Optimal Injection Parameters for Enhancing Coalbed Methane Recovery: A Simulation Study from the Shizhuang Block, Qinshui Basin, China

The injection of N 2 into coal reservoir has great potential in improving recovery of coalbed methane (CBM). In this study, a numerical model was established based on the GEM component model to evaluate the in ﬂ uences of di ﬀ erent N 2 injection parameters (production injection well spacing, gas injection timing, gas injection duration, gas injection rate, and the bottom-hole injection pressure) on the production of CBM in the Shizhuang Block of Qinshui Basin, China. Based on the economic bene ﬁ t of CBM production, the production increasing rate and nitrogen replacement ratio were established to optimize the N 2 injection parameters. The results show that (1) the production injection well spacing had the greatest in ﬂ uence on CBM production, followed by injection duration and the bottom-hole injection pressure, and injection timing and injection rate had a relatively small in ﬂ uence. (2) With increasing gas injection duration, injection rate, and the bottom-hole injection pressure, the rate of production increased and the nitrogen replacement ratio decreased. (3) The optimal N 2 injection scheme was revealed with the production injection well spacing of 180 m, the injection timing of a second year after gas production, an injection duration of 7 years, an injection rate of 5000m 3 /d, and a bottom-hole injection pressure of 10MPa. Under these conditions, the rate of production increasing rate, the nitrogen displacement ratio, and the regional recovery of the four production wells were 18.14%, 0.5, and 48.96%, respectively, some 8.88% higher than that without nitrogen displacement, showing good e ﬀ ect in terms of CBM production.


Introduction
Coalbed methane (CBM) is an important unconventional natural gas resource, and it is abundant in China. According to the fourth round of CBM resource assessment, the geological resources of shallow CBM at a burial depth of 2 km are 29:82 × 10 12 m 3 in China [1][2][3][4][5]. There are about 20,000 CBM wells at the end of 2020, and the CBM production is about 57:67 × 10 8 m 3 . The average gas production per well is generally low. It is not only affected by the complex geological conditions but also depends on the adaptability of CBM development technology. By the end of the 13 th Five-Year Plan, the production of CBM has gradually increased, but the increase is small. The CBM production still has not exceeded 10 billion cubic meters. At present, China's CBM industry is characterized by the low exploration and development, low adaptability of agent technology, low return on investment, small development scale, etc. [6][7][8][9]. Under the background of "peak carbon and carbon neutralization," clean energy is in high demand. CBM industry needs to be closely linked around the value chain in terms of "how to improve the single CBM well production and the overall CBM recovery." Therefore, CBM development needs to conduct the refine exploitation geology research and the development of more targeted engineering technology research. This strengthens the geological and engineering technology integration evaluation and implements technology industrialization, which can achieve the goal of improving the development benefit of CBM and promote the development of China's CBM industry. Therefore, efficient techniques are needed to improve CBM recovery [10].
Exploitation of CBM mainly depends on drainage and pressure reduction, which promotes desorption of methane [11,12]. Injecting N 2 can reduce the partial pressure of methane in a coal reservoir [13] and improve the permeability of coal reservoir [14], thus significantly improving the CBM production. Based thereon, a gas-injection technique is proposed, which is called "enhancing CBM recovery by injecting N 2 (N 2 -ECBM)" [15,16]. Many laboratory and field tests have been conducted [17][18][19][20][21][22][23]. The adsorption of N 2 will cause the shrinkage of coal matrix when the N 2 is injected into coal, which mainly changes the mechanical properties and permeability of coal. After N 2 injection, the permeability of coal increases, and it can promote the diffusion and migration of CBM. Meanwhile, the mechanical strength of coal changes readily, which is conducive to improving CBM recovery. Additionally, some scholars explored and compared the results of N 2 injection and the mixture of N 2 and CO 2 injection [24]. The process is nonpiston displacement when N 2 displaces CH 4 . The breakthrough of N 2 occurs rapidly, and the two-element transition zone is narrow. The CH 4 and N 2 are produced for a long time after breakthrough. The ratio of N 2 injection is higher when the mixture of N 2 and CO 2 is injected into the coal, which can increase the permeability of the coal and is beneficial to CBM recovery. Most of the previous studies focused on the mechanism analysis of N 2 injection to enhance CBM recovery, however, less work on the effect of N 2 injection parameters on CBM recovery and the optimization of N 2 injection scheme has been undertaken.
The Shizhuang Block has realized the industrial development of CBM which shows considerable production volumes in the Qinshui Basin [25][26][27]. However, with the development of CBM, many CBM wells have been found to have low efficiency and low rates and amounts of overall productivity [28,29]. To promote the long-term stable production of CBM in the area, it is necessary to enhance the recovery based on an N 2 -ECBM technique.
Therefore, in the present research, the production variations under different N 2 injection parameters (including the production injection well spacing, gas injection timing, gas injection duration, gas injection rate, and the bottom-hole injection pressure) in coal reservoir were studied using numerical simulation, to optimize the N 2 injection parameters and enhance CBM recovery. The results may provide theoretical guidance for an optimal N 2 -ECBM scheme in the study area.

Model Establishment
2.1. Geological Model. The Cartesian coordinate system was adopted for the reservoir grid model. The grid distribution is 51 × 51 × 1. The length, width, and height of a single grid are 10 m × 10 m × 6 m, and the model measures 510 m × 510 m × 6 m. Based on the five point well pattern, an N 2 injection well is located in the middle of the model, four production wells are located around the injection well, and the well spacing between the injection well and the four production wells is equal (Figure 1).
The Shizhuang Block is located in the south of Qinshui Basin ( Figure 2). The target layer is the no. 3 coal seam. Previous studies have shown that its burial depth is 500-1300 m, the coal thickness is 4-10 m, and the gas content is 8-28 m 3 /t [30,31]. Based on the above, basic parameters of the basic model are described as follows: the depth of the coal seam is 1000 m, the thickness of the coal seam is 6 m, and the gas content is 24 m 3 /t. Thus, the geological reserves of CBM in this area amount to 57:8 × 10 6 m 3 ; other basic parameters are listed in Table 1.

Numerical Model.
A coal reservoir is the dual porosity system composed of matrix pores and fracture [32]. Matrix pores are the main gas storage area where CBM is present as an adsorption phase, and fracture controls the permeability of coal reservoir [33]. Therefore, the Gliman and Kazemi dual porosity model was adopted, which assumes that the matrix does not consider flow, and the fractures does [34].
In addition, the GEM component model was used to simulate the multicomponent fluid flow state in the process of N 2 -ECBM. According to the occurrence conditions of coal reservoir, the assumptions proposed by our predecessors were employed to set some basic settings of simplified operation in the model, namely: (1) there are two-phase flows of water and gas in the coal reservoir [35]. (2) The free gas in coal reservoir is an ideal gas [36]. (3) CBM experiences desorption, diffusion, and seepage processes, in which the desorption process conforms to the Langmuir model, the diffusion process is Fickian, and seepage in fractures conforms to Darcy's law [37,38].
According to the conservation of mass and continuity equation，the balance equation of gas-water two-phase flow in fractured systems can be expressed as The equilibrium equation of gas-water two-phase flow in the matrix system can be expressed as

Geofluids
where ϕ represents the porosity, ρ w is the density of water, ρ g is the density of gas, S w is the saturation of water, S g is the saturation of gas, μ w is kinematic viscosity of water, μ g is kinematic viscosity of gas, g is gravity acceleration, d is the coal burial depth, q w is the production of water, q g is the production of gas, q cwmf is the water exchange capacity between the matrix and fracture, q cgmf is the gas exchange capacity between the matrix and fracture, B w is the water volume factor, B g is the gas formation volume factor, ρ ga is the gas density at standard conditions, ρ c is the coal density, V is the average residual gas content in coal matrix, and subscripts f and m denote fracture and matrix. Based on the studies of Redlich and Kwong [39] and Soave [40], the equations of state for gases are a T ð Þ = 0:42748 where R denotes the universal gas constant of 8.314 J/ðmol •KÞ, T c is the critical temperature in K, P c is the critical pressure in Pa, and ω is the acentric factor. Binary mixed gas migrates in coal reservoir in the process of N 2 displacement [36]. Here, the subscript 1 and the subscript 2 represent CBM and injected nitrogen, respectively. The gas in coal reservoir is stored in adsorbed state and free state, and the content of adsorbed component can be expressed by the generalized Langmuir equation [41]: where C is adsorption gas volume, V L denotes the Langmuir volume constant, p represents gas pressure in matrix, and b is the Langmuir constant for gas component 1 and 2 which is equal to the reciprocal of the Langmuir volume, V L . Palmer and Mansoori [42] established a model to predict the change in coal permeability caused by coal shrinkage, which is applicable to the mixed gas adsorption/desorption equation: where ϕ represents the porosity, subscript 0 is the initial conditions, p L is the Langmuir pressure, ε L is the strains at infinite pressure, subscripts 1 and 2 denote CBM and injected nitrogen, c f represents the fracture pore volume compressibility, M represents the constrained axial modulus, K is the bulk modulus, p is the pressure, y 0,1 and y 0,2 stand for the composition of components 1 and 2 at the initial or reference conditions, and y 1 and y 2 refer to the composition of components 1 and 2 with pressure p.

Simulation Scheme.
Previous studies have shown that the factors affecting the production increase of N 2 injection in coal reservoirs are mainly limited by the spacing between production wells and injection wells, the timing of N 2 injection, the duration of gas injection, the rate of gas injection, and the bottom hole pressure of gas injection [13]. Therefore, the productivity of coal reservoir under different nitrogen injection production parameters was simulated based on the above factors. According to the geological conditions of the Shizhuang Block, the basic nitrogen injection parameters were set as follows: the production injection well spacing is 150 m, the injection timing is the third year after gas production, the gas injection duration is 5 years, the gas injection rate is 4000 m 3 /d, and the bottom-hole injection pressure is 10 MPa. Compared with these, the influences of various nitrogen injection production parameters on CBM Recovery were analyzed to optimize the N 2 -ECBM production scheme.
To select the optimal parameters of N 2 injection for increasing production, the coefficient of production increasing rate (I) was established, and the increasing production effect of CBM under the influences of different factors was expounded, which provides a favorable basis for optimizing productivity.
where C i represents the total cumulative gas rate of parameter i, and C 0 is the total cumulative gas rate of coal reservoir without N 2 injection. The larger the value of I, the greater the effect of N 2 injection on increased production, the higher the recovery. The value of I can characterize the stimulation effect of N 2 injection in coal reservoir, however, the economic benefit of coal reservoir should be considered, that is, the total amount of nitrogen needed to be consumed. Therefore, the establishment of the coefficient replacement ratio (R) reflects the volume of methane that can be replaced by 1 m 3 of N 2 , to study N 2 injection into coal reservoir and consider the ensuing economic benefits.
where N i represents the total amount of N 2 injection with parameter i. The larger the value of R, the better the displacement effect of CH 4 by N 2 , and the higher the economic benefit.

Results
First, the real productivity of coal reservoir without N 2 displacement was simulated, and then the productivity of coal reservoir with basic N 2 injection parameters was taken as the control group for simulation, to provide the basis for analyzing different N 2 injection conditions when aiming to enhance CBM recovery. Based on the application of the above reservoir parameters and nitrogen injection production parameters, the bottom-hole injection pressure was controlled by the pressure drop rate of 0.1 MPa/d. When the bottom-hole injection pressure dropped to 0.2 MPa, the bottom-hole injection pressure was kept unchanged and CBM production continues [43]. The model simulated the production capacity of four production wells in 15 years, and the gas-production time ranged from 2021 to 2036. Since the parameters of the four production wells were the same, Well-1 was taken as an example (Figure 3). When the coal reservoir was not stimulated by N 2 injection, the cumulative gas flow per single well in 15 years was 5:79 × 10 6 m 3 , the peak gas rate was 1486.8 m 3 /d, and the     : CBM production curves and N 2 injection curves under different N 2 injection production conditions: (a, c, and e) are CBM production curves of production injection well spacing, gas injection timing, and gas injection duration, respectively; (b, d, and f) are the N 2 injection curves of production injection well spacing, gas injection timing, and gas injection duration, respectively. PIWS stands for production injection well spacing, GR denotes daily gas production, CGR represents cumulative gas production, IR denotes daily gas injection, and CIR denotes cumulative gas injection. SC refers to surface condition. 6 Geofluids average gas production amounted to 1057.65 m 3 /d. The cumulative gas rate of the four wells was 23:18 × 10 6 m 3 , and the recovery factor was 40.08%. When the control group was subject to N 2 injection displacement production, the cumulative gas flow from a single well in 15 years increased to 6:46 × 10 6 m 3 , the peak gas rate was 1909.43 m 3 /d, and the average gas rate was 1178.61 m 3 /d. The cumulative gas rate of the four wells was 25:83 × 10 6 m 3 , the value of I was 10.26%, the value of R was 0.39, the recovery factor was 44.68%, the cumulative gas rate net increase was 2:65 × 10 6 m 3 , and the recovery factor was increased by 3.88%.

Production Injection Well
Spacing. The simulation conditions are the same as the other parameters. On this basis, the productivity of production wells and N 2 injection wells with a spacing of 90 m, 120 m, 150 m, 180 m, and 210 m could be simulated, respectively. The simulation results indi-cated that the longer the interval between production wells and injection wells, the longer the time to reach the peak gas rate. When the production injection well spacing was greater than 180 m to 210 m, the peak gas rate tended to decrease from 1922.42 m 3 /d to 1884.44 m 3 /d. The increase in cumulative gas rate was also small. The total cumulative gas rate of four wells was only increased by 19:08 × 10 6 m 3 (Figure 4(a)). Meanwhile, the smaller the production injection well spacing, the shorter the time for N 2 to reach the maximum N 2 injection rate, but the higher the total amount of N 2 injection (Figure 4(b)). The CBM recovery factor was then 36.62%, 41.03%, 44.68%, 46.98%, and 47.31% according to the respective well spacing.

Gas Injection Timing.
To analyze the influences of different injection timings on N 2 -ECBM, the N 2 injection productivity of injection wells in 0, 1, 2, 3, 4, and 5 years after gas  Figure 5: CBM production curves and N 2 injection curves under different N 2 injection production conditions: (a and c) are CBM production curves of gas injection rate and the bottom-hole injection pressure, respectively; (b and d) are N 2 injection curves of gas injection rate and the bottom-hole injection pressure, respectively. IBHP denotes the bottom-hole injection pressure, GR refers to daily gas production, CGR denotes cumulative gas production, IR represents daily gas injection, and CIR denotes cumulative gas injection. SC denotes surface condition. , the higher the bottom-hole injection pressure, the larger the peak gas production, the maximum value was 1976.9 m 3 /d, and the shorter the time to reach the gas rate peak value. At the same time, the cumulative gas rate and the total amount of N 2 injection were larger, but the increase was smaller, which indicated that higher injection pressure was not an ideal parameter for optimization of the technique. The CBM recovery factors were then 41.65%, 43.92%, 44.68%, and 44.72%, respectively.

Discussion
The results show that the production parameters of N 2 injection, such as production injection well spacing, gas injection timing, gas injection duration, gas injection rate, and the bottom-hole injection pressure, have a significant impact on N 2 -ECBM. Therefore, it is necessary to use the values of I and R to analyze the stimulation and economic applicability of various control factors for N 2 injection in a coal reservoir in more depth.

Production Injection Well
Spacing. Both N 2 injection and CBM drainage were realized by reducing the pressure of coal reservoir through drainage. When the well spacing was less Production increasing rate Replacement ratio Production increasing rate (%) (e) Figure 6: (a-e), respectively, describe the production increasing rate and replacement ratio of production injection well spacing, gas injection timing, gas injection duration, gas injection rate, and the bottom-hole injection pressure. 9 Geofluids than the radius of influence of each well, the depression funnels formed in the drainage process of production wells would overlap, resulting in inter-well interference, which would increase the corresponding development cost and worsen the economic effect. However, if the well spacing was too large, the drainage and depressurization effect would be affected, and the N 2 injectability would be reduced [44]. Therefore, choosing the right spacing between production  Figure 7: The CBM production curves and N 2 injection curves of N 2 injection optimized displacement and no N 2 injection displacement. GR denotes daily gas production, and CGR denotes cumulative gas production. SC denotes surface condition.
10 Geofluids wells and injection wells was conducive to obtaining the best N 2 -ECBM effect. Based on numerical simulations of productivity, the production increasing rate I and the replacement ratio R of different production injection well spacings were calculated (Figure 6(a)), and the production increase and replacement efficiency under five spacings were revealed.
The results indicate that I and R increased with the increase of production injection well spacing, which indicated that the increase of well spacing was beneficial to the increase of production and economy of coalfield. However, when the well spacing exceeded 180 m, I tended to remain unchanged and R increased greatly. Considering the boundary problem of geological model, the optimal production injection well spacing should be 180 m.

Gas Injection
Timing. By changing the timing of gas injection, its influences on the production increasing rate of coal reservoir N 2 injection and its economics could be studied ( Figure 6(b)). The results show that the later the gas injection timing was, the smaller the R was, and the less economical it was, but I first increased, then decreased, reaching its peak in the second year after gas production. It showed that the best time for gas injection was the second year after gas production, but the economic benefit was general. Considering that the main benefit of coal field was the increase of production, the best time of gas injection was the second year after gas production.

Gas Injection Duration.
Through the numerical simulation of the production capacity under different injection durations, the control of the injection duration on the production increasing of N 2 injection and the economy of the total amount of N 2 injection were obtained. The results ( Figure 6(c)) showed that, with the increase of injection duration, I increased and R decreased, indicating with the increase of N 2 injection amount, the production increasing rate of coal reservoir increased, but the efficiency of use of N 2 decreased, and the amount of waste increased. Moreover, the longer the gas injection duration, the rate of production increase tended to be flat. Considered comprehensively, the production capacity with a gas injection duration of 7 years should be selected.

Gas Injection
Rate. By changing the gas injection rate, the productivity simulation results (Figure 6(d)) imply that when the injection rate was less than 4000 m 3 /d, with the increase of the injection rate, I increased rapidly, R decreased sharply, and finally tended to slow down. The finding showed that increasing the gas injection rate was beneficial to the increase of coalfield production, but it would reduce the rate of utilization of N 2 and weaken the economic effect of coalfield production. Considered comprehensively, a rate of injection of 5000 m 3 /d was optimal.
4.5. The Bottom-Hole Injection Pressure. By changing the bottom-hole injection pressure, the increases in production benefit and economic benefit of N 2 injection in the coal field were analyzed. The results (Figure 6(e)) show that the influences of the bottom-hole injection pressure, injection rate, and injection timing on N 2 injection in coalfield had a sim-ilar trend. With the increase of the bottom-hole injection pressure, I increased and R decreased, and when the pressure exceeded 10 MPa, the rate of production increase and replacement ratio tended to be constant. On the one hand, the higher N 2 injection pressure in the fracture would increase the N 2 diffusion from the fracture system to the coal matrix system and lead to the earlier breakthrough of N 2 , which would increase the industrial cost of N 2 and CH 4 separation in the N 2 -ECBM process. On the other hand, if the N 2 injection pressure was too low, it was not conducive to gas injection and migration. Considered comprehensively, it was more appropriate to choose a bottom-hole injection pressure of 10 MPa.
4.6. Scheme Optimization. As mentioned above, the injection of N 2 reduced the partial pressure and concentration of methane in the fracture system, caused desorption of methane on the coal surface and contraction of the coal matrix [45,46], promoted the exploitation of methane, and improved the recovery of CBM. Therefore, according to the above summary, the production parameters of N 2 injection optimization scheme were designed as follows: the production injection well spacing was 180 m, the injection timing was two years after gas production, the injection duration was 7 years, the injection rate was 5000 m 3 /d, and the bottom-hole injection pressure was 10 MPa. The simulation results are shown in Figure 7. Figure 7 demonstrates that, compared with the case of no nitrogen displacement production, the average gas rate, daily gas peak value, and cumulative gas rate increased significantly when nitrogen injection displacement production was implemented under the proposed scheme. The cumulative gas rate per single well in 15 years was 7:07 × 10 6 m 3 , increasing by 22.1%, the peak gas rate was 2011.44 m 3 /d, increasing by 35.3%, and the average gas rate was 1291.27 m 3 /d, increasing by 9.6%. The cumulative gas rate of the four production wells was 28:29 × 10 6 m 3 , I was 18.34%, R was 0.5, and recovery factor was 48.95%. Compared with the case with no displacement, the cumulative gas rate net was increased by 5:11 × 10 6 m 3 , and the recovery factor was increased by 8.88%. The simulation results were well verified in the physical experiment [47].

Conclusion
In this study, an N 2 -ECBM numerical model was established to study the effects of various N 2 injection parameters on the production of CBM, and the values of I and of R were established to optimize the N 2 injection parameters. The following conclusions were drawn: (1) The stimulation effect of N 2 displacement is related to the production injection well spacing, injection timing, injection duration, injection rate, and the bottom-hole injection pressure. Among them, the production injection well spacing has the greatest influence on methane cumulative gas rate, followed by injection duration and the bottom-hole injection 11 Geofluids pressure, while injection timing and injection rate have relatively little effect (2) In the process of displacement, N 2 injection can significantly improve the gas production of CBM. The gas production of production wells increases rapidly in the early stage, reaches its peak value, and then decreases. At the end of N 2 injection, the gas rate decreases greatly and then decreases steadily in the later stage (3) With the increase of the production injection well spacing, the production increasing rate and nitrogen replacement ratio of coal reservoir increase. However, with a delay to the timing of the gas injection, the replacement ratio of nitrogen injection in a coal reservoir decreases, and the rate of production first increases and then decreases. Injection duration, injection rate, and the bottom-hole injection pressure have similar controlling effects on N 2 -ECBM, manifest as an increased rate of production and a decrease in the nitrogen replacement ratio (4) The best nitrogen injection scheme is as follows: the production injection well spacing should be 180 m, the injection should occur in the second year after gas production, the injection duration should be 7 years, the injection rate should be 5000 m 3 /d, and the bottom-hole injection pressure should be 10 MPa. Under these conditions, the cumulative gas rate of four production wells is 28:29 × 10 6 m 3 , which is 5:11 × 10 6 m 3 greater than that without nitrogen displacement, the recovery rate is 48.96%, and the net increase therein is 8.88%.

Data Availability
The data used to support the findings of this study are included within the article.

Conflicts of Interest
The authors declare no conflicts of interest.