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To accurately and reliably predict the time of spontaneous combustion of fractured coal around a borehole induced by gas drainage along the seam, this study performed an orthogonal test taking the No. 10 Coal Mine of Pingdingshan as the research object, in terms of the suction negative pressure and coal seam buried depth. COMSOL Multiphysics was used to model the orthogonal test results, and a multielement statistical analysis of four factors and their relationships with the spontaneous combustion of coal around the borehole and a single-factor analysis in line with the site conditions were performed on the modeling results through multiple regression. The results showed a nonlinear regression relationship between the sealing hole length, sealing hole depth, negative pressure, and coal seam depth and the spontaneous combustion of the coal around the gas drainage borehole; the prediction regression model is significant. Taking the field gas drainage in the No. 10 Coal Mine of Pingdingshan as an example, the relationship between the time of spontaneous combustion of gas drainage and the drainage pressure follows a power of two. When the drainage negative pressure is less than 45 kPa, the coal around the borehole is more likely to undergo spontaneous combustion with increasing pressure, and the sealing hole length has a positive linear correlation with the time of spontaneous combustion of the coal around the borehole. When the sealing hole length is 23 m, the time of spontaneous combustion of the coal around the gas drainage hole is >500 days, and the coal around the borehole does not easily undergo spontaneous combustion. When the sealing depth is 15 m, the time of spontaneous combustion of the coal around the gas drainage hole is 76 days, which is most likely to cause spontaneous combustion.

Coal is a basic form of energy in China, and gas leakage has been the main factor threatening the safety of coal production with increasing mining depth. Bedding gas drainage is an important method for solving the problem of gas leakage at the mining face. The mainly used methods to improve the gas drainage efficiency include enlarging the borehole diameter [

Accurately predicting the temperature [_{2} concentration as the indicator. Gao et al. [

In summary, several studies have been conducted on the time of spontaneous combustion in the gob and coal seam [

The No. 10 Mine of Pingdingshan is located in the northeast of Pingdingshan City, approximately 6 km from the downtown center. The mine field is approximately 6.0 km long in the north–south direction and 2.0–4.7 km wide in the east–west direction. The operation of the No. 10 Mine was commenced in August 1958, with an annual production capacity of 1.2 million tons and a service life of 68 years. The mining method includes advancing the mining area, backward section, up and down of the mountain layout of the long wall roof, and full caving. The mining method is fully mechanized mining. The main mining coal seam is the No. 15 coal seam, and the second group coal seam is mainly distributed in the 24070, 24100, and 24130 mining faces with buried depths of approximately 635, 981, and 1239 m, respectively. The gas pressure is in the range of 0.1–1.85 MPa, the gas content is in the range of 2.15–20.0374 m^{3}/t, the permeability of the coal seam is 0.0019 mD, and the attenuation coefficient is 0.068 D^{−1}.

The spontaneous combustion of coal around the borehole induced by gas drainage is affected not only by geological factors, mining technology, coal quality, and ventilation mode, but also by the gas drainage technology and hole sealing parameters [

Although gas drainage-induced spontaneous combustion of coal is affected by internal factors, external factors can be decisive in that they determine whether the coal around the gas drainage borehole will undergo a spontaneous combustion. In the gas drainage process, an excessively high negative pressure can reduce the gas concentration in the borehole, increase the energy loss, and easily result in a spontaneous combustion of the coal around the borehole. If the negative pressure is too low, the gas drainage concentration in the borehole is reduced, the drainage period is increased, and the probability of spontaneous combustion around the borehole is increased. A too short sealing hole length can cause the gas in the roadway to enter the drainage borehole, reduce the amount of gas drainage, and cause the surrounding coal to undergo spontaneous combustion. If the sealing hole length is too long, it increases the difficulty of sealing the hole in terms of the time required and the complexity of the parameters involved, which reduces the work efficiency. When the hole sealing depth is too large, the plugging section exceeds the peak stress value, and some coal seams are around the plugging section, resulting in a blind area in the gas drainage process. When the sealing length is too small and the sealing section of the drainage hole is located within the plastic zone of the roadway, the surrounding coal body is broken to a higher degree. In the drainage process, the gas concentration is easily diluted by the gas flowing into the drainage hole through the plastic zone, and it is easy to cause a spontaneous combustion of the coal body around the plugging section.

Based on the above analysis, to study the influence of gas drainage on the spontaneous combustion of coal around the borehole, the CO concentration was detected in three boreholes adjacent to the 24070, 24100, and 24130 working faces of Pingdingshan No. 10 Mine. The detection results were then averaged to obtain the relationship between the average CO concentration in the borehole and the gas drainage time, as shown in Figure

Variation in CO concentration with time in the different mining faces.

The spontaneous combustion of coal around the borehole can be reflected by monitoring the CO concentration. Figure

To study the influence of the sealing parameters on the spontaneous combustion of coal around the borehole, eight experimental boreholes with different sealing parameters were designed in the 24130 working face. The specific sealing parameters of the 1# and 2# boreholes are (15, 6), those of the 3# and 4# boreholes are (15, 8), those of the 5# and 6# boreholes are (23, 8), and those of the 7# and 8# boreholes are (23, 10). Here, (15, 8) means that the hole sealing depth is 15 m and that the hole sealing length is 8 m. The CO concentration in the gas drainage borehole was detected within 40 days; Figure

Change curve of average CO concentration in a single borehole under different sealing parameters.

As shown in Figure

Typically, if the negative pressure applied during coal seam drainage is constant, to reflect the different drainage from the coal body around the drilling holes under negative pressure changes over time, we conducted a simulation based on COMSOL software on the 24130 mining face under a hole sealing depth of 18 m, sealing hole length of 10 m, and drainage pressures of 15, 20, 23, 28, and 35 kPa to study the spontaneous combustion situation around the borehole. Figure

Relationship between maximum temperature of coal around the drilling hole and the drainage time under different negative pressure conditions.

Based on the different negative pressures of field pumping, sealing parameters, and buried depth of the mining face, orthogonal tests at four levels were set for the four factors. Table

Parameters and their values.

Serial number | Negative pressure drainage (_{1}/kPa) | Sealing length (_{c}/m) | Sealing depth (_{s}/m) | Seam temperature (K) |
---|---|---|---|---|

1 | 18 | 6 | 15 | 308.15 |

2 | 23 | 8 | 18 | 312.15 |

3 | 30 | 10 | 20 | 316.15 |

4 | 35 | 13 | 23 | 321.15 |

Spontaneous combustion time.

Serial number | Negative pressure drainage (kPa) | Sealing length (m) | Sealing depth (m) | Seam temperature (K) | Time (d) |
---|---|---|---|---|---|

1 | 23 | 10 | 23 | 321.15 | 250 |

2 | 23 | 8 | 18 | 308.15 | 109 |

3 | 35 | 8 | 20 | 316.15 | 66 |

4 | 35 | 13 | 23 | 308.15 | 551 |

5 | 35 | 6 | 18 | 321.15 | 39 |

6 | 18 | 8 | 23 | 312.15 | 401 |

7 | 35 | 10 | 15 | 312.15 | 76.5 |

8 | 18 | 6 | 15 | 308.15 | 83 |

9 | 30 | 10 | 20 | 308.15 | 145 |

10 | 30 | 13 | 18 | 312.15 | 151 |

11 | 23 | 13 | 15 | 316.15 | 98 |

12 | 23 | 6 | 20 | 312.15 | 82 |

13 | 18 | 13 | 20 | 321.15 | 594 |

14 | 30 | 8 | 15 | 321.15 | 60 |

15 | 30 | 6 | 23 | 316.15 | 69 |

16 | 18 | 10 | 18 | 316.15 | 164 |

The 16 groups of orthogonal experimental results listed in the table were simulated using COMSOL Multiphysics software; Figure

Simulation results under different scenarios. (a) 2. (b) 4. (c) 6. (d) 8. (e) 10. (f) 12.

Relevant experiments were carried out based on the orthogonal experimental design, and 16 groups of experimental data were simulated to obtain the time required for the temperature of the coal around the borehole to reach 70°C. Because of the number of experiments, cloud maps could not be attached individually. Figure

In practice, the regression equation expressing the functional relationship between the variables should be accurately established. If there are a large number of variables in the regression equation or if there is a certain degree of similarity between the variables, this will decrease the degree of freedom of the regression equation due to estimate increase and have a certain influence on the accuracy of the regression equation. Therefore, to establish an optimal regression equation, it is necessary to filter variables that have significant influence on the independent variables.

The regression methods include forward, backward, and step-by-step regression methods. Each method has its own advantages and disadvantages; however, the step-by-step regression method is the most convenient and can be used to quickly conduct a regression analysis of the variables. With the step-by-step regression method applied to construct an optimal regression equation, we can obtain the optimal solution.

If

A standardized regression equation for

The maximum partial regression

As listed in Tables

The new variables obtained from the normalization of the variables are denoted by

The set of data obtained by the nonlinear data transformation of the new variable is

The variables were introduced and eliminated according to the principle of the F test where

Entered/removed variables.

Model | Input variable | Removed variable | Methods |
---|---|---|---|

1 | _{P}_{Tc} | Step (input | |

2 | _{P}^{2} | Step (input | |

3 | _{Fs} | Step (input | |

4 | _{P} | Step (input | |

5 | _{Fc} | Step (input | |

6 | _{P}_{Tc}. | _{P}_{Tc} | Step (input |

7 | _{Tc}^{2} | Step (input | |

8 | _{Fs}_{Tc} | Step (input |

In Step 8, the results of each parameter are listed in Table

Model variances.

Model | ^{2} | Adjusted ^{2} | Error in standard estimation | Change in the statistical metrics | |||
---|---|---|---|---|---|---|---|

^{2} variation | Degrees of freedom 1 | ||||||

1 | 0.634^{a} | 0.402 | 0.359 | 0.80064328 | 0.402 | 9.400 | 1 |

2 | 0.741^{b} | 0.549 | 0.479 | 0.72164473 | 0.147 | 4.233 | 1 |

3 | 0.817^{c} | 0.667 | 0.584 | 0.64475177 | 0.119 | 4.286 | 1 |

4 | 0.867^{d} | 0.751 | 0.660 | 0.58278835 | 0.083 | 3.687 | 1 |

5 | 0.904^{e} | 0.817 | 0.726 | 0.52346855 | 0.066 | 3.634 | 1 |

6 | 0.904^{f} | 0.817 | 0.750 | 0.49992426 | −0.001 | 0.033 | 1 |

7 | 0.934^{g} | 0.872 | 0.808 | 0.43806416 | 0.055 | 4.326 | 1 |

8 | 0.955^{h} | 0.912 | 0.853 | 0.38307345 | 0.040 | 4.077 | 1 |

In the process of model building and stepwise regression, a standardized residual analysis was carried out by default using the SPSS software, and the histogram and normal probability diagrams of the standardized residual were drawn. As shown in Figure

Histogram and P–P diagram of simulation results. (a) Histogram. (b) P–P figure.

The eight-step regression process is also where the variables are introduced and removed, where the first correlation test of the variables is conducted, and where the coefficients are generated. Finally, the coefficients of the relevant variables are obtained from Model 8. Given the length constraints, only the coefficients of Step 8 are listed in Table

Coefficients of the relevant variables.

Model | Unnormalized coefficient | Normalized coefficient | Significance | |||
---|---|---|---|---|---|---|

Standard error | Beta | |||||

8 | (Constant) | −0.797 | 0.202 | −3.953 | 0.003 | |

_{P}^{2} | 0.558 | 0.144 | 0.383 | 3.876 | 0.004 | |

_{Fs} | 0.549 | 0.099 | 0.549 | 5.555 | 0.000 | |

_{P1} | −0.367 | 0.106 | −0.367 | −3.457 | 0.007 | |

_{Fc} | 0.494 | 0.101 | 0.494 | 4.898 | 0.001 | |

_{Tc}^{2} | 0.292 | 0.123 | 0.235 | 2.378 | 0.041 | |

_{Fs}_{Tc} | −0.225 | 0.112 | −0.218 | −2.019 | 0.074 |

As listed in Table

The variables in (

Fitting equation (

To study the influence of a single factor on the drilling spontaneous ignition time, a control variable method is adopted to control three factors, and only the influence of the single factor on the drilling spontaneous ignition time is studied. The coal seam ground temperature of the 24130 mining face in the field is generally 321.15 K. Therefore, we only analyzed and studied the influences of the suction negative pressure, hole sealing length, and hole sealing depth on the ignition time of the drilling holes.

To analyze the influence of suction negative pressure _{1} on the spontaneous ignition time

With (

Influence of pumping negative pressure on the natural ignition time of borehole.

To analyze the influence of hole sealing length

With (

Influence of sealing length on the natural ignition time of borehole.

To analyze the influence of sealing depth on the spontaneous ignition time of the drilling holes, the suction negative pressure, sealing hole length, and ground temperature were fixed to study the influence rule. Based on the sealing parameters determined by the simulation analysis and field tests, the negative pressure of pumping was −23 kPa, the sealing length was 10 m, and the ground temperature was 321.15 K. Substituting the known conditions into (

Using (

Influence of sealing depth on natural ignition time of borehole.

In view of the lack of current methods for determining the spontaneous combustion time of broken coal around the borehole induced by bedding gas drainage, a multiple stepwise regression method based on a combination of orthogonal test and numerical simulation was proposed to predict the time pattern of the spontaneous combustion of coal around the borehole.

We plotted the nonlinear regression relationship between four factors, namely the sealing hole length, sealing hole depth, suction negative pressure, and coal seam depth, and the spontaneous combustion time of coal around the borehole fissure. The sealing length and depth of the holes were found to have a linear positive correlation with the spontaneous ignition time of the drilling holes, whereas the negative pressure of pumping and ground temperature had a quadratic negative correlation.

Taking the actual gas drainage situation at the 24130 mining face of the No. 10 Mine of Pingdingshan as an example, we derived an equation relating the gas drainage negative pressure with the natural combustion time of the borehole:

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

There are no conflicts of interest regarding the publication of this paper.

The authors would like to thank Rodrigo Cabanero for its linguistic assistance during the preparation of this manuscript. This work was supported by the National Key R&D Plan Key Special Funding Project (grant no. 2018YFC0807900), the China Coal Technology & Engineering Group Co., Ltd. (2019-2-ZD003), the National Natural Science Foundation Youth Project of China (grant no. 51804161), the National Natural Science Foundation of China (grant no. 52074156), and China Postdoctoral Science Foundation (2020M680490).