas into the coal seam. Generally, the injected gas includes CO 2 , N 2 , and flue gas (Wu et al., 2019). The adsorption capacity of coal for CO 2 , N 2 , and CH 4 is CO 2 > CH 4 > N 2 through a series of studies, which provides a certain theoretical basis for coal seam gas injection , Fan et al., 2019a, Yi et al., 2013. N 2 mainly displaces coal bed methane by changing the pressure gradient in the coal-rock fractures (Lin et al., 2018), and the competitive adsorption effect is small. CO 2 can not only displace the free CH 4 in fractures, but also compete with the gas on the adsorption site to replace it (Liu et al., 2017;Fang et al., 2019a). Busch et al. (2003) carried out CO 2 and CH 4 mixed binary gas adsorption and desorption experiments on different coal ranks under the same conditions, and found that the adsorption capacity of CO 2 is stronger than that of CH 4 Wang et al., 2018). Reznik et al. (1984) conducted experiments by injecting CO 2 into bituminous coal containing CH 4 and bituminous coal containing water under high pressure, and proved that CO 2 injection can increase the recovery rate of CH 4 by 2-3 times and obtained higher gas injection pressure can lead to higher recovery rate of CH 4 (Chattaraj et al., 2016, Lin et al., 2017. Baran et al. (2014) used the volumetric method to conduct adsorption experiments under lower and higher pressures, and proved that CO 2 is the best gas that can penetrate into the internal structure of coal. The above experiments show that CO 2 injection can flood or displace coal seam CH 4 and improve the efficiency of CH 4 drainage. To explore the mechanism of CO 2 injection enhanced CH 4 recovery, scholars from various countries have carried out numerical simulation on the basis of physical experiments. Vishal et al. (2015) studied the effect of adsorption time on CO 2 enhanced coal bed methane recovery (CO 2 -ECBM). Zhou et al. (2012) and Fang et al. (2019b) used COMSOL Multiphysics software to analyze the evolution of permeability in the CO 2 -ECBM process, and the results show that the effective stress changes, matrix shrinkage, and swelling caused by pumping pressure of drainage and CO 2 injection pressure are the key factors affecting permeability. Gas injection pressure and temperature are the two key factors that affect the efficiency of CH 4 extraction (Fang et al., 2019c). Fan et al. (2018) considered non-isothermal adsorption and analyzed the effects of different injection pressures and initial temperatures on CO 2 -ECBM. Additionally, Pan et al. (2019) studied the evolution of its microstructural changes under high-pressure methane adsorption/desorption. Wang et al. (2020) revealed the specific process of coal macromolecular rearrangement caused by CO 2 injection through molecular dynamics.
However, predecessors have seldom studied the deformation law of coal skeleton in the process of gas injection to displace coal seam CH 4 . In this article the coal mass is considered a dual pore structure composed of pores and fractures, and a fluid-solid coupling model for gas injection enhanced methane drainage is established. The COMSOL Multiphysics software is used to study the coal skeleton strain law in the process of CO 2 injection to displace coal seam CH 4 on the background of Zhangcun coal mine in Shanxi Provence. The results will provide a reference for improving the CH 4 drainage from coal seams during underground mining.

Basic Assumptions
According to the occurrence characteristics of gas in coal reservoirs, the following assumptions are made Li et al., 2016;Ren et al., 2017;Fan et al., 2019b): 1) The coal mass is a porous medium with double pores composed of pores and fracture; 2) The gas migration in the matrix satisfies Fick's law of diffusion, and the gas migration process in the fracture satisfies Darcy's law; 3) CH 4 and CO 2 are regarded as ideal gases; 4) Water only migrates in the fractures; 5) The adsorption and desorption of CH 4 and CO 2 in coal mass are carried out under constant temperature conditions.

Permeability Evolution Model
Assume that the coal seam is a dual-porosity unidirectional permeable medium composed of a matrix, as shown in Figure 1. Matrix pores are the main storage space for CH 4 and CO 2 , and the change of fractures affects the evolution of permeability. Therefore, the changes of pores and fractures are the key factors in the process of CO 2 down whole injection enhanced CH 4 drainage by effects of flooding and displacement.Where a 0 is the initial matrix width, m; q is the initial fracture width, m.
The coal matrix porosity model can be expressed as : where S ε v + p mg /(K s + ε a ) is the matrix porosity strain variable; ε v is the volume strain in the coal; p mg is the gas mixture pressure, MPa; K s E s /3(1 − 2v) is the skeleton bulk modulus, GPa; ε a is the skeleton adsorption gas strain; E s is the skeleton elastic modulus, GPa; v is Poisson ratio; α m 1 − K/K s is the Biot coefficient for the porosity; K D/3(1 − 2v) is the bulk modulus, GPa; D 1/[(1/E) + 1/(a 0 · K n )] is the effective elastic modulus, GPa; E is the elastic modulus, GPa; K n is fracture Frontiers in Earth Science | www.frontiersin.org October 2021 | Volume 9 | Article 766011 stiffness, GPa; and the subscript "0" represents the initial value of the parameter. Expression of matrix swelling strain caused by gas adsorbed on coal (Cao et al., 2019): where ρ c is the density of coal, kg/m 3 ; R is gas molar constant, J/(mol·K); T is the temperature in the coal seam, K; a i is the limit adsorption capacity of gas component i, m 3 /kg; b i is the adsorption equilibrium constant of gas component i, MPa −1 ; p mgi is pressure of gas component i in the matrix, Pa; V m is the molar volume of gas, L/mol. Considering the influence of stress and seepage effects, the fracture porosity model can be obtained as (Fan et al., 2019b): where φ f0 is the initial fracture porosity; K f qK n is the equivalent fracture stiffness, GPa; q is the initial fracture width, m.
According to the cubic law, the relationship between porosity and permeability is: where k 0 is the initial permeability of the coal seam, m 2 . Substituting Eq. 3 into Eq. 4 can obtain the dynamic evolution equation of permeability: The relative permeability model of gas-water two-phase flow is (Xu et al., 2014): where k rg0 is the endpoint relative permeability of the gas; s w is the saturation of water; s wr is the irreducible water saturation; s gr is the residual gas saturation fraction; k rw0 is the endpoint relative permeability of water.

Gas Transport in the Coal Matrix
According to the ideal gas state equation, the density of each component gas under standard conditions is: where p a is standard atmospheric pressure, kPa. Generalized Langmuir equation for binary gas adsorption equilibrium: where c pi is the content of gas component i in coal, kg/m 3 ; ρ gi is the density of gas component i under standard conditions, kg/m 3 ; M gi is the molar mass of gas component i, g/mol. The gas content in the coal matrix per unit volume equals the sum of the free gas content and the adsorbed gas content, which is obtained from the Langmuir equation and the ideal gas equation of state: Owing to the influence of gas injection and drainage, the original equilibrium state of gas in the coal seam is broken. Forced by the concentration gradient, the gas in the coal matrix migrates into the fractures by diffusion. According to Fick's law of diffusion, the gas mass in the matrix can be conserved. The equation is : where p fgi is the pressure of gas component i in the fracture, MPa; τ i is the desorption time of gas component i, d. Substituting Eqs 7-9 into Eq. 10, the gas transport equation in the matrix can be obtained as:

Transport of Gas and Water in the Fractures
Considering the gas slippage effect and the generalized Darcy law of gas-water two-phase flow, the transport flows of gas and water are gained respectively (Fan et al., 2019c): where b is the Klinkenberg factor, MPa; μ gi is the dynamic viscosity of gas component i, MPa·s; μ w is the dynamic viscosity of water, MPa·s. Then, the mass conservation equation for gas migration in the fractures is: where s g is the gas saturation in fracture, s g + s w 1. The water seepage controlling equation is:

Stress Field Controlling Equation
Considering that the total strain of coal mass is the sum of strain caused by stress, fluid pressure in matrix pores and fractures, and coal matrix swelling resulted from CH 4 and CO 2 adsorption. The stress field controlling equation is : is the shear modulus of coal, GPa; e i,ij are in tensor form (e can be displacement u, pressure p, or strain ε).
The first subscript represents the i-direction component of variable e. The second subscript represents the partial derivative of e i in the i-direction. The third subscript represents the partial derivative of e i,ij in the j direction; a f 1 − K/(a 0 · K n ) is the Biot coefficient; F i is the volume force, GPa; p f s w · p fw + s g · p fg is the fracture fluid pressure, Pa.

Physical Model and Definite Solution Conditions
Taking the 2,606 roadway of Zhangcun Coal Mine in Shanxi Provence as the background, the feasibility of CO 2 injection to increase gas drainage was studied in terms of its high gas and enrich water combined condition. COMSOL Multiphysics software is adopted to numerically solve the established fluidsolid coupling mathematical model. The 2,606 roadway is buried in a depth of 537 m, the coal seam temperature is 298.15 K, and the gas content during advancing is 8.5-10.0 m 3 /t. As shown in Figure 2  in other articles Fan et al., 2019a;Fan et al., 2019b;Fang et al., 2019b;Fang et al., 2019c). Figure 3 shows the contour map of coal bed gas pressure at 10, 60, 120, and 180 days of regular gas drainage and CO 2 enhanced gas drainage. In Figure 3A, without CO 2 injection, the gas pressure continues to decrease with the increase of extraction time. The vertical direction decreases faster than the horizontal direction leading by the supplemental gas sources in the horizontal direction. The vertical direction is closer to the coal seam boundary and there is no supplementary gas source. As CO 2 is continuously injected into coal seam, the gas pressure shows a downward tendency in whole, but the changes near the drainage borehole and the gas injection borehole are different, as illustrated in Figure 3B. The pressure around the gas injection borehole is also gradually decreasing. The pressure around the gas injection borehole drops slower than that near the extraction borehole. And the drop rate in the vertical direction is slower than that in the horizontal direction. This is because the vicinity of the injection borehole is largely affected by CO 2 flows. Although the CH 4 pressure decreases with the effects of extraction, the CO 2 pressure is rising, resulting in slowly drops of pressure. The gas pressure in the vertical direction of injection borehole is less affected by the pumping pressure of the drainage. Figure 4 presents the contour of CH 4 content at 10, 60, 120, and 180 days of both regular and CO 2 enhanced gas drainage in coal seam. Figure 4A shows the variation of CH 4 content after regular gas drainage. The CH 4 content reduction area expands from the center of drainage borehole, but the reduction region and rate are relatively slow. On the contrary, the reduction region and rate of CH 4 content at the same duration for CO 2 injection enhanced CH 4 drainage have been significantly improved. This is caused by the combined action of CO 2 injection and CH 4 drainage. The potential pressure gradient in the coal seam drives the seepage of CO 2 and displacement of free CH 4 in the fractures. When most of the free CH 4 in the fractures is driven out, the injected CO 2 will compete with the CH 4 adsorbed inside and on the surface of the  coal, and then replace the adsorbed CH 4 . This accelerates the desorption rate of CH 4 . In Figure 4B, CH 4 presents the trend of change. Figure 5 presents the evolution of the CH 4 content on the observation line A-B with time. In Figure 5A CH 4 content of both regular gas drainage and CO 2 enhanced gas drainage gradually decreases with time, and the decreasing rate is highest between 10 and 60 days. CH 4 pressure in coal seam gradually decreases (pressure gradient between the drainage borehole and coal seam) as the extraction time prolongs. In other words, the pressure gradient and the CH 4 flow rate gradually decrease, slowing down the decreasing rate of CH 4 content. Compared with the regular gas drainage, the effect of CO 2 enhanced gas drainage in coal seam is more obvious with greater amount of CH 4 extracted out. The reason is that CO 2 drives and competitively adsorbs with CH 4 , which enhances the efficiency CH 4 drainage.

CH 4 Content Evolution
The peak CH 4 content between the extraction borehole and the gas injection borehole for 10, 60, 120, and 180 days of regular gas drainage are 8.62, 6.87, 5.55, and 4.57 m 3 /t, respectively. The peak CH 4 content of CO 2 enhanced gas drainage are 8.17, 5.69, 4.24, and 3.35 m 3 /t respectively, which reduced by 5.2, 17.2, 23.6, and 26.7% compared with that of regular gas drainage, respectively. The drainage efficiency has been significantly improved. Figure 6 shows the strain and permeability of coal skeleton adsorbed gas during regular gas drainage and CO 2 enhanced gas drainage. From Figure 6A, the strain value of coal skeleton behaves a gradual downward trend on the reference points (C, D, E) for the regular gas drainage. This is because the free CH 4 in fractures flows out driven by the pressure gradient, and the decrease of gas pressure in fractures triggers desorption of adsorbed gas in coals, as a result that coal matrix will shrink and deform. The strain at point E is slightly smaller than that at other points at the same time due to the influence of a single drainage hole. There is a short period of plateau on the coal permeability curve at the beginning followed by gradual increase. The change in permeability is mainly affected by effective stress and matrix shrinkage. On the one hand, with the pumping pressure of drainage, the free CH 4 in fractures is  Frontiers in Earth Science | www.frontiersin.org October 2021 | Volume 9 | Article 766011 7 discharged, and the adsorbed CH 4 begins to desorb. As a result, CH 4 pressure in coal seam drops. The effective stress increases, to compress the seepage channel in coal mass, and subsequently coal permeability decreases. On the other hand, the permeability increases caused by the CH 4 desorption induced shrinkage of coal matrix. The two opposite aspects work together to decide the change of coal seam permeability. In early stage, the seepage effect dominates, and the desorption rate of CH 4 is slow, leading to the infinitesimal change in coal permeability. When the free CH 4 is gradually discharged, the desorption rate begins to increase, and the permeability begins to rise.

Evolution of Coal Skeleton Strain and Permeability
In Figure 6B, the strain on reference points C and D shows a slight decrease-rapid increase-slow increase trend in the process of CO 2 enhanced gas drainage. CH 4 desorption under the combined action of CO 2 displacement and pumping pressure of drainage at the initial stage plays a leading role. Then, free CH 4 in the coal fractures decreases and CO 2 increases. CO 2 competes with the CH 4 in matrix for adsorption, and the strain value of coal skeleton increases as the coal matrix undergoes swelling deformation caused by the stronger adsorption affinity of CO 2 than that of CH 4 . Finally, CO 2 gradually reaches adsorption equilibrium, and the strain curve gradually slows down. Point E is mainly affected by the drainage hole, and its strain value continues to decrease. Figure 6B shows that the evolution curve of permeability is opposite to that of coal skeleton strain.
The CH 4 desorption in coal matrix contracts leading to the decrease of coal skeleton strain. Then, as the free CH 4 in the coal fractures decreases, CO 2 increases and CO 2 competes with the CH 4 in the matrix to adsorb. The coal matrix expands and deforms, and the strain value of the coal skeleton rapidly increases. Finally, the competitive adsorption of CO 2 gradually tends to balance since most of the adsorbed CH 4 in the matrix is replaced. The competitive adsorption of CO 2 gradually tends to balance. The CO 2 adsorption rate slows down, and the strain value of coal skeleton slowly increases.

INFLUENCE OF DIFFERENT FACTORS ON THE DEFORMATION OF COAL SKELETON
We will explore different factors affecting the deformation of coal skeleton during CO 2 injection to enhanced CH 4 drainage from coal seam. The controlled single variable method was used to   15, 288.15, 298.15, 308.15 Frontiers in Earth Science | www.frontiersin.org October 2021 | Volume 9 | Article 766011 8 analyze the influence of different gas injection pressures, pumping pressures, initial water saturations, and coal seam temperatures on coal skeleton deformation. The simulation schemes of different influencing factors are shown in Table 2. Figure 7A presents the strain curve on the reference point D under different gas injection pressures during CO 2 enhanced gas drainage. In general, higher gas injection pressure will lead to greater strain of coal skeleton. Higher injection pressure under the same condition will lead to greater amount of adsorbed CO 2 , as well as greater swelling deformation of coal matrix. If the injection pressure is low, the matrix contraction in the early stage is great, and the curve is easy to slow down. When the initial injection pressure is higher than CH 4 pressure in coal seam, CO 2 cannot transport from high pressure to low pressure area. At this time, the coal skeleton strain is mainly affected by the desorption of CH 4 . CH 4 pressure in coal seam gradually decreases as the action of pumping pressure. When CH 4 pressure drops below the injection pressure, CO 2 can flow under the action of the pressure gradient. The lower the injection pressure of CO 2 , the smaller the pressure gradient formed. As a result, the adsorption equilibrium reaches earlier.
In Figure 7B, the change of pumping pressure of drainage affects the deformation of coal skeleton slightly. Figure 7C shows the strain curve of coal skeleton on the reference point D at different initial water saturations. Greater initial water saturation will lead to greater deformation of the coal skeleton in the early stage, and the strain value of coal skeleton gradually tends to be consistent as the operation time of gas injection prolongs. The reason is the water in fractures flow out will carry out part of the free CH 4 and CO 2 in the coal. As a result, the desorption rate of CH 4 is accelerated and the adsorption rate of CO 2 is slowed down. The shrinkage scale of the coal matrix becomes larger. As most of the water flows out of the borehole, the water saturation of coal seams with different water saturations tends to be consistent, and the deformation of coal skeleton also tends to be consistent. Figure 7D shows the coal skeleton strain on the reference point D at different initial temperatures. The higher initial temperature will lead to greater reduction in the coal skeleton strain value, particularly when the operation time of gas injection prolongs.

CONCLUSION
1) A fluid-solid coupling mathematical model of CO 2 injection enhanced CH 4 drainage in coal seam was Frontiers in Earth Science | www.frontiersin.org October 2021 | Volume 9 | Article 766011 9 established based on Fick's law, Darcy's law, ideal gas state equation, and Langmuir equation. Meanwhile, numerical simulations on CO 2 injection enhanced CH 4 drainage during underground mining were carried out using the established model.
2) The CH 4 content of both regular and CO 2 enhanced gas drainage gradually decreases with time, and the decreasing rate is high between 10 and 60 days. Compared with regular gas drainage, CO 2 enhanced gas drainage effect is more obvious with greater amount of CH 4 extracted out. When the CH 4 in coal seam is extracted for 10, 60, 120, and 180 days, the CH 4 content in coal seam is reduced by 5.2, 17.2, 23.6, and 26.7%, respectively. 3) For regular gas drainage, the deformation of the coal skeleton is dominated by the contraction of coal matrix induced by gas desorption, and the strain curve shows a continuous downward trend. In the process of CO 2 enhanced gas drainage, the strain curve of coal skeleton showed a slight decrease-rapid increase-slow increase trend. The evolution curve of permeability is opposite to that of coal skeleton strain. 4) Higher gas injection pressure will lead to greater coal skeleton strain. The pumping pressure affects the deformation of coal skeleton slightly compared with the initial water saturation and initial temperature. Greater initial water saturation will lead to larger deformation of coal skeleton in the early stage, and the strain value of coal skeleton gradually tends to be consistent as the operation time of gas injection prolongs. Higher initial temperature leads to greater reduction in coal skeleton strain, particularly when the gas injection prolongs continuously.

DATA AVAILABILITY STATEMENT
The raw data supporting the conclusion of this article will be made available by the authors, without undue reservation.

AUTHOR CONTRIBUTIONS
CF write and financially support this paper; LY design the research scheme and write this paper; GW financially support and correct this paper; QH derive the equations of this paper; HW carry out simulations.