Identification of Limestone Aquifer Inrush Water Sources in Different Geological Ages Based on Trace Components

Abstract

In the process of mining Carboniferous coal resources in China’s coal mines, catastrophic water inrush from the floor often occurs. The water inrush source is mainly the fifth limestone aquifer of Carboniferous or Ordovician limestone aquifers. Conventional elements cannot effectively identify the source of water inrush as limestone aquifers of different geological ages. Against the background of floor water inrush in Baizhuang Coal Mine in Feicheng Coalfield, water samples of the fifth-layer limestone aquifer, Ordovician limestone aquifer and water inrush point water samples of Feicheng Coalfield were collected. Trace components F⁻, Br⁻, I⁻, H₃BO₃ and Rn were selected for compositional analysis. The minimum deviation method was used to combine and weight the weights obtained by the entropy weight method, principal component analysis method and analytic hierarchy method. An improved grey correlation model was established for water inrush source identification. The model discrimination result shows that the water inrush source comes from the Ordovician limestone aquifer, and the discrimination accuracy is high.

1. Introduction

Human development is inseparable from energy consumption, and coal is the world’s second largest energy source [1,2]. China has always been a country with coal as its main energy source and is currently the world’s largest coal producer [3]. In the process of coal mining, mine water inrush accidents occur frequently, causing great economic losses and casualties [4]. Therefore, in order to ensure the safe mining of coal mines, the need for prevention and control of mine water inrush cannot be ignored [3]. The rapid and accurate identification of mine water inrush sources is an important prerequisite for the follow-up mine water inrush prevention and control work [5].

Traditional water source identification methods mainly include chemical composition analysis [6,7,8], isotope determination [9], the water-level dynamic observation method [10], similar simulation test [11], etc. In recent years, with the development of big data and artificial intelligence, machine learning has been applied to more and more industries [12,13]. Many experts and scholars at home and abroad have applied machine learning models such as the neural network method [14,15], support vector machine [16] and particle swarm optimization [17] to the field of water source identification. The machine learning model has obvious advantages when dealing with a large amount of data, but insufficient advantages in its recognition accuracy and the processing speed of a small amount of data, so the traditional water source identification method cannot be completely replaced. During the formation of coal mine water, it is subjected to various physical and chemical effects [2]. Therefore, the chemical composition analysis method is the most common and easiest to use water inrush source identification method.

The commonly used water chemical composition analysis methods include Piper three-line diagram [18], cluster analysis method [19], grey correlation method [20], fuzzy comprehensive evaluation [21], and water temperature and water quality identification [22]. Among them, the grey correlation method has low requirements for data sample size, and the results are simple and reliable. It has great advantages in the field of mine water inrush source identification with relatively few data samples and high recognition speed requirements. The traditional grey correlation method does not consider the index weight, and the effect is not good, so some scholars [23,24] have improved the gray correlation method in terms of weight.

In previous studies on the identification of mine water inrush sources, conventional chemical components or isotopes were used as discriminant indexes. Conventional chemical components are more suitable for identifying water inrush sources in aquifers with different lithologies [25], and their discrimination effect for aquifers with the same lithologies is poor [26]. For different lithologic aquifers, isotopes can more accurately identify water inrush sources [27,28], but for the same lithologic aquifers, the isotopes they contain are also roughly the same, resulting in unsatisfactory discrimination. In addition to conventional chemical components and isotopes, trace components are widely used and easily obtained for water chemical analysis.

At present, the grey correlation model established using conventional components as discriminant indexes in the field of mine water inrush has the disadvantages of a slow recognition speed and low accuracy. By improving the grey correlation and selecting trace components, the recognition accuracy and speed when discriminating mine water inrush sources can be improved, offering high sustainable application value in subsequent mine water prevention and control work. Therefore, this paper takes the water inrush case of Baizhuang Coal Mine in Feicheng Coalfield, central and eastern China, as the research background. Five trace components (F⁻; Br⁻; I⁻; H₃BO₃; Rn) with obvious changes in different limestone aquifers were selected as discriminant indexes. With the help of the minimum deviation method [29], the weights obtained by the entropy weight method [30], the principal component analysis method [31] and the analytic hierarchy process [32] were combined and weighted. An improved grey correlation model was established to distinguish the mine water inrush situation when the water inrush source is limestone aquifer in different geological ages.

2. Study Area

Feicheng Coalfield is located in Feicheng City, Shandong Province, in the east of China. The fault structure of Feicheng Coalfield is very developed, and Baizhuang Coal Mine is located in the middle of Feicheng Coalfield (Figure 1). The stratigraphic structure of Baizhuang minefield is shown in Figure 2. The coal-bearing strata are Carboniferous-Permian. Among them, No.3 and No.4 coal seams of the Permian Shanxi Formation and the No.5, No.6, No.7 and No.8 coal seams of the Carboniferous Taiyuan Formation have been mined out. At present, the No.9 coal seam of the Taiyuan Formation is mainly mined. The mining of the No.9 coal seam is threatened by water inrush from the fifth limestone aquifer of the Carboniferous Benxi Formation and the Ordovician limestone aquifer. On 26 July 2021, water inrush from the floor occurred during the mining of the No.9 coal seam in Baizhuang Coal Mine, and the maximum water inrush was 545 m³/h. According to the hydrogeological profile (Figure 3a), schematic diagram (Figure 3b) and long-term practical field experience in Baizhuang Coal Mine, the technical personnel judged that the water inrush source is either the fifth limestone aquifer or the Ordovician limestone aquifer. Knowing how to accurately identify the source of water inrush is very important to guide the on-site technicians in taking effective water prevention measures.

In Feicheng coalfield, the fifth limestone water and Ordovician limestone water samples were collected and sent for inspection by the Feicheng Mining Group. The specific sampling points are shown in Figure 4. After the occurrence of water inrush, the relevant person in charge of Baizhuang Coal Mine collected and inspected the water samples of water inrush points.

3. Methods

3.1. Piper Three-Line Diagram

The Piper three-line diagram is a common analytical graph in the field of water chemistry analysis. It can directly reflect the type of water chemistry [33], and is generally drawn by Origin software.

3.2. Correlation Heat Map

Correlation heat map is a common graph in the field of chemical analysis, which can directly reflect the correlation between factors. It can be drawn by Origin (v2023) software.

3.3. Grey Correlation Analysis

Grey correlation analysis is a multi-factor statistical analysis method [20]. Simply speaking, we want to know the relationship between an indicator and other factors. By sorting the correlation between factors and obtaining an analysis result, we can learn which factors are more relevant to the indicator with which we are concerned. When using water chemical composition analysis for water source identification, each water sample has multiple indicators, which can be used to form an orderly sequence and then construct a related model, before the water inrush sample to be judged and compared with the known results to obtain the discriminant effect.

Because the content of each component in the aquifer is quite different, the direct analysis effect is not good; therefore, the normalization theory of grey correlation analysis is used to ensure the content data of each component are dimensionless before analysis. The specific formula is shown in Equation (1) below.

$$X(k)=\frac{X^{(0)}(k)}{X_0(k)}$$

(1)

In the equation, $X\left(k\right)$ is the normalized sequence, $X^{\left(0\right)}\left(k\right)$ is the original data sequence, and $X_0\left(k\right)$ is the parent sequence.

The equation for calculating the correlation coefficient is shown in Equation (2):

$${\zeta }_i(k)=\frac{\underset{i}{\min } \underset{k}{\max }\left|x_0(k)-x_i(k)\right|+\rho \cdot \underset{i}{\min } \underset{k}{\max }\left|x_0(k)-x_i(k)\right|}{\left|x_0(k)-x_i(k)\right|+\rho \cdot \underset{i}{\min } \underset{k}{\max }\left|x_0(k)-x_i(k)\right|}$$

(2)

In the equation, $\underset{i}{\min } \underset{k}{\min }\left|x_0\left(k\right)-x_i\left(k\right)\right|$ is the minimum absolute difference between absolute difference, $\underset{i}{\max } \underset{k}{\max }\left|x_0\left(k\right)-x_i\left(k\right)\right|$ is the two-stage maximum absolute difference, and $\rho$ is the resolution coefficient.

In the research process, to avoid the error caused by the different values of the resolution coefficient $\rho$, the resolution coefficient is improved by the variance method [34], which can reduce the influence of the two-stage maximum absolute difference. The improved correlation coefficient formula is shown in Equation (3):

$${\zeta }_i(k)=\frac{\underset{i}{\mathrm{c}·\min } \underset{k}{\max }\left|x_0(k)-x_i(k)\right|+d·\underset{i}{\min } \underset{k}{\max }\left|x_0(k)-x_i(k)\right|}{\left|x_0(k)-x_i(k)\right|+d·\underset{i}{\min } \underset{k}{\max }\left|x_0(k)-x_i(k)\right|}$$

(3)

Among them, $c=\frac{{\sigma }_{min}}{{\sigma }_{min}+{\sigma }_{max}}$, $d=\frac{{\sigma }_{max}}{{\sigma }_{min}+{\sigma }_{max}}$, the normalized standard deviation of each column of water chemistry index is ${\sigma }_i\left(i=\mathrm{1,2},\cdots ,n\right)$, ${\sigma }_{max}$ is the maximum standard deviation obtained by comparison, ${\sigma }_{min}$ is the minimum value.

3.4. Entropy Weight Method

The weight matrix $W=w_i$ of each water quality index was calculated by the entropy weight method [30]. The entropy weight method is used in the absence of expert weight, in order to reduce the influence of subjective factors: according to the degree of variation of each index, the entropy weight of each index is calculated using information entropy, and the weight of the evaluation index is determined by the judgment matrix composed of the evaluation value.

3.5. Principal Component Analysis

Principal component analysis [31] is a statistical method of dimension reduction. With the help of an orthogonal transformation, it transforms the original random vector related to its component into a new random vector unrelated to its component, and then reduces the dimension of the multi-dimensional variable system to convert it into a low-dimensional variable system. By constructing an appropriate value function, the low-dimensional system is further transformed into a one-dimensional system.

3.6. Analytic Hierarchy Process

The analytic hierarchy process is a subjective weighting method [32]. The specific calculation steps are as follows. Firstly, a judgment matrix $A={\left(a_{ij}\right)}_{m\times n}$ is constructed for each level, and the maximum eigenvalue and corresponding eigenvector of the judgment matrix are solved. Then, the maximum eigenvector of the judgment matrix is normalized to obtain the weight coefficient of each index. Finally, the consistency index $CI$ is calculated to determine whether the matrix has satisfactory consistency. If $CI\le 0.1$, the consistency requirement is satisfied; otherwise, it is not satisfied, and the judgment matrix line must be adjusted.

3.7. Combination Weight of Minimum Deviation Method

In the previously improved grey correlation model, the weights obtained by the entropy weight method and analytic hierarchy process are selected, and combination weighting is carried out by linear weighting. The entropy weight method regards different indicators as having an independent existence and does not consider the correlation between indicators. The objective weight obtained by principal component analysis is added to the combination weighting as a supplement to the objective weight, and the weighting result is better. For multi-objective decision-making problems, the linear programming method has obvious limitations, and the minimum deviation method [29] obtains better results. Therefore, this paper uses the minimum deviation method to combine the index weights obtained by the entropy weight method, principal component analysis and analytic hierarchy process. The specific principle and formula of the minimum deviation method for combined weighting are shown in Equations (4)–(8).

For a multi-attribute decision making problem, there are a total of $n$ indicators, using $l$ weighting methods. The attribute weight vector is used as shown in Equation (4):

$${\mu }_k=\left\{{\mu }_{k1},{\mu }_{k2},\cdots ,{\mu }_{kn}\right\},k=1,2,\cdots ,l$$

(4)

Of which ${\sum }_i^n{\mu }_{ki}=1,k=\mathrm{1,2},\cdots ,l$. Let the combination weight of the $i$th index be ${\omega }_i$, and the weight value corresponding to the combination weight is $\left({\alpha }_1,{\alpha }_2,\cdots ,{\alpha }_l\right),{\sum }_{i=1}^l{\alpha }_i=1$. Then:

$$w_i={\alpha }_1{\mu }_{1i}+{\alpha }_2{\mu }_{2i}+\cdots +{\alpha }_l{\mu }_{li},i=1,2,\cdots ,n$$

(5)

The index weighting method based on minimum deviation aims to make the deviation of weighted weight obtained by this weighting method as small as possible, so the optimization model is constructed:

$$\min P({\alpha }_1,{\alpha }_2,\cdots ,{\alpha }_l)={\displaystyle {\sum }_{j=1}^m{\displaystyle {\sum }_{k=1}^l{\displaystyle {\sum }_{i=1}^n({\alpha }_k{\mu }_{ki}}}}-{\alpha }_j{\mu }_{ij}{)}^2$$

(6)

$$s.t.\left\{\begin{array}{l}{\alpha }_i\ge 0,i=1,2,\cdots ,l\\ {\displaystyle \sum _{i=1}^l{\alpha }_i=1}\end{array}\right.$$

This is followed by the reintroduction of the Lagrange function:

$$L({\alpha }_1,{\alpha }_2,\cdots ,{\alpha }_l,\lambda )={\displaystyle {\sum }_{j=1}^m{\displaystyle {\sum }_{k=1}^l{\displaystyle {\sum }_{i=1}^n({\alpha }_k{\mu }_{ki}}}}-{\alpha }_j{\mu }_{ij}{)}^2+\lambda ({\displaystyle {\sum }_{i=1}^l{\alpha }_i-1)}$$

(7)

The following equations are obtained by deriving ${\alpha }_1,{\alpha }_2,\cdots ,{\alpha }_l,\lambda ,$ respectively:

$$\left\{\begin{array}{l}((l-1){\displaystyle {\sum }_{i=1}^n{\mu }_{1i}^2)}{\alpha }_1-({\displaystyle {\sum }_{i=1}^n{\mu }_{2i}^{}{\mu }_{1i}^{})}{\alpha }_2-\cdots -({\displaystyle {\sum }_{i=1}^n{\mu }_{li}^{}{\mu }_{1i}^{})}{\alpha }_l+\frac{\lambda }{2}=0\\ -({\displaystyle {\sum }_{i=1}^n{\mu }_{1i}^{}{\mu }_{2i}^{})}{\alpha }_1+((l-1){\displaystyle {\sum }_{i=1}^n{\mu }_{2i}^2)}{\alpha }_2-\cdots -({\displaystyle {\sum }_{i=1}^n{\mu }_{li}^{}{\mu }_{1i}^{})}{\alpha }_l+\frac{\lambda }{2}=0\\ \begin{array}{ccc}\begin{array}{c}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} \end{array}& ⋮& \end{array}\\ -({\displaystyle {\sum }_{i=1}^n{\mu }_{1i}^{}{\mu }_{li}^{})}{\alpha }_l-({\displaystyle {\sum }_{i=1}^n{\mu }_{2i}^{}{\mu }_{li}^{})}{\alpha }_2-\cdots +((l-1){\displaystyle {\sum }_{i=1}^n{\mu }_{li}^2)}{\alpha }_l+\frac{\lambda }{2}=0\\ {\alpha }_1+{\alpha }_2+\cdots +{\alpha }_l=0\end{array}\right.$$

(8)

This can be introduced to Equation (9) to find the grey weighted correlation degree:

$$W_i={\displaystyle {\sum }_{i=1}^n{w}_i{\zeta }_{ij}}$$

(9)

where ${\omega }_i$ is the combination weight and ${\zeta }_{ij}$ is the grey correlation degree.

The process of creating an improved grey correlation mine water inrush source identification model based on minimum deviation combination weight is shown in Figure 5.

4. Results and Discussion

4.1. Apply Conventional Chemical Components to Identify Water Inrush Sources

We first used the conventional chemical composition to draw the Piper three-line diagram to identify the water inrush source of Baizhuang Coal Mine. The conventional water quality analysis results of the fifth limestone water and Ordovician limestone water in Baizhuang Coal Mine of Feicheng Coalfield are shown in

Table 1. Analysis of conventional chemical components of water quality in the fifth limestone of Baizhuang Coal Mine in Feicheng Coalfield (unit: mg·L⁻¹).

Number	Ca2+	Mg2+	K+ + Na+	Cl−	SO42−	HCO3−
1f	229.64	60.71	302.08	86.99	1211.75	105.81
2f	200.84	46.91	319.70	86.99	1119.55	125.70
3f	189.48	54.95	259.30	76.75	1019.94	132.29
4f	203.13	66.69	294.61	100.64	1132.31	112.46
5f	203.89	84.61	284.95	81.89	1205.16	132.29
6f	10.17	6.96	12.39	2.31	25.09	2.17
7f	203.89	84.61	284.95	81.89	1205.16	132.29
8f	165.99	59.78	281.98	76.75	1027.77	115.75
9f	192.78	65.58	286.97	140.00	1052.77	94.83
10f	171.94	46.61	316.04	124.00	1008.32	94.83
11f	171.94	46.61	316.04	124.00	1008.32	94.83
12f	230.62	51.50	323.63	94.94	1195.70	138.88

and

Table 2. Analysis of conventional chemical components of Ordovician limestone water in Baizhuang Coal Mine of Feicheng Coalfield (unit: mg·L⁻¹).

Number	Ca2+	Mg2+	K+ + Na+	Cl−	SO42−	HCO3−
1O	184.79	59.33	285.25	78.49	1053.70	145.53
2O	250.86	67.84	313.88	92.10	1292.01	138.88
3O	358.50	65.30	328.11	107.48	2291.79	224.92
4O	172.04	53.81	268.36	73.35	988.66	112.46
5O	200.84	4.78	290.38	80.19	1064.40	132.29
6O	181.14	54.50	264.06	76.75	1000.19	125.70
7O	266.03	71.05	319.26	86.99	1375.98	119.05
8O	181.14	54.50	264.06	76.75	1000.19	125.70
9O	266.03	71.05	319.26	86.99	1375.98	119.05
10O	95.49	62.09	318.86	192.78	78.20	139.65
11O	169.34	79.80	235.59	116.00	988.57	81.28
12O	164.13	53.73	319.85	124.00	1005.03	121.92

, and the conventional water quality analysis results of this water inrush sample are shown in

Table 3. Conventional chemical composition analysis of water inrush water samples from Baizhuang Coal Mine in Feicheng Coalfield (unit: mg·L⁻¹).

Number	Ca2+	Mg2+	K+ + Na+	Cl−	SO42−	HCO3−
1	194.89	56.31	288.23	76.46	1063.75	155.55
2	259.82	65.84	303.81	82.10	1192.11	158.88
3	368.51	64.30	308.12	105.49	2191.77	234.92
4	172.54	52.85	278.36	77.35	998.66	142.46
5	201.85	14.88	280.38	80.89	1024.40	162.21
6	191.14	52.50	234.06	77.75	1001.11	135.71
7	195.39	64.00	288.53	136.00	1073.35	109.05
8	223.95	23.88	275.33	2.12	1020.93	177.50
9	220.50	31.07	269.65	76.54	1006.77	105.99
10	37.08	12.86	49.97	9.36	1082.88	177.00
11	169.34	79.80	235.59	116.00	988.57	81.28
12	164.13	53.73	319.85	124.00	1005.03	121.92

. Among them, X^f (X = 1, 2, ..., 12) represents 12 water samples of limestone water in the fifth layer, and X^O (X = 1, 2, ..., 12) represents 12 water samples of Ordovician limestone water.

According to Table 1, Table 2 and Table 3 the Piper three-line diagram (Figure 6) is drawn. It can be seen from the diagram that the water quality of the fifth limestone aquifer (Figure 6a), the Ordovician limestone aquifer (Figure 6b) and the water inrush water samples of Baizhuang Coal Mine (Figure 6c) is ClSO₄-Mg type. This shows that, in the case of mine water inrush from limestone aquifers of different geological ages, the conventional components of water chemistry are not effective as discriminant indicators for water inrush source discrimination. Selecting appropriate trace components for subsequent discrimination is a powerful way to improve the accuracy of discrimination.

4.2. A Simple Study on the Correlation of Trace Components in the Study Area

In the Baizhuang mine field, 12 water samples of the fifth limestone aquifer, 12 water samples of the Ordovician limestone aquifer and 12 water samples of water inrush were taken for trace component analysis. The analysis components mainly include F⁻, Br⁻, I⁻, H₃BO₃ and Rn. The results are shown in

Table 4. Analysis of trace components in water quality of the fifth limestone in Baizhuang Coal Mine, Feicheng Coalfield (unit: mg·L⁻¹).

Number	F−	Br−	I−	H3BO3	Rn
1	0.99	0.42	0.01	2.97	4.70
2	1.14	2.48	0.14	8.15	4.75
3	0.44	3.20	0.32	7.17	2.51
4	0.61	0.50	0.01	1.19	0.69
5	1.10	0.46	0.01	0.49	1.13
6	2.09	0.66	0.71	8.41	5.06
7	1.03	0.69	0.26	1.24	0.10
8	0.89	1.01	0.42	5.42	3.21
9	1.28	0.98	0.22	6.13	2.12
10	0.87	0.75	0.32	3.24	4.05
11	0.56	0.64	0.31	4.35	4.78
12	0.93	0.72	0.10	7.13	0.89

,

Table 5. Analysis of trace components of Ordovician limestone water in Baizhuang Coal Mine of Feicheng Coalfield (unit: mg·L⁻¹).

Number	F−	Br−	I−	H3BO3	Rn
1	1.10	0.40	0.01	2.47	4.01
2	1.04	0.43	0.01	8.41	3.21
3	1.01	0.43	0.01	9.65	6.73
4	1.02	0.78	0.01	1.98	5.31
5	1.51	0.88	0.01	2.97	1.00
6	1.48	0.34	0.07	2.20	3.32
7	0.99	1.18	0.07	6.18	6.03
8	1.21	0.53	0.05	7.89	5.42
9	0.89	0.64	0.05	7.65	5.89
10	1.32	0.48	0.04	6.89	6.14
11	1.21	0.46	0.02	2.97	4.01
12	0.98	0.49	0.02	8.45	2.34

and

Table 6. Micro component analysis of water quality of water inrush samples from Baizhuang coal mine in Feicheng coalfield (unit: mg·L⁻¹).

Number	F−	Br−	I−	H3BO3	Rn
1	0.98	0.09	0.07	1.41	1.36
2	0.84	0.13	0.08	1.10	0.98
3	0.97	0.09	0.01	1.21	0.95
4	1.29	0.11	0.09	1.51	1.46
5	0.98	0.14	0.03	1.31	0.98
6	1.21	0.31	0.08	1.91	1.46
7	0.99	0.18	0.02	2.18	5.42
8	1.11	0.56	0.03	3.89	4.03
9	0.98	0.66	0.01	4.65	5.49
10	1.22	0.58	0.02	1.89	6.44
11	1.21	0.56	0.04	1.97	5.01
12	1.08	0.79	0.05	5.45	5.34

.

According to the data of Table 4, Table 5 and Table 6, the correlation heat maps (Figure 7) of the five trace components of the fifth limestone water, Ordovician limestone water and water inrush samples are drawn, respectively. According to the correlation heat maps of F⁻ (Figure 7a), Br⁻ (Figure 7b), I⁻ (Figure 7c), H₃BO₃ (Figure 7d) and Rn (Figure 7e), there is a big difference in the correlation coefficient between the fifth limestone water, Ordovician limestone water and water inrush samples in Baizhuang Coal Mine, which further shows that the trace components have a good application value in distinguishing the water source of limestone water inrush in different geological ages.

4.3. The Outlier Test of Data

The outlier test uses the five statistics of the minimum, lower quartile, median, upper quartile and maximum in the sample data to draw a box line diagram of the sample and then compare the symmetry and dispersion degree of the sample to describe the sample data. Using its outliers, we can find outliers in the box line diagram.

To ensure the representativeness of the application data in the subsequent example test, the micro-component values of the aquifer water samples of the fifth limestone water and the Ordovician limestone water were tested for outliers, and the outliers were found. The test results are shown in Figure 8 and Figure 9. Figure 8 shows that, in the water sample of the fifth layer of limestone water, there is one abnormal value of F⁻, two abnormal values of Br⁻, and no abnormal values of I⁻, H₃BO₃ and Rn. Figure 9 shows that, in the water sample of Ordovician limestone water, there is one abnormal value of Br⁻, and no abnormal values of F⁻, I⁻, H₃BO₃ and Rn. The abnormal values were eliminated to ensure the accuracy of the follow-up study.

4.4. Application of Improved Grey Correlation Model to Identify the Source of Water Inrush

After the outlier test, the mean value of the trace components of the fifth layer of limestone water aquifer water sample without outliers is the parent sequence $X_{L0}\left(k\right)$, and the mean value of the trace components of the Ordovician limestone water aquifer water sample without outliers is the parent sequence $X_{\mathrm{O}0}\left(k\right)$. The trace components of the 12 aquifer water samples of the water inrush water samples are taken as the original data sequence $X_i^0\left(k\right)$, and the specific data are shown in

Table 7. Discrimination sequence of trace components in water quality of the fifth limestone in Baizhuang Coal Mine, Feicheng Coalfield.

Constructing Sequences	F−	Br−	I−	H3BO3	Rn
$X_{L0}\left(k\right)$	0.92	0.69	0.18	3.57	2.4
$X_1^0\left(k\right)$	0.98	0.09	0.07	1.41	1.36
$X_2^0\left(k\right)$	0.84	0.13	0.08	1.10	0.98
$X_3^0\left(k\right)$	0.97	0.09	0.01	1.21	0.95
$X_4^0\left(k\right)$	1.29	0.11	0.09	1.51	1.46
$X_5^0\left(k\right)$	0.98	0.14	0.03	1.31	0.98
$X_6^0\left(k\right)$	1.21	0.31	0.08	1.91	1.46
$X_7^0\left(k\right)$	0.99	0.18	0.02	2.18	5.42
$X_8^0\left(k\right)$	1.11	0.56	0.03	3.89	4.03
$X_9^0\left(k\right)$	0.98	0.66	0.01	4.65	5.49
$X_{10}^0\left(k\right)$	1.22	0.58	0.02	1.89	6.44
$X_{11}^0\left(k\right)$	1.21	0.56	0.04	1.97	5.01
$X_{12}^0\left(k\right)$	1.08	0.79	0.05	5.45	5.34

and

Table 8. Discrimination sequence of trace components of Ordovician limestone water in Baizhuang Coal Mine, Feicheng Coalfield.

Constructing Sequences	F−	Br−	I−	H3BO3	Rn
$X_{O0}\left(k\right)$	1.16	0.53	0.03	5.59	4.31
$X_1^0\left(k\right)$	0.98	0.09	0.07	1.41	1.36
$X_2^0\left(k\right)$	0.84	0.13	0.08	1.10	0.98
$X_3^0\left(k\right)$	0.97	0.09	0.01	1.21	0.95
$X_4^0\left(k\right)$	1.29	0.11	0.09	1.51	1.46
$X_5^0\left(k\right)$	0.98	0.14	0.03	1.31	0.98
$X_6^0\left(k\right)$	1.21	0.31	0.08	1.91	1.46
$X_7^0\left(k\right)$	0.99	0.18	0.02	2.18	5.42
$X_8^0\left(k\right)$	1.11	0.56	0.03	3.89	4.03
$X_9^0\left(k\right)$	0.98	0.66	0.01	4.65	5.49
$X_{10}^0\left(k\right)$	1.22	0.58	0.02	1.89	6.44
$X_{11}^0\left(k\right)$	1.21	0.56	0.04	1.97	5.01
$X_{12}^0\left(k\right)$	1.08	0.79	0.05	5.45	5.34

.

The data were brought into Equation (1) and normalized to obtain the standardized fifth limestone parent sequence $X_L\left(k\right)$ and the standardized Ordovician limestone parent sequence $X_O\left(k\right)$, as well as the standardized sequence $X_i^L\left(k\right)$ of the fifth limestone water corresponding to the 12 water inrush water samples and the standardized sequence $X_i^O\left(k\right)$ corresponding to the Ordovician limestone water. The specific values are shown in

Table 9. Standardized sequence table of water quality trace components in the fifth limestone of Baizhuang Coal Mine in Feicheng Coalfield.

Constructing Sequences	F−	Br−	I−	H3BO3	Rn
$X_L\left(k\right)$	1.00	1.00	1.00	1.00	1.00
$X_1^L\left(k\right)$	1.07	0.13	0.39	0.39	0.57
$X_2^L\left(k\right)$	0.91	0.19	0.44	0.31	0.41
$X_3^L\left(k\right)$	1.05	0.13	0.06	0.34	0.40
$X_4^L\left(k\right)$	1.40	0.16	0.50	0.42	0.61
$X_5^L\left(k\right)$	1.07	0.20	0.17	0.37	0.41
$X_6^L\left(k\right)$	1.32	0.45	0.44	0.54	0.61
$X_7^L\left(k\right)$	1.08	0.26	0.11	0.61	2.26
$X_8^0\left(k\right)$	1.21	0.81	0.17	1.09	1.68
$X_9^0\left(k\right)$	1.07	0.96	0.06	1.30	2.29
$X_{10}^L\left(k\right)$	1.33	0.84	0.11	0.53	2.68
$X_{11}^L\left(k\right)$	1.32	0.81	0.22	0.55	2.09
$X_{12}^L\left(k\right)$	1.17	1.14	0.28	1.53	2.23

and

Table 10. Standardized sequence table of trace components of Ordovician limestone water in Baizhuang Coal Mine of Feicheng Coalfield.

Constructing Sequences	F−	Br−	I−	H3BO3	Rn
$X_O\left(k\right)$	1.00	1.00	1.00	1.00	1.00
$X_1^O\left(k\right)$	0.84	0.17	2.33	0.25	0.32
$X_2^O\left(k\right)$	0.73	0.25	2.67	0.20	0.23
$X_3^O\left(k\right)$	0.84	0.17	0.33	0.22	0.22
$X_4^O\left(k\right)$	1.11	0.21	3.00	0.27	0.34
$X_5^O\left(k\right)$	0.84	0.26	1.00	0.23	0.23
$X_6^O\left(k\right)$	1.04	0.58	2.67	0.34	0.34
$X_7^O\left(k\right)$	0.86	0.34	0.67	0.39	1.26
$X_8^O\left(k\right)$	0.96	1.06	1.00	0.70	0.94
$X_9^O\left(k\right)$	0.84	1.25	0.33	0.83	1.27
$X_{10}^O\left(k\right)$	1.05	1.09	0.67	0.34	1.49
$X_{11}^O\left(k\right)$	1.04	1.06	1.33	0.35	1.16
$X_{12}^O\left(k\right)$	0.93	1.49	1.60	0.97	1.24

.

The grey correlation coefficient ${\zeta }_{ij}^L$ between the water inrush water sample and the fifth limestone water and the grey correlation coefficient ${\zeta }_{ij}^O$ between the water inrush water sample and the Ordovician limestone water can be obtained by bringing the standardized data into Equation (3). The specific values are shown in

Table 11. Grey correlation coefficient of trace components in the fifth limestone of Baizhuang Coal Mine, Feicheng Coalfield.

Water Sample	F−	Br−	I−	H3BO3	Rn
${\zeta }_{i1}^L$	0.85	0.47	0.62	0.50	0.80
${\zeta }_{i2}^L$	0.81	0.48	0.64	0.47	0.74
${\zeta }_{i3}^L$	0.89	0.47	0.50	0.48	0.73
${\zeta }_{i4}^L$	0.47	0.47	0.67	0.52	0.82
${\zeta }_{i5}^L$	0.85	0.49	0.54	0.50	0.74
${\zeta }_{i6}^L$	0.53	0.58	0.65	0.58	0.82
${\zeta }_{i7}^L$	0.83	0.51	0.52	0.62	0.55
${\zeta }_{i8}^L$	0.63	0.80	0.54	0.89	0.71
${\zeta }_{i9}^L$	0.85	0.96	0.50	0.68	0.55
${\zeta }_{i10}^L$	0.52	0.83	0.52	0.57	0.48
${\zeta }_{i11}^L$	0.53	0.80	0.55	0.58	0.59
${\zeta }_{i12}^L$	0.68	0.85	0.57	0.54	0.56

and

Table 12. Grey correlation coefficient of trace components of Ordovician limestone water in Baizhuang Coal Mine, Feicheng Coalfield.

Water Sample	F−	Br−	I−	H3BO3	Rn
${\zeta }_{i1}^O$	0.61	0.48	0.53	0.49	0.51
${\zeta }_{i2}^O$	0.48	0.50	0.47	0.47	0.48
${\zeta }_{i3}^O$	0.61	0.48	0.69	0.48	0.46
${\zeta }_{i4}^O$	0.70	0.49	0.43	0.50	0.52
${\zeta }_{i5}^O$	0.61	0.50	1.00	0.48	0.48
${\zeta }_{i6}^O$	0.87	0.64	0.47	0.52	0.52
${\zeta }_{i7}^O$	0.64	0.53	0.82	0.54	0.73
${\zeta }_{i8}^O$	0.87	0.93	1.00	0.71	0.93
${\zeta }_{i9}^O$	0.61	0.75	0.69	0.81	0.73
${\zeta }_{i10}^O$	0.84	0.90	0.82	0.52	0.59
${\zeta }_{i11}^O$	0.87	0.93	0.82	0.53	0.82
${\zeta }_{i12}^O$	0.79	0.61	0.71	0.96	0.75

.

After obtaining the grey correlation coefficient, the entropy weight method and the principal component analysis method are used to obtain the objective weight of trace elements, and the analytic hierarchy process is used to obtain the subjective weight of trace elements. Then, the combination weighting method based on the minimum deviation is used to obtain the combination weight of trace elements in water inrush water samples of Feicheng coalfield. The specific values are shown in Figure 10.

After the grey correlation coefficient and the weight value of each index are brought into Equation (9), the grey weighted correlation degree between the water inrush source and the fifth limestone water is 0.65, and the grey weighted correlation degree with the Ordovician limestone water is 0.89. Therefore, it is judged that the source of water inrush from the floor in Baizhuang Coal Mine is Ordovician limestone water. According to the judgment results, on-site technicians carried out grouting and water-plugging projects on the Ordovician limestone near the water inrush point, and achieved a remarkable water-plugging effect in a short time. This proves the correctness of the judgment of the water inrush source at this time, and verifies the high accuracy of the application of the improved grey correlation model to identify the water inrush source of limestone at different geological ages through trace components.

5. Conclusions

(1)

Conventional chemical composition should not be used as a discriminant indicator in the discrimination of water inrush sources for limestone aquifers of different geological ages. Therefore, in the identification of water inrush sources under similar conditions, the analysis and determination of conventional components can be omitted, which saves a lot of time and economic costs, and has high economic value and sustainable application value.

(2)

The five trace components of F⁻, Br⁻, I⁻, H₃BO₃ and Rn were used as the discriminant indicators of water inrush sources in limestone aquifers of different geological ages, and good discriminant results were obtained. This shows that the use of trace elements as discriminant indicators can be considered in the subsequent case of similar water inrushes, which can save time and economic costs, and ensure the safety of mining personnel. It has high social value and sustainable application value.

(3)

In this study, the weights obtained by the entropy weight method, principal component analysis method and analytic hierarchy process are combined and weighted by the minimum deviation method, and then an improved grey correlation model based on trace components is established. With regard to the discrimination of water inrush sources in limestone aquifers of different geological ages, the discrimination accuracy is high, the requirements regarding the number of samples is low, and it has strong practical significance and sustainable application value.

(4)

With the depletion of shallow coal resources, the importance of research on deep coal mining has continuously increased. This is of great practical significance for ensuring the sustainable and safe mining of deep coal mines to establish a water inrush source identification model that can be used to identify the water inrush source at the same lithology aquifer in different geological years.