A new model for accurate estimation of gas content and pressure based on Langmuir adsorption equation in Guizhou,China

Abstract

In order to obtain the functional relationship of gas content and gas pressure, and to accurately calculate the two values which fitting the characteristics of coal seam, the destruction coefficient (X) and the index (ΔP) of the initial velocity of gas emission are introduced to establish the new model with higher precision based on Langmuir equation and destruction type of coal. The applicability of classic model (W-P model) and new optimization model in Guizhou mining areas are studied through the statistics of basic parameter data from 107 groups of coal-seam gas in eight mining areas. The results show that the gas content calculated by the classical model is lower than the measured value, while the gas pressure value is larger than that. The average relative error of gas content and pressure data reach 23.98% and 97.86%, respectively. The gas content and pressure data calculated by the optimization model are well fitted with the measured value. The fitting degree gradually rises with the increase of the sample size, and the average relative errors are 6.44% and 14.27%, respectively. Compared with the classical model, the average relative errors of gas content and pressure calculated by the optimization model reduce by 17.54% and 83.59%, respectively. The optimization model controls the tendency of calculated value error which significantly rises as the ΔP increases. For the coals with different destruction types, the average relative error of calculated gas content in optimization model ranges from 4.40% to 11.99%. And the average relative error of calculated pressure value ranges from 9.84% to 25.80%, both of them are far superior to that of classical model. The optimization model is more accurate for calculating the gas content and pressure in Guizhou.

Keywords

Gas outburst Langmuir equation gas content gas pressure optimization model

Introduction

Coal seam gas content is an important basic parameter in the field of gas disaster prevention, gas pre-extraction effect evaluation, coalbed methane resource evaluation and so on (Bodden and Ehrlich, 1998; Clarkson and Bustin, 2011; Hamilton et al., 2012; McGlade et al., 2013). Based on the relevant law in China, the gas content and gas pressure are traditionally used to classify the outburst-prone of coal seam, which decides the gas prevention level. Therefore, the accurate determination of the gas content is the foundation of gas control and utilization. Various methods have been developed to estimate the gas content of in-situ coal, and the determination techniques generally fall into two categories: direct methods and indirect methods.

The direct methods depend on the actual measurement of the volume of gas released from a coal sample, which requires on site gas desorption underground and the multiple measurements of residual gas in the laboratory. Since the direct gas content measurement method was introduced by Bertrard (1970), many modified methods have been developed to measure the gas content of coal for direct methods (Diamond and Schatzel, 1998; Xue and Yuan, 2017). The coalbed gas content testing procedure commonly referred to as the USBM direct method (Kissell et al., 1973). Direct methods can be further divided into closed sampling and desorption method (Wang and Wang, 2012). The closed sampling method refers to a special sampling device, which is characterized in that the coal sample can be automatically sealed under the original state in it. Then, the gas content is measured in the laboratory, and the measurement result is more realistic. However, the low success rate, high price and complicated process limit its popularity. On the other hand, the desorption method is currently widely used in the coal mining industry and promoted in many countries. The total gas content of a coal sample usually falls into three parts: lost, desorbed and residual gas. Each of these parts is generally measured or estimated by a different procedure, and then composes the total gas content of the sample. The method associated with the modified devices by Kissell et al. (1973) is referred to as the USBM direct method. For the similar process, the Chinese standard is GB/T23249-2009 (Chinese Standards, 2009a) during geological exploration period and GB/T23250-2009 (Chinese Standards, 2009b) for underground mine operations, and the American standard is ASTM D7569/D7659M-10 (ASTM International, 2010).

The key to the method is to eliminate or reduce the gas loss during sampling, which is the fundamental difference between the desorption method and other methods (Jin et al., 2010). The accuracy of the desorption method depends on the exposure time of coal sample during sampling and the accurate sampling location. Whether the conditions of the desorption law are completely or close to the conditions of the coal sample exposure process. Therefore, the direct desorption method needs a long measurement time and lots of work especially when a large number of measured coal seam gas contents are necessary based on the China’s law. These disadvantages make the current direct method low efficient and even influence the production schedule of coal mines (Wang et al., 2015).

The indirect methods are based upon empirical correlations or adsorption isotherm data related to gas pressure, gas emission rate, coal rank, porosity, etc. The gas content consists of the adsorbed and free gas in the methods. Gas content can be rapidly obtained by the measurement of adsorption constant and proximate analysis, and no need to seal the samples and gas desorption on site underground. Typically, the original gas pressure must first be measured on site or deduced according to the empirical correlations. Coal samples were collected for coal industry analysis, adsorption constant measurement and pore volume testing in the laboratory. Finally, the classic model (W-P model) which is deduced by the modified Langmuir equation is often used to quickly obtain the gas content and pressure as follows (Cheng et al., 2010; Guo et al., 2017; Li et al., 2008a, 2008b).

W = \frac{abp}{1 + bp} \cdot \frac{1}{1 + 0.31 M_{ad}} \cdot \frac{100 - M_{ad} - A_{d}}{100} + \frac{10 π P}{γ}

(1)

where W is the gas content, cm³/g; a and b are the Langmuir adsorption constants, dimensionless; p is the gas pressure, MPa; A_d is the ash content, %; M_ad is the moisture content, %. γ is the apparent density of coal, g/cm ³ ; and π is the porosity.

The indirect method has been preferably used in some mines because of the convenient operating process which only measuring the sorption isotherm in lab. In recent years, the correlation between gas content and geophysical log characteristics was established to apply in some mine area (Fu et al., 2009; Mullen, 1989). Based on gas desorption laws and the basic determination principle of coal seam gas content, Wang et al. (2015) proposed a method to theoretically measure the content of lost gas and residual gas. They are all essentially the empirical estimation curve technique and have a successful application in some mines.

W-P classic model can quickly and conveniently obtain the gas content or pressure data. This feature has significant theoretical and practical value to predict the risk of coal and gas outburst, discuss the occurrence condition of gas resources and guide the safe production for coal mine. According to the practical application and based on equation (1), there are certain errors between gas content or gas pressure obtained from calculated with the measured values (Jiang et al., 2016). In practical engineering application of Guizhou mine area of China, there is a large error between the gas content in No. 9 coal seam in Linhua mine calculated by equation (1) with the actual value. In addition, under the condition of 0.74 MPa gas pressure and 8.0 m³/t gas content in outburst coal seam in Guizhou, there is also a great difference for gas content and gas pressure in corresponding coal seam. The critical values of gas pressure and gas content (0.74 MPa and 8.0 m³/t, respectively) recommended in the Regulations for Prevention and Control of Coal & Gas Outburst in China cannot truly reflect the outburst risk of coal seam in Guizhou. For instance, the gas pressures of No. 5 and No. 19 coal seam in Xiangshui coal mine are under 0.74 MPa, however, the corresponding gas content are 11.28 m³/t and 6.76 m³/t, respectively. And for No. 9 coal seam in Linhua coal mine, the corresponding gas content and gas pressure are 16.10 m³/t and 0.40 MPa, respectively. There exists a great mismatch in the critical values of gas content and pressure in different coal seams. Therefore, it is of great significance for guiding production to improve the accuracy of W-P model and obtain reliable data of gas pressure and gas content.

Theoretical analysis

The previous study indicated that the relation between the gas adsorption content of coal combustibles and gas pressure could be described by the Langmuir equation (Cao et al., 2013; Langmuir, 1918; Levy et al., 1997; Liu et al., 2012; Ruppel et al., 1974; Zhou et al., 2016). There is a linear relationship between free gas content and the gas pressure in coal, and gas pressure can be inversely calculated by the Langmuir equation with gas content when the coal seam is intact or relatively intact. When the coal seam is in a broken and discrete state, it presents a lump state, and the Langmuir equation is not suitable for the inverse calculation for gas pressure and gas content.

The basic hypothesis of establishing Langmuir classical physical model is that the molecules are monolayer adsorption state with uniform solid surface. There is no intermolecular interaction among the adsorbed molecules on the solid surface, and the free and adsorbed gas keep the dynamic equilibrium state (Clarkson and Bustin, 2000; Jiang et al., 2016; Langmuir, 1918). During many years of research, many scholars have found that there are some limitations in the accuracy of W-P classical model based on the Langmuir equation (Jiang et al., 2016; Zhang, 2012; Zhang et al., 2005; Zhao and Tang, 2002). First of all, one of the foundations of Langmuir equation is that gas adsorption occurs on the nonporous solid surface. However, nano-pore in coal provides main adsorption space for CH₄ based on the study of pore structure (Cai et al., 2013; Clarkson and Bustin, 1999; Karacan and Okandan, 2001; Radlinski et al., 2004). Moreover, fractal characterization of adsorption-pores of coals indicates that there is a high heterogeneity in nano-pore of coal (Friesen and Mikula, 1987; Fu et al., 2005; Yao et al., 2008). Although the coal-based adsorbed methane molecules can reveal the characteristics of Langmuir adsorption isotherm, the porous condition of coal matrix is not based on the hypothesis of Langmuir theory. Second, there are both surface adsorption and volume filing when coal matrix adsorbs the methane molecule (Debelak and Schrodt, 1979). Zhao and Tang (2002) point out the gas molecules are not simply covered on the surface of coal matrix in the manner of monolayer; methane molecules will fully fill the inner space of microporous pores when the pressure rises to a certain limit, i.e. the “Volume filling Theory”. Micropores are characterized by volume filling (Dubinin and Radushkevich, 1947; Jaroniec and Choma, 1989; Mahajan and Walker Jr, 1978), whereas larger pores fill with adsorbed gas layer by layer on the internal surface of the pores. Therefore, the volume of micropores is thought to be the main control upon gas adsorption (Dubinin, 1975). Third, there exists a possibility that gas occurs within the coal matrix in the state of solid-solution of cage-type crystal compound (Zhao and Tang, 2002). As ”excess” gas exists in case of gas outburst, Li et al. (2008a, 2008b) analyzed the molecular structure and formation mechanism of methane hydrate and pointed out that methane hydrate may exist in porous medium coal. The excess adsorption indicates that the gas may exist in coal in similar form to natural gas hydrate, that is, the form of solid-solution state of cage-type crystal compound (Bae and Bhatia, 2006; Mosher et al., 2013; Zhang et al., 2014).

Actually, the gas occurrence regularity in coal is controlled by pore structure and gas diffusion, especially for the tectonically deformed coals (TDCs). The TDCs are unstable and easily lead to catastrophic failures, such as outbursts, during mining due to the relatively unconsolidated characteristic of the granular coal and a large amount of gas contained within them (Cao et al., 2000; Ju et al., 2005). The tectonic deformation usually controls the pore size distributions (PSDs) and further influences the seepage-porosity and the variation in adsorption-porosity (Li et al., 2015a, 2015b; Song et al., 2017a). Tectonic deformation has the significant effect on the nano-scale structure of coal for both the macro-molecule and nano-pores. Though the nano-pore structure determines the differences in structure diversity in TDCs, the transformation effect of tectonic deformation on the surface heterogeneity gradually weakened with the decreasing of the pore scale (Song et al., 2017b, 2018). The pore volume, pore surface area, micro-pore volume and pore connectivity increase with the increase in deformation extent. The CH₄ adsorption capacity of coals shows an increasing trend from brittle deformation to ductile deformation. The coal structure, pore and fracture characteristics of TDCs control the gas adsorption capacity of coals (Yao et al., 2014). The physical and chemical texture of TDCs produced by various formational mechanisms is different from those of primary coals, thus resulting in major differences among the physical properties of the reservoirs of these coals. The adsorption/desorption process of methane in the deformed coals is not consistent with primary coals, which form an effect of hysteresis in different kinds of TDCs (Ju et al., 2009). The adsorption capacity of methane is higher for the deformed coal samples than for the intact ones. The adsorption capacity of different structure coals can be arranged in a descending order: mylonitized > granulated > cataclastic > intact. Both the specific surface area and the pore volume increase with the increase of deformation degree. The adsorption potential and surface free energy for different-structure coals under the same adsorption space volume increase with the increase of deformation degree (Meng et al., 2016).

The pore system in the coal seam is the place where gas is adsorbed and enriched, and it plays a role in the diffusion process of gas. The micropores and specific surface area are indicators that reflect the adsorption capacity of methane. The pore size also reflects the change in the desorption velocity of gas in coal. The macropore and mesopore are developed well in low rank coal, and the pore volume is greater, the desorption velocity of gas is greater. While the micropore develop well in high rank coal, the desorption velocity is relatively lower (Gamson et al., 1996). Diffusion is the movement of molecules from a region of high concentration (or high chemical potential) to a region of low concentration (or low chemical potential) as a result of random motion of the molecules. Diffusion is driven by a gradient in chemical potential of the diffusing species. The pore size controls the diffusion rate which is greater in large-pore, and the diffusion is inhibited in small-pore. The fracture system acts as the main bridge, and the subsystems of the pores are connected to form the main subsystem structure of the gas migration. The fracture system connects or communicates the pores in the matrix into a network. Diffusion and seepage occur alternately, forming a mutually complementary and mutually controlled gas flow situation. The permeability of coal seam controls the desorption and migration of gas, and also depends entirely on the development of fracture system. The seepage is the dominant flow in fracture system and thus gas flow volume is controlled by fracture characteristics. The dual-porosity structure is a unique medium property of coalbed methane, and its distribution and changes control the migration of gas in coal. The previous studies also prove that the interior coal is full of multi-scale pores with varied sizes (Chen et al., 1998; Jiang et al., 2011; Song et al., 2014). Based on this analysis, it is believed that the main source of gas is the filling free gas in pores during the first minute of gas diffusion when testing the index (ΔP) of the initial velocity of gas emission. The ΔP indicates the difference between the gas discharge amount of 45–60 s expressed by nmHg and the gas discharge amount within 0–10 s after adsorbing gas at one atmosphere. The ΔP is one of the coal quality indicators of coal, which characterizes the microstructure of coal. It not only reflects the diffusion ability of gas, but also reflects the law of gas infiltration and flow, which plays an important role in the prediction of gas outburst.

The above analysis demonstrates that there are both the objective factors of test error and the limitation of model accuracy in respect of the reasons for error between the calculated value and measured value of gas pressure and content (Busch and Gensterblum, 2011; Hao et al., 2014). Thus, it is necessary to consider multiple factors to optimize the model. Based on the theories and existing problems above, the above influencing factors are all related to deformation feature and gas diffusion. Therefore, we choose the destruction coefficient of coal (X) and the index (ΔP) of the initial velocity of gas emission as the additional parameters to establish the W-P optimization model.

Methodology

Data collection and statistics

In Guizhou, the main coal-bearing strata belong to the Paleozoic Permian Upper Longtan Formation (P2l) and the Wangjiazhai Formation (P2c), which contains 5–80 coal seams. There are 1–7 main recoverable coal seams and the average thickness is 1.1–2.0 m, and the coal resources account for 98% of the total amount in Guizhou. The main coal accumulation period in Guizhou is the Late Permian. Based on the analysis of the regional tectonic evolution, the area is significantly affected by the Anyuan orogeny of the Indosinian period and the Yanshan movement of the Yanshan period, as well as the late Himalaya movement. The main coal-rich areas in Guizhou are distributed on the edge of the Yangtze block, which belongs to interactive marine and terrestrial deposit. The Yangtze block is pushed by the block of Tibet-Yunan in the west, the south is pushed by the Indo-China plate, and the east is pushed by the long-term collision of the Pacific plate from the southeast to the northwest. Therefore, the Yangtze plate is squeezed and sheared particularly in Guizhou, and the northwest-south-east direction extrusion and shearing action are the most significant. The Permian coal-bearing strata in Guizhou Province generally belong to the high gas and outburst coal seams. The distribution of coal mine in the research area is shown in Figure 1.

Figure 1.

The distribution of coal mine in the west of Guizhou, China.

The sample covers eight mining areas in Guizhou, including Panjiang, Shuicheng, Liuzhi, Zhina, Qianbei, Qianxibei, Lindong and Puxing. They include the main mining coal seams in various mining areas in Guizhou, with a total of 55 layers of coal. The coal structures of these coal samples include intact, cataclastic, granulated and mylonitized coal (Cao et al., 2000; Ju et al., 2005). According to the morphological features of coal under different tectonic stress regimes, coal structures can be classified into five types, including integrated, blocky, cataclastic, granulated and mylonitized structures as shown in Table 1 (GB/T 30050-2013).

Table 1.

The characteristics of different destruction types of coals.

	Intact coals		Deformed coals
Characteristics contrast	Integrated coal (I)	Blocky coal (II)	Cataclastic coal (III)	Granulated coal (IV)	Mylonitized coal (V)
Visibility of macroscopic lithotype	Clearly visible	Clearly visible	Visible	Not easy to identify	Unable to identify
Texture and Structure	Layered and blocky structures with distinct bands	Stripe texture and horizontal bedding structure	Traceable stripe structure and angular nubby structure	Broken into pieces and no significant angular structure	Compressed into blocks or solid particles, oriented into foliation and mostly scaly, with crumpled slip surface and mirror surface
Basic granule size/mm			>2–10	1–2	<1
Broken state	Integrated, great hardness, blocky	Easy to peel into small pieces by hand, medium hardness	Angular, no significant orientation arrangement and displacement	Broken into tablets and occasionally including intact coal shivers, orientation arrangement and displacement	Powder, pulverized into solid block, powder
Cracks and permeability	Completed fracture, high permeability	Completed fracture and relatively high permeability	Well-developed cleats, high permeability	Less developed cleats and cracks, low permeability	No cleats, cracks filled by coal powder, very low permeability
Adsorption and emission	High hardness, low ΔP	High hardness, relatively low ΔP	Strong adsorption capability, with the increase of deformation, coal strength decreases and ΔP increases

The gas content and pressure are obtained by actual measurement according to the China’s standard (Chinese Standards, 2007, 2009b). The moisture, volatile matter, ash, and the fixed carbon of all coal samples are determined based on ASTM standards (ASTM International, 2015). The adsorption parameters are obtained by Chinese Standards (2008). The ΔP is measured according to the industrial standard of Chinese Standards (2009c). The gas and coal parameters of the typical area are shown in Table 2.

Table 2.

The gas parameters of coal seam in the typical mining area of Guizhou.

Mining area	Mine	Destruction type	△P (mmHg)	a (cm³/g)	b (MPa⁻¹)	Moisture content, M_ad (%)	Ash content, A_d (%)	Porosity (%)	Gas pressure (MPa)	Gas content (m³/t)
Liuzhi	Xinhua	III–IV	25.00	36.91	1.03	1.92	22.73	7.02	1.65	14.02
Liuzhi	Pumao	III–IV	57.00	26.47	1.00	1.81	8.04	4.79	1.23	14.50
Panjiang	Longxin	III–IV	17.94	38.59	1.17	1.02	14.71	5.84	0.24	7.62
Panjiang	Maidi	II–III	13.88	29.35	0.98	1.48	13.62	3.50	0.69	8.22
Shuicheng	Miluo	III	11.00	35.12	0.89	2.3	15.28	4.24	1.04	9.84
Shuicheng	Dongfeng	III	16.10	34.11	0.96	1.37	19.45	5.14	1.02	12.84
Zhina	Fenghuang	II–III	16.94	41.18	1.50	3.70	7.26	4.61	0.22	6.25
Zhina	Fukang	II–III	14.00	33.75	0.54	0.82	17.32	3.42	2.13	13.39
Qianbei	An’neng	II–III	28.14	39.63	1.43	2.23	20.71	5.45	1.05	14.11
Qianbei	Guixing	III	28.46	32.88	1.58	2.25	18.91	5.45	0.96	12.80
Qianxibei	Guiqing	III–IV	16.87	43.58	0.99	3.16	21.58	7.06	0.59	10.83
Qianxibei	Yuxing	II–III	20.75	34.11	1.31	1.45	12.94	4.61	0.41	7.27
Lindong	Nanshan	II–III	29.00	31.63	0.72	2.25	29.58	4.85	0.48	5.34
Lindong	Xinqiao	III	21.50	35.65	0.98	2.35	14.80	4.49	0.32	5.18
Puxing	Yonggui	II–III	14.06	32.46	1.53	2.67	26.26	5.75	0.24	5.25
Puxing	Luxing	II–III	19.10	32.64	0.72	1.58	15.73	6.54	0.67	9.08

W-P optimization model

Li et al. (2016) developed the new diffusion model for dynamic diffusivity, and the description accuracy of this model for diffusion process is much better than that of the classical diffusion model. The basic hypothesis of theory of new diffusion model for dynamic diffusivity is that the inner coal is constituted of numerous pores with varied scales. Following the pore classification method (Hotot, 1966; Sing, 1985), coal pores could be classified into micropores (pore size d ⩽ 10 nm), mesopores (10 nm < d < 1000 nm), and macropores (d ⩾ 1000 nm). The pore structure of coal, mainly consists of the matrix pore and the cleat system, which controls the gas transport in coal seam (Cui et al., 2004). It is generally assumed that gas through a crack system relates to a seepage or laminar flow process which is pressure-driven and may be described using Darcy’s law, whereas gas through the matrix relates to a diffusion process which may be described using Fick’s law. There are three distinct diffusion mechanisms: Fickian diffusion, Knudsen diffusion, and surface diffusion (Pan et al., 2010). The diffusion coefficients are generally obtained based on Fick’s second law, with various porous models including the unipore bidisperse, and modified bidisperse. The gas diffusion in coal is controlled by pressure and temperature, the coal matrix swells may be ignorable and the main transport model is the surface diffusion under low pressure (Charrière et al., 2010). Molecular simulations show that diffusion in micropores is predominant for gas transport in coal, and the transport diffusion coefficient increases first and then decreases with the rising of pressure, because dominating mechanism changes from surface to configurational diffusion (Hu et al., 2017; Song et al., 2017c; Zhao et al., 2016). Meanwhile, the gas pressure, gas content, pore structure of coal, specific surface area and ΔP show that these parameters have some inherent correlations (Du et al., 2012; Jia and Sun, 2013; Lin et al., 2016; Peng et al., 2009). Du et al. (2012) investigated the relationship between the gas expansion energy, gas pressure and ΔP. Jia and Sun (2013) and Zhang et al. (2016) examined the difference of ΔP with different destruction degree. Lin et al. (2016) analyzed the influence of adsorption hole structure on the ΔP. Cheng et al. (2017) established the high-precision calculation model for the ΔP which includes the ash content, volatile matter, porosity, sturdiness coefficient and other parameters. In this study, in order to establish a succinct and scientific model, we choose the destruction type and the ΔP as the key parameters through the comprehensive analysis.

Based on the statistical data, the relationships between the average measured gas content (pressure) and the ΔP are shown in Figure 2. The relationships between the average measured gas content (pressure) and the different destruction types are shown in Figure 3.

Figure 2.

The average measured value of gas content/pressure in different ΔP intervals.

Figure 3.

The average measured gas content/pressure of coal with different destruction types.

Figure 2 indicates that the average measured gas content and pressure in different ΔP intervals first decrease and then increase as the ΔP increases. Figure 3 shows that average measured gas content and pressure of coal with different destruction types tend to decrease with the increase of coal's destruction degree.

Based on achievements of many scholars, the destruction types of coal and the ΔP are the macroscopic characterization of coal property. In combination with the analysis on the effect of destruction type and diffusion velocity, the multi-parameter and overall properties of W-P model can be reflected by the destruction type and ΔP. Through the analysis and fitting of basic parameters of 107 groups of coal-seam gas in coal mine area of Guizhou, the concept of destruction coefficient is introduced based on destruction type of coal. Combined with the ΔP which can reflect the diffusion characteristics of free gas, the W-P optimization model is established:

W = \frac{abp}{1 + bp} \cdot \frac{1}{1 + 0.31 M_{ad}} \cdot \frac{100 - M_{ad} - A_{d}}{100} + \frac{10 π P}{γ} + \frac{Δ P}{3 X}

(2)

where W is the gas content, cm³/g; a and b are the adsorption constants; p is the gas pressure, MPa; A_d is the ash content, %, M_ad is the moisture content,%. γ is the apparent density of coal, g/cm ³ ; π is the porosity; ΔP is the index of initial velocity of gas emission, nmHg; X is the destruction coefficient, dimensionless.

The destruction coefficient of different destruction types of coal is shown in Table 3.

Table 3.

The destruction coefficient of different destruction types.

Destruction types of coal	Destruction coefficient (dimensionless)
I	1
II	2
III	3
IV	4
V	5

If the destruction type of coal in the test area is between two types of destruction, the mean value of destruction coefficients is selected.

Results

Gas content

Based on the measured gas pressure, the statistical 107 sets of gas parameter data shall be substituted into W-P classical model and optimization model respectively for calculating and acquiring the gas content. The contrast distribution of calculated data and the measured data of these two models are shown in Figures 4 and 5, respectively.

Figure 4.

The calculated value of gas content based on the W-P classical model.

Figure 5.

The calculated value of gas content based on the W-P optimization model.

Figures 4 and 5 show that the gas content calculated from the measured gas pressure based on W-P classical model is less than the gas content measured in field. The gas content calculated by W-P optimization model is fitted well with the measured gas content, and the data mainly fluctuate around the measured gas content. As the measured gas content is greater, the fitting degree of gas content calculated by W-P optimization model with the measured content rises, and the fluctuation error reduces.

In order to quantify the differences between the two models, the normal distribution of relative error between the gas content and the measured gas content data calculated by the two models are investigated, respectively, as shown in Figures 6 and 7.

Figure 6.

The relative error normal distribution of gas content calculated by the W-P classical model.

Figure 7.

The relative error normal distribution of gas content calculated by the optimization model.

According to Figure 6, the relative errors of the gas content data of each group calculated by W-P classical model and the measured gas content data are mainly distributed between 10% and 35%. The highest relative error is up to 60%, and the average relative error is 23.98%. Figure 7 shows that the relative errors of the gas content data of each group calculated by W-P optimization model and the measured gas content data are mainly distributed between 0% and 5%. The highest relative error is up to 55%, and the average relative error is 6.44%.

Gas pressure

Based on the measured gas content, the statistical 107 sets of gas parameter data shall be subdivided into the W-P classical model and the optimization model for calculating and acquiring the gas pressure, respectively. The contrast distribution of the calculated pressure and the measured pressure of two models are shown in Figures 8 and 9, respectively.

Figure 8.

The calculated value of gas pressure based on the W-P classical model.

Figure 9.

The calculated value of gas pressure based on the W-P optimization model.

Figure 8 shows that the gas pressure calculated by W-P classical model is greater than that of the measured gas pressure. The calculated pressure fluctuates in a large range and the error increases with the increase of gas pressure. Figure 9 shows that the gas pressure calculated by W-P optimization model fluctuates around the measured gas pressure, and the fitting degree gradually rises with the increase of gas pressure.

In order to quantify the differences of two models, the normal distribution of relative errors of gas pressure calculated by classical model/optimization model and the measured gas pressure data are shown in Figures 10 and 11, respectively.

Figure 10.

The relative error normal distribution of gas pressure calculated by the W-P classical model.

Figure 11.

The relative error normal distribution of gas pressure calculated by the W-P optimization model.

Figure 10 indicates that the relative errors of the gas pressure data of each group calculated by W-P classical model and the measured gas pressure data are mainly distributed between 0% and 100%. The highest relative error in this statistical data is up to 700%, and the average relative error is up to 97.86%. Figure 11 shows that the relative errors of the gas pressure data of each group calculated by W-P optimization model and the measured gas pressure data are mainly distributed between 0% and 10%. The highest relative error in this statistical data is 100%, and the average relative error is 14.27%. According to the comparison, the relative error of predictive values of W-P optimization model is significantly lower than that of the classical W-P model. It is more accurate to predict the measured gas content and gas pressure in coal seam.

Discussion

Application comparison of coal with different types of destruction

The 107 sets of data are classified according to the destruction types of coal. In these statistical data, the coal of type I and V is very few. The types II, III and IV account for 17.70%, 61.62% and 20.52%, respectively. The application of two models in different types of coal is investigated. The relationship between the average relative error of the calculated gas content with destruction types is shown in Figure 12. The relationship between the average relative error of the calculated gas pressure with destruction types is shown in Figure 13.

Figure 12.

The average relative error of the calculated gas content changes with destruction types.

Figure 13.

The average relative error of the calculated gas pressure changes with destruction types.

Figures 12 and 13 demonstrate that the average relative error has no uniform variation as the destruction degree increases, which is calculated by the classic model. The average relative error of gas content and pressure calculated by the optimization model rises as the destruction degree increases. However, the average relative error of the calculated values is less than that of the classical model, and the average relative error of the calculated gas content increases from 4.40% to 11.99%, which is lower than the minimum mean relative error of the classical model 24.84%. The average relative error of the calculated pressure increases from 9.84% to 25.80%, which is lower than the minimum mean relative error of the classical model 87.00%. It indicates that the destruction type of coal is a key factor affecting the model accuracy, and the introduction of destruction type in the optimization model can promote the model accuracy.

Application comparison of different ΔP

The ΔP in this study ranges from 5.435 mmHg to 57.000 mmHg. The ΔP is divided into different intervals from small to large, and the average relative error of the calculated values of two models at different ΔP intervals is investigated. The average relative error of the calculated gas content is shown in Figure 14, and the average relative error of the calculated gas pressure is shown in Figure 15.

Figure 14.

The average relative error of the calculated gas content changes with ΔP.

Figure 15.

The average relative error of the calculated gas pressure changes with ΔP.

Figure 14 indicates that the average relative error of the calculated gas content of classical model increases from 20.19% to 30.45% with the increase of ΔP, and that of the optimization model is stable with few fluctuations, ranging from 4.97% to 6.94%. Figure 15 shows that the average relative error of the calculated gas pressure of classical model increases from 49.00% to 278.31% with the increase of ΔP, and that of the optimization model rises with the increase of ΔP. However, the average relative error of the calculated pressure at different ΔP intervals reduces to 11.56–20.06%.

In general, the error of the calculated value of the classical model rises progressively with the increase of ΔP. The introduction of X and ΔP in the optimization model can significantly control the trend that the error of the calculated values rises with the increase of ΔP.

Conclusion

Through the analysis and fitting of basic parameters of coal seam gas in coal mine areas of Guizhou, the destruction coefficient is introduced to establish W-P optimization model based on the destruction type of coal. The fitting of the W-P classic model and optimization model for statistical data demonstrates that W-P optimization model is better than the classic model in both respects of error fluctuation range and average relative error.

Based on gas content calculated by the measured gas pressure, the average relative error of W-P optimization model reduces by 17.54% than that of W-P classic model. Based on gas pressure calculated by the measured gas pressure, the average relative error of W-P optimization model reduces by 83.59% than that of W-P classic model.

For the coals with different destruction types, the calculated values of the optimization model still tend to rise with the increase of destruction degree. However, the average relative error of the calculated gas content is 4.40–11.99%, which is lower than the minimum mean relative error of the classical model. The average relative error of the calculated gas pressure is 9.84–25.80%, which is also lower than the minimum mean relative error of classical model.

The error of the calculated values of classical model significantly increases with the increase of ΔP. The optimization model significantly controls the trend that the error rises with the increase of ΔP.

The average relative errors of the calculated gas content and pressure in optimization model are 4.97–6.94% and 11.56–20.06%, respectively, which are superior to 9.84–25.80% and 49.00–278.31% of classic model. It can be acquired that the W-P optimization model established in this paper is more suitable for investigating the relationship between the gas content and gas pressure than the classical model in Guizhou. Meanwhile, it can provide more accurate calculated values of gas content and gas pressure for safe production in coal mines.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the laboratory staffs of Guizhou Institute of Mine Safety and Science for the assistance in experimental data processing, the National Natural Science Foundation of China (General Program, 51574231), the Guizhou Science and Technology Fund (Guizhou Science & Cooperation Base [2016]1083), the Guizhou Province Science and Technology Hall Significant Special Plan Project ([2018]3003-2, [2018]3004). The authors wish to thank these organizations for the financial support.

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