Yi Xue , Faning Dang Rongjian Li and Fei Liu

Abstract: Adsorption deformation significantly affects the seepage characteristics of coal.However, effect of sorption time on coal permeability and gas pressure has not been investigated systematically. In this study, the sorption experiment of coal samples is conducted to elaborate the importance of sorption equilibration time. Then a coupled coal deformation and gas flow model is established considering the sorption characteristic and permeability evolution. This coupled model is implemented through finite element method to analyze the effect of sorption time on coal permeability and gas pressure. The simulation results reveal that the gas pressure of the coal will change with the adsorption time. The fracture pressure maintains a high level while the matrix pressure is relatively low during the adsorption process. The sorption time has a great influence on the distribution of gas pressure. The smaller the adsorption time is, the lower the gas pressure becomes.

Keywords: Permeability, porosity, gas pressure, adsorption time.

1 Introduction

Coal bed methane is a low-cost fuel and an unconventional source of energy, which can also pose a danger to coal production. Therefore, the pre-extraction of coal seam gas before coal seam mining can not only eliminate the risk of gas outburst, the methane also can be used as an energy source [Yu, Cheng, Jiang et al. (2004); Cao and Zhou (2015); Domingues,Baptista and Diogo (2017)]. The permeability of coal is a vital parameter in the process of coalbed methane drainage. The permeability of coal is affected by intrinsic and extrinsic factors, including effective stress, gas pressure and adsorption deformation [Cao, Du, Xu et al. (2017); Xue, Ranjith, Gao et al. (2017)]. Therefore, studying the characteristics of adsorption deformation is important for analyzing the seepage characteristics of coal [Li,Qi, Liang et al. (2010); Yin, Jiang, Hu et al. (2011); Xue, Gao and Liu (2015); Newman,Agioutantis and Leon (2017)].

Many researchers have studied the sorption characteristics of coal with different kinds of technological means. Majewska et al. [Majewska, Ceglarska-Stefańska, Majewski and Zi?tek (2009)] studied the gas sorption/desorption characteristics of coal with CH4and CO2through the sorption experiments with acoustic emission system. Zhang et al. [Zhang, Ju,Wei et al. (2015)] measured the macromolecule structure and adsorption capacity of different kinds of metamorphic-deformed coal and suggested that internal structures determine the adsorption capacity of coal. Connell et al. [Connell, Sander, Camilleri et al.(2017)] simulated the gas drainage process by using a triple porosity model with the SIMED software and analyzed the sorption based on core flooding experiments. Peng et al. [Peng, Liu, Pan et al. (2017)] divided the matrix strain into two different parts, including internal swelling and global strain, and suggested these two swellings affected the permeability at different stage respectively. However, these studies ignore the effect of sorption time on coal permeability and it may cause a great deviation in the estimation of gas pressure.

In this study, the importance of sorption equilibration time is elaborated firstly through the sorption experiment of coal samples. Then a coupled hydro-mechanical model is established considering the sorption characteristic and permeability evolution. Finally, the effect of sorption time on coal permeability and gas pressure is studied based on this coupled model.

2 Adsorption characteristic analyses

The coal samples used in the experiment are the raw coal samples with different structural characteristics obtained from Zhao Zhuang mine at Jincheng mining area. In order to study the difference of gas adsorption capacity of coal samples, gas adsorption experiments were carried out. The adsorption experiment adopts high pressure adsorption device. First, the coal sample is placed in a vacuum drying box, and then dried and cooled to the room temperature. Then the coal sample is pumped into a coal sample tank for vacuum pumping.After the vacuum extraction is completed, the gas is filled into the coal sample tank according to the set pressure, and the experiment data are measured.

Figure 1: Sorption-induced strain against sorption time

Fig. 1 is the adsorption deformation curve of three kinds of coal samples. It can be seen from the figure that coal samples adsorbs the methane and emerges volume expansion.After a long period of time, coal deformation enters into a stable state. At the same time, it can be seen that the adsorption equilibrium time of these three coal samples is different.The coal sample ZZ-1 quickly reaches the adsorption equilibrium, while the coal sample ZZ-3 reaches equilibrium after a long time. However, the importance of adsorption equilibrium time found from the experiments did not get considerable attention. There is no effective model which can consider this characteristic of adsorption equilibrium. The coal seam is a typical dual-porosity medium reservoir which is consisted of coal matrix blocks and coal fractures.Different gas pressures exist at every point: fracture pressureand matrix pressure . During the adsorption process, when these two pressures reach the same value, it means the adsorption finishes. The difference betweenandwill result in a long-term response to adsorption. Therefore, in the following section we investigate the sorption equilibrium characteristic based on a fully coupled hydromechanical (HM) model and analyze the effect of sorption equilibrium on gas pressure and coal permeability.

3 Equations of coupled model

3.1 Gas flow in fractures

The non-Darcy flow caused by inertial effect has a significant influence on gas reservoir performance and it can be expressed as [Xia, Gao, Kang et al. (2016)]

The above equation can be expressed as the following form

For the porous media, the flow equilibrium equation can be expressed as

The gas absorption volume can be expressed as

Where VLand PLare the Langmuir volume constant and the Langmuir pressure constant.The sorption induced volumetric shrinkage strainis assumed as

The ideal gas law is described as

Then the gas flow equation can be rewritten as

3.2 . Gas diffusion in coal matrix

The source term from the adsorption of coal matrix can be expressed as

The gas concentration in matrix and fractures can be expressed as

The methane exchange rate is related with the current gas content and the equilibrium gas content, therefore, the following equation is introduced to calculate the exchange rate

3.3 Klinkenberg effect

The effective gas permeabilitycan be expressed as a as

3.4 Mechanical equilibrium equation

For the dual porosity media, the effective stress can be expressed as

The strain-displacement relation of coal is expressed as

The Navier-type equation is yielded as

3.5 Coal permeability

The general porosity model is defined as [Zhang, Liu and Elsworth (2008)]

Then the porosity is expressed as

Besides, the permeability is correlated to the porosity according to the following exponential function

The apparent permeability in fracture system is obtained as

The change rate of porosity can be expressed as

4 Model establishment and analysis

4.1 Model establishment

In order to analyze the influence of adsorption on the distribution of coal permeability and gas pressure, a calculation model is established as shown in Fig. 2. The length of model is 0.1 m and width of model is 0.1 m. The upper, lower and left boundaries are restrained by normal displacement, and the right boundary is free. The zero fluxes are applied to these three boundaries, and the condition of the right boundary is the constant gas pressure 6.2 MPa. The initial pressure of the coal seam is 0.1 MPa, and the parameters in the calculation are listed in Tab. 1. A monitoring line is selected in the middle of coal mass and three monitoring points (A,B and C) are used to analyze the change law of coal permeability and gas pressure.

Table 1: Property parameters used in the simulation model

Figure 2: Geometry and boundary conditions of the calculation model

4.2 Effect of adsorption deformation on gas pressure

The gas pressure of the coal will change with the adsorption time. The effective stress and adsorption deformation of coal also affect the distribution of gas pressure. Fig. 3 shows the distribution of gas pressure in coal at different times. The same color bar is used in Fig. 3.The maximum is 6.2 MPa, and the minimum is 0.1 MPa. It can be seen from the figure that the highest gas pressure appeared on the right boundary firstly. The initial pressure in the coal seam is 0.1 MPa. With the entry of the gas fromthe right side, the gas pressure of the coal mass increased continuously. Bothand increase with time, and eventually reach the same pressure. There is also a difference between the matrix pressure and the fracture pressure. The pressure of coal fracture is greater than the pressure of coal matrix at 1 h, 3 h and 6 h. At the same time, with the increase of time, the difference between the matrix pressure and the fracture pressure is decreasing. Finally, the two pressures reached to 6.2 MPa at 18 h.

Figure 3: Gas pressure distribution at different times

The gas pressure distribution on the monitoring line is shown in Fig. 4. The gas pressure increases gradually with time. The minimum pressure of coal fracture is 3.15 MPa and 5.31 MPa corresponding to the time of 3 h and 6 h. It can be seen that the fracture pressure maintains a high level while the matrix pressure is relatively low during the adsorption process. The ratios of fracture pressure minimum and matrix pressure minimum are 100%,371%, 167% and 100% at times 1 h, 3 h, 6 h and 18 h. Fracture pressure and matrix pressure are different in most adsorption time. However, most studies only consider the fracture pressure and neglect the matrix pressure.

4.3 Effect of adsorption deformation on permeability distribution

The permeability distribution at the monitoring line at different times is shown in Fig. 5.The permeability evolution is affected by the effective stress and the adsorption deformation. With the increase of time, the permeability of coal decreases continuously. It can be seen from the figure that the permeability of coal mass begins to decrease, and the decrease speed is fast. Finally, the decline rate changes and finally maintains a stable level.The permeability of the left side is relatively higher, while the permeability of the coal seam of the right side is relatively lower. This is because the coal of the right side is firstly adsorbed and expanded, and the fracture aperture reduces, resulting in the decrease of permeability. It shows that the influence of adsorption swelling on the right side exceeds that of the left side. Meanwhile, the influence zone of the adsorption swelling extends to the left side. Finally, more than 18 h after the gas adsorption the coal rock permeability reached a balance and remained constant.

In order to analyze the evolution characteristics of coal permeability, the permeability evolution curves of three monitoring points in the model are studied, as shown in Fig. 6.The coordinates of the three monitoring points are A (0.01 m, 0.05 m), B (0.05 m, 0.05 m)and C (0.09 m, 0.05 m). The permeability of all these monitoring points decreases with time, and finally reaches the same level. With the adsorption deformation of coal, the permeability of coal changes continuously. Finally, the adsorption deformation reaches a balanced state, and the permeability remains unchanged. The size of the permeability at three points is in order of k (A)＞k (B)＞k (C), and the permeability at C point finally reaches stability. The permeability evolution of different points in coal is mainly caused by gas migration and adsorption deformation of coal.

Figure 4: Gas pressure distribution along the monitoring line

As shown in Fig. 7, the deformation of coal varies with time due to gas adsorption. When the pore pressure increases, the coal sample expands in the horizontal direction. These results show that the deformation characteristics of the calculation model are consistent with the experimental results of gas desorption. The volumetric strain caused by gas adsorption plays a vital role in the change of porosity and permeability of coal. Small variations in porosity can lead to much greater changes in permeability. The variation of permeability is affected by opposite effects of effective stress and gas desorption, and gas adsorption may decrease permeability. If the effect of gas adsorption is neglected, pore pressure of coal seam may be underestimated.

Figure 5: Permeability distribution along the monitoring line

Figure 6: Permeability distribution of the monitoring points

Figure 7: Evolution of the coal volume with gas desorption

4.4 Effect of adsorption time on permeability distribution

Fig. 8 shows the gas pressure distribution under different sorption time. It can be seen from the diagram, the sorption time has a great influence on the distribution of gas pressure. The smaller the adsorption time is, the lower the gas pressure becomes. The difference of the gas pressure between adsorption time 0.1 d and 1 d is greater than the difference between the adsorption time 10 d and 1 d. Fig. 9 shows the permeability distribution at different sorption times. It can be seen from the figure that the influence of sorption time on the permeability distribution is obvious, and the different sorption time also has obvious influence on the distribution of coal permeability. Similar to the gas pressure distribution,the difference of the permeability between adsorption time 0.1 d and 1 d is greater than the difference between the adsorption time 10 d and 1 d. Therefore, adsorption time is a vital factor which needs to be considered in analyzed the seepage characteristic of coal. It will affect the diffusion rate between matrix blocks band fractures. Both experiential results and simulation results indicate adsorption time significantly affect the diffusion rate and gas pressure.

5 Conclusions

(1) The gas pressure of the coal will change with the adsorption time. Bothandincrease with time, and eventually reach the same pressure. The fracture pressure maintains a high level while the matrix pressure is relatively low during the adsorption process.

Figure 8: Gas pressure distribution with different sorption time

Figure 9: Permeability distribution with different sorption time

(2) With the increase of time, the permeability of coal decreases continuously. The permeability of coal mass begins to decrease, and the decrease speed is fast. Finally, the decline rate changes and finally maintains a stable level. The permeability of the left side is relatively higher, while the permeability of the coal seam of the right side is relatively lower.

(3) The sorption time has a great influence on the distribution of gas pressure. The smaller the adsorption time is, the lower the gas pressure becomes. Similar to the gas pressure distribution, the difference of the permeability between adsorption time 0.1 d and 1 d is greater than the difference between the adsorption time 10 d and 1 d.

Acknowledgments:This study is sponsored by the National Natural Science Foundation of China (No. 51679199), the Special Funds for Public Industry Research Projects of the Ministry of Water Resources (No. 201501034-04 and 201201053-03) and the Key Laboratory for Science and Technology Coordination & Innovation Projects of Shaanxi Province (No. 2014SZS15-Z01).