Univariate and Multivariate Analyses of Influencing Factors on Methane Adsorption Capacity of Semianthracite

Methane adsorption isotherm experiments on semianthracite (2.00-2.33% R o , max ) collected from the Xin’an coal mine, Henan Province, China, were conducted to investigate the effects of pore structure, coal quality, coal maceral, and coal rank on methane adsorption capacity with applications of univariate and multivariate analyses. Methane adsorption capacity varies significantly from 12.03 to 28.40 cm3/g. In univariate analysis, methane adsorption capacity has a strong positive correlation with pore specific surface area, weak positive correlations with pore volume and ash content, and weak negative correlations with moisture content and inertinite content. No correlation is observed between methane adsorption capacity and coal rank. In multivariate analysis, the mathematical model of methane adsorption capacity affected by the combined individual variables is established based on quantification theory I. There are similarities and differences between the two analyses. The similarities are that pore specific surface area has the greatest contribution to methane adsorption capacity, while coal rank has the least contribution. The differences are reflected in two aspects. Firstly, the other influencing factors contribute differently to methane adsorption capacity. Secondly, the positive or negative correlations of some influencing factors present the opposite. The mathematic model synthetically covers the combined effects of the influencing factors, which is more representative in evaluating methane adsorption capacity.

Many researches have been performed to investigate factors affecting methane adsorption capacity.In the traditional view, the influencing factors can be divided into two aspects: inherent properties of coal (e.g., coal rank, coal maceral, coal quality, and coal lithotype) and external conditions (e.g., temperature, pressure, burial history, sequence stratigraphy, water occurrence states, and water invasion) [6-8, 13, 19-36].Additionally, other parameters of coal property, including coal deformation [29], macromolecular structure or crystallite structure characteristics of coal [37,38], chemical structure of coal organic matters (e.g., aromatic structure, aliphatic structure, and coal surface functional group) [6,14,28,39], and pore structure characteristics (e.g., pore specific surface area, pore volume, pore size distribution, and fractal characteristics) [7,28,30,[40][41][42][43][44], also play important roles in methane adsorption capacity.Coal rank is generally considered to be the dominant parameter affecting methane adsorption capacity [12,45].Coal samples used in previous studies, however, show wide range of variation in coal rank [25,39,46], which may mask the effects of other influencing factors.Therefore, for coals with similar rank, more in-depth analyses are essential to understand influencing factors on methane adsorption capacity and to establish a comprehensive mathematical model of methane adsorption capacity.This paper examines the variation of methane adsorption capacity and its influencing factors of the No. 2 1 coal in the Xin'an coal mine, Henan Province, China.The two major objectives are to (1) individually analyze the effects of influencing factors in terms of pore structure, coal quality, coal maceral, and coal rank on methane adsorption capacity and (2) comprehensively establish a mathematic model containing the influencing factors of methane adsorption capacity using multivariate statistical analysis.The research result may serve as an important geological basis for the safety production of the unmined area in the coal mine.

Experiments and Methods
The study area, the Xin'an coal mine, is located in northwestern Henan Province, China (Figures 1(a) and 1(b)).It spans within a homocline, with NE strike and SE trend.The No. 2 1 coal within the Lower Permian Shanxi Formation is economically minable.The coal underwent extreme tectonic deformation and is classified as tectonically deformed coal.A total of eleven coal samples were collected from six working faces (Figure 1(c)).One of the samples belongs to the working face 12201, two to the working face 13151, five to the working face 14211, one to the working face 14221, and the remaining two to the working faces 15051 and 15061, respectively.The samples were sieved directly and reduced in size to 2 mm (maximum particle size).Several subsamples of each coal sample were obtained by coning and quartering for proximate analysis, petrographic analysis, low-pressure N 2 adsorption analysis, and methane adsorption isotherm experiment.
Proximate analysis was conducted in accordance with ASTM Standards D3173-11 [47], ASTM Standards D3175-11 [48], and ASTM Standards D3174-11 [49].The polished samples for petrographic analysis were prepared according to the procedure described in Mardon et al. [50].Maceral analysis (500 point counts) and mean maximum vitrinite reflectance (R o,max ) measurements were conducted on the same polished sections using a Leitz MPV-3 photometer microscope.
Low-pressure N 2 adsorption analysis was performed to obtain pore structure parameters including Brunauer-Emmett-Teller (BET) specific surface area (S BET ) using BET model [51], Barrett-Joyner-Halenda (BJH) pore volume (V BJH ), and pore size distribution (PSD) according to BJH model [52].The samples between 0.18 mm and 0.25 mm were used for the experiment with a Micromeritics ASAP 2020 surface area and porosity analyzer.Prior to analysis, the samples were first degassed under vacuum at 105 °C for 12 h.Both adsorption and desorption isotherms were measured at 77.35 K for the relative pressure ranging from 0.01 to 0.995.The adsorption isotherms were used to interpret S BET , V BJH , and PSDs.
Methane adsorption isotherm experiments on coal samples were conducted on an Isotherm Adsorption/Desorption System ISO-200, following Chinese National Standard GB/T 19560-2008 [53].The coal samples on the air dry basis were sieved into a particle size fraction of 0.18-0.25 mm and moisture equilibrated under the controlled relative humidity (RH) condition using saturated salt solutions of K 2 SO 4 (97% RH) for at least four days.The pretreated moisture-equilibrated samples were put into the sample cell of the ISO-200 for the adsorption isotherm experiment.The experimental temperature and equilibrium pressure were 30 °C and up to 8 MPa, respectively.The measured adsorption data were fitted by the Langmuir model [54] to determine the Langmuir constants, i.e., Langmuir volume (V L ) and Langmuir pressure (P L ), and the analytical results were reported on the air dry basis.

Results and Discussion
3.1.Methane Adsorption Capacity.Coal rank of the samples varies in a relatively small range with R o,max of 2.00-2.33%(Table 1).However, methane adsorption capacity (as indicated by V L ) varies widely from 12.03 cm 3 /g to 28.40 cm 3 /g (averaging at 19.66 cm 3 /g) (Table 1), which suggests a remarkable difference for the coal samples with similar rank.The observation is consistent with Zou et al. [55], where they demonstrated a significant change in methane adsorption capacity of the isorank coals.Methane adsorption capacity greater than 25 cm 3 /g is located in the working face 13151.Methane adsorption capacity of 20-25 cm 3 /g is concentrated in the working faces 14221, 15051, and 15061.Methane adsorption capacity less than 20 cm 3 /g is distributed in the remaining two working faces 12201 and 14211.
Methane adsorption capacity of different rank coals has been researched in previous publications.For low-rank coal, methane adsorption capacity of coals with 0.34-0.69%R o,max varies from 3.33 cm 3 /g to 17.22 cm 3 /g in Moore et al. [56], and that of coals with 0.46-0.73%R o,max is between 5.06 cm 3 /g and 13.37 cm 3 /g in Xu et al. [57].For mediumhigh-rank coal, methane adsorption capacity is from 9.59 cm 3 /g to 21.38 cm 3 /g of coals with 0.68-1.51%R o,max in Li et al. [58], from 18.28 cm 3 /g to 23.20 cm 3 /g of coals with 1.23-1.90%R o,max in Meng et al. [59], from 12.01 cm 3 /g to 25.36 cm 3 /g of coals with 1.60-2.50%R o,max in Yao et al. [34], and from 14.16 cm 3 /g to 43.36 cm 3 /g of coals with 0.96-2.93%R o,max in Liu et al. [37].Compared with the data in the literature mentioned above, the experimental results in our study suggested that the No. 2 1 coal has mediumhigh methane adsorption capacity.Table 1: Summarized results of petrographic analysis, proximate analysis, pore structure parameters, and Langmuir constants of the No. 2 1 coal in the Xin'an coal mine.at the relative pressure from 0.45 to 0.995 is considered to be associated with capillary condensation in mesopores [61,62].The shape of hysteresis loop is identified with the particular pore structure [63].The adsorbed nitrogen quantity at the maximum relative pressure varies among coal samples from different working faces, with the maximum value of 7.91 cm 3 /g at the sample 15051-1 and the minimum value of 2.18 cm 3 /g at the sample 14211-3.This substantial difference translates into the evident variations in S BET , V BJH , and PSD.As shown in  Pore structure parameters including pore specific surface area and pore volume have significant implications on methane adsorption capacity [7,12,20,34,44,55,64], with distinctly different mechanisms (surface adsorption versus pore volume filling) [65].Moore [12] and Zhou et al. [44] suggested that pore specific surface area is the most important parameter in determining methane adsorption capacity, whereas Clarkson and Bustin [7] concluded that pore volume is more important.It is of great importance to have a better understanding of their roles in methane adsorption capacity in our study.The scatter plot (Figure 3(a)) displays that there is a significant positive correlation between methane adsorption capacity and S BET with the correlation coefficient of r = 0:87.This is because gas is predominantly adsorbed on the surface of coal matrix [4,6,12,43].The larger surface area supplies substantial adsorption sites [24,66] and stron-ger adsorbate-adsorbent interaction energy to methane [65] because of the adsorption force on the surface area [5].This results in the strong positive correlation between methane adsorption capacity and S BET .Compared with S BET , the weak positive correlation between methane adsorption capacity and V BJH (r = 0:21) (Figure 3(b)) suggests that the effect of V BJH on methane adsorption capacity may be covered by that of S BET .[39,40].The results of proximate analysis of the samples are listed in Table 1.The No. 2 1 coal displays low moisture content (0.56-0.98%, 0.72% on average).The scatter plot (Figure 3(c)) shows that methane adsorption capacity has an insignificant negative correlation with moisture content with the r = −0:32.Generally, 6 Adsorption Science & Technology methane adsorption capacity decreases with the increasing moisture content until a certain critical moisture content (equilibrium moisture) is reached, after which no influence on methane adsorption capacity is observed [8,23].The presence of moisture weakens the interaction between coal and methane [17,67] and competes with methane for adsorption sites [13,25,68].Because of the polarity of water molecule, moisture is preferentially adsorbed [69,70], which leads to less space available for methane [17].Once all possible adsorption sites for moisture are occupied, methane adsorption capacity will not decrease any further [23,70].Meanwhile, moisture may block the accesses of gas to micropores [13,71].As a result, methane adsorption capacity decreases with an increase in moisture content [8,19,25,31,68,69].Inorganic matter (as indicated by ash content) plays a critical role in methane adsorption capacity [8,10,19,25,44,68,[72][73][74].Ash content of studied samples ranges from 8.16% to 26.26% (Table 1), which is classified as special low ash to medium ash coal according to Chinese National Standard GB/T 15224.1-2010(Ash yield <10% for special low ash coal, 10.01-20% for low ash coal, and 20.01-30% for medium ash coal).There is a positive association between ash content and methane adsorption capacity but the relationship lacks statistical significance (r = 0:14) (Figure 3(d)).Methane is mainly adsorbed on organic matter rather than mineral matter [31,56,75].Acting as the simple diluent, mineral matter reduces the affinity of methane to the surface of coal matrix [39] and is not likely contribute to methane adsorption sites [13,21,25].The increase in ash content results in the decrease in methane adsorption capacity [7,19,35,56,69].However, methane adsorption capacity presents an increasing trend with an increase in ash content in our study.This anomaly suggests that the effect of ash content on methane adsorption capacity may be masked by other influencing factors.1, coal maceral is dominated by vitrinite, followed by inertinite, with no occurrence of liptinite.Vitrinite and inertinite range from 86.65% to 95.10% and from 4.90% to 13.35%, averaging at 92.50% and 7.50%, respectively.Submaceral of vitrinite is mainly telinite and telocollinite, while that of inertinite contains mainly fusinite and some sclerotinite.

Coal Maceral. As indicated in Table
The influence of coal maceral on methane adsorption capacity is rank dependent, but with controversies.Laxminarayana and Crosdale [13] indicated that methane adsorption capacity increases with the increasing vitrinite content at high-volatile bituminous coal and decreases at semianthracite and anthracite, whereas methane adsorption capacity is not associated with coal maceral at low-medium-volatile bituminous coal.Liu et al. [26] suggested that methane adsorption capacity of vitrinite is weaker than that of inertinite for low-rank coal, and the opposite is true for highrank coal.Flores [73] concluded that vitrinite-rich coal is characterized by greater methane adsorption capacity than inertinite-rich coal up to low-volatile bituminous coal.In contrast, Ettinger et al. [76] supported the opposite.But they have the consensus that methane adsorption capacity of coal maceral is similar at higher-rank coal (Ettinger et al. [76]; [73]).Chalmers and Bustin [45] suggested that there is no significant difference in methane adsorption capacity of coal maceral for lower-rank coal, but for higher-rank coal, vitrinite-rich coal has higher methane adsorption capacity.For the high-rank coal in our study, the negative correlation (r = −0:44) occurs in inertinite content and methane adsorption capacity (Figure 3(e)), which is in support of the findings of Chalmers and Bustin [45] and Liu et al. [26].Vitrinite-rich coal is characterized by much more mesopores and micropores than inertinite-rich coal [7,19,45,64] and can provide more adsorption sites for methane [70], which results in the decreasing methane adsorption capacity with an increase of inertinite content.

Coal Rank.
As the most important indicator of metamorphism, R o,max varies from 2.00% to 2.33% with the average value of 2.17% (Table 1).The coal is classified as semianthracite, according to the ASTM classification [77].Coal rank is generally considered to be the dominant parameter affecting methane adsorption capacity [8,12,13,25,31,34,38,45].A correlation of second-order polynomial trend ("U" shaped) exists between coal rank and methane adsorption capacity with the minimum value occurring at high-or medium-volatile bituminous coal [10,13,19,39,46,71].Coal rank in our study exceeds medium-volatile bituminous coal, and methane adsorption capacity is supposed to increase with the increasing coal rank.Nevertheless, there is no correlation between coal rank and methane adsorption capacity (r = −0:005, Figure 3(f)).The extremely weak negative correlation coefficient suggests that coal rank is not the main factor affecting methane adsorption capacity because of its relatively small variation range.

Mathematic Model of Methane Adsorption Capacity.
Methane adsorption capacity is affected by these various factors, and the contributions of the individual variables to methane adsorption capacity may interact and be likely to be incorrect in univariate analysis.It is necessary to develop a computational scheme of methane adsorption capacity affected by the combined individual variables.Quantification theory I belongs to multivariate statistical analysis method, which can associate quantitative and qualitative variables simultaneously.The CBM geological mathematical model software was developed on the basis of quantification theory I and used to relate methane adsorption capacity to the combined effects of the independent variables in our study.The quantitative variables including S BET , V BJH , moisture content, ash content, inertinite content, and R o,max were selected as the independent variables, while methane adsorption capacity as the dependent variable.There are no qualitative variables in the independent variables.The mathematical model containing all analytical factors for methane adsorption capacity established by the software is y = 14:3877d1 + 211:9483d2 + 12:4757d3 − 0:2695d4 where y is methane adsorption capacity, cm 3 /g; d1 is S BET , Adsorption Science & Technology m 2 /g; d2 is V BJH , cm 3 /g; d3 is moisture content, %; d4 is ash content, %; d5 is inertinite content, %; d6 is R o,max , %.The model was checked using ANOVA (i.e., analysis of variance, F-test) method [78].The F-distribution for F-test of the mathematical model is 12.98, which is larger than the F 0:1 = 4:01 (the value of the F-distribution at the 10% significance level).The F-test suggests that the mathematical model is proved to be significant.Consequently, the mathematical model can be used to evaluate methane adsorption capacity of the No.2 1 coal in our study area.
The measured values from the experiment and the predicted values from the mathematical model of methane adsorption capacity are listed in Table 2.The deviation of the measured values to the predicted values varies from -1.75 cm 3 /g to 2.06 cm 3 /g.The maximum and minimum deviations are belonging to the working face 13151, which is mainly attributed to the relatively high methane adsorption capacity.The relative error varies from 0.08% to 9.31% with the average value of 4.59%.The correlation coefficient between the measured values and the predicted values of methane adsorption capacity is 0.98, as illustrated in Figure 4, indicating there is a good consistency between the mathematical model prediction and the experimental measurement.

Comparison of Univariate Analysis and Multivariate
Analysis.For the univariate analysis expressed by the scatter plots, the correlation coefficients suggest that the contributions of the analytical factors to methane adsorption capacity in a descending order are as follows: S BET , inertinite content, moisture content, V BJH , ash content, and R o,max .Methane adsorption capacity is positively correlated with S BET , V BJH , and ash content, is negatively correlated with inertinite content and moisture content, and has no correlation with R o,max .For the multivariate analysis expressed by the mathematical model, the partial correlation coefficients of independent variables are, in same order as the mathematical model, 0.96, 0.28, 0.74, 0.73, 0.43, and 0.18, respectively.This implies that the contributions of independent variables to methane adsorption capacity from large to small are S BET , moisture content, ash content, inertinite content, V BJH , and R o,max .Methane adsorption capacity has positive relationships with  S BET , V BJH , moisture content, and R o,max and negative relationships with ash content and inertinite content according to the mathematical model.There are similarities and differences between the univariate analysis and the multivariate analysis.The similarities are that S BET has the greatest contribution to methane adsorption capacity, while R o,max has the least contribution.The differences are reflected in two aspects.Firstly, the contributions of the other influencing factors (S BET and R o,max not included) are in different orders.Taking inertinite content as an example, it ranks second in the univariate analysis but fourth in the multivariate analysis.Secondly, the positive or negative relationships of some influencing factors such as ash content present the opposite in the two analyses.Because the mathematic model synthetically covers the combined effects of the influencing factors, it is more representative in evaluating methane adsorption capacity.

Conclusions
Methane adsorption isotherm experiments on semianthracite collected from the Xin'an coal mine, Henan Province, China, were conducted to investigate the effects of pore structure, coal quality, coal maceral, and coal rank on methane adsorption capacity using univariate analysis expressed by the scatter plots and multivariate analysis expressed by the mathematical model.The key conclusions are summarized as follows: (1) Methane adsorption capacity varies widely from 12.03 cm 3 /g to 28.40 cm 3 /g, suggesting a remarkable difference for the coal with similar rank (2.00-2.33%R o,max ) where y is methane adsorption capacity; d1 to d6 represent S BET , V BJH , moisture content, ash content, inertinite content, and R o,max , respectively (4) S BET has the greatest contribution to methane adsorption capacity, while R o,max has the least contribution in both univariate analysis and multivariate analysis.The differences in the two analyses are that the other influencing factors contribute differently to methane adsorption capacity, and the positive or negative correlations of some influencing factors present the opposite (5) The mathematic model is more representative in evaluating methane adsorption capacity because it covers the combined effects of the influencing factors

3. 2 . 1 .Figure 1 :
Figure 1: (a) Location of the Henan Province.(b) Location of the Xin'an coal mine.(c) Map showing sampling points, working faces, and burial depth of the No. 2 1 coal in mining area of the Xin'an coal mine.

Figure 2 :
Figure 2: (a-c) Low-pressure N 2 adsorption and desorption isotherms of the No. 2 1 coal samples from different working faces in the Xin'an coal mine.(d) Pore size distributions obtained from adsorption branches of low-pressure N 2 adsorption isotherms.

Figure 3 :
Figure 3: Scatter plots of (a) BET specific surface area, (b) BJH pore volume, (c) moisture content, (d) ash content, (e) inertinite content, and (f) coal rank versus methane adsorption capacity of the No. 2 1 coal in the Xin'an coal mine.

Figure 4 :
Figure 4: Scatter plot of measured versus predicted methane adsorption capacity of the No. 2 1 coal in the Xin'an coal mine.

Table 1
, the S BET and V BJH of the samples are in the range of 0.36-1.64m 2 /g (0.76 m 2 /g, on average) and 0.0032-0.0122cm 3 /g (0.0053 cm 3 /g, on average), respectively.This is mainly attributed to the heterogeneous pore structure of the coal samples in different locations due to the intense tectonic deformation.The largest S BET and V BJH are present in the sample 13151-1 and sample II (represented by the samples 14211-2, 14211-3, 14211-4, 15051-1, and 15061-1) shows the minor peak(s) at the beginning (approximately 2 nm) and/or the end (approximately 200-240 nm) of PSD.Type III (represented by the samples 12201-1, 14211-1, 14211-5, and 14221-1) exhibits no peak with respect to PSD.

Table 2 :
Comparison of measured values and calculated values of methane adsorption capacity of the No. 2 1 coal in the Xin'an coal mine.