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Abstract

The capacity of coal to adsorb methane is greatly affected by temperature and, in recent years, temperature-dependent adsorption has been studied by many researchers. Even so, comprehensive conclusions have not been reached and conflicting experimental results are common. This paper reviews the current state of research regarding the temperature-dependent adsorption of methane in coal and catalogs the conclusions from experiments conducted on that subject by 28 researchers, as published between 1995 and 2017. Probability theory and statistics are used to show that the conclusion generally accepted by most researchers is that the amount of methane adsorbed by coal decreases with increasing temperature. It is highly likely that the Langmuir volume decreases as the temperature rises, and it is also probable that the Langmuir pressure increases at higher temperatures. Equations are presented that express the relationships between methane adsorption, Langmuir volume, Langmuir pressure, and temperature. Future research should be directed toward determining the relationship between Langmuir pressure and temperature. The results of the study presented herein provide a theoretical basis for predicting the gas content in coal seams and improving the efficiency of coalbed methane development.

Keywords

Methane coal adsorption temperature statistical analysis experiment

Introduction

Coal mine methane (CMM) adsorption is an important topic associated with the study of coal gas outbursts, and is also relevant to the exploration, development, and utilization of coalbed methane. Temperature is one of many important factors that influence the capacity of coal to adsorb CMM (Pan et al., 2012; Sakurovs et al., 2008; Tang et al., 2015; Wang et al., 2015). Recently, especially over the last 20 years, research concerning temperature-dependent CMM adsorption has greatly increased and many studies have been conducted. There are three main reasons for this increase in interest. First, coalbed and shale methane reservoirs have become an important source of natural gas, and a significant proportion of the gas in these reservoirs exists in an adsorbed state. Because gas adsorption is temperature-dependent, the geothermal gradient in a reservoir affects the adsorption capacity of the host rocks or coal. Thus, accurately accounting for the temperature dependence of gas adsorption is important for reliable gas-in-place estimates (Feng et al., 2018; Pongtorn et al., 2015). In addition, temperature also affects gas desorption–diffusion during coal sample collection when drilling (Sakurovs et al., 2008; Wang et al., 2015). The second reason for increased interest is related to gas desorption. One state-of-the-art coal seam degasification technique used to lower a coal seam’s methane content and pressure employs thermal effects. Specifically, increasing the internal energy of the CMM accelerates gas adsorption and diffusion. This thermal effect can be produced by hot-water injection, flue gas injection, water jetting, an electromagnetic field, or ultrasonic vibrations (Ge et al., 2011; He, 1996; He et al., 2010; Li et al., 2011; Yang et al., 2008, 2010, 2013). For all of these techniques, the effect of temperature on gas adsorption and diffusion should be considered. Third, the geological sequestration of CO₂ is one means of reducing CO₂ emissions and their effect on atmospheric temperatures (Gasparik et al., 2014; Holloway, 2005; Liang et al., 2018). Research has shown that deep, unmineable coal seams are a favorable geological environment for CO₂ sequestration. CO₂ injection into coalbed methane reservoirs has also been used to enhance coalbed methane recovery (Kronimus et al., 2008; Morsi and Schroeder, 2005; Van Bergen et al., 2006). The combination of reservoir temperature and pressure also determines the phase of the stored CO₂ (gas, liquid, or supercritical fluid) as well as the capacity of the storage reservoir (Gensterblum et al., 2014; Sakurovs et al., 2008).

Many researchers worldwide have conducted numerous experiments concerning CMM temperature-dependent adsorption. These investigations have generated a large amount of data regarding the effect of temperature on methane adsorption in coal. The results from some of these studies agree, but other studies reach divergent conclusions. There does seem to be a general consensus that the methane adsorption capacity of coal decreases as temperature increases (Chen et al., 1995; Crosdale et al., 2008; Cui et al., 2003; Hao et al., 2014; Liang, 2000; Pini et al., 2010; Sakurovs et al., 2008; Wang et al., 2012; Yu et al., 2015; Zhang and Tao, 2011; Zhao et al., 2001; Zhong et al., 2002), but the effects of temperature on the Langmuir volume (V_L) and Langmuir pressure (P_L) remain controversial. Some researchers believe that V_L decreases but P_L increases with increasing temperature (Lin et al., 2012; Pini et al., 2010; Zhang and Tao, 2011; Zhao et al., 2001; Zhu et al., 2010), while some maintain that both V_L and P_L decrease with increasing temperature (Chen et al., 1995; Lin et al., 2014). Still others have concluded that both V_L and P_L increase with increasing temperature (Hao et al., 2014; Wang et al., 2012).

All the above viewpoints were acquired based on the results of experiments performed by many different researchers and so it is difficult to judge which hypotheses are valid. Variations in experimental conditions, laboratory apparatus, and the type of coal samples used in the experiments performed in assorted laboratories by different investigators undoubtedly have a significant effect on the results. In addition, results acquired through a single set of experiments performed by one research group have potential one-sidedness and randomness, and so it is understandable that a lack of consensus could arise.

The aim of this paper is to eliminate the effects of uncertainty on the results of individual experimental programs and to thoroughly and comprehensively assess the effects of temperature on methane adsorption capacity. The conclusions regarding temperature-dependent CMM adsorption reached by 28 scholars based on experimental work between 1995 and 2017 have been tabulated and analyzed, employing probability theory and statistical processes. The aim of this work was to determine the overall effect of temperature on methane adsorption, to point out shortcomings in current experimental procedures, and to propose improvements that will make experiments performed in different laboratories easier to compare.

Qualitative summary of published experimental results regarding methane adsorption, V_L, P_L, and temperature

Between 1995 and 2017, 28 groups from various countries conducted 62 series of experiments on the temperature dependence of CMM adsorption. The results from these 62 trials are summarized in Table 1. A total of 25 of these researchers (representing 56 groups of experiments) were from the People’s Republic of China, while three investigators (representing six groups of experiments) were from other countries.

Table 1.

Summary of experimental results reported between 1995 and 2017 concerning the effect of temperature on the quantity of methane adsorbed by coal.

No.	Adsorbent	Location	Coal rank	Pressure range (MPa)	Temperature range (K)	RMACTP/NDP	RLVTP/NDP	RLPTP/NDP	References
1	Hongni coal	Sichuan, China	Anthracite	0.1–4	252–323	Decrease/32	Decrease/6	Decrease/ 6	Chen et al. (1995)
2	Xiangshan coal	Shanxi, China	Meagre coal	0.16–5.02	298–318	Decrease/30	Decrease/5	Disorder/5	Liang (2000)
3	Loutian coal	Liaoning, China	Long flame coal	0.1–6	303–343	Decrease/27	Decrease/3	Increase/3	Zhao et al. (2001)
4	Aiweier coal	Sinkiang, China	Coking coal	0.1–6	303–343	Decrease/27	Decrease/3	Increase/3
5	Shuoli coal	Anhui, China	Meagre coal	0.1–6	303–343	Decrease/27	Decrease/3	Increase/3
6	\	China	Gas coal	0.1–8	298–323	Decrease/24	Increase–decrease/4	Increase/4	Zhong et al. (2002)
7	\	China	Anthracite	0.1–8	298–323	Decrease/24	Constant/4	Increase/4	Zhong et al. (2002)
8	\	China	Gas coal	1–8	293–323	Decrease/24	Decrease/4	Increase/4	Cui et al. (2003)
9	\	China	Coking coal	1–8	293–323	Decrease/24	Constant 4	Increase/4
10	\	China	Meagre coal	1–8	293–323	Decrease/24	Decrease/4	Increase/4
11	\	China	Anthracite	1–8	293–323	Decrease/24	Decrease–increase/4	Increase/4
12	Qinshui coal	Shanxi, China	Gas coal	1.3–8	293–323	Decrease/24	Disorder/4	Increase/4	Zhang et al. (2004)
13	Shouyang coal	Shanxi, China	Coking coal	1.3–8	293–323	Decrease/24	Constant/4	Increase/4
14	Liuling coal	Shanxi, China	Meagre coal	1.3–8	293–323	Decrease/24	Decrease/4	Increase/4
15	Xinji coal	Huainan, China	Anthracite	1.3–8	293–323	Decrease/24	Decrease–increase/4	Increase/4
16	Wangjiahe coal	Shanxi, China	Coking coal	0.5–8	298–323	Decrease/24	Decrease/4	\	Xie and Chen (2007)
17	Xiayukou coal	Shanxi, China	Coking coal	0.5–7	293–323	Decrease/24	Decrease/4	Constant/4	Zhang et al. (2009)
18	Xiayukou coal	Shanxi, China	Meagre coal	0.5–7	293–323	Decrease/24	Decrease/4	Decrease/4
19	Cuijiagou coal	Shanxi, China	Long flame coal	0.5–7	293–323	Decrease/24	Decrease/4	Constant/4
20	Xinji coal	Huainan, China	Gas coal	1–8	293–323	Decrease/24	Decrease/4	Increase/4	Zhu et al. (2010)
21	Songzao coal	Chongqing, China	Anthracite	1–5	303–343	Decrease/35	Decrease/5	Increase/5	Zhang and Tao (2011)
22	Zhaolou coal	Shandong, China	Coking coal	0.1–5.2	293–323	Decrease/56	Increase/7	Increase/7	Wang et al. (2012)
23	Sihe coal	Shanxi, China	Anthracite	0.5–8	288–313	Decrease/48	Decrease/6	Increase/6	Lin et al. (2012)
24	Zhaiyadi coal	Shanxi, China	Coking coal	0.1–9	288–313	Decrease/71	Decrease/6	Increase/6	Lin et al. (2012)
25	Beizao coal	Shandong, China	Lignite	1–16	303–323	Decrease/30	Decrease/3	Decrease/3	Liu et al. (2012)
26	Caiyuan coal	Shandong, China	Gas coal	1–16	303–323	Decrease/30	Increase–decrease/3	Decrease/3
27	Xiqu coal	Shanxi, China	Coking coal	1–16	303–323	Decrease/30	Increase/3	Increase–decrease/3
28	Guhanshan coal	Henan, China	Anthracite	1–16	303–323	Decrease/30	Increase–decrease/3	Decrease/3
29	Jiulishan coal	Henan, China	Anthracite	\	303–333	Decrease	Constant/4	Increase/4	Li et al. (2012)
30	Xingqing coal	Qinghai, China	Fat coal	0–3.5	298–328	Decrease/21	Decrease/3	Increase–decrease/3	Feng et al. (2012)
31	Xutong coal	Anhui, China	Gas coal	0.1–10	303–343	Decrease/27	Decrease/3	Disorder/3	Pan et al. (2012)
32	Xutong coal	Anhui, China	Gas coal	0.1–10	303–343	Decrease/27	Decrease/3	Disorder/3
33	Xutong coal	Anhui, China	Gas coal	0.1–10	303–343	Decrease/27	Decrease/3	Disorder/3
34	Xinji coal	Anhui, China	Gas coal	1–8	293–323	Decrease/24	Decrease/4	\	Jiang (2014)
35	Miaowan coal	Shanxi, China	Coking coal	1–8	293–323	Decrease/24	Decrease/4	\
36	Quzhuang coal	Shanxi, China	Meagre coal	1–8	293–323	Decrease/24	Decrease/4	\
37	Zhengcun coal	Shanxi, China	Anthracite	1–8	293–323	Decrease/24	Decrease/4	\
38	Xingqing coal	Qinghai, China	Long flame coal	1–8	303–323	Decrease/24	Increase/3	Increase/3	Hao et al. (2014)
39	Qinghua coal	Qinghai, China	Long flame coal	1–8	303–323	Decrease/24	Increase/3	Increase/3
40	Xujiadong coal	Hunan, China	Long flame coal	1–8	303–323	Decrease/24	Increase/3	Increase/3
41	Leiyang coal	Hunan, China	Anthracite	1–8	303–323	Decrease/24	Increase/3	Increase/3
42	\	Shanxi, China	Coking coal	0.7–6.5	293–323	Decrease/24	Decrease/4	Decrease/4	Lin et al. (2014)
43	Pingdingshan coal	Henan, China	Fat coal	1.5–8	293–313	Decrease/21	Decrease/3	Increase/3	Yu et al. (2015)
44	Pingdingshan coal	Henan, China	Fat coal	2–8	293–313	Decrease/21	Decrease/3	Decrease/3	Yu et al. (2015)
45	Datong coal	Chongqing, China	Anthracite	0.1–5	303–333	Decrease/28	Decrease/4	Increase/4	Zhang (2015)
46	Wangpo coal	Shanxi, China	Anthracite	0.1–5	293–333	Decrease/35	Decrease–increase/5	Increase/5
47	Zhaozhuang coal	Shanxi, China	Anthracite	0.1–5	293–333	Decrease/35	Constant/5	Increase/5
48	Liziya coal	Sichuan, China	Anthracite	0.1–5	303–328	Decrease/21	Constant/3	Increase/3	Zhang (2015)
49	Yuyang coal	Chongqing, China	Anthracite	0.1–5	303–333	Decrease/28	Decrease/4	Increase/4
50	Sihe coal	Shanxi, China	Anthracite	0.1–5	303–333	Decrease/28	Decrease–increase/5	Increase/5
51	Daning coal	Shanxi, China	Anthracite	0.1–5	303–333	Decrease/28	Constant 5	Increase/5
52	Gaoqiao Kangda coal	Sichuan, China	Coking coal	0.1–5	293–333	Decrease–increase–decrease/35	Disorder/5	Increase/5
53	Zhaogu coal	Henan, China	Anthracite	\	303–333	\	Constant/4	Increase/4	He (2016)
54	Datong coal	Chongqing, China	Anthracite	0.1–6	293–333	Decrease/35	Increase–decrease/5	Increase/5	Guo (2016)
55	Gucheng coal	Shanxi, China	Meagre coal	0.1–5	293–363	Decrease/48	Increase/8	\	Cai et al. (2017)
56	Gaocun coal	Shanxi, China	Meagre coal	0.1–5	293–363	Decrease/48	Increase/8	\	Cai et al. (2017)
57	Ruawar coal	Huntly Coalfield, New Zealand	Subbituminous coal	0.1–8	298.7–333.1	Decrease/45	Decrease/5	Disorder/5	Crosdale et al. (2008)
58	Jasper coal	Huntly Coalfield, New Zealand	Subbituminous coal	0–8	305–323.4	Decrease/18	Increase/2	Increase/2	Crosdale et al. (2008)
59	I1	Italy	Subbituminous coal	0.2–0.22	306–333	Decrease/15	Decrease/3	Increase/3	Pini et al. (2010)
60	A1	Australia	Subbituminous coal	0.21–0.218	318–328	Decrease/18	Decrease/2	Increase/2
61	A2	Australia	Subbituminous coal	0.21–0.218	318–328	Decrease/18	Decrease/2	Increase/2
62	Pocahontas #3 coal	West Virginia, USA	Subbituminous coal	0–15	308–328	Decrease/28	\	\	Sakurovs et al. (2008)
Total number						1765	252	216	28

Note: RMACTP, RLVTP, and RLPTP are the changes in the coal methane content, the Langmuir volume, and the Langmuir pressure with increasing temperature at a constant pressure. NDP denotes the number of data points while a slash symbol denotes no information available.

The Chinese groups classified the coal samples used in their experiments based on the Chinese National Standard for coal classification (GB/T 5751–1986). According to this standard, coal is divided into seven types. In these 56 trials, the coal types comprised anthracite (18 groups and 635 data points), meager coal (8 groups and 309 data points), coking coal (10 groups and 419 data points), fat coal (3 groups and 81 data points), gas coal (6 groups and 192 data points), long flame coal (2 groups and 65 data points), and lignite (1 group and 36 data points). The remaining three research groups classified their coal samples based on different criteria, and all were classified as subbituminous coal.

Based on the 62 groups of experiments, a large database containing 2233 data points regarding the temperature dependence of methane adsorption by coal was compiled. This database incorporated 1765 data points concerning the amount of methane adsorbed by coal with increasing temperature at the same pressure, 252 data points related to V_L values at increasing temperatures at the same pressure, and 216 data points for P_L values at increasing temperatures at the same pressure. All coal samples for the experiments tabulated herein were crushed and sieved to obtain specific particle sizes, although the particle sizes were not consistent between the different experiments. The pressures used in the various trials ranged from 0.1 MPa to 16 MPa and the temperatures were between 288 K and 363 K. The experimental conditions and a summary of the results from these 62 groups of experiments are provided in Table 1.

Of the 62 groups of experiments, 59 identified an inverse relationship between methane adsorption and temperature at a constant pressure (representing 95% of the trials). Only one group found a decrease–increase–decrease trend between adsorption and increasing temperature, while the other two observed no clear correlation. With regard to changes in V_L with increasing temperature, 36 studies showed that V_L decreased, nine showed that V_L did not change appreciably, 10 found that V_L increased, four reported an initial decrease followed by an increase, three showed the opposite (an early increase followed by a decrease), and two reported no consistent relationship. Concerning the behavior of P_L with increasing temperature, 37 groups reported an increase, seven found a decrease, three found no change, two reported an initial increase followed by a decrease, and five reported no information for this parameter.

From the data summarized in the preceding paragraph, it can be concluded that it is generally accepted by most researchers that, at constant pressure, CMM adsorption decreases with increasing temperature. A decrease in V_L as the temperature increased was observed by 55.7% of the studies, whereas only a few studies reported some other relationship between V_L and temperature. These results demonstrate that V_L is most likely decreased as the temperature rises. In addition, 68.5% of the studies found that P_L increases along with temperature while only a few reported some other behavior, suggesting that in most instances, P_L increases with temperature.

Statistical analyses of adsorbed methane, V_L, and P_L data at different temperatures

To allow a statistical analysis of the range of coal methane adsorption values at different temperatures, data were obtained from the results of the 62 groups of experiments listed in Table 1. From these data, a histogram for the amount of methane adsorbed by coal samples having various ranks at different temperatures under 3 MPa pressure was constructed. These data were also used to create histograms for both V_L and P_L over a range of temperatures. The histograms are presented herein as Figures 1 to 3, respectively.

Figure 1 shows that the quantities of methane adsorbed by coal samples of different ranks ranged from 3 cm³/g to 37 cm³/g under 3 MPa pressure at temperatures between 288 K and 343 K. In the same pressure and temperature range, the amounts of methane adsorbed by anthracite and meager coal (coals with higher metamorphic grades) were larger than those adsorbed by fat, gas, and long flame coals (with lower metamorphic grades). This finding demonstrates that adsorption increases with the degree of metamorphism. Figure 1 also shows that, at 3 MPa, the methane adsorbed by a coal with a given metamorphic grade decreases with increasing temperature.

Figure 1.

Graph showing methane adsorbed by coal samples of different ranks at various temperatures under 3 MPa pressure.

V_L, also known as the saturation adsorption content, is the maximum amount of methane that can be adsorbed by a coal under infinite pressure at a given temperature and reflects the greatest quantity of methane that the coal can physically hold. This is generally estimated to be between 15 cm³/g and 55 cm³/g (Liang, 2000; Wang et al., 2012). From Figure 2, at temperatures between 288 and 343 K, the V_L’s are in the range of 5–57 cm³/g, and so are reasonably close to the estimated range. The V_L values for the anthracite and meager coals, both with a higher metamorphic grade, are in the range of 25–57 cm³/g, while the values for the coking, fat, and gas coals (with middle metamorphic grades) are in the range of 10–29 cm³/g. The values for the long flame coal and lignite (with low metamorphic grades) are in the range of 5–22 cm³/g. These generalizations provide a means of estimating the methane saturation points of coals having different metamorphic grades. From Figure 2, it is apparent that, in the 293–323 K temperature range, the V_L of coals with the same metamorphic grade does not change with increasing temperature. In fact, overall, the V_L values appear to decrease slightly as the temperature increases, indicating that the effect of temperature on V_L is not significant at lower temperatures.

Figure 2.

Langmuir volumes of coal samples of different ranks at various temperatures.

P_L, also termed the critical desorption pressure, is the pressure at which one-half of the V_L can be filled. As shown in Figure 3, the P_L values of samples of coal of the same rank differ significantly and do not correlate with temperature. At the same temperature, the P_L values of anthracite and meager coal are low, whereas the P_L values for coking, fat, and gas coal are high. This is the opposite of the coal rank–V_L relationship.

Figure 3.

Langmuir pressures of coal samples of different ranks at various temperatures.

Regression equations for adsorbed methane, V_L, P_L, and temperature

To analyze the relationship between adsorption and temperature quantitatively, it is necessary to find equations that fit the relationships between a variable expressing the amount of methane adsorbed (Q), V_L, P_L, and temperature (T). Ideally, these equations should be generated based on coals of the same rank (that is, coals with the same degree of metamorphism). In the present work, prior to fitting the data points, the experimental data were processed to reject outliers so as to eliminate the effect of random factors in the individual experiments on the results. This processing was accomplished using Grubbs’ test (Grubbs, 1969; Stefansky, 1972). After the outliers were rejected, the remaining data collected at the same temperature were averaged and these numbers were regarded as the correct values for adsorbed methane, V_L, and P_L for that temperature. These averaged, outlier-free values were used to produce Figures 4 to 6 and to fit curves for coals of different rank at the same temperature.

Regression model for adsorbed methane and temperature

Most researchers believe that the relationship between methane adsorption and temperature is exponential (Feng et al., 2012; Liang, 2000). According to the monolayer location adsorption model proposed by Wang et al. (2012), the methane adsorbed per unit surface area per unit mass of coal, Q, can be expressed as

Q = C (1 - θ) c \exp (T^{- 1}) T^{- \frac{1}{2}}

(1)

where Q is the methane adsorbed per unit surface area per unit mass of coal (cm³/g), θ is surface coverage (%), c is a condensation coefficient, T is the absolute temperature of the coal (K), and C is a constant based on the coal rank, the adsorbate, and the gas pressure.

Based on the analysis presented by Liang (2000) and Feng et al. (2012), this paper defines the relationship between Q and temperature as exponential. From the data used to prepare Figure 4, regression models relating Q and temperature for unit masses of coal of different ranks were used to derive the equations

Anthracite : Q = 66.538 \exp (- 0.004 T), R^{2} = 0. 6059

(2)

Meager coal: Q = 1898 \exp (- 0.015 T), R^{2} = 0. 889

(3)

Coking coal: Q = 58.165 \exp (- 0.005 T), R^{2} = 0. 6628

(4)

Fat coal: Q = 35.022 \exp (- 0.0051 T), R^{2} = 0. 8703

(5)

Gas coal : Q = 93.656 \exp (- 0.008 T), R^{2} = 0. 8969

(6)

Long-flame coal : Q = 2304.3 \exp (- 0.017 T), R^{2} = 0. 9936

(7)

and

Lignitous coal : Q = 433.941 \exp (- 0.014 T), R^{2} = 0. 7136

(8)

Figure 4.

Outlier-free, averaged data for adsorbed methane as functions of temperature for coals of different rank.

In both the above and subsequent equations, R² is the determination coefficient for the curves.

With regard to the magnitudes of the determination coefficients for the seven coal ranks, two are between 0.6 and 0.7, one is between 0.7 and 0.8, while the values for the other four ranks are greater than 0.8 (with one equal to 0.9936). The average determination coefficient is 0.8046 and the absolute value of the average correlation coefficient is 0.8970. Although the average determination coefficient is somewhat low, these fits are still considered acceptable given the size of the data set.

Regression model for V_L and temperature

It is generally believed that, in the case that there is only a single adsorbate gas, V_L is insensitive to changes in temperature and is only affected by the coal rank. According to the experimental data used to prepare Figure 5, the relationships between V_L and temperature for different coals can be expressed by the following quadratic polynomials

Anthracite : V_{L} = - 0.00 49 T^{2} + 2.8807 T - 381.27, R^{2} = 0. 8968

(9)

Meager coal : V_{L} = 0.00 25 T^{2} - 2.2996 T + 503.99, R^{2} = 0. 9435

(10)

Coking coal : V_{L} = - 0.00 28 T^{2} + 1.6885 T - 227.9, R^{2} = 0. 885

(11)

Fat coal : V_{L} = - 0.00 59 T^{2} + 3.3713 T - 466. 1, R^{2} = 0. 9723

(12)

Gas coal : V_{L} = 0.00 14 T^{2} - 1.0165 T + 197. 95, R^{2} = 0. 6963

(13)

Long-flame coal : V_{L} = 0.00 47 T^{2} - 3.265 T + 5 71.25, R^{2} = 0. 9999

(14)

and

Lignitous coal : V_{L} = - 0.00 74 T^{2} - 4.4406 T - 659. 7, R^{2} = 0. 9999

(15)

Figure 5.

Outlier-free, averaged data for Langmuir volume (V_L) as functions of temperature for coals of different rank.

Only the determination coefficient for gas coal, at 0.6963, was low, although even this relatively low number was close to 0.7. The other values were all above 0.88, with two groups giving values of 0.9999. The average determination coefficient, including that of the gas coal, was 0.9134, indicating that these equations fit the data very well.

Regression model for P_L and temperature

For a given adsorbate gas, P_L is related to temperature, adsorption pressure, and the physical properties of the absorbent (in this case, coal). According to the data in Figure 6, the changes in P_L with increasing temperature can be summarized as increases in the case of the anthracite, meager, coking, gas, and long flame coals but decreases in the case of the fat and lignitious coals. Zhang and Tao (2011) and Li et al. (2012) proposed a linear relationship between P_L and temperature, and the linear regression equations for P_L and temperature derived in the present study are

Anthracite : P_{L} = 0.0191 T - 4.0755, R^{2} = 0. 9723

(16)

Meager coal : P_{L} = 0.0225 T - 4.7299, R^{2} = 0. 8204

(17)

Coking coal : P_{L} = 0.034 T - 8 .0 738, R^{2} = 0. 6734

(18)

Fat coal : P_{L} = 0.038 T +1 . 8444, R^{2} = 0. 9974

(19)

Gas coal : P_{L} = 0.0529 T - 10.502, R^{2} = 0. 9505

(20)

Long-flame coal : P_{L} = - 0.012 T + 5.6317, R^{2} = 0. 7015

(21)

and

Lignitous coal : P_{L} = - 0.016 T + 53.377, R^{2} = 0. 9948

(22)

Figure 6.

Outlier-free, averaged data for Langmuir pressure (P_L) as functions of temperature for coals of different rank.

Two of the determination coefficients here are less than 0.8, one is between 0.8 and 0.9, and four are greater than 0.9. The average determination coefficient is 0.8729, indicating that overall, the goodness of fit is fairly high.

Discussion

As the coal temperature is increased, collisions between molecules become more intense as the kinetic energy of the molecules increases, and the probability that a given molecule will have an energy greater than the adsorption potential energy increases (Pan et al., 2012). Thus, the probability that methane molecules will desorb from the coal increases and the quantity of adsorbed methane should decrease. However, an increase in temperature can also decrease the activation energy associated with methane adsorption on the surfaces of the pores in the coal. At higher temperatures, methane molecules will not remain on the pore surfaces but instead will migrate into the pores, increasing the pore pressure (Cui et al., 2003). As a consequence, there will be more free methane at higher temperatures. Thus, overall, an increase in temperature will result in the adsorbed methane being more easily desorbed. Both our statistical analysis and the above regression analysis and equations support this hypothesis.

The parameter V_L is the methane adsorption capacity of the coal at a given temperature. Theoretically, for the same adsorbent (coal in the present study), V_L is only related to the properties of the coal and not directly correlated with temperature. However, the adsorption of methane by coal is primarily a physical process. For the same adsorption equilibrium system, with an increase in temperature, the methane adsorption rate accelerates and an adsorption equilibrium can be reached within a finite time (Zhang and Tao, 2011). Moreover, methane adsorption by coal is exothermic so, on the whole, V_L decreases with increasing temperature (Li et al., 2012). In addition, because almost all the components that make up the coal and rock are reactive with oxygen, the properties of the coal will change at extremely low oxygen partial pressures when the temperature changes (Wang et al., 2012). These changes will result in fluctuations in the coal’s specific surface area and thus in changes in V_L. The relationship between V_L and temperature obtained by the present statistical analysis and the regression equations show that, for coals of the same rank, V_L is less affected by changes in temperature than is the amount of adsorbed methane, and the response of V_L for coals of different rank is less consistent. Only the long flame coal exhibits different responses as the temperature changes.

The P_L can reflect the adsorption capacity of internal surfaces in the coal. According to Langmuir adsorption theory, P_L can be considered to represent the ratio of the desorption rate to the adsorption rate. Because adsorption is exothermic and desorption is endothermic (Li et al., 2012; Zhang et al., 2004), higher temperatures will promote desorption while limiting adsorption. Thus, theoretically, higher temperatures should lead to higher P_L values. However, in actuality, P_L is affected by many other factors, including non-ideal adsorbents and adsorbates, temperature, and adsorption gas pressure. These factors thus complicate the relationship between P_L and temperature. The relationship between P_L and temperature obtained herein demonstrates that P_L generally increases as temperature increases, even though this relationship does not hold for all ranks of coal. As an example, the P_L for lignitious coal decreases as the temperature increases, although it is possible that this result is due to the limited quantity of experimental data (that is, there are only three data points).

With regard to the effect of coal rank on adsorption, it is thought that higher rank coals will generate greater quantities of micropores as the temperature increases. These micropores play a dominant role in methane adsorption, and so adsorption would be expected to increase with temperature. The accuracy of the statistical method proposed in this paper was evaluated by comparing the results from the equations presented herein to results obtained from equations previously reported in the literature. No equations for the relationship between adsorbed methane and temperature were found in any of the references cited, but relevant equations for V_L versus T (for anthracite and coking coal) and P_L versus T (for anthracite) were found. Several representative equations have been selected and are provided in Tables 2 and 3. Graphs comparing the curves generated from these equations to curves generated using equations (9), (11), and (16) from this paper are shown in Figures 7 and 8.

Table 2.

Equations from this paper and from the literature for V_L versus temperature (for anthracite and coking coal).

Coal rank	Equations	Sources
Anthracite	V_L=−0.0049T² + 2.8807T-381.27	This paper
	V_L=−0.0021T² + 1.0924T-95.05	Guo (2016)
	V_L=−0.0031T² + 1.9223T-266.9	Zhang and Tao (2011)
Coking coal	V_L=−0.0028T²+1.6885T-227.9	This paper
	V_L=27.54 × 1.01^(297.48- ^T ⁾+3.96	Zhang et al. (2009)
	V_L=29.655 × 0.993278⁽ ^T ^-273.15)	Zhao et al. (2001)

Table 3.

Equations from this paper and from the literature for P_L versus temperature (for anthracite).

Coal rank	Equations	Sources
Anthracite	P_L = 0.0191T−4.0755	This paper
	P_L = 0.000417T²−0.17418T+17.02	Guo (2016)
	P_L = 0.0147T−2.8468	He (2016)
	P_L = 0.0125T−2.0369	Li et al. (2012)
	P_L = 0.0094T−1.4544	Zhang and Tao (2011)

Figure 7.

Comparisons of V_L vs temperature curves generated from equations published by different authors for anthracite and coking coal.

Figure 8.

Comparisons of P_L vs temperature curves generated from equations published by different authors for anthracite.

Figures 7 and 8 demonstrate that, regardless of the V_L–T or P_L–T equation used, the differences between the resulting curves are significant. The curves from the equations generated by this study using statistical and regression methods are basically in the middle of the range of those from the equations taken from the literature. The equations generated by this study could therefore, to some extent, act to average out differences and reduce the errors caused by various factors, because they are based on probability and statistical analysis. The new equations presented in this paper are thus more accurate.

Conclusions

The analysis of experimental data concerning the effect of temperature on the methane adsorption capacity of coal from numerous different researchers over the last two decades allows the following conclusions.

At constant pressure, the amount of methane adsorbed by samples of coal of the same rank decreases as temperature increases. At constant pressure and temperature, higher rank coals can adsorb more methane than lower rank coals.

The V_L’s of anthracite and meager coal (higher metamorphic grade coals) are in the range of 25–57 cm³/g. The V_L’s of medium metamorphic grade coals, including coking, fat, and gas coals, are in the range of 10–29 cm³/g. The V_L’s of low rank/low metamorphic grade coals, such as long flame and lignitious coals, are most commonly between 5 cm³/g and 22 cm³/g. In the case of trials performed at lower temperatures (288–343 K), the effect of temperature on V_L is minimal.

According to the data collected for this study, P_L will increase with increases in temperature in the case of anthracite, meager, coking, gas, and long flame coals, while P_L decreases for fat and lignitious coals. From these trends, it is evident that the P_L–temperature relationship is complex and a universal conclusion that would apply to all ranks of coal cannot be established using existing data.

Using the data compiled for Q, temperature, V_L, and P_L, a regression model was used to define equations that fit those parameters to curves. Three sets of seven curves were constructed: Q versus temperature, V_L versus temperature, and P_L versus temperature. Each set of curves contained one plot for each of the seven different ranks of coal. The majority of the determination coefficients for these regression equations were above 0.7, indicating that the equations show good relativity and sensitivity. Comparisons of the curves obtained from some equations generated by this study and those from equations found in prior publications showed that the new equations presented in this paper are more accurate. Therefore, these fitting equations can be used to predict the methane adsorption variables Q, V_L, and P_L for the different ranks of coal at various temperatures.

The methane adsorption capacity of coal is affected by many factors, including rank (meaning the degree of coal metamorphism), coal structure, ash and moisture contents, air pressure, temperature, and physical or electromagnetic stimuli applied to enhance gas extraction. At a constant temperature and for coal of the same rank, experiments performed by different investigators using varying experimental conditions, equipment, and/or procedures can return markedly different results. Therefore, uniform experimental standards should be established to guarantee the accuracy and, to some extent, the comparability of experimental results. In addition, at present, according to the data compiled for this study, it is not possible to conclusively establish the relationship between P_L and temperature. Experimental research regarding this aspect of CMM adsorption should therefore continue.

Footnotes

Acknowledgments

We thank David Frishman, PhD, from Liwen Bianji, Edanz Group China (), for editing the English text of a draft of this article.

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 financially supported by the National Natural Science Foundation of China (51404101), Foundation for University Key Teacher by Education Department of Henan Province (2014GGJS-062), China Postdoctoral Science Foundation (2015M572106), Henan Postdoctoral Foundation (2015056), and the State Key Laboratory Cultivation Base for Gas Geology and Gas Control (Henan Polytechnic University) (WS2017B09, WS2013B02).

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The influence of temperature on methane adsorption in coal: A review and statistical analysis

Abstract

Keywords

Introduction

Qualitative summary of published experimental results regarding methane adsorption, VL, PL, and temperature

Statistical analyses of adsorbed methane, VL, and PL data at different temperatures

Regression equations for adsorbed methane, VL, PL, and temperature

Regression model for adsorbed methane and temperature

Regression model for VL and temperature

Regression model for PL and temperature

Discussion

Conclusions

Footnotes

Acknowledgments

Declaration of Conflicting Interests

Funding

References

Qualitative summary of published experimental results regarding methane adsorption, V_L, P_L, and temperature

Statistical analyses of adsorbed methane, V_L, and P_L data at different temperatures

Regression equations for adsorbed methane, V_L, P_L, and temperature

Regression model for V_L and temperature

Regression model for P_L and temperature