A Study on the Mechanical Mechanism of Injection Heat to Increase Production of Gas in Low-Permeability Coal Seam
Abstract
:1. Introduction
2. Coal and Rock Damage-Heat-Gas-Solid Multi-Field Coupling Theory
2.1. Damage and Deformation Control Equation of Coal and Rock Mass
2.2. Effective Stress Theory of Coal Containing Gas
2.3. Damage and Deformation Control Equation of Coal Containing Gas
2.4. Migration Theory of Gas in Coal Seam
2.4.1. Gas Content Equation in Coal Seam
2.4.2. Control Equation of Gas Migration
Fick Diffusion Equation
Knudsen Diffusion Equation
Nonlinear Seepage Equation
2.4.3. Continuity Equation of Gas Migration in Coal Seam
2.5. Control Equation of Temperature Field of the Coal Containing Gas
2.6. Evolution Mechanism of Permeability of Damaged Coal Mass
2.7. Heat-Gas-Solid Coupling Model of Damaged Coal Seam
3. Numerical Solution of Damage-Heat-Gas-Solid Coupling Model of Coal and Rock Mass
3.1. Finite Element Equation for Calculating the Damage and Deformation of Coal and Rock
3.1.1. Calculation of Equivalent Nodal Load
3.1.2. Calculation of Damage Stiffness Matrix of Coal and Rock
3.2. Finite Element Equation of Temperature Field of Coal Containing Gas
The Finite Element Equation of the Transient Temperature Field
3.3. Finite Element Equation of Gas Seepage
4. Numerical Simulation of Gas Drainage by Borehole Injection Heat
4.1. Numerical Model
4.2. Effect of Heat Injection Temperature on Gas Production Efficiency
4.3. The Influence of Injection Heat Temperature on the Distribution of Gas Pressure
4.4. Effects of theThermal Expansion Coefficient on Gas Production
5. Conclusions
- (1)
- When considering the effects of the temperature, the gas migration and the redistribution of mining stress comprehensively, this paper proposes using the effective strain field to define the damage field of the coal body. This variable is a quantitative description for the degree of coal rupture and damage. A new mathematical model of coal damage-heat-gas-solid multi-field coupling is developed.
- (2)
- Based on the multi-physical field coupling theory that was established in this paper, according to the numerical solution method, the finite element source program is developed twice by using FORTRAN language, and the multi-field coupling analysis program is compiled when considering temperature, gas seepage, damage, and deformation of coal and rock. Subsequently, it was applied for the analysis of borehole thermal stimulation for coal-bed methane mining. The results show that, when the injection heat temperature increased from 350 K to 400 K, the rate of gas production and total gas production increased by more than 110% and 90%, respectively. As gas drainage is carried out, the efficiency of gas production is gradually increased. When the drainage time changed from 30 d to 90 d, the total gas production increased from 90% to 110%, and the amount of gas production significantly increased.
- (3)
- The thermal stimulation of boreholes caused the rise of coal seam temperature, which promoted the decrease of gas pressure and the increase of the effective extraction radius of boreholes. For example, when the gas is extracted for 60 days, the effective extraction radius without heat injection is 1.31 m. When the injection temperatures are 350 K, 375 K, and 400 K, the effective extraction radius are 1.38 m, 1.395 m, and 1.41 m, respectively. The thermal expansion coefficient of coal seam has significant effect on the gas production rate of coal-bed methane. The main reason is that the thermal expansion coefficient changes the effective stress of coal body and the inward thermal expansion deformation of coal pores. The former factor makes the permeability of coal seam increase first and then decrease, while the latter makes the permeability of coal seam decrease first and then increase, resulting in the trend that the gas production rate first decreases and then increases.
- (4)
- In this paper, the effect of coal fracture and damage on the deformation of solid structure and gas migration is investigated, and the paper has made great progress when compared with previous studies. This paper utilizes the damage variable to describe the development of coal fracture since the finite element theory adopted is based on the continuous mechanics. Whereas, the development and expansion of multiple fractures of coal body under the action of multiple physical fields cannot be accurately studied. To simplify the mechanical model, the gas-liquid two-phase flow that occurred during the heat injection process has not been considered, which poses a great challenge to our future work.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Different temperature | Model 1:350 K |
Model 2:375 K | |
Model 3:400 K | |
Different coefficient of thermal expansion | Model 1:1 × 10−7 K−1 |
Model 2:5 × 10−7 K−1 | |
Model 3:1 × 10−6 K−1 |
Strata Formation Name | Thickness h /m | Elastic Modulus E /GPa | Poisson Ratio | Internal Cohesion /MPa | Internal Friction angle /(°) | Tensile Strength /MPa | Density /kg·m3 |
---|---|---|---|---|---|---|---|
roof | 8 | 5.89 | 0.16 | 3.2 | 40.9 | 3.7 | 2721 |
Coal seam | 1.8 | 2.4 | 0.29 | 0.2 | 20 | 0.28 | 1450 |
foundation | 12 | 5.89 | 0.16 | 3.2 | 40.9 | 3.7 | 2721 |
Lengthvariable | 1 m = 3.281 feet |
Gas production | 1 m3 = 1000 L = 6.29 bbl |
Temperature | 1 K = 1 °C + 273.15 |
Quality | 1 t = 1000 kg |
Permeability | 1 m2 = 1.013 × 1015 md |
Pressure | 1 MPa = 106 Pa |
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Cheng, H.; Zhang, N.; Yang, Y.; Peng, W.; Chen, H. A Study on the Mechanical Mechanism of Injection Heat to Increase Production of Gas in Low-Permeability Coal Seam. Energies 2019, 12, 2332. https://doi.org/10.3390/en12122332
Cheng H, Zhang N, Yang Y, Peng W, Chen H. A Study on the Mechanical Mechanism of Injection Heat to Increase Production of Gas in Low-Permeability Coal Seam. Energies. 2019; 12(12):2332. https://doi.org/10.3390/en12122332
Chicago/Turabian StyleCheng, Hongmei, Ning Zhang, Yugui Yang, Weihong Peng, and Heng Chen. 2019. "A Study on the Mechanical Mechanism of Injection Heat to Increase Production of Gas in Low-Permeability Coal Seam" Energies 12, no. 12: 2332. https://doi.org/10.3390/en12122332