Experimental Study on Rapid Determination Method of Coal Seam Gas Content by Indirect Method

Abstract

In view of the problems of heavy work, long cycle, high cost and low efficiency in the process of indirect determination of coal seam gas content, the basic gas parameters and coal quality indexes of 24 coal samples from 5 coal mines in the Hancheng area of Shanxi Province are measured by the laboratory measurement method. The raw coal gas content–gas desorption index of drilling cuttings (W–K₁) relationship model is characterized by logarithmic function. Using SPSS data analysis software, a stepwise multiple linear regression method is used for statistical analysis. The results show that the factors that have a significant impact on the regression slope C in the W–K₁ relationship model are gas adsorption constant (a), apparent density (ARD), initial velocity of gas diffusion (Δp) and consistent coefficient (f). The factors that have a significant impact on the regression constant D are Δp and atmospheric adsorption (Q). Then, the mathematical model of rapid prediction of coal seam gas content is determined. Compared with the measured values, the average absolute error rate is 12.84%, which meets the prediction requirements and provides a simple and easy method for rapid determination of coal seam gas content in coal mines in the Hancheng area.

1. Introduction

Coal seam gas content directly affects the amount of coal seam gas and the amount of mine gas emission, which are of great significance for the correct design of mine ventilation, gas drainage and outburst risk assessment [1,2,3,4]. Coal seam gas content is an important parameter to characterize the occurrence of coal seam gas. Accurate prediction of coal seam gas content plays a vital role in the prevention and control of coal mine gas disasters. The determination method of coal seam gas content is divided into the direct method and indirect method. The direct method [5,6,7] is to measure the amount of desorbable gas and normal pressure gas in the underground field and laboratory and then calculate the gas loss in the sampling process. The sum of the three parts is the gas content of the coal seam. The indirect method [8,9,10] is to measure the basic gas parameters such as gas adsorption constant, industrial analysis, density and porosity in the laboratory. Combined with the measured coal seam gas pressure in the underground field, the adsorbed gas amount and free gas amount of coal are calculated by the Langmuir equation. The sum of the two parts is the coal seam gas content. Because there are many factors affecting the gas content of coal seams [1,11,12,13,14,15], and the gas occurrence has the characteristics of complexity, nonlinearity, dynamics and random uncertainty, it is difficult to accurately determine the gas content of a coal seam. In recent years, for the prediction of coal seam gas content, Zhang et al. [16] used the method of multiple linear regression analysis. Chen et al. [17,18,19] adopted the grey theory method. Zhang et al. [20,21] used the neural network analysis method. Wang et al. [22,23] used a machine learning algorithm. They studied different mathematical models for predicting coal seam gas content. The prediction model mainly focuses on the relationship between the influencing factors such as coal seam depth, coal seam thickness, floor elevation, fault distance, coal rock dip angle and coal seam gas content. These scholars are using direct methods to predict coal seam gas content. However, there are few studies on predicting coal seam gas content by indirect methods in a laboratory. Li [24] used the drilling cuttings gas desorption index method to predict coal seam gas content. Through the study, the exponential mathematical model for predicting coal seam gas content was obtained, which avoided the determination of coal seam gas pressure. However, the regression coefficient of the exponential mathematical model is not accurately determined. Compared with the direct method, the gas basic parameters measured by the indirect method are all measured values, and the gas pressure of the coal seam is also measured. There are fewer influencing factors in the measurement process, the measurement error is small, and the measurement data is relatively reliable. However, the disadvantage of using an indirect method to measure coal seam gas content is that it is necessary to measure coal seam gas pressure underground. This is relatively heavy work, and the measurement period is long (about one month). Especially in the gently inclined coal seam or the coal seam with poor surrounding rock density, it is difficult to measure the gas pressure of the coal seam. In short, it is common that the results of a direct method are low, while the results of indirect methods in many mines are close to reality [25]. To solve the problem of accurate determination of coal seam gas pressure in the indirect determination of coal seam gas content, 24 coal samples from 5 coal mines in the Hancheng area of Shanxi Province are selected. The relationship model between gas basic parameters, coal quality index, drilling cuttings gas desorption index and gas pressure of these coal samples was measured in the laboratory. The SPSS data analysis software was used, and the stepwise multiple linear regression analysis method was used. A mathematical model for predicting the gas content of coal seams in the Hancheng area unrelated to gas pressure was established. This method can quickly and accurately determine the gas content of the coal seam in this area, and provide technical guidance and reference for mine gas disaster prevention, coal and tile outburst prediction, gas emission prediction and so on.

2. Indirect Method to Determine the Coal Seam Gas Content

2.1. Coal Seam Gas Content Calculation

The most commonly used indirect determination method of coal seam gas content at home and abroad is to calculate the coal seam gas content according to the known coal seam gas pressure and the gas adsorption constant value of coal measured in the laboratory [26]. The calculation formula is:

$$W=\frac{abp\left(100-A_{ad}-M_{ad}\right)}{100\left(1+bp\right)\left(1+0.31M_{ad}\right)}+\frac{10kp}{ARD}$$

(1)

where W is the raw coal gas content, m³/t. a is gas adsorption constant, cm³/g. b is the gas adsorption constant, MPa⁻¹. p is coal seam gas pressure, MPa. A_ad is the ash content of coal, %. M_ad is the moisture of coal, %. k is the porosity of coal, %. ARD is the apparent density of coal, t/m³.

2.2. Coal Sample Taking and Test

Four and five coal samples are taken from different sampling sites of 3# coal seam and 5# coal seam, respectively, in the Xiangshan Coal Mine in the Hancheng area of Shanxi Province. Two and three coal samples are taken from 2# coal seam and 3# coal seam, respectively, in the Xiayukou Coal Mine. Three and two coal samples are taken from 3# coal seam and 5# coal seam, respectively, in the Xinglong Coal Mine. Three coal samples are taken from 3# coal seam in the Sangbei Coal Mine. Two coal samples are taken from 3# coal seam in the Sangshuping Coal Mine. A total of 24 coal samples are taken. According to the GB/T482–2008 ‘coal seam coal sample taking method’, GB/T474–2008 ‘coal sample preparation method’, GB/T477–2008 ‘coal sample screening test method’ and other national standards, about 5 kg mixed coal samples are taken from freshly exposed coal seams, indicating the sampling location, and the packaging is strictly sent to the laboratory for drying, crushing and screening, and coal samples of different particle sizes are prepared for inspection, according to the MT/T752–1997 ‘Determination method of methane adsorption in coal’, GB/T212–2008 ‘Industrial analysis method of coal’, GB/T 217–2008 ‘Truth relative density determination method of coal’, GB/T6949–2008 ‘Apparent relative density determination method of coal’, AQ1080–2009 ‘Determination method of initial velocity index (Δp) of gas emission in coal’, GB/T23561.12–2010 ‘Determination method of firmness coefficient of coal’ and other coal industry standards and national standards. The HCA-type high-pressure capacity method gas adsorption device, industrial analysis tester, density tester, gas emission initial velocity tester, WTC gas outburst parameter tester and other instruments and equipment are used. In the laboratory, the moisture M_ad, ash A_ad, volatile V_daf, true density TRD, apparent density ARD, porosity k, atmospheric adsorption Q and gas adsorption constant a and b of 24 coal samples from 5 coal mines in the Hancheng area are measured. The results of gas basic parameters of 24 coal samples are summarized.

The variation ranges of each parameter of 24 coal samples measured in

Table 1. Summary of basic gas parameters of 24 coal samples measured.

Coal Sample Number	Sampling Site	Moisture Mad/%	Ash Aad/%	Volatile Vdaf/%	True Density TRD/(g·cm−3)	Apparent Density ARD/(g·cm−3)	Porosity k/%	Atmospheric Adsorption Capacity Q/(cm3·g−1)	Gas Adsorption Constant a/(cm3·g−1)	Gas Adsorption Constant b/MPa−1
M01	Xiangshan mine 3# coal seam 22301 return airway	0.79	26.87	17.59	1.57	1.51	3.82	3.0595	24.5904	0.9459
M02	Xiangshan Mine 5# coal seam track downhill	0.93	16.67	14.26	1.48	1.43	3.38	3.4328	25.8505	1.1127
M03	21220 mining face of 2# coal seam in Xiayukou Mine	0.65	9.36	16.20	1.39	1.34	3.60	3.0190	22.8960	1.1560
M04	Xiayukou mine 3# coal seam 23306 Yunshun	0.81	4.30	14.44	1.32	1.29	2.27	3.3520	26.6249	0.9581
M05	21301 open-off cut of 3# coal seam in Xinglong Coal Mine	0.70	11.73	18.61	1.46	1.43	2.05	2.4276	17.0599	1.2944
M06	Xinglong Mine 5# coal seam 4501 Yunshun	0.65	15.64	17.90	1.50	1.45	3.33	3.1282	22.3545	1.251 5
M07	Sangbei Mine 3# coal seam 11308 transport trough	0.68	12.08	14.22	1.41	1.37	2.84	3.0605	19.7706	1.2854
M08	Sangbei Mine 3# coal seam 11308 return air trough	0.82	10.06	14.95	1.39	1.35	2.88	3.2195	22.7722	1.2786
$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$
M23	4301 control roadway of 3# coal seam in Sangshuping Mine	0.73	9.61	14.89	1.41	1.37	2.84	3.0570	22.4181	1.0547
M24	South belt roadway of 3# coal seam in Sangshuping Mine	0.84	15.53	15.20	1.48	1.44	2.70	3.7367	22.1534	1.5578

are as follows: M_ad is 0.54~1.59%, A_ad is 4.30~26.87%, V_daf is 13.10~18.61%, TRD is 1.32~1.57 g·cm⁻³, ARD is 1.29~1.51 g·cm⁻³, k is 2.05~5.84%, Q is 2.1624~3.8969 cm³·g⁻¹, a is 17.0599~26.6249 cm³·g⁻¹, and b is 0.8217~1.7279 MPa⁻¹. From the distribution characteristics of the measured data, the selected coal samples are universal and extensive.

3. K₁–p Relation Model

The drilling cuttings gas desorption index K₁ characterizes the characteristic parameters of the coal gas desorption speed. It reflects the coal seam gas content and the size of the initial pressure relief gas desorption rate. Scholars at home and abroad have carried out extensive and in-depth research on the law of gas desorption from drilling cuttings in the laboratory [27,28]. They mainly studied the influence of mathematical fitting of gas desorption law and gas pressure on the gas desorption index of drilling cuttings. The research results show that the gas desorption law of drilling cuttings is the law of gas desorption amount of drilling cuttings changing with time. It can not only reflect the gas adsorption pressure and desorption gas content in coal but also reflect the damage degree of coal; that is, it can be used for outburst prediction. It is also used to determine the gas pressure and tile content of a coal seam. According to Zhao’s research results [29], there is a power function relationship between the gas desorption index of drilling cuttings and the gas pressure of adsorption equilibrium:

$$K_1=m{p}^n$$

(2)

where K₁ is the gas desorption index of drilling cuttings, mL·g⁻¹·min^−0.5. p is the adsorption equilibrium gas pressure, MPa. m and n are undetermined constants, 0 < n < 1.

The instrument used to determine K₁ in the underground field and laboratory is a WTC gas outburst parameter instrument. The underground site is measured according to the AQ/T 1065–2008 drilling cuttings gas desorption index determination method. The laboratory determination of the K₁–p relationship model test process is based on the test method adopted by Lei [30]. According to Equation (2), the key to determine the gas desorption index of drilling cuttings is to determine the undetermined constants m and n. The essence of laboratory determination of the K₁–p relationship model is to determine the undetermined constants m and n. The measured K₁–p relationship model results of 24 coal samples, gas basic parameters such as gas initial velocity Δp, coal firmness coefficient f and coal quality index measurement results are summarized in

Table 2. Measured 24 coal samples relational model and other parameters summary table.

Coal Sample Number	Sampling Site	Initial Velocity of Gas Diffusion Δp/mmHg	Consistent Coefficient of Coal f	K1–p Relation Model	(K1)p = 1	W–K1 Relation Model
M01	Xiangshan mine 3# coal seam 22301 return airway	21	0.49	K1 = 0.5086 p0.5761	0.5086	W = 5.408 lnK1 + 11.39
M02	Xiangshan Mine 5# coal seam track downhill	25	0.30	K1 = 0.6598 p0.5652	0.6598	W = 6.310 lnK1 + 11.94
M03	21220 mining face of 2# coal seam in Xiayukou Mine	20	0.32	K1 = 0.4093 p0.6163	0.4093	W = 6.053 lnK1 + 15.23
M04	Xiayukou mine 3# coal seam 23306 Yunshun	26	0.10	K1 = 0.9097 p0.5427	0.9097	W = 7.722 lnK1 + 11.35
M05	21301 open-off cut of 3# coal seam in Xinglong Coal Mine	14	0.22	K1 = 0.4400 p0.6535	0.4400	W = 4.000 lnK1 + 10.46
M06	Xinglong Mine 5# coal seam 4501 Yunshun	12	0.43	K1 = 0.3438 p0.6871	0.3438	W = 4.911 lnK1 + 14.35
M07	Sangbei mine 3# coal seam 11308 transport trough	14	0.39	K1 = 0.2696 p0.6147	0.2696	W = 5.015 lnK1 + 14.96
M08	Sangbei mine 3# coal seam 11308 return air trough	13	0.39	K1 = 0.2704 p0.6040	0.2704	W = 5.755 lnK1 + 17.00
$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$
M23	4301 control roadway of 3# coal seam in Sangshuping Mine	10	0.44	K1 = 0.2646 p0.6634	0.2646	W = 5.271 nK1 + 12.04
M24	South belt roadway of 3# coal seam in Sangshuping Mine	16	0.31	K1 = 0.2678 p0.7174	0.2678	W = 4.368 lnK1 + 14.84

below.

The variation ranges of each parameter of 24 coal samples measured in Table 2 are as follows: Δp is 7~37 mmHg, f is 0.10~0.55, K₁–p relationship model coefficient m is 0.217~0.9371, and index n is 0.4431~0.7740.

4. Test Result Analysis

4.1. Relationship between K and Coal Quality Index

Coal quality indexes mainly include gas emission initial velocity Δp, firmness coefficient f, volatile matter V_daf, ash A_ad, etc. They macroscopically reflect some essential characteristics related to coal and gas desorption. Among them, Δp and f are commonly used in regional outburst risk prediction. Because Δp, f, V_daf, A_ad, etc. are all coal quality indicators unrelated to gas pressure, the relationship between them and the values under certain gas pressure conditions can only be considered. In Table 2, the K₁ value is calculated when the gas pressure p = 1 MPa. Through nonlinear fitting of the data in Table 1 and Table 2, the relationship between (K₁)_p=1 and Δp, f, V_daf, A_ad is obtained, as shown in Figure 1.

It can be seen from Figure 1a that the relationship between (K₁)_p=1 and Δp conforms to the power function increasing relationship. With the increase in Δp, the value of (K₁)_p=1 also increases correspondingly. The correlation coefficient R² is 0.812, indicating that there is a significant correlation between K₁ and Δp, and Δp significantly affects the positive (K₁)_p=1. It can be seen from Figure 1b that (K₁)_p=1 is in accordance with the logarithmic function attenuation relationship. As f increases, the value of (K₁)_p=1 decreases accordingly. The correlation coefficient R² is 0.657, indicating that there is also a certain correlation between (K₁)_p=1 and f, and f affects negative (K₁)_p=1, but the significance is lower than Δp. It can be seen from Figure 1c that the distribution of 24 coal samples represented by 24 points in the figure is relatively disordered. The relationship between (K₁)_p=1 and A_ad is an approximately logarithmic function, and the correlation coefficient R² is only 0.129, indicating that the correlation between (K₁)_p=1 and A_ad is not close. It can be seen from Figure 1d that 24 points are concentrated in the range of 13.10~18.61 of V_daf, and (K₁)_p=1 has no correlation with V_daf.

From the above analysis, it can be seen that under the same gas pressure condition, the value of K₁ mainly depends on Δp. In theory, K₁ is the same as Δp, which is an index to reflect the risk of outburst by the amount of initial gas desorption. Their fundamental difference is only the difference of adsorption gas pressure; that is, K₁ index reflects the change of adsorption gas pressure more than Δp. The firmness coefficient f mainly reflects the ability of coal to resist damage. In many cases, the lower the strength of a coal seam, the greater the initial gas desorption. The regression analysis shows that under the condition of certain gas pressure, K₁ decreases with the increase in f in a negative exponential law. The volatile matter V_daf of coal reflects the metamorphic degree of coal, and the ash A_ad reflects the yield of effective carbon. Both of them are not closely related to the initial gas desorption amount. In short, K₁ is most affected by Δp and less affected by V_daf and A_ad. Therefore, Δp is the main influencing factor of K₁, and f, V_daf and A_ad are secondary influencing factors.

4.2. The Relationship between Coal Seam Gas Content W and K₁

The coal seam gas content W in Equation (1) and the drilling cuttings gas desorption index K₁ in Equation (2) are directly related to the gas pressure p, and as the gas pressure increases, K₁ and W increase. To find the relationship between K₁ and W, gas pressure p is set to 0.1, 0.5, 1.0, 2.0, 3.0, 4.0, 5.0 MPa. Equations (1) and (2) are used to calculate 7 K₁ and 7 W corresponding to 7 gas pressures, and then, the nonlinear fitting is carried out. The W–K₁ relationship model is obtained, and the correlation coefficient R² is greater than 0.9900. The results are summarized in Table 2. One coal sample each (limited to the length of the article) was selected from the Xiangshan Coal Mine, Xiayukou Coal Mine, Xinglong Coal Mine, Sangbei Coal Mine and Sangshuping Coal Mine for nonlinear fitting. The fitting relationship curve is shown in Figure 2.

It can be seen from Figure 2 that there is a significant correlation between coal seam gas content W and drilling cuttings gas desorption index K₁, which is characterized by logarithmic function. The W–K₁ relationship model can be expressed by Equation (3):

$$W=C\ln K_1+D$$

(3)

where W is the gas content of raw coal, m³/t. K₁ is the gas desorption index of drilling cuttings, mL·g⁻¹·min^−0.5. C is regression slope. D is regression constant.

In the process of adsorption and desorption of coal, the change of coal seam gas content W and drilling cuttings gas desorption index K₁ is caused by the change of coal seam gas pressure. This change eventually leads to the continuous change of diffusion coefficient in the process of coal desorption, which leads to the unique nonlinear relationship between W and K₁. Figure 2 shows that when the gas desorption index K₁ of the five coal mines is the same, the coal seam gas content W of the Xiangshan Coal Mine is the largest, and the coal seam gas content W of the Xiayukou Coal Mine is the smallest. From Table 2, the W–K₁ relationship model coefficient C is 4.000~7.722, and D is 9.829~17.98.

4.3. Determination of Regression Coefficient of W–K₁ Relation Model

It can be seen from Equation (3) that the key is to determine the regression coefficients C and D, whether it is to determine the coal seam gas content W through the drilling cuttings gas desorption index K₁ or to determine K₁ through W. Although the regression coefficients C and D of the W–K₁ relationship model of a specific sampling site in a coal mine can be obtained through the laboratory, combined with the measured data of the underground site, this is the result based on a large amount of experimental data such as 11 gas basic parameters and coal quality indexes measured in the laboratory and the measured coal seam gas pressure and drill cuttings gas desorption index K₁ in the coal mine. The determination of these parameters is heavy, long cycle, high cost and low efficiency. For the coal mines in the Hancheng area, only by finding out the universal law of the regression coefficients C and D in the W–K₁ relationship model and establishing a regression coefficient relationship model suitable for the area can the coal seam gas content be predicted quickly and accurately, and a simple and easy method for predicting the coal seam gas content in the Hancheng area is provided.

Taking 24 coal samples from 5 coal mines in the Hancheng area as samples, 24 regression coefficients C and 24 regression coefficients D (as shown in Table 2) obtained by the W–K₁ relationship model are taken as dependent variables, respectively. M_ad, A_ad, V_daf, TRD, ARD, k, Q, a, b, Δp, f and another 11 gas basic parameters and coal quality indexes corresponding to coal samples are used as independent variables. The SPSS data analysis software is used. The stepwise multiple linear regression method is used for statistical analysis. According to the order of input parameters, 11 independent variables are introduced into the regression formula one by one. The regression results show that for the dependent variable C, after eliminating the seven parameters that cannot have a significant impact, the final model introduces four parameters a, ARD, Δp and f. Similarly, for the dependent variable D, after eliminating the nine parameters that cannot have a significant impact, the final model introduces two parameters such as Δp and Q. Through SPSS data analysis, the multiple linear regression model of regression coefficients C and D in the W–K₁ relationship model is:

$$C=11.031+0.148a+0.084\Delta p-7.919ARD+2.263f$$

(4)

$$D=4.724-0.339\Delta p+4.725Q$$

(5)

4.4. Multiple Linear Regression Model Test

The prerequisites for the establishment of multiple linear regression models (4) and (5) are that there is no serious autocorrelation between series, there is no strong multicollinearity between independent variables and the residual distribution basically obeys the normal distribution. Only when these three assumptions are satisfied at the same time can it be proved that (4) and (5) have certain validity and reliability. SPSS data analysis software is used for statistical analysis of the output results (as shown in

Table 3. Model summary.

Regression Model	Adjusted R2	Sig	Durbin-Wastson
(4)	0.833	0.038	2.082
(5)	0.631	0.001	1.377

). The coefficient of determination of the regression model (4) in Table 3 is 0.833, indicating that the four independent variables a, ARD, Δp and f can explain 83.3% of the change of the dependent variable C, R² is close to 1, and the goodness of regression fitting is better. That is to say, there is a very close linear correlation between C and a, ARD, Δp and f. The coefficient adjustment R² of the regression model (5) is only 0.631, indicating that the two independent variables such as Δp and Q can explain 63.1% of the change in the dependent variable D, and there is a certain linear correlation between D and Δp and Q.

Regression model (4) significance level (t statistics corresponding probability value) Sig = 0.038 < 0.05. The probability that 11 independent variables cannot have a significant impact on the dependent variable C is 0. Rejecting the null hypothesis, there are at least four independent variables, a, ARD, Δp and f, that have a significant impact on C in the 11 independent variables. Among them, a, Δp and f significantly affect positive C, and ARD significantly affects negative C. The significance level of regression model (5) (the probability value corresponding to t statistics) Sig = 0.001 < 0.05, indicating that there are at least two independent variables, Δp and Q, that have a significant impact on D, where Δp significantly affects negative D and Q significantly affects positive D.

Regression models (4) and (5) Durbin-Wastson in Table 3. are 2.082 and 1.377, respectively, which are close to 2. In statistics, when the Durbin-Wastson value is significantly close to 0 or 4, the sequences are not independent of each other, and there is a serious autocorrelation. Therefore, it can be considered that the series in regression models (4) and (5) are independent of each other and there is no serious autocorrelation.

In statistics, it is generally believed that there is no strong multicollinearity between independent variables when the variance inflation factor VIF is less than 5. The output result of statistical analysis using SPSS data analysis software is that the variance expansion factor VIF of the four independent variables of a, ARD, Δp and f in the regression model (4) is 1.761, 1.771, 3.262, and 3.133, respectively, all less than 5. The variance expansion factor VIF of the two independent variables, such as Δp and Q, are 1.488 and 1.488, respectively, which are also less than 5. It shows that there is no strong multicollinearity between a, ARD, Δp and f, between Δp and Q; that is, there is no strong correlation.

From the standard P–P diagram and scatter diagram of the regression standardized residuals of the dependent variables C and D in Figure 3 and Figure 4, it can be seen that the standardized residuals are basically distributed around the asymptote, the scatters are basically linear, and the data and models are basically matched. The distribution of sample points is scattered and irregular, the residuals are random, and there is no heteroscedasticity. This shows that the residual basically obeys the normal distribution.

The main factors that significantly affect the regression coefficient C are a, ARD, Δp and f, and the main factors that significantly affect the regression coefficient D are Δp and Q. There is no serious autocorrelation between the tested series, and there is no strong multicollinearity between the independent variables. The residual distribution is basically normal distribution. Therefore, the C and D regression models (4) and (5) established by SPSS data analysis software have certain validity and reliability.

5. Mathematical Model Prediction Correction of Coal Seam Gas Content

Through the above research and analysis, the regression models (4) and (5) of regression coefficients C and D are established. Substituting (4) and (5) into Equation (3), the mathematical model (6) for predicting coal seam gas content in coal mines in the Hancheng area is finally obtained:

$$\begin{array}{l}{W}^{\prime }=(11.031+0.148a+0.084\Delta p-7.919ARD+2.263f)\ln K_1\\ +(4.724-0.339\Delta p+4.725Q)\end{array}$$

(6)

where W′ is the predicted value of coal gas content, m³/t.

Three coal samples are taken from the Xiangshan Coal Mine, Xiayukou Coal Mine and Sangbei Coal Mine in the Hancheng area. Eleven gas basic parameters and coal quality indexes of M_ad, A_ad, V_daf, TRD, ARD, F, Q, a, b, Δp, f, etc. of three coal samples are measured in the laboratory. At the same time, the K₁–p relationship model of three coal samples is measured by a WTC gas outburst parameter instrument [31]. The gas content of the coal seam is predicted by mathematical model (6). The gas pressure p is set as 0.5, 1.0, 2.0, 3.0, 4.0 and 5.0 MPa, respectively. The predicted value W′ of the mathematical model of coal seam gas content is compared with the measured value W (as shown in

Table 4. Comparison of predicted and measured values of the mathematical model of coal bed methane content.

Gas Pressure p/MPa	Xiayukou Coal Mine 23208 Working Face of 2# Coal Seam			Sangbei Coal Mine 3# Coal Seam 11308 Transport Trough			Xiangshan Coal Mine 5# Coal Seam South Wing Belt Transport Roadway
	Measured Value (W)/(m3·t−1)	Predicted Value (W′)/(m3·t−1)	Error Rate/%	Measured Value (W)/(m3·t−1)	Predicted Value (W′)/(m3·t−1)	Error Rate/%	Measured Value (W)/(m3·t−1)	Predicted Value (W′)/(m3·t−1)	Error Rate/%
0.5	4.9836	3.7021	−25.71	4.8044	4.1224	−14.20	5.4155	5.4867	1.31
1.0	7.4337	5.7095	−23.19	7.0595	6.1035	−13.54	7.8719	7.5497	−4.09
2.0	9.9104	7.7169	−22.13	9.3171	8.0845	−13.23	10.2810	9.6128	−6.50
3.0	11.2080	8.8912	−20.67	10.5292	9.2434	−12.21	11.5566	10.8196	−6.38
4.0	12.0432	9.7243	−19.25	11.3446	10.0656	−11.27	12.4092	11.6758	−5.91
5.0	12.6496	10.3760	−17.97	11.9672	10.7033	−10.56	13.0581	12.3400	−5.50

Remarks: error rate = (W′–W)/W × 100%.

).

It can be seen from Table 4 that when the gas pressure is 0.5 MPa, 1.0 MPa, 2.0 MPa, 3.0 MPa, 4.0 MPa and 5.0 MPa, the variation range of the predicted value W′ of the mathematical model of coal seam gas content and the measured value W is 3.7021~13.0581 m³/t. The predicted value W′ and the measured value W increase with the increase in gas pressure. When the gas pressure is in the range of 0.5~5.0 MPa, the maximum deviation between the predicted value W′ and the measured value W is −2.3189 m³/t when the gas pressure is 4.0 MPa in the Xiayukou Coal Mine. The minimum deviation is 0.0711 m³/t corresponding to the gas pressure of 0.5 MPa in the Xiangshan Coal Mine. The average deviation is −1.2178 m³/t. The maximum error rate is −25.71%. The minimum error rate is 1.31%. The average error rate is −12.84%.

In Figure 5, the trend of the predicted value W′ of the mathematical model of coal seam gas content in the three coal mines is generally consistent with the measured value W, which conforms to the characteristics of logarithmic function. The predicted value W′ of the Xiangshan Coal Mine is very close to the measured value W, and the change trend of the Xiayukou Coal Mine deviates far. In the low-pressure state, the coincidence degree is high, close to coincidence, and the average absolute error rate is 12.84%, which can meet the prediction requirements. It can be seen that the mathematical model of multiple linear regression has high reliability in predicting coal seam gas content in the Hancheng area. Because the average deviation is −1.2178 m³/t, the predicted value W′ is generally lower than the measured value W. Therefore, Equation (6) is modified by the average deviation of −1.2178 m³/t. The modified mathematical model is:

$$\begin{array}{l}{W}^{\prime }=(11.031+0.148a+0.084\Delta p-7.919ARD+2.263f)\ln K_1\\ +(4.724-0.339\Delta p+4.725Q)+1.2178\end{array}$$

(7)

6. Conclusions

(1)

Through the experimental study and analysis of coal samples in the Hancheng area of Shanxi, it is found that W and K₁ have a significant correlation. SPSS data analysis software is used for statistical analysis, and the main influencing factors of the regression coefficient C of the W–K₁ relationship model are a, ARD, Δp and f. Among them, a, Δp and f significantly affect positive C, and ARD significantly affects negative C. The main factors of regression coefficient D are Δp and Q, where Δp significantly affects negative D and Q significantly affects positive D. After testing, the multiple linear regression model has certain validity and reliability.

(2)

When the gas pressure is 0.5, 1.0, 2.0, 3.0, 4.0 and 5.0 MPa, the maximum deviation between the predicted value W′ of the mathematical model of coal seam gas content and the measured value W is −2.3189 m³/t, the minimum deviation is 0.0711 m³/t, and the average absolute error rate is 12.84%. It can meet the prediction requirements.

(3)

The mathematical model of predicting coal seam gas content is only related to six parameters, such as a, ARD, Δp, f, Q and K₁, and has nothing to do with coal seam gas pressure. It avoids the problems of heavy task, long cycle, high cost and low efficiency in measuring coal seam gas pressure in a coal mine. The prediction model can quickly and accurately determine the gas content of a coal seam and provide a simple and feasible method for predicting the gas content of coal seams in the Hancheng area.