^{1}

^{2}

^{2}

^{3}

^{1}

^{2}

^{3}

Understanding the influence of temperature on the gas seepage of coal seams is helpful to achieve the efficient extraction of underground coal seam gas. Thermal coal-gas interactions involve a series of complex interactions between gas and solid coal. Although the interactions between coal and gas have been studied thoroughly, few studies have considered the temperature evolution characteristics of coal seam gas extraction under the condition of variable temperature because of the complexity of the temperature effect on gas drainage. In this study, the fully coupled transient model combines the relationship of gas flow, heat transfer, coal mass deformation, and gas migration under variable temperature conditions and represents an important nonlinear response to gas migration caused by the change of effective stress. Then, this complex model is implemented into a finite element (FE) model and solved through the numerical method. Its reliability was verified by comparing with historical data. Finally, the effect of temperature on coal permeability and gas pressure is studied. The results reveal that the gas pressure in coal fracture is generally higher than that in the matrix blocks. The higher temperature of the coal seam induces the faster increase of the gas pressure. Temperature has a great effect on the gas seepage behavior in the coal seams.

Coal seam gas is an important natural source and an important part in the clean energy structure in China [

The thermal stimulation of gas reservoir triggers the complex interaction between coal, gas, and temperature. It changes the deformation behavior of coal, as well as the heat and gas flow. Temperature has an obvious effect on the adsorption capacity of coal seam gas, which is negatively correlated with the increase of temperature [

The interaction mechanism of heat injection has not yet fully understood for the design of engineering. It is indispensable to study the coal-gas interaction under variable temperature. In this study, a coupled thermal-hydrological-mechanical model is established, considering the sorption characteristic and permeability evolution. Then, this complex model is implemented into a finite element (FE) and solved through the numerical method. Finally, the effect of temperature on coal permeability and gas pressure is studied based on this coupled model.

For the coal seam reservoir, the non-Darcy flow can be expressed as

The above equation can be expressed in the following form:

The mass conservation equation of gas migration can be expressed as

In the coal seams, the gas absorption volume can be expressed as

The Sorption Strain

The gas density can be obtained as

The mass conservation equation can be expressed as

The gas migration process experiences three substeps: flow in fracture, gas diffusion, and sorption in matrix [

A conceptual model for gas storage and transport in the coal seams. (a) Natural fracture networks. (b) Stage 1: desorption from internal surfaces. (c) Stage 2: flow/diffusion in the matrix. (d) Stage 3: flow in the natural fracture network.

The relationship of gas concentration and gas pressure is written as

The diffusion equation can be written as

Then, the diffusion equation can be expressed as

The permeability

The stress equation of coal seam can be written as

The stress-strain equation can be written as

The overall stress balance equation can be written as

The relationship between porosity and effective stress can be expressed as [

Then, the porosity is expressed as

By substituting the porosity, it can be rewritten as

The evolution characteristics of permeability can be expressed as

Total heat flux

The thermal balance can be written as [

The conservation of mass yields

Considering

These equations (

Couplings in the gas migration process.

To verify the validity of the model established in this paper in the calculation of simulated extraction, the numerical simulation is carried out according to the practical example of coal seam extraction. The actual size of the coal seam is 568 × 568 m^{2}, and the parameters are obtained from Mora and Wattenbarger [

Comparison between numerical result and field test.

A model is established to analyze the effect of adsorption on the distribution of coal permeability and gas pressure. The size of the model is 0.1 m × 0.1 m, as shown in Figure

Calculation model.

Parameters of the model.

Parameter | Value | Sources | Parameter | Value | Sources |
---|---|---|---|---|---|

Young’s modulus of coal, |
2713 | [ |
CH_{4} Langmuir volume constant, _{L} (m^{3}/kg) |
0.043 | [ |

Young’s modulus of the coal grains, _{s} (MPa) |
4070 | [ |
Specific heat capacity of gas, _{g} (J/kg·K) |
1.625 × 10^{3} |
[ |

Initial porosity, |
0.01 | [ |
Specific heat capacity of coal, _{s} (J/kg·K) |
1.25 × 10^{3} |
[ |

Density of coal, ^{3}) |
1250 | [ |
Pressure coefficient, _{1} (MPa^{−1}) |
0.07 | [ |

Poisson’s ratio of coal, |
0.34 | [ |
Sorption strain coefficient, ^{3}) |
0.06 | [ |

Initial gas permeability, ^{2}) |
1.09 × 10^{−18} |
[ |
Volumetric coefficient of matrix, ^{−1}) |
2.4 × 10^{−5} |
[ |

Density of CH_{4} at standard condition, ^{3}) |
0.717 | [ |
Klinkenberg effect, |
1.44 × 10^{5} |
[ |

Gas dynamic viscosity, ^{2}) |
1.84 × 10^{−5} |
[ |
Temperature coefficient, _{2} (K^{−1}) |
0.02 | [ |

CH_{4} Langmuir pressure constant, _{L} (MPa) |
1.57 | [ |
Thermal conductivity of coal, |
0.2 | [ |

There are two different pressures between matrix blocks and coal fractures. Because of the high permeability in coal fractures, gas can quickly flow through the fractures. The gas pressure in fractures is generally higher than that in the matrix blocks in the calculation model. The matrix also continues to adsorb gas, and the pressure rises gradually. As the gas is injected from the top of the model, the crack pressure reaches 2.5 MPa firstly at the upper boundary, and the matrix permeability is also increasing. Finally, pore pressure and matrix pressure reach the equilibrium state. Figure

Gas pressure change law of the model.

Figure

Gas pressure distribution along the monitoring line.

Based on the dual-porous medium model, the fracture pressure and the matrix pressure are calculated through different equations. Therefore, we can further understand the dual-porous medium model by analyzing the evolution rule of permeability. Figure

Permeability distribution along the monitoring line.

Coal mass expends and the fracture aperture decreases when it absorbs gas. Meanwhile, the coal mass is limited by the boundary conditions, so coal deforms under the combined influence of the change of gas pressure, expansion stress, and effective stress [^{3}/kg to 0.0481 m^{3}/kg when the time increased from 1 h to 8 h. As time goes, the permeability of coal gradually stabilizes and tends to be at a uniform state.

The changes of permeability and porosity of a point are analyzed. The point is at the center of the model, and its coordinates are (0.05 m, 0.05 m). Figure

Permeability distribution of the monitoring point A.

Figure

Temperature change law of the model.

Evolution of the coal volume with time under the effect of temperature.

The distributions of gas pressure and permeability under different temperatures are given in Figures

Gas pressure distribution with different temperatures.

Permeability distribution with different temperatures.

In order to quantify the influence of gas diffusion behavior, the fracture pressure distribution without Klinkenberg effect and different adsorption times was also plotted as shown in Figure

Gas pressure distribution under different cases.

A new model about heat transfer was developed to study the dynamic problem of gas adsorption in coal seam under variable temperature conditions. In the model, the coal mass was regarded as a dual-porous medium, and each point of the coal mass has two different pressures, i.e., pore pressure and matrix pressure. The relationship between adsorption equilibrium and permeability evolution was analyzed through the numerical method. The main results are as follows:

The gas pressure in fractures is generally higher than that in the matrix blocks in the calculation model. The matrix also continues to adsorb gas, and the pressure rises gradually. Finally, pore pressure and matrix pressure reach the equilibrium state.

The adsorption of coal increases with the increase of gas pressure, and the gas content increases continuously. The porosity of coal mass decreases with the increase of time, while the temperature and gas content increase with the increase of time.

The higher temperature induces the faster increase of the gas pressure. Temperature has a greater impact on the gas migration. As the coal seam gas pressure approaches the setting pressure, the influence of temperature is reduced.

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

The authors declare that they have no conflicts of interest.

This work was supported by the China Postdoctoral Science Foundation (Grant no. 2018M633549), Fundamental Research Funds for the Central Universities (Grant no. 2015XKZD06), and National Natural Science Foundation of China (Grant nos. 51674247 and 51804302).