# Modeling of Coalmine Methane Flows to Estimate the Spacing of Primary Roof Breaks

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

_{4}).

_{3}CJSC “Mine named after. A.F. Zasyadko” (development depth exceeded 1300 m, longwall length of 300–305 m) during the mining of the 18th eastern longwall. A series of 3 wells with different parameters of spatial orientation (“pads”) were sunk at a frequency of 20–25 m, while in each pad, there were two wells (No. 2 and No. 3) oriented to the overlying massif (with re-drilling of gas-bearing sandstone) and one “axial” (No. 4, with a zero turn), or “on the goaf” (No. 4). To assess the features of methane emission flows, two types of wells were selected—type No. 2 and No. 4 due to the fact that the angle of their turn to the bottom of the longwall was the same (β = 60°). Moreover, the ascent angles relative to the horizon were also equal (α = 60°, Figure 1), which determines the similarity in the development of deformation processes in the conditions of the previously undermined massif and the beginning development of reserves.

^{2}), was used in the first stage—the selection of filtering/smoothing parameters according to the method given in [39]. In contrast to the criteria approach [40], artificial neural networks (ANN) [41], the multivariate regression method (with the application of SPSS software) [42], or the finite element method (FEM) [43], further, already smoothed data (on a distributed grid) were interpolated similarly to the study [39], after which the parameters of high-degree polynomials were selected (regression) by the method of least squares. The algorithms were first written in “Vi Improved” (version 9.0, open-source software from Bram Moolenaar, Holland) in Python (version 2.7.10., Python Software Foundation, DE, USA). To improve the quality of modeling at each stage, the residuals on the projections (Z = ƒ(X;Y)) were analyzed, and the presentation of graphical results (vectorization) was programmed in the “gnuplot” program (version 5.4, Thomas Williams & Colin Kelley). To assess the quality of the final models, at the last stage, quantile–quantile (Q-Q) plots were additionally built in MS Excel.

_{4})—well type No. 2—and 261 points—type No. 2 (due to the fact that wells in goaf were drilled through one picket). The “data set” fragment is presented in Table 1.

## 3. Results

_{3}seam is shown in Figure 3.

_{4}≥ 60% (the area limited by the black curve) from −120 to −30 m before the stope.

_{4}= 100–90%, the area bounded by the dark yellow curve) can be traced from −120 to −40 m, followed by its sharp decrease from −38 to −14 m (from 80 to 40%), which is replaced by a more gentle decline to −4 m (from 40 to 30%). Stabilization and constancy of the methane concentration = 30%, which began −4 m ahead of the longwall, continues up to 50 m behind it, while this trend does not change during the first 63 m (S = 1320 m) of the longwall. When the stoping face line approaches the mark S = 1320 m, up to S = 1268 m, the area of the local maximum decreases from the area −120 to −43 m to the area −106 to −98 m. Further, the area of the maximum concentration disappears and begins to be traced only from the range S = 1218–1165 m, at distances from −120 to −110 m to −60 to −43 m ahead of the longwall. Behind the longwall of the studied area, it does not exist up to S = 1197, while it is localized at the level L = 50 m. With subsequent mining of the reserves, the area of the local maximum gradually increases in size. It reaches its maximum expansion (L = from 30 to 50 m) at S = from 1180 to 1160 m relative to the beginning of the extraction column. Further, from S = 1160, the studied area sharply decreases and shifts again to L = 50 m at S = 1140 m.

_{4}≥ 60%), starting from S = 1320 m, is removed relative to the distance to the bottom hole (L = −110 to −85 m) and decreases in size, after which, up to S = 1220 m, the size and localization of this zone remain stable. A very interesting mining area is S = 1218–1200 m, which is characterized by the presence of CH

_{4}≥ 60% for any distance from the stope, both in front and behind the longwall. After S = 1200 m, the zone is removed relative to the distance to the face L = from −120 to −10 m and decreases in size L = from −120 to −53 m in front of the longwall at S = 1140 m.

_{4}≤ 20%, limited by the orange curve in Figure 3) begins to form from 1310 m from the beginning of the extraction column at L = −28 m in front of the longwall and gradually expands in size. The maximum width of the region (L = from −60 to −8 m) is traced at S = 1250 m, after which it sharply narrows to a point (S = 1240 m L = −35 m). Further, the area of the minimum concentration disappears and begins to be traced only from S = 1183 m, at a distance of −11 m in front of the longwall. The maximum width of the region (L = from −37 to 7 m) is traced at S = 1162 m, after which it sharply narrows to a point (S = 1140 m L = −15 m). Behind the longwall, this area is essentially absent.

^{2}= 0.97):

- -
- The definition domain of the points (orthogonality interval of the approximating polynomials) corresponds to S = S′ for all S′ ∈ [0, π] and L = L′ for all corresponds to S = S′ for all S′ ∈ [0, π] and L = L′ for all L′ ∈ [0, π].

_{3}seam are shown in Figure 4.

_{4}≥ 60%) begins from points S = 1323 m and L = 4 m behind the longwall. The maximum width of the region (L = from −6 to 15 m) is traced at S = 1305 m, after which sharp narrowing to a point (S = 1298 m L = from 2 m) is observed. Further, insignificant dimensions of the studied zone begin to be traced only from the range S = 1197–1194 m, at distances from −12 to −9 m ahead of the longwall. Subsequently, behind the longwall, the zone begins to form from 1172 m from the beginning of the site at L = −50 m in front of the longwall and gradually expands in size. The maximum width of the region (L = from 20 to 50 m) is observed at S = 1140 m, after which it sharply narrows to a width of L = from 33 to 50 m at S = 1120 m.

_{4}≥ 60%), starting from S = 1340 m, is stably traced at a distance L = −10 m in front of the longwall and in the entire range L = 0–50 m behind it (which means the width of the area is 60 m) to the picket S = 1298 m. Subsequent mining of the reserves leads to a decrease in the width of the area to the point S = 1261 m L = 5 m. Of particular interest is the area of the extraction column S = 1260–1218 m, which is characterized by the presence of CH

_{4}≤ 60% for any distance from the stoping face, both in front of and behind the longwall. Moreover, several zones of the “local minimum” are dispersed on one line in this range. Further, the area of high productivity of degassing begins from the point (S = 1218 m; L = −13 m), expanding sharply up to 50 m behind the longwall (starting from S = 1208 m) and up to −34 m in front of the longwall (S = 1200 m). Further, ahead of the longwall, there is a slight decrease in the width of the zone of high methane content, followed by stabilization at a value of L = −25 m, from S = 1168 m to S = 1120 m.

_{4}≤ 20%) in front of the longwall can be traced from a picket of 1340 m, at a distance L = from −120 to −18 m and gradually decreasing (at the first stage) in size to S = 1278 m (L = from −120 to −35 m). Further, the area expands to maximum values of −120 to −13 m at picket 1239 m, after which the width of the area again begins to decrease to minimum values (L = from −120 to −84 m) at S = 1200 m. In the last stage, the growth and stabilization of the zone width up to L = from −120 to −39 m after the picket = 1168 m is typical. Behind the longwall, the area of the local minimum begins to form from 1260 m from the beginning of the excavation column to 50 m ahead of the longwall and gradually expands in size. The maximum width of the region (L = 20 to 50 m) is traced at S = 1239 m, after which it sharply narrows to a point (S = 1220 m L = 50 m).

## 4. Discussion

## 5. Conclusions

- Deformation-wave processes in geo-environments produce cyclic non-linearities in the nature of the air–gas regime of mine methane emissions into anthropogenic rock masses, while only a part of the gas flows is captured by the degassing network in the extraction area.
- It has been established for the first time that a decrease in the distance of the stoping face line from the start of mining of the extraction column S = from 1340 to 1120 m and the distance in front of the longwall L = from −120 to 0 m leads to undulating changes in gas release (in wells No. 2), according to a polynomial dependence.
- The influence of situational geomechanical conditions of reserve mining on the area and the shape of the local extrema of the models was clarified. These models are transformed in proportion to the development of the stoping front and are displaced at certain angles to the alignment with the longwall.

_{3}seam mining in Donbass. The main constraints include a development depth of 1250–1350 m, natural methane content of 23 m

^{3}/t dry ash-free mass and above, a coal seam thickness of 1.3–1.55 m, (the main limiting mining and technical factor) a rock temperature that exceeds 41 °C.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**The sink scheme of wells of various types in the excavation area: 1—gray sandstone; 2—dark gray siltstone; 3—mudstone; 4—seam m

_{3}; 5—mined-out space of previously worked out longwall; 6—bi-support; 7—belt road of 17th eastern longwall; 8—contour deformations; 9—casing; 10—air drift of 18th eastern longwall.

**Figure 2.**The distribution of methane concentration in the previously mined rock mass during reverse development of the m

_{3}seam (according to well type No. 2): L is the distance to the stopping face line of the 18th eastern longwall, m; S is remoteness of the face of the 18th eastern longwall relative to the beginning of the extraction column (pickets), m; P is main roof span, at a different point in time; CH

_{4}is the concentration of methane in the extracted mixture, %.

**Figure 3.**Evolution of the intensity of emission flows of coalmine methane during reverse mining of the m

_{3}seam (according to data from wells type No. 4).

**Figure 5.**Scatter of modeling residuals (M) in relation to experimental data (O) for well type No. 2.

N | Wells No. 4 | Wells No. 2 | ||||
---|---|---|---|---|---|---|

L, m | S, m | Measurements CH_{4}, % | L, m | S, m | Measurements CH_{4}, % | |

1 | −20 | 1330 | 2 | −30 | 1330 | 60 |

2 | −18 | 1330 | 10 | −28 | 1330 | 40 |

3 | −6 | 1330 | 100 | −26 | 1330 | 27 |

4 | 8 | 1330 | 88 | −24 | 1330 | 30 |

5 | 10 | 1330 | 86 | −22 | 1330 | 13 |

6 | 16 | 1330 | 86 | −20 | 1330 | 25 |

7 | 28 | 1330 | 65 | −18 | 1330 | 24 |

8 | 46 | 1330 | 48 | −6 | 1330 | 44 |

9 | −26 | 1310 | 15 | 8 | 1330 | 30 |

10 | −12 | 1310 | 72 | 10 | 1330 | 27 |

11 | −10 | 1310 | 100 | 16 | 1330 | 15 |

12 | −4 | 1310 | 95 | 28 | 1330 | 15 |

13 | 8 | 1310 | 90 | 46 | 1330 | 15 |

14 | 26 | 1310 | 80 | 50 | 1330 | 14 |

15 | 34 | 1310 | 72 | −50 | 1310 | 90 |

N | Wells No. 4 | Wells No. 2 | ||
---|---|---|---|---|

Model, % | Measurements, % | Model, % | Measurements, % | |

1 | 6.51 | 2 | 60.77 | 60 |

2 | 20.19 | 10 | 56.72 | 40 |

3 | 76.19 | 100 | 53.30 | 27 |

4 | 87.34 | 88 | 50.37 | 30 |

5 | 85.77 | 86 | 47.82 | 13 |

6 | 79.08 | 86 | 45.51 | 25 |

7 | 65.99 | 65 | 43.36 | 24 |

8 | 60.70 | 48 | 31.43 | 44 |

9 | 5.62 | 15 | 24.47 | 30 |

10 | 73.84 | 72 | 24.57 | 27 |

11 | 79.95 | 100 | 25.89 | 15 |

12 | 92.23 | 95 | 27.30 | 15 |

13 | 94.23 | 90 | 20.46 | 15 |

14 | 79.06 | 80 | 20.29 | 14 |

15 | 77.16 | 72 | 72.92 | 90 |

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**MDPI and ACS Style**

Brigida, V.S.; Golik, V.I.; Dzeranov, B.V.
Modeling of Coalmine Methane Flows to Estimate the Spacing of Primary Roof Breaks. *Mining* **2022**, *2*, 809-821.
https://doi.org/10.3390/mining2040045

**AMA Style**

Brigida VS, Golik VI, Dzeranov BV.
Modeling of Coalmine Methane Flows to Estimate the Spacing of Primary Roof Breaks. *Mining*. 2022; 2(4):809-821.
https://doi.org/10.3390/mining2040045

**Chicago/Turabian Style**

Brigida, Vladimir Sergeevich, Vladimir Ivanovich Golik, and Boris Vitalievich Dzeranov.
2022. "Modeling of Coalmine Methane Flows to Estimate the Spacing of Primary Roof Breaks" *Mining* 2, no. 4: 809-821.
https://doi.org/10.3390/mining2040045