# Coupled Effects of Stress, Moisture Content and Gas Pressure on the Permeability Evolution of Coal Samples: A Case Study of the Coking Coal Resourced from Tunlan Coalmine

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## Abstract

**:**

_{4}-containing coal samples. Therefore, considering the coupled effects of compressing and infiltrating on the gas permeability of coal could be more accurate to reveal the CH

_{4}gas seepage characteristics in CBM reservoirs. In this study, coal samples sourced from Tunlan coalmine were employed to conduct the triaxial loading and gas seepage tests. Several findings were concluded: (1) In this triaxial test, the effect of confining stress on the permeability of gas-containing coal samples is greater than that of axial stress. (2) The permeability versus gas pressure curve of coal presents a ‘V’ shape evolution trend, in which the minimum gas permeability was obtained at a gas pressure of 1.1MPa. (3) The gas permeability of coal samples decreased exponentially with increasing moisture content. Specifically, as the moisture content increasing from 0.18% to 3.15%, the gas permeability decreased by about 70%. These results are expected to provide a foundation for the efficient exploitation of CBM in Qinshui basin.

## 1. Introduction

^{12}m

^{3}[3]. With respect to CBM extraction, the permeability evolution of gas-containing coal under the in-situ stress should be fully understood before commencing a commercial CBM project. The permeability of coal is influenced by many factors, such as in situ stress, moisture content, gas adsorption and loading/unloading conditions. Normally, the porosity of coal decreases with increasing buried depth, resulting in the low permeability of CBM reservoirs, thus affecting the effective extraction of CBM. Previous studies have indicated that the permeability of CBM reservoirs always presents an exponential decay trend with increasing burial depth [4]. However, some studies showed that coal permeability does not always decrease with the increase of stress, because after the stress increases to a certain degree, the coal body enters the elasto-plastic stage, which results in the generation of new micro-cracks and enhancing its permeability [5]. Therefore, further understanding the influence of stress on the permeability of coal containing water and gas is significant to the exploitation of CBM.

_{4}gas. Pan et al. [6] found that the permeability declined with increasing pore pressure at a constant effective stress. Yin et al. [7,8] established the relationship between permeability and the effective stress of coal under loading/unloading conditions. The results indicated that the permeability of gas-containing coal decreases with the increase of axial stress and confining stress. Conversely, the permeability increases with increasing gas pressure. Yuan et al. [9] pointed out that the permeability first decreases and then increases with increasing CH

_{4}pressure in coal during loading. A turning point was obtained at a gas pressure of around 1.2 MPa. Similarly, Cao et al. [10] found a ‘V’-shaped permeability versus gas pressure curve for outburst-prone coal. Li et al. [11] studied the changes in porosity and permeability of coal samples under various confining pressures. They found that the porosity drops faster than permeability with the increase of confining stress. By filling the coal with Helium gas to measure its permeability, Li et al. [12] found that the coal permeability first decreases and then increases with decreasing pore pressure. Furthermore, when the pore pressure is less than 1.9 MPa, the effective stress and gas slippage effects simultaneously control the coal permeability. Meanwhile, when the pore pressure is greater than 1.9 MPa, the effective stress plays a major role in controlling the coal permeability.

## 2. Theoretical Foundations

_{4}gas mainly migrates by diffusion in the coal matrix, while it migrates by seepage in the pores and fractures of coal. The speed of gas migration by seepage is much greater than that by diffusion. Generally, gas flow in coal pores and fractures obeys Darcy’s law, and the permeability model can be expressed as:

^{−3}μm

^{2}; P

_{0}is the standard atmospheric pressure, 10

^{5}Pa; Q is flow flux, cm

^{3}/s; μ is the dynamic viscosity of CH

_{4}gas, which is determined as 1.08 × 10

^{−5}Pa·s at room temperature; P

_{1}and P

_{2}are inlet and outlet gas pressures, respectively, Pa; l is the length of the sample, cm; A is the cross-sectional area of sample, cm

^{2}.

## 3. Methodology

#### 3.1. Sample Preparation

^{3}/min, and the NO. 8 and NO. 9 coal seams are closely overlapped with a total thickness of about 10 m and with a vertical spacing distance between 0.1 and 2.4 m. The employed coal blocks were taken from the NO. 8 coal seam at a buried depth of more than 800 m. The sourced coal blocks were processed into ISRM suggested samples with a dimension of φ50 mm × 100 mm (Figure 2a). It should be noted that we tried to drill intact coal without cleats during the sampling procedures. Samples were rejected if obvious cleats were found or if a cleat penetrated the coal sample. Finally, 40 samples were made and tested in this study. The basic properties of the coal sourced from the NO. 8 coal seam of the Tunlan coalmine are listed in Table 1 in detail.

#### 3.2. Experimental Apparatus and Methods

_{4}gas into the coal sample. After this has been fully absorbed and desorbed on the coal sample, remove the residual air in pipes and open the outlet and inlet flow valves. Then, measure the gas permeability. (4) Close the outlet flow valve and finish a test. (5) Repeat step 1 to step 4 for the remaining coal samples to complete all tests. Overall, the confining stress in these tests varies from 2 to 8 MPa, and the gas pressure varies from 0.5 to 1.4 MPa.

## 4. Results and Discussion

#### 4.1. Effect of Axial Stress on the Gas Permeability of Coal Samples

^{−5}μm

^{2}and 0.6 × 10

^{−5}μm

^{2}, respectively.

#### 4.2. Effect of Confining Stress on the Gas Permeability of Coal Samples

#### 4.3. Coupled Effects of Axial and Confining Stresses on the Gas Permeability of Coal Samples

^{2}fitted by the exponential function are all higher than 0.977. The average values of the fitting parameter a for the permeability–axial stress and permeability–confining stress curves were 2.20442 and 3.53507, respectively. The average values of the fitting parameter b were −0.054285 and −0.08749, respectively. Therefore, it can be concluded that the influence of confining stress on the permeability of gas-containing coal samples is greater than that of axial stress.

#### 4.4. Effect of Gas Pressure on the Gas Permeability of Coal Samples

^{−5}μm

^{2}, 0.2 × 10

^{−5}μm

^{2}, 0.35 × 10

^{−5}μm

^{2}and 0.25 × 10

^{−5}μm

^{2}, respectively. Therefore, an obvious inflection point at a gas pressure of 1.1 MPa can be concluded.

#### 4.5. Effect of Moisture Content on the Gas Permeability of Coal Samples

^{−5}μm

^{2}to 1.039368 × 10

^{−5}μm

^{2}with an increase in moisture content from 0.18% to 3.15%, which represents a decrease of 69%. Therefore, it can be easily concluded that the permeability of gas-containing coal can be significantly limited by increasing its moisture content. This is because the drilled coal is relatively hydrophilic, and water/vapor is adsorbed on the surface of coal particles, thus occupying the internal pore/fracture structures of coal body.

^{−5}μm

^{2}; a and b are fitting parameters, w is the moisture content of coal.

_{4}gas drainage, the permeability can be evaluated by the proposed fitting equations. These results could help predict gas emission amounts and for developing reasonable gas extraction plans.

## 5. Conclusions

_{4}gas outburst disasters. In this study, the WYS-800 triaxial gas seepage apparatus was employed to investigate the evolution of gas permeability in the Tunlan coal samples under various stresses, moisture contents and gas pressures. The following conclusions can be drawn:

- (1)
- The permeability of coal samples first decreases and then increases with increasing axial stress, which corresponds to the compressed sealing and failing effects of coal samples under the triaxial compression test. The permeability of coal samples always decreases with increasing confining stress in a negative exponential manner. Furthermore, in our triaxial test, the inhibition impact of confining stress on the permeability of coal samples was greater than that of axial stress.
- (2)
- Similarly, the permeability of coal samples first decreases and then increases with increasing gas pressure, which may be a result of the Klinkenberg effect. The lowest permeabilities of Tunlan coal samples were observed at a gas pressure of 1.1 MPa.
- (3)
- Water or vapor could be adsorbed onto the surface of the coal particles and occupy the internal pore/fracture structures of the coal body, leading to a negative exponential decreasing trend in permeability. For the employed Tunlan coal samples, the coal permeability decreased by about 70% with an increase in moisture content from 0.18% to 3.15%.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Sample preparation setups. (

**a**) Line cutting machine; (

**b**) coal samples; (

**c**) drying oven; (

**d**) water injection apparatus.

**Figure 4.**Gas permeability versus axial stress curves of coal (

**a**) and coal samples after failure (

**b**).

**Figure 5.**Gas permeability–confining stress curves of coal with viable moisture contents (0.18%–3.15%) and gas pressures (0.5MPa (

**a**), 0.8MPa (

**b**), 1.1MPa (

**c**) and 1.4MPa (

**d**)).

**Figure 6.**Coupled effects of axial stress (

**a**) and confining stress (

**b**) on the gas permeability of coal.

**Figure 8.**Effect of moisture content on the permeability of compressed gas-containing coal. (

**a**) confining stress 2 MPa; (

**b**) confining stress 4 MPa; (

**c**) confining stress 6 MPa; (

**d**) confining stress 8 MPa.

Properties | Detail | Unite | Value |
---|---|---|---|

Physical | Density, ρ | g/cm^{3} | 1.32 |

Porosity, φ | % | 2.86 | |

Mechanical | Tension strength, τ | MPa | 1.29 |

Uniaxial compression strength, σ_{c} | MPa | 10.1 | |

Elastic modulus, E | GPa | 5.1 | |

Poisson’s ratio, v | N/A | 0.33 | |

Cohesive strength, c | MPa | 1.83 | |

Internal friction angle, φ_{o} | ° | 35 | |

Proximate analysis | Air-dried moisture, M_{ad} | % | 1.61 |

Dry base ash, A_{ad} | % | 6.86 | |

Dry ash-free volatiles, V_{daf} | % | 26.09 | |

Gas parameters | Gas content | ${m}^{3}/t$ | 8.631–15.49 |

Absorption constant, a | ${\mathrm{cm}}^{3}/{\mathrm{g}}_{daf}$ | 23.12 | |

Absorption constant, b | ${\mathrm{MPa}}^{-1}$ | 1.08 |

NO. | Axial Stress ${\mathit{\sigma}}_{\mathit{v}}$/MPa | Confining Stress ${\mathsf{\sigma}}_{\mathbf{h}}$/MPa | Fitting Equation | R^{2} |
---|---|---|---|---|

$\mathit{K}=\mathit{a}{\mathit{e}}^{\mathit{b}\mathit{\sigma}}$ | ||||

1 | 2, 4, 6, 8 | 6 | $K=2.39567{e}^{-0.05282{\sigma}_{v}}$ | 0.97712 |

2 | 2, 4, 6, 8 | 8 | $K=2.01317{e}^{-0.05575{\sigma}_{v}}$ | 0.99075 |

3 | 8 | 8, 10, 12, 14 | $K=3.63198{e}^{-0.08550{\sigma}_{h}}$ | 0.98421 |

4 | 10 | 8, 10, 12, 14 | $K=3.43816{e}^{-0.08948{\sigma}_{h}}$ | 0.99241 |

NO. | Confining Stress/MPa | CH4 Pressure/MPa | Fitting Equation | R^{2} |
---|---|---|---|---|

$\mathit{K}=\mathit{a}{\mathit{e}}^{\mathit{b}\mathit{w}}$ | ||||

1 | 2 | 0.5 | $K=4.42076{e}^{-0.31086w}$ | 0.99069 |

2 | 2 | 0.8 | $K=3.73810{e}^{-0.29813w}$ | 0.98118 |

3 | 2 | 1.1 | $K=3.03553{e}^{-0.44614w}$ | 0.99296 |

4 | 2 | 1.4 | $K=3.31513{e}^{-0.39121w}$ | 0.98668 |

5 | 4 | 0.5 | $K=3.96484{e}^{-0.34131w}$ | 0.96775 |

6 | 4 | 0.8 | $K=3.25065{e}^{-0.32497w}$ | 0.96543 |

7 | 4 | 1.1 | $K=2.51570{e}^{-0.42524w}$ | 0.98817 |

8 | 4 | 1.4 | $K=2.66752{e}^{-0.36704w}$ | 0.9905 |

9 | 6 | 0.5 | $K=3.61192{e}^{-0.34790w}$ | 0.94446 |

10 | 6 | 0.8 | $K=2.82434{e}^{-0.36339w}$ | 0.99271 |

11 | 6 | 1.1 | $K=2.18501{e}^{-0.48835w}$ | 0.98134 |

12 | 6 | 1.4 | $K=2.40452{e}^{-0.37905w}$ | 0.98305 |

13 | 8 | 0.5 | $K=3.14023{e}^{-0.34455w}$ | 0.93777 |

14 | 8 | 0.8 | $K=2.36980{e}^{-0.34400w}$ | 0.96184 |

15 | 8 | 1.1 | $K=1.76251{e}^{-0.46914w}$ | 0.97761 |

16 | 8 | 1.4 | $K=2.01755{e}^{-0.40367w}$ | 0.98748 |

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**MDPI and ACS Style**

Li, G.; Wang, Y.; Wang, J.; Zhang, H.; Shen, W.; Jiang, H.
Coupled Effects of Stress, Moisture Content and Gas Pressure on the Permeability Evolution of Coal Samples: A Case Study of the Coking Coal Resourced from Tunlan Coalmine. *Water* **2021**, *13*, 1653.
https://doi.org/10.3390/w13121653

**AMA Style**

Li G, Wang Y, Wang J, Zhang H, Shen W, Jiang H.
Coupled Effects of Stress, Moisture Content and Gas Pressure on the Permeability Evolution of Coal Samples: A Case Study of the Coking Coal Resourced from Tunlan Coalmine. *Water*. 2021; 13(12):1653.
https://doi.org/10.3390/w13121653

**Chicago/Turabian Style**

Li, Guofu, Yi Wang, Junhui Wang, Hongwei Zhang, Wenbin Shen, and Han Jiang.
2021. "Coupled Effects of Stress, Moisture Content and Gas Pressure on the Permeability Evolution of Coal Samples: A Case Study of the Coking Coal Resourced from Tunlan Coalmine" *Water* 13, no. 12: 1653.
https://doi.org/10.3390/w13121653