**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 [1–4]. 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 [5–7] 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 [8–10] 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 [1,11–15], 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. [17–19] 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

**Citation:** Lei, H.; Dai, L.; Cao, J.; Li, R.; Wang, B. Experimental Study on Rapid Determination Method of Coal Seam Gas Content by Indirect Method. *Processes* **2023**, *11*, 925. https://doi.org/10.3390/pr11030925

Academic Editor: Qingbang Meng

Received: 25 February 2023 Revised: 15 March 2023 Accepted: 16 March 2023 Published: 17 March 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

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:

$$\mathcal{W} = \frac{alp(100 - A\_{ad} - M\_{ad})}{100(1 + bp)(1 + 0.31M\_{ad})} + \frac{10kp}{ARD} \tag{1}$$

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. *Aad* is the ash content of coal, %. *Mad* 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 (Δ*p*) 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 *Mad*, ash *Aad*, volatile *Vdaf*, 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 are as follows: *Mad* is 0.54~1.59%, *Aad* is 4.30~26.87%, *Vdaf* is 13.10~18.61%, *TRD* is 1.32~1.57 <sup>g</sup>·cm−3, *ARD* is 1.29~1.51 g·cm−3, *<sup>k</sup>* is 2.05~5.84%, *<sup>Q</sup>* is 2.1624~3.8969 cm3·g−1, *<sup>a</sup>* is 17.0599~26.6249 cm3·g<sup>−</sup>1, and *<sup>b</sup>* is 0.8217~1.7279 MPa<sup>−</sup>1. From the distribution characteristics of the measured data, the selected coal samples are universal and extensive.

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

