Effects of Injection Pressure and Duration on Alternate High-Pressure Water-Gas Sequestration of Coalbed Methane

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Introduction
The CBM production in China is significantly lower than that in other coal-rich countries, such as Australia and the United States [1]. Due to the different geological conditions, the permeability of some coal seams is low, which determines the difficulty of methane extraction and drainage [2]. Many researchers put forward a series of enhanced coalbed methane recovery (ECBM) techniques to solve the above problems, such as large-diameter borehole drainage [3], hydraulic punching [4], pulsating shock [5], hydraulic cutting [6] (or ultra-high pressure hydraulic slitting), hydraulic fracturing [7], CO 2 -ECBM [8] and pre-split blasting [9]. The basic mechanism of these techniques is to generate artificial fractures in coal seams, which can improve the permeability of coal seams and thus increase the methane recovery rate. However, methane is mainly adsorbed in nanopores of coal with high adsorption ability, which makes it difficult to effectively extract methane adsorbed [10]. There-fore, the problem of low methane recovery rate in coal seam cannot be fundamentally solved. Water displacement is considered an effective method to recover methane from small coal pores [11].
Water flooding has encountered some problems in the field practice, such as poor methane recovery rate [12]. The water diffusion in coal seam is affected by viscous force, friction force, and normal stress of fracture wall, and water lock occurs in coal seam due to capillary effect and Jiamin phenomenon [13]. Recently, some researchers use acidbase salt solutions to improve the injected water [14], which still does not completely solve the water lock damage, and only to reduce the effect of bound water [15]. CO 2 enhanced coalbed methane recovery (CO 2 -ECBM) is a good alternative method to obtain a high coalbed methane recovery rate [16], involving CO 2 injected into deep coal seams [17,18]. However, CO 2 injection can cause coal matrix expansion, which has decreased gas permeability of coal [19]. The adsorption capacity of CO 2 in coal is higher than that of methane, which may lead to high risk of coal and gas outburst or accidental emission of CO 2 during coal mining. Considering the potential hazard of CO 2 -ECBM, nitrogen injection into coal seam was proposed [14]. N 2 is mainly produced by separation from the atmosphere or decomposition of nitrogenous compounds, which requires a cost to produce, store and transport. The production of large amounts of N 2 and CO 2 is not economical. The adsorption of CH 4 and N 2 on coal matrix belongs to physical adsorption, and the adsorption capacity of CH 4 on coal matrix is stronger than that of N 2 . Air containing 78% nitrogen is commonly used in field practice.
Thus, we proposed a new technique named highpressure water and gas alternating sequestration (H-P-WGAS) in our previous work [20]. In that work, we discussed the effectiveness of the H-P-WGAS technique and verified that the H-P-WGAS technique can enhance methane migration in coal seam. The field tests indicated that the average methane drainage flow rate of single borehole increased significantly and consequently the residual methane content in coal seam decreased dramatically as a result. In the present work, the effect of injection pressure and duration on water and gas alternating sequestration of coalbed methane will be discussed, which is important to the engineering practice.

Numerical Model
In our study, water and air are successively injected into coal seam to displace methane. Based on the theory of multiphase-flow in porous media, the model considered fluid seepage and capillary force in coal seam, and the basic assumptions were as follow: (1) Coal is a double porous medium rich in pores and fractures. The pore system and fracture system are assumed to be continuum systems (2) The coal seam is homogeneous, porous, and isotropic. In-situ methane pressure and methane content are uniform everywhere in the coal seam (3) The initial volume fraction of methane in the coal seam is 85%, and the water and air saturation are 10% and 5%, respectively (4) Temperature of the coal seam is constant (293.15 K), and there is no heat exchange between the boundary and the coal seam  Figure 1. A single borehole model is established. It is a 0.1 m borehole located in the center of calculated zone (X =150 m, Y =100 m). Eight detection points (A to H) are arranged at different distances away from injection borehole along line L. As shown in Figure 2, the boundary pressure of coal seam is set to 2 MPa. Coal seam parameters are shown in Table 1.

Calculation Model of Fluid Seepage in Porous Media.
The multiphase flow in coal seams follows Darcy's law with the continuity equation [21,22]: where ρ l is density of fluid, kg/m 3 ; u l is seepage velocity of each phase, m/s, Q ls is mass source of the fluid, kg/(m 3 ·s). m l is liquid mass in the coal matrix per unit volume, which can be calculated by: In the present work, the swelling and deformation of the coal matrix due to water absorption are not considered, so the porosity can be expressed as: where R = ε v + ðp/K s Þ;R 0 = ε v0 + ðp 0 /K s Þ ; ε v and ε v0 are volumetric strain and initial volumetric strain of coal seam, respectively; K s is bulk modulus of coal skeleton. The equation of permeability and porosity obtained by simultaneous formula is as follows: where k f and k f 0 are the permeability and initial permeability of coal seam, respectively; ϕ and ϕ 0 are the porosity and initial porosity of coal seam, respectively. Darcy's law for seepage in porous media is as follows: where q i is seepage velocity of pressure water, m/s; μ i is hydrodynamic viscosity, Pa·s; k is permeability, mD; ρ i is density of pressure water, kg/m 3 ,∇D is gravitational potential difference, m; g is gravitational acceleration, 9.8 m 2 /s. (1) and (3) can be derived as where u is fluid velocity, m/s; μ i is dynamic viscosity of the fluid, Pa·s; κ is effective permeability, mD; κ ri is relative permeability, mD; ∇p i is pressure gradient (Pa/m). The effective permeability (κ) is related to relative permeability (κ ri )and can be calculated by: Total methane including adsorbed methane and free methane in the coal matrix can be calculated by: where q is mass of methane per unit volume in coal matrix, kg/m 3 ; ρ is coal density, kg/m 3 ; V L is Langmuir volume (maximum adsorption capacity of coal), m 3 /t; p L is Langmuir pressure, MPa; ∅ m is porosity of the coal matrix, %; V m is molar volume of methane under standard conditions, m 3 /mol [24]. Multiphase fluid transport is based on macroscopic mass conservation equation of each phase. The average volume fraction (also known as saturation) of each phase is found.   Describe single-phase fluid transport: s i is volume fraction (dimensionless); u i represents the velocity vector of phase i, m/s; Q i is mass source of phase i, kg/(m 3 ·s).
Assuming that the sum of the volume fractions of each phase is 1 (100%), the volume fraction of the remaining phase S j is obtained by:    Geofluids where S i is volume fraction of phase i; S j is volume fraction of phase j.
Combining (8) and (11), other N-1 phase fluid motion equations can be obtained:  Figure 3 shows the evolution of methane volume fraction recorded every 2 hours. The injected water expanded from the borehole to far-field area of coal seam. The influence range of water injection expanded with the increase of injection time.
As shown in Figure 4, methane fraction volume (V CH 4 ) near the injection borehole (point A, X =3 m) decreased significantly from 85% to 73.31% after 2 hours and decreased to 70.50% after 22 hours. After 24 hours water injection, V CH 4 at point F to H still fluctuated around 85% and showed a slight upward trend, indicating a weak disturb by water injection. The influence effective radius of water injection is about 13 m.

Geofluids
V CH 4 at all detection points increased at the initial stage (less than 5%) and then decreased sharply. The phenomenon also appears in the experimental studies of other scholars [11]. A reasonable explanation is: under water injection, affected by high injection pressure, pressure gradient forces the methane carried by water and the methane V 1 displaced by water to passively flow to the outside, plus the external coalbed methane V 2 that has not been affected by hydraulic permeability. Both V 1 and V 2 overlap, and the V CH 4 increases briefly and in a small range. Figure 5 gives time-dependent pore pressures at different detection points. Pore pressures increased rapidly in the first two hours under high-pressure water injection, which indicates that pore pressures quickly covered all detection points  7 Geofluids under water injection. Pore pressure is higher in areas closer to the injection hole, which will be beneficial to fracture the coal body and extend the primary fractures. Figure 6, the reduction of V CH 4 is lower than that of water displacement.

Air Injection Displacement. As shown in
The injected air expanded faster than water and had a wider displaced area. As shown in Figure 7 under air injection displacement, the decrease of V CH 4 fluctuated little at all detection points. V CH 4 decreased sharply within 2 h. The total V CH 4 at detection point A decreased by 90% at the first 2 h, indicating a high displacement velocity. The air expansion in coal seam is relatively uniform.
The pore pressures at different detection points finally reached a stable value when air was continuously injected.

Geofluids
The average stable pore pressure of different detection points is 8.85 MPa (as shown in Figure 8), which is slightly higher than 8.05 MPa under water injection. As shown in Figure 9, the pore pressures and influence range under air injection are both significantly larger than water injection at the same injection time (12 h) along line L. The velocity of pressure propagation is obviously faster than that of water injection.

Characteristics of Water-Air Alternating Displacement.
Water was injected into coal seam in the first 12 hours and air in the next 12 hours. As shown in Figure 10, the V CH 4 near the borehole decreased significantly under air injection. And the influence range was larger compared with water injection at the same time. As shown in Figure 11, V CH 4 at detection points A, B, and C decreased twice and stabilized at about 43%, while the average stable V CH 4 of other  9 Geofluids detection points was 58.5%. Under air injection (14-24 h), V CH 4 at different detection points did not change much, indicating that the air injection completed the displacement within two hours. This phenomenon is consistent with air injection. Therefore, WGA-ECBM technique is combined with the advantages of air injection. Under the water-air altering displacement, the average V CH 4 of all detection points decreased to 52.9%, while that of water injection and air injection under the same conditions decreased to 79.3% and 74.9%, respectively.
Under the water-air alternating displacement, pore pressures first increased under water injection. Pore pressures firstly decreased and then increased under air injection, as shown in Figure 12. At the time of air injection (t =12-13 h), pore pressures decreased because injected air drives the multiphase flow to migrate. According to Bernoulli equation: p + ρgz + ð1/2Þ * ρv^2 = C, part of pressure potential energy is converted to kinetic energy. And the other part is lost when pressure gradient fractures coal body to expand the cracks and break through the water-blocked migration channel. Figure 13 shows the 3D distribution of pore pressures in coal seam. The decrease rate of pore pressure gradually slows down from borehole to the boundary.

Comprehensive Comparison of Three Displacement
Methods. Figure 14 shows V CH 4 reduction at each detection  As shown in Figure 15, V CH 4 in the borehole decreased to 67.16% and 72.28% under water injection and air injection, respectively. The water-air alternating displacement decreased to 40.38%. V CH 4 decreased again by 26.94% based on 17.84% reduction of water injection. After water injec-tion, the aid of air injection on displacement is significant, and the second decrease in methane volume is greater. As shown in Figure 15, the influence ranges are 24.68 m, 149.73 m and 135.21 m (the diameter on L line) under water injection, air injection and water-air alternating displacement, respectively. As shown in Figure 16, pore pressure distribution under three displacement methods is similar at 24 h. This indicates that the injection pressure has completed a relatively uniform spread within 24 h. 11 Geofluids pressure and the permeability in coal seam is an important engineering parameter. As shown in Figure 17, the pore pressure in the contour appears to be reduced at t =12 h compared to t =8 h. The injected air pushes the methanewater in the pore space to seep outward and overcomes the capillary pressure. Resolving water-lock damage causes the pore pressures to temporarily decrease and then increase.
As shown in Figure 18, V CH 4 decreases gradually as injection pressure increases in a pressure gradient of 5 MPa. However, V CH 4 decreases slightly under water displacement. The   influence range under air injection is greater than that under water injection.
As shown in Figure 19, at the end of water injection (t = 8 h), the influence ranges from 10  As shown in Figure 20,with the foundation of the water injection, the displacement effect of the air injection is obviously better. V CH 4 Figure 19, the influence range is obviously expanded.

Water-Air Alternating Displacement under Different
Injection Durations. As shown in Figure 21, the influence range increases continuously with the increasing injection duration. The area expansion of the contours is significantly larger under air injection than under water injection. The air injection is more dramatically influenced by injection duration.
As shown in Figure 22, As injection duration increases in the WGA-ECBM, V CH 4 in the displaced area is less and less affected by the injection duration. V CH 4 in the borehole are  However, As the wetting area of coal seam becomes larger, the seepage channels increase, and the displacement velocity gradually slows down, as shown in Figure 23. The injection duration has little effect on pore pressures. The pore pressure can propagate to the model boundary at t =8 h in Figure 24. The pore pressure distribution characteristics are similar under different injection durations.

Conclusions
The WGA-ECBM provide a new high-efficiency technique for the methane recovery. And in the multiphase fluidsolid coupling model, the influences of different parameters on fluid migration, pore pressure and methane content are discussed, which has important guidance value in field practice.
(1) The WGA-ECBM eliminated the high methane area generated by water injection while it also helped water injection to further expand the influence range. The influence ranges (diameter) are 24.68 m, 149.73 m and 135.21 m under water injection, air injection and water-air alternating injection, respectively. Under the same conditions, the pore pressure distribution characteristics of three methods are similar at 24 h (2) Water-air alternating injection can quickly reduce V CH 4 again based on methane reduction under water injection. V CH 4 in the borehole are 67.16%, 72.28% and 40.38% under water injection, air injection and water-air alternating injection, respectively. The methane reduction effect of WGA-ECBM is the best among three methods (3) The influence range of air injection is wider than water injection. The curve fluctuation of V CH 4 under air injection was smaller at each detection point. However, water injection is better than air injection in V CH 4 reduction.
(4) The influence of injection pressure and injection duration under air injection is greater than under water injection. High pressure water injection for long time is not effective. In the WGA-ECBM technique, V CH 4 decreases and influence range expands as the injection pressure increases in a pressure gradient of 5 MPa. With the increase of injection duration, the influence range expands significantly but the pore pressure distribution changes little. And V CH 4 decreases slightly in the displacement area and the displacement velocity gradually slows down

Data Availability
The data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. 14 Geofluids