Numerical Simulation of Coal Deformation and Gas Flow Properties Around Borehole

Yi Xue

1 Introduction

Coal seam gas (CSG) is an important kind of clean energy, which plays an important role in the world energy structure. Underground well and ground drilling is usually used in the pre-extraction process, and the underground drainage is the main method for the actual reservoir conditions [Barenblatt, Zheltov and Kochina (1960); Cao, Zhou and Zhang et al.(2015); Xue, Gao and Liu (2015)]. However, many coal seams in the world are low-permeability coal seams, and methane stored in coal seams cannot be effectively extracted. Many technological means are adopted to increase the permeability of coal seam and achieve the efficient gas extraction. For example, hydraulic fracturing technology, carbon dioxide flooding, hot injection, and other engineering technologies have been successfully applied to enhance the extraction of coalbed methane [Douglas,Hensley and Arbogast (1991)], as shown in Fig. 1.

Hot injection extraction techniques have gained great attention in recent years because of its superiority [Gray (1987); Mavor and Vaughn (1998); Hong, Koo and Park (2012);High, Budianto and Oda (2016); Xue, Cao and Cai et al. (2017)]. However, the effect of temperature on coal-gas interactions in coal seam gas extraction is still not clear.Therefore, the thermal evolution characteristic evolution during the extraction of coalbed methane needs to be studied.

In this study, a gas-solid coupled model is established to describe coalbed methane migration, which combines with methane diffusion law, seepage law in coal matrix,permeability evolution model and coal seam deformation equation. The model is used to simulate the whole process of methane extraction, and the effect of diffusion on methane migration is analyzed.

2 Governing equations

2.1 Coal seam deformation

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

2.2 Gas flow equation

The non-Darcy flow caused by inertial effect has a significant influence on gas reservoir performance and it can be expressed as

The above equation can be expressed as the following form

The gas absorption volume can be expressed as

where VL and PL are the Langmuir volume constant and Langmuir pressure constant at temperature Tt, respectively; Tar the absolute reference temperature in the stress-free state; Tt the reference temperature for the desorption/adsorption test of gas; (Tar+T) the temperature of the coal seam; c1 the pressure coefficient; and c2 the temperature coefficient.

The sorption induced volumetric shrinkage strainis assumed as whereis the content of absorbed gas;is the coefficient of sorption-induced strain.

The ideal gas law is described as

2.3 Gas diffusion in coal matrix

The gas transport experiences three stages: flow in the fractures, gas diffusion and sorption in the matrix. Figure 1 shows a conceptual model for gas transport. The source term from the adsorption of coal matrix can be expressed as

The gas concentration in matrix and fractures can be expressed as

Then the diffusion equation can be expressed as

The effective gas permeabilitycan be expressed as a as [Kumar, Elsworth and Mathews et al. (2016)]

2.4 Coal permeability

The general porosity model is defined as [Soofastaei, Aminossadati and Kizil et al.(2016)]

Then the porosity is expressed as

where subscript 0 denotes the initial state of variables.

Substituting the porosity can be rewritten as

The permeability is correlated to the porosity according to the following exponential function

The apparent permeability in fracture system is obtained as

2.5 Energy conservation

Neglecting the thermal-filtration effect, the total heat fluxis given by

Neglecting the interconvertibility of thermal and mechanical energy, the thermal balance can be expressed as Valliappan and Wohua (1996)

3 Model verification and establishment

3.1 Analytical validation

In order to verify the effectiveness of this coupled model in the calculation of gas flow in porous media, the finite element model is applied and the numerical results are compared with the simplified analytical solutions. The one-dimensional linear steady gas flow model has a length of 20m. A single phase gas is injected into the rock with a constant rate of gas at the inlet and gas pressure keeps constant at outlet. Assuming that the porosity of the rock remains constant, the gas will eventually reach a steady state.Equation for one-dimensional linear flow can be reduced from Eq. (6) to:

The boundary conditions are

The parameters used in numerical calculation are listed in Table 1, and these parameters are also adopted in analytical solutions. This comparison shows that the numerical solutions agree well with the analytical solutions, which verifies the validity of the numerical model.

Table 1 Parameters used for one-dimensional linear steady gas flow

3.2 Model establishment

In order to analyze the influence of heat injection on the gas extraction, a calculation model is established as shown in Figure 2. The length of model is 100m and width of model is 100m. The four boundaries are restrained by normal displacement. The zero fluxes are applied to these boundaries. The initial pressure of the coal seam is 6.2MPa,the initial temperature of the coal seam is 293K and the parameters in the calculation are listed in Table 2. A monitoring line is selected in diagonal line of coal mass and three monitoring points A (30m, 30m), B (55m,55m) and C (80m, 55m) is used to analyze the change law of production rate, coal permeability and gas pressure.

Table 2: Property parameters used in the simulation model

Figure 2: Computational model and the schematic diagram of heat injection well.

4 Result and discussion

4.1 Effect of diffusion on diffusion rate

Figure 3: Gas diffusion rate distribution at different times

Figure 4: Gas diffusion rate along the diagonal line

Figure 3 shows the gas diffusion rate distribution at different times and Figure 4 shows the gas diffusion rate along the diagonal line. The effect of diffusion on gas extraction can be seen from these figures. In the initial gas extraction process, the gas in the fractures can flow to the borehole quickly under the influence of pressure gradient.Therefore, the gas diffusion rate is relatively high in the initial stage. With the increase in time, the difference between coal fractures and coal matrix blocks becomes lower and the gas diffusion rate decreases gradually. It can be seen from the figure that the gas diffusion rate decreases significantly near the borehole and the decrease degree becomes small when it is far away from borehole.

4.2 Effect of diffusion on seepage rate

Figure 5: Gas seepage rate distribution at different times

Figure 6: Gas seepage rate along the diagonal line

Figure 5 shows the gas seepage rate distribution at different times and Figure 6 shows the gas seepage rate along the diagonal line. The change law of gas seepage rate is obvious different from that of gas diffusion rate. The gas seepage rate is mainly controlled by the pressure gradient of coal fractures and the gas diffusion rate is mainly controlled by the pressure gradient of coal fractures and matrix blocks. The gas seepage rate increases gradually with the increase of time. Similar to the change law of gas diffusion rate, the gas seepage rate decreases significantly near the borehole and the decrease degree becomes small when it is far away from borehole.

4.3 Effect of diffusion on drainage rate

Figure 7: Gas drainage rate at different times

Figure 7 shows the gas drainage rate at different times. The influence of diffusion time on gas drainage rate can be seen from this figure. The influence of diffusion time on gas drainage rate is not obvious. When the diffusion time increases from the 0.1d to 10d, the gas drainage rate increases slightly. It may be caused by the fact that the gas drainage last many years and the diffusion time only is some days. There is a far distance difference in the order of magnitude.

5 Conclusions

(1) In the initial gas extraction process, the gas in the fractures can flow to the borehole quickly under the influence of pressure gradient. The gas diffusion rate is relatively high in the initial stage. With the increase in time, the difference between coal fractures and coal matrix blocks becomes lower and the gas diffusion rate decreases gradually.

(2) The change law of gas seepage rate is obvious different from that of gas diffusion rate.The gas seepage rate increases gradually with the increase of time. The gas seepage rate decreases significantly near the borehole and the decrease degree becomes small when it is far away from borehole.

(3) The influence of diffusion time on gas drainage rate is not obvious. It may be caused by the fact that the gas drainage last many years and the diffusion time only is some days.There is a far distance difference in the order of magnitude.

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