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New insights into the CH4 adsorption capacity of coal based on microscopic pore properties
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New insights into the CH4 adsorption capacity of coal based on microscopic pore properties ⁎
Biao Hua,b,c, Yuanping Chenga,b,c, , Xinxin Hea,b,c, Zhenyang Wanga,b,c, Zhaonan Jianga,b,c, Chenghao Wanga,b,c, Wei Lia,b,c, Liang Wanga,b,c a
Key Laboratory of Coal Methane and Fire Control, Ministry of Education, China University of Mining and Technology, Xuzhou, Jiangsu 221116, China National Engineering Research Center for Coal and Gas Control, China University of Mining and Technology, Xuzhou 221116, China c School of Safety Engineering, China University of Mining and Technology, Xuzhou 221116, China b
G R A P H I C A L A B S T R A C T
A R T I C LE I N FO
A B S T R A C T
Keywords: Coal Methane Adsorption Langmuir volume Micropore filling Surface coverage
The objective of this study is to quantitatively describe the CH4 adsorption capacity of coal through microscopic pore properties. In this work, the micropore volume distributions (MPVDs) of granular coal samples from six collieries were obtained by low-pressure CO2 adsorption (LPGA-CO2), and the external specific surface areas (SSAs) were calculated using low-pressure N2 adsorption (LPGA-N2). Based on micropore filling and monolayer coverage theories, the micropores were assumed to be cylindrical to obtain the distribution of CH4 in pore structures with different scales. For the coal samples used in this study, micropores were common, whose SSAs accounted for most of the total SSAs (90.39–99.58%), and the micropore volumes accounted for 75.61–96.55% of total pore volumes. The quantity of CH4 adsorbed in the form of micropore filling account for 74–99% of the total amount adsorbed, while the amount of CH4 adsorbed by micropores in the size range of 0.38–0.76 nm was 38–55% of the total amount adsorbed and accounted for the largest proportion in the nine adsorption areas partitioned according to the number of CH4 molecules occupying micropores with different scales. Based on a combination of the high-pressure CH4 adsorption (HPGA-CH4) results, the estimated Langmuir volumes are in close agreement with the measured Langmuir volumes, which demonstrates that the CH4 adsorption capacity of the coal is determined by both the accessible MPVD and external SSAs. The results of this study may be significant for understanding the pore networks and the CH4 adsorption mechanism in coal under in situ conditions.
⁎ Corresponding author at: Key Laboratory of Coal Methane and Fire Control, Ministry of Education, China University of Mining and Technology, Xuzhou, Jiangsu 221116, China. E-mail address: [email protected] (Y. Cheng).
https://doi.org/10.1016/j.fuel.2019.116675 Received 18 August 2019; Received in revised form 19 October 2019; Accepted 14 November 2019 0016-2361/ © 2019 Elsevier Ltd. All rights reserved.
Please cite this article as: Biao Hu, et al., Fuel, https://doi.org/10.1016/j.fuel.2019.116675
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structures in the form of micropore filling due to the enhanced adsorbent-adsorptive interactions [13,28], and they are adsorbed on the external surface in the form of surface coverage. Because of the importance of characterization of the CH4 adsorption capacity of coal, the main objective of this work was to quantitatively characterize the CH4 adsorption capacity using the microscopic pore properties. In this study, we intended to conduct a comprehensive investigation of CH4 adsorption on coal by considering the different adsorption forms of CH4 molecules in pore structures on different scales. We obtained the micropore volume distributions (MPVDs) of granular coal samples from six collieries using the LPGA-CO2 method. The micropores in coal were assumed to be cylindrical herein, and the number of CH4 molecules captured by the microporous structures on different scales is different. The number of CH4 molecules adsorbed in the micropores based on micropores filling theory was calculated by dividing the range of the MPVD. We obtained the external SSAs by the LPGA-N2 method, and the CH4 molecules were captured by the adsorption sites on the surface of the mesopores and macropores by monolayer absorption. Based on the micropore filling and monolayer adsorption theory, quantitative relationships between the microscopic pore characteristics of coal and the CH4 adsorption capacity were constructed and verified by the measured Langmuir volume. The research results are of great significance for understanding the pore networks in coal and their influencing factors and for studying the CH4 adsorption mechanism.
1. Introduction Coalbed methane (CBM), a clean and high-efficiency energy source, is composed primarily of CH4 [1]. Compared with conventional shale reservoirs, coal reservoirs are dominated by pores of nanometer dimensions [2,3], and the CH4 is mainly stored in an adsorption state on the surface of these pores in the coal [4]. Therefore, understanding the pore networks and CH4 adsorption mechanism in micro- and mesoporous coal has practical application in the accurate prediction of CBM [5,6], CBM development and utilization [7,8], coal and gas outburst prevention and control [9,10], and geological CO2 storage [11]. Before discussing the effects of pore structures on the CH4 adsorption capacity of coal, it is beneficial to give a brief background of coal porosity and CH4 adsorption in coal. Coal is a heterogeneous material with complex pore networks, containing pores varying in size from large cracks of micron dimensions to micropores of nanometer dimensions [12,60]. The quantity of CH4 adsorbed in coal under different pressures follows the Langmuir model, whereat the Langmuir volume obtained by fitting the adsorption data using the Langmuir equation is widely used to describe the CH4 adsorption capacity of coal [13–15]. To better understand the adsorption mechanism of CBM and to accurately predict the occurrence regularity of CBM in coal seam, it is worthwhile to study the relationship between the CH4 adsorption capacity and the microscopic pore properties in coal. For many years, researchers have made considerable efforts to understand the effects of the pore structures in coal on the CH4 adsorption capacity, and the focus of these studies was mainly on the specific surface areas (SSAs) [16–18], micropore volume [19,20], and micropore size distribution (MPSD) [19,21]. The first widely accepted view is that the larger the SSAs are, the more adsorption sites are available, resulting in a higher CH4 sorption capacity of the coal [2]. Tao et al. [22,23] found a linear relationship between the Langmuir volume at 298 K and the SSAs based on the Brunauer-Emmett-Teller (BET) method (BET-SSA) using high-pressure CH4 adsorption (HPGA-CH4) and lowpressure N2 adsorption (LPGA-N2) measurements. However, Byamba et al. [24,25] found that the plot of CH4 adsorption capacity versus BET-SSA fails for adsorbents of microporosity. Comparing the results of LPGA-N2 and low-pressure CO2 adsorption (LPGA-CO2) measurements, Zhao et al. [2,26,27] noted that micropores are common in coal whose SSAs account for most of the total SSA (> 99%), and the CH4 adsorption capacity is positively related to the SSAs of the micropores. The second view is that the CH4 adsorption capacity of coal is significantly and positively related to the micropore volume [18,20,26]. On the basis of this view, Lozano-Castello et al. [17,19,21] studied the effect of the pore size distribution (PSD) on the adsorption characteristics and found that the CH4 adsorption capacity in coal not only depends on the micropore volume but also strongly depends on the MPSD. It should be noted that some fallacies are introduced when the pore characteristics obtained by LPGA-N2 and LPGA-CO2 methods are used to represent the CH4 adsorption capacity of coals. (1) Due to activation diffusion [12], BET-SSAs based on the LPGA-N2 method only measure the external surface area in the presence of microporosity [2,28]. Thus, the BET-SSAs of coal are only a very small part of the total SSA [2,27,29]; it is meaningless to characterize the CH4 adsorption capacity of microporous solids using the BET-SSAs alone. (2) The LPGA-CO2 method is widely used to obtain the properties of micropores in the size range of 0.33–1.5 nm [30]. However, for CH4 molecules with a kinetic diameter of 0.38 nm [31], the micropore structures obtained by LPGACO2 include some inaccessible areas (0.33–0.38 nm), resulting in an overestimation of the CH4 adsorption capacity of coal. In addition, the LPGA-CO2 method overestimates the surface areas because it induces swelling in coals [12]; therefore, the surface areas may be meaningless to characterize the CH4 adsorption capacity on coals. (3) The CH4 adsorption mechanisms in the micropore structures obtained by LPGACO2, and on the external surface obtained via the LPGA-N2 method are different [2,28]. The CH4 molecules are adsorbed inside the micropore
2. Materials and methods 2.1. Materials collection and preparation Fresh coal blocks were collected directly from the working faces of six collieries in China, i.e., Daning colliery in Shanxi province, Xiaoqing colliery in Liaoning province, Taoyuan and Qinan collieries in Anhui province, Pingba colliery in Henan province, and Haishiwan colliery in Gansu province (see Fig. 1). The coal samples were transported to the laboratory, crushed, and sequentially sieved into a 60–80 mesh (0.18–0.25 mm) particle size through a set of screens. 2.2. Experimental methods Proximate analysis was conducted for moisture, ash, volatile material, and fixed carbon according to the China National Standard GB/T 212-2008 via an automatic industrial analyzer (5E-MAG6600; Changsha Kaiyuan Instruments, China). Vitrinite reflectance was obtained according to the China National Standard GB/T 6948-2008 via a microscope photometer. Three replicate analyses were performed, and the proximate analysis and vitrinite reflectance results for the coal samples are listed in Table 1. HPGA-CH4 measurements were conducted by the manometric method at a constant temperature of 303 K according to the China National Standard GBT 19560-2008. The experimental instruments were similar to those used in previous studies [32] (see Fig. 2). The uncertainty in the CH4 pressure measurement was 0.001 MPa, and the uncertainty in the volume measurement was 0.05 mL. Three replicate analyses of the free volume of each reference tank and adsorption tank were performed according to the China National Standard GB/T 195602008 using the helium expansion method to minimize and assess the composition uncertainty. Coal samples weighing approximately 60 g with 60–80 mesh (0.18–0.25 mm) particle sizes were used for the HPGA-CH4 measurements, and the maximum pressure of the adsorption tests was set at 7 MPa. The adsorbed volume of CH4 was calculated by subtracting the volume of gas occupying the free volume after adsorption equilibrium was reached from the total volume of gas that was present in the reference cell [32]. The Langmuir volume was calculated by linear fitting the adsorption data using the Langmuir equation [14], and the results are shown in Table 1. 2
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Fig. 1. Schematic diagram of the sampling locations and sample preparation steps.
3. Results and discussion
Granular coal samples of the same size were used for LPGA-N2 and LPGA-CO2 measurements to avoid the effect of particle size on the microscopic pore characteristics and CH4 adsorption capacity. Before the N2 and CO2 adsorption started, the coal samples were predried (323 K for 48 h) to prevent moisture in the samples from damaging the turbomolecular pump. At the beginning of the experiment, to remove the adsorbed moisture and volatile matter, coal samples weighing approximately 0.4 g were placed in the degassing station of the automatic industrial analyzer (Autosorb-iQ2; Quantachrome Instruments, United States) and degassed at 383 K for 10 h. The uncertainty in the mass measurement was 0.0002 g, based on replicate measurements. The sample tube was then transferred to the analysis station, and the N2 and CO2 adsorption isotherms of the coal samples were measured at constant temperatures of 77 K and 273 K. The N2 adsorption/desorption isotherms were obtained at relative pressures (P/P0) ranging from 0.001 to 0.995, which consisted of 80 adsorption points and 50 desorption points. The CO2 adsorption isotherms were measured in a relative pressure range of 3 × 10-5 to 0.0289, which consisted of 50 adsorption points. For the LPGA-N2 and LPGA-CO2 measurements, the equilibrium interval was set for 4 min, the relative pressure tolerance and absolute pressure tolerance were set to 0.08% and 0.608 mmHg (0.0811 kPa), respectively.
3.1. Microscopic pore characteristics of coal determined by the LPGA-N2 and LPGA-CO2 methods 3.1.1. N2 adsorption/desorption isotherms The N2 adsorption/desorption isotherms of the six coal samples from different mines are shown in Fig. 3. The adsorption potential energy of two parallel pore walls reached approximately 3.5 times the desorption potential energy according to calculations based on the potential energy model in which the distance between the walls was almost the size of a molecule [33]. Thus, a steep uptake at a very low P/ P0 due to enhanced adsorbent-adsorptive interactions in narrow micropores indicated that there were micropores of molecular dimensions in the coal samples, resulting in micropore filling at a very low P/P0 [34]. Monolayer coverage began on the surface with comparable potential energy when the high potential energy region was filled with gas molecules. At low P/P0, Point B (the beginning of the middle almost linear section) usually corresponded to the completion of the monolayer coverage [28]. Capillary condensation was accompanied by hysteresis at moderate and high P/P0, which was dependent on the adsorption system and temperature (for the N2 adsorption isotherm, hysteresis started to occur in pores wider than 4 nm) [35,36]. When P/ P0 was close to 1, the adsorption isotherms rose sharply without limit,
Table 1 Proximate analysis and CH4 adsorption test results. Sample number
DN XQ TY QN PB HSW
Coal
Daning colliery Xiaoqing colliery Taoyuan colliery Qinan colliery Pingba colliery Haishiwan colliery
Proximate analysis (wt%)
Langmuir parameters
R0 (%)
Mad
Ad
Vdaf
FCad
VL (mL/g)
PL (MPa)
1.94 4.04 1.82 1.38 1.13 0.95
9.28 11.16 19.94 12.07 21.73 5.88
7.05 37.61 36.31 37.84 32.45 40.98
82.54 52.91 49.84 53.81 52.12 55.00
35.76 28.76 22.82 16.46 14.47 13.30
0.61 1.58 2.52 1.20 1.30 1.85
2.89 0.81 0.82 0.79 0.92 0.73
Note: Mad is the moisture content on the air-dry basis; Ad is the ash content on a dry basis; Vdaf is the volatile matter content on the dry-ash-free basis; FCad is the fixed carbon content on the air-dry basis; VL is the Langmuir volume; PL is the Langmuir pressure; R0 is the vitrinite reflectance. 3
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Fig. 2. Schematic diagram of the experimental instruments for the high-pressure CH4 adsorption test.
agglomerates of micropores and plate-like particles [38,39]. The hysteresis loop was resolved to a type H2 loop for the XQ samples. The very steep desorption branch can be attributed to pore-blocking/percolation in a narrow range of pore necks or to cavitation-induced evaporation [28], indicating that the coal samples may have contained some inkbottle pores [28,40]. In addition, for the DN and XQ coal samples, the hysteresis loops were not closed. This phenomenon is often associated with the expansion and contraction of adsorbents, especially for highrank and low-rank coals with complex pore structures [38,41,42].
indicating that a macroporous structure (pores wider than 300 nm) appeared in the coal. Based on the classification criteria for pores recommended by the International Union of Pure and Applied Chemistry (IUPAC) [28], the coal samples used in this study, as typical porous solid materials, contained micropores (< 2 nm), mesopores (2–50 nm) and macropores (> 50 nm) [37]. According to the six hysteresis loops shapes recommended by IUPAC [28], the N2 adsorption/desorption isotherms for the TY, QN, PB, and HSW coal samples exhibited type H4 hysteresis loops, indicating that the coal samples were mainly composed of non-rigid
Fig. 3. Results of the N2 adsorption/desorption isotherms: (a) DN sample; (b) XQ sample; (c) TY sample; (d) QN sample; (e) PB sample; (f) HSW sample. 4
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Fig. 4. Results of the CO2 adsorption isotherms: (a) DN sample; (b) XQ sample; (c) TY sample; (d) QN sample; (e) PB sample; (f) HSW sample.
3.1.2. CO2 adsorption isotherms For the LPGA method, LPGA-N2 measurements are not satisfactory for the quantitative assessment of the microporosity, especially in the range of ultramicropores (pore widths < 0.7 nm), due to the activation diffusion [12,43,44]. The LPGA-CO2 method focuses on studying the micropore features of adsorbents by measuring the adsorption characteristics of samples during micropore filling. The CO2 adsorption isotherms of the six coal samples from different mines are shown in Fig. 4. These CO2 adsorption isotherms had similar shapes for the DN, XQ, TY, and PB coal samples and exhibited type Ⅰ isotherms. The bump trends in the isotherms of the QN and HSW samples were not consistent with the other samples; they were closer to linear changes.
adsorption, the BET-SSAs of the six samples ranged from 0.317 to 24.539 m2/g, while the SSAs of the micropores ranged from 75.898 to 230.736 m2/g. The pore volumes obtained by LPGA-N2 were in the range of 0.001–0.021 cc/g, while the micropore volumes obtained by the LPGA-CO2 method were in the range of 0.028–0.069 cc/g. Thus, micropore structures were common for the coal samples used in this paper and accounted for most of the total SSAs (90.39–99.58%), and the micropore structures accounted for 75.61–96.55% of the total pore volumes in these coal samples. These conclusions are similar to the results obtained in the previous studies [2,47]. 3.2. Quantitative characterization of CH4 adsorption capacity based on micropore filling and surface coverage
3.1.3. Pore volumes and specific surface areas Density functional theory (DFT) and the BET methods were used to analyze the N2 adsorption isotherms of the six coal samples and to get the pore volumes and the external surface areas [18,23]. Additionally, the DFT method was adopted to analyze the CO2 adsorption isotherms and for obtaining the micropore volumes, SSAs, and MPVDs of the coal samples [45,46]. The results are displayed in Table 2. According to the comparison of the SSAs and pore volumes obtained by N2 and CO2
3.2.1. Quantitative methods Numerous studies of HPGA-CH4 on coal have shown that the Langmuir equation is the most straightforward and widely accepted model to describe the relationship between the gas pressure and the quantity of CH4 adsorbed on coal [14,48,49]. The external surface of a coal sample is assumed to be energetically homogenous on the basis of Langmuir theory, where the CH4 molecules are adsorbed only on the
Table 2 Pore volumes and SSAs of the pulverized coal samples. Methods
Fitting parameters
DN
XQ
TY
QN
PB
HSW
LPGA-N2 (BET)
Slope (1/g) Intercept (1/g) Correlation coefficient Surface area (m2/g) C constant Pore volume (cc/g) Surface area (m2/g) Fitting error (%) Pore width (nm) Pore volume (cc/g) Surface area (m2/g) Fitting error (%) Pore width (nm)
921.168 35.73 0.99995 3.639 26.78 0.006 3.264 4.276 4.52 0.067 230.605 0.731 0.349
139.843 2.072 0.99999 24.539 68.49 0.021 19.033 0.587 1.096 0.069 230.736 0.8 0.524
1284.54 54.16 0.99921 2.601 24.72 0.004 1.989 0.482 4.22 0.041 124.769 0.101 0.548
1844.64 181.8 0.99947 1.719 11.15 0.004 1.372 4.623 4.52 0.038 111.85 0.127 0.479
717.424 16.63 0.99999 4.744 44.15 0.01 3.942 0.38 4.22 0.031 96.755 0.08 0.6
10174.5 811.6 0.99897 0.317 13.54 0.001 0.252 5.049 4.22 0.028 75.898 0.257 0.627
LPGA-N2 (DFT)
LPGA-CO2 (DFT)
Note: C constant is related to the energy of adsorption in the first adsorbed layer and consequently its value is an indication of the magnitude of the adsorbent/ adsorbate interactions. 5
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Fig. 6, and the pore length of each part was calculated separately according to the pore size distribution obtained based on the LPGA-CO2 results. Micropores with cross-section diameters ranging from 0.38–0.76 nm, 0.76–0.82 nm, 0.82–0.92 nm, 0.92–1.03 nm, 1.03–1.14 nm, 1.14–1.26 nm, 1.26–1.37 nm, and 1.37–1.49 nm, can accommodate 1, 2, 3, 4, 5, 7, 8, 9, and 11 CH4 molecules, respectively. To simplify the calculation, it was assumed that CH4 molecules are arranged in a close-packed array in the micropores and the equivalent height of each layer of CH4 is 0.33 nm [27]. Finally, the quantity of CH4 adsorbed in 8 areas can be calculated according to the pore length of each part and equivalent height respectively. n
Nmic =
∑ ih i=1
Li CH4
(1)
where Nmic is the quantity of CH4 molecules adsorbed in the micropore structures; i is the theoretical number of CH4 molecules accommodating the cross-section of the cylindrical micropores; Li is the total length of the assumed cylindrical micropores; and hCH4 is the equivalent height of the CH4 molecules on the axis of assumed cylindrical micropores.
Fig. 5. Distribution of the CH4 molecules in the adsorption areas of micropores with different scales based on the MPVD of LPGA-CO2.
Li =
external surface in the form of monolayer coverage [50,51], and the quantity of CH4 adsorbed depends on the external SSA [23]. Due to the enhanced adsorbent-adsorptive interactions in micropores [13], it is assumed that the CH4 molecules are only adsorbed inside the micropore structures in the form of micropore filling [52,53], and the amount of CH4 adsorbed is limited by the micropore volumes [23,54]. Therefore, the estimated Langmuir volume was obtained by calculating the total amount of CH4 adsorbed on the external surface and inside the micropore structures. Since the kinetic diameters of CO2 (0.33 nm) and CH4 (0.38 nm) molecules are not the same [31], the probe-accessible surface measured by the LPGA-CO2 method does not coincide with the adsorption space that CH4 molecules can enter [15,24]. Therefore, the micropore volumes measured by CO2 adsorption cannot be directly converted into the amount of CH4 adsorbed inside micropore structures. Additionally, because the number of CH4 molecules that can be adsorbed inside micropores of different sizes is not the same, it was assumed that the micropores in the coal samples were cylindrical, and eight adsorption areas were identified according to the number of CH4 molecules occupying the micropores with different scales, as shown in Fig. 5 and
4Vi πdi2
(2)
where Vi is the total micropore volumes in a certain adsorption area and di is the average micropore diameter of this adsorption area.
Nmes & mac =
SSA(N2 − BET ) SACH4
(3)
where Nmes & mac is the quantity of CH4 molecules adsorbed on the external surface in the form of monolayer adsorption; SSA(N2 − BET ) is the external SSA calculated by the BET method for LPGA-N2; and SACH4 is the equivalent surface area occupied by a CH4 molecule arranged in a close-packed array [28] and has a value of 1.251 × 10−19 m2. 3.2.2. CH4 molecule distribution characteristics in pore structures with different scales The numbers of CH4 molecules in micropore structures with different sizes were calculated by Eq. (1) and Eq. (2). Based on the BETSSAs obtained by the LPGA-N2 method, the total numbers of CH4 molecules adsorbed on the external surface were calculated by Eq. (3). The distribution characteristics of the CH4 molecules adsorbed in the adsorption areas with different scales are shown in Fig. 7. For the six coal samples, the number of CH4 molecules adsorbed by micropores in the size range of 0.38–0.76 nm accounted for 38–55% of the total amount adsorbed and made up the largest proportion in the nine adsorption areas. The quantity of CH4 adsorbed in the form of micropore filling accounted for 74–99% of the total amount adsorbed, and the XQ coal sample had the largest external SSA, so that the amount of CH4 adsorbed on the external surface in the form of monolayer coverage accounted for 26% of the total amount adsorbed. Similar calculated results were obtained in other studies [52], but the CH4 molecules in the micropore structures were not adsorbed on the surface of the micropores in the form of surface coverage. 3.3. Discussion of the microscopic pore properties and CH4 adsorption capacity 3.3.1. Correlations between the microscopic pore characteristics and the Langmuir volume The relationships between the microscopic pore characteristics and the measured Langmuir volumes obtained from the HPGA-CH4, LPGAN2, and LPGA-CO2 measurements (Tables 1 and 2) are shown in Fig. 8. There was not a good correlation between the CH4 adsorption capacity of the coals and the pore volumes or external SSAs obtained by the LPGA-N2 measurements, as shown in Fig. 8 (a) and (d). However, a very good correlation between the CH4 adsorption capacity of the coals and
Fig. 6. Numbers of CH4 molecules in micropores with different scales. 6
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Fig. 7. Distribution of the adsorbed CH4 molecules in pore structures with different scales.
3.3.2. Correlations between the measured and estimated Langmuir volume To facilitate a comparison with the HPGA-CH4 results, the quantity of CH4 molecules adsorbed in the coal was converted into the adsorbed volume of CH4 under the standard conditions using Eq. (4).
the micropore volumes or SSAs obtained by the LPGA-CO2 measurements existed for the six coal samples used in this study. Similar calculated results were obtained in previous studies [46,55,56]. Finally, the total pore volumes and total SSAs were calculated by adding the pore volumes and SSAs obtained by the LPGA-N2 and LPGA-CO2 methods. Compared with the micropore volumes and SSAs obtained by LPGA-CO2, the total pore volumes and total SSAs did not better express the CH4 adsorption capacity, as shown in Fig. 8 (c) and (f). The reason may be that different adsorption forms in the micropore structures and on the external surface of the coal led to different effects on the CH4 adsorption capacity [23,28,54]. In addition, according to the micropore volumes of the DN and XQ samples (Table 2), the samples have larger micropore volumes but smaller adsorption capacities (Fig. 7), which can be attributed to the different MPVDs and micropore volumes of the areas inaccessible to the CH4 molecules (see Fig. 5) [57]. Therefore, although the best relationship exists between the micropore properties and the measured Langmuir volume, we still do not recommend the direct comparison of the CH4 adsorption capacity with the pore properties obtained by LPGA-CO2.
Vmic − PV & BET − SSA = =22.4 ×
Nmic + Nmes & mac Na
(4)
where Vmic-PV&BET-SSA is the estimated Langmuir volume based on micropore filling and monolayer adsorption theory and Na is Avogadro's number, with a value of 6.02 × 1023. In this paper, the adsorption was assumed to be two-dimensional and to take place on an imaginary surface (Gibbs dividing surface) [28]. The adsorbed volumes of CH4 were calculated based on the SSAs obtained by the LPGA-N2 and LPGACO2 methods using Eqs. (5) and (6).
Vmic − SSA = =22.4 ×
SSA(CO2− DFT ) Na SACH4
(5)
VBET − SSA = =22.4 ×
Nmes & mac Na
(6)
Fig. 8. Correlations between the microscopic pore characteristics and the measured Langmuir volume. 7
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intrusion tests have been extensively studied [15,56,58,59]. However, similar to the BET-SSAs, the fractal dimension based on N2 adsorption can only characterize the surface properties of pores in a limited range. Therefore, confirmation of the ability of these properties to represent the overall pore structures in coal is need.
Table 3 Measured and estimated Langmuir volumes calculated using the microscopic pore properties. Sample
DN XQ TY QN PB HSW
Measured Langmuir volume
Estimated Langmuir volume
VL (mL/g)
VBET-SSA (mL/g)
Vmic-SSA (mL/g)
Vmic-PV&BET-SSA (mL/g)
4. Conclusions
35.76 28.76 22.82 16.46 14.47 13.30
1.08 7.30 0.77 0.51 1.41 0.09
68.62 68.65 37.12 33.28 28.79 22.58
33.33 28.19 20.78 18.93 16.13 14.68
In this study, a new quantitative method for estimating the CH4 adsorption capacity of coal was proposed. Based on micropore filling and monolayer coverage theory, nine adsorption areas with different scales were constructed for the coal, and the distribution of the CH4 molecules in pore structures with different scales was obtained. By a comparison with the Langmuir volumes obtained from HPGA-CH4 measurements, this quantitative method was verified. The conclusions can be summarized as follows: (1) The probe-accessible area of the LPGA method is determined by the type of probe, temperature, and the pressure range. The surface characteristics of coal obtained by N2 and CO2 adsorption are not compatible. In this study, the external SSAs and pore volumes obtained by LPGA-N2 ranged from 0.317 to 24.539 m2/g and from 0.001 to 0.021 cc/g, respectively, while the SSAs and micropore volumes obtained by the LPGA-CO2 method ranged from 75.898 to 230.736 m2/g and from 0.028 to 0.069 cc/g, respectively. (2) The quantity of CH4 adsorbed in the form of micropore filling accounted for 74–99% of the total amount adsorbed, and the amount of CH4 adsorbed by the micropores in the size range of 0.38–0.76 nm accounted for 38–55% of the total amount adsorbed and made up the largest proportion in the nine adsorption areas. (3) CH4 molecules were adsorbed on the external surface in the form of monolayer coverage, and they were adsorbed on the micropore structures in the form of micropore filling. Thus, the SSAs and micropore volumes obtained by CO2 adsorption correlated better with the CH4 adsorption capacity of coal than the total SSAs and pore volumes, and the ratio of the SSAs of the micropores to the total SSA was higher than the ratio between the quantity of CH4 adsorbed in the micropores and the total amount adsorbed in the coal. (4) The estimated Langmuir volumes based on micropore filling and monolayer coverage theory were very similar to the measured Langmuir volumes. Therefore, the CH4 adsorption capacity of coal is determined by both the accessible MPVD and external surface areas in coal.
Fig. 9. Comparison of the measured and estimated adsorbed volume of CH4.
where VBET-SSA is the estimated Langmuir volume based on the BETSSAs obtained by the LPGA-N2 method and Vmic-SSA is the estimated Langmuir volume based on the DFT-SSAs obtained by the LPGA-CO2 method. The estimated Langmuir volumes based on different methods were obtained and are shown in Table 3. The relationships between the estimated Langmuir volumes and the measured Langmuir volumes are shown in Fig. 9. The estimated Langmuir volumes obtained based on the SSAs obtained by the LPGA-N2 measurements were much smaller than the measured values, indicating that only a very small portion of CH4 adsorbed in coal is present on the external surface. Regarding the estimated Langmuir volume obtained based on the SSAs obtained by the LPGA-CO2 measurements, the estimated Langmuir volumes were much larger than the measured values, indicating that the amount of CH4 adsorbed in the micropores is limited by the pore volume rather than the surface area, and it is not suitable to use the surface area to characterize the adsorption amount. Therefore, regardless of the adsorption forms of CH4 in different pore structures, it is unreliable to simply compare the SSAs with the CH4 adsorption capacity of coal. Similar views have been published stating that surface areas of coals obtained by CO2 adsorption are meaningless and should not be reported [12]. When the CH4 adsorption capacities of coal samples are compared, the BET-SSAs obtained by N2 adsorption should not be reported, due to the presence of micropores [15]. A very good relationship existed between the measured Langmuir volumes and the estimated Langmuir volumes based on micropore filling and surface coverage theory (see Fig. 9), which demonstrated that the adsorption capacity of coal was determined by both the accessible MPVD and the external surface areas of the CH4 molecules. Note that the relationships between the Langmuir parameters and the fractal characteristics obtained by the LPGA-N2 and mercury
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Full Length Article
New insights into the CH4 adsorption capacity of coal based on microscopic pore properties ⁎
Biao Hua,b,c, Yuanping Chenga,b,c, , Xinxin Hea,b,c, Zhenyang Wanga,b,c, Zhaonan Jianga,b,c, Chenghao Wanga,b,c, Wei Lia,b,c, Liang Wanga,b,c a
Key Laboratory of Coal Methane and Fire Control, Ministry of Education, China University of Mining and Technology, Xuzhou, Jiangsu 221116, China National Engineering Research Center for Coal and Gas Control, China University of Mining and Technology, Xuzhou 221116, China c School of Safety Engineering, China University of Mining and Technology, Xuzhou 221116, China b
G R A P H I C A L A B S T R A C T
A R T I C LE I N FO
A B S T R A C T
Keywords: Coal Methane Adsorption Langmuir volume Micropore filling Surface coverage
The objective of this study is to quantitatively describe the CH4 adsorption capacity of coal through microscopic pore properties. In this work, the micropore volume distributions (MPVDs) of granular coal samples from six collieries were obtained by low-pressure CO2 adsorption (LPGA-CO2), and the external specific surface areas (SSAs) were calculated using low-pressure N2 adsorption (LPGA-N2). Based on micropore filling and monolayer coverage theories, the micropores were assumed to be cylindrical to obtain the distribution of CH4 in pore structures with different scales. For the coal samples used in this study, micropores were common, whose SSAs accounted for most of the total SSAs (90.39–99.58%), and the micropore volumes accounted for 75.61–96.55% of total pore volumes. The quantity of CH4 adsorbed in the form of micropore filling account for 74–99% of the total amount adsorbed, while the amount of CH4 adsorbed by micropores in the size range of 0.38–0.76 nm was 38–55% of the total amount adsorbed and accounted for the largest proportion in the nine adsorption areas partitioned according to the number of CH4 molecules occupying micropores with different scales. Based on a combination of the high-pressure CH4 adsorption (HPGA-CH4) results, the estimated Langmuir volumes are in close agreement with the measured Langmuir volumes, which demonstrates that the CH4 adsorption capacity of the coal is determined by both the accessible MPVD and external SSAs. The results of this study may be significant for understanding the pore networks and the CH4 adsorption mechanism in coal under in situ conditions.
⁎ Corresponding author at: Key Laboratory of Coal Methane and Fire Control, Ministry of Education, China University of Mining and Technology, Xuzhou, Jiangsu 221116, China. E-mail address: [email protected] (Y. Cheng).
https://doi.org/10.1016/j.fuel.2019.116675 Received 18 August 2019; Received in revised form 19 October 2019; Accepted 14 November 2019 0016-2361/ © 2019 Elsevier Ltd. All rights reserved.
Please cite this article as: Biao Hu, et al., Fuel, https://doi.org/10.1016/j.fuel.2019.116675
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structures in the form of micropore filling due to the enhanced adsorbent-adsorptive interactions [13,28], and they are adsorbed on the external surface in the form of surface coverage. Because of the importance of characterization of the CH4 adsorption capacity of coal, the main objective of this work was to quantitatively characterize the CH4 adsorption capacity using the microscopic pore properties. In this study, we intended to conduct a comprehensive investigation of CH4 adsorption on coal by considering the different adsorption forms of CH4 molecules in pore structures on different scales. We obtained the micropore volume distributions (MPVDs) of granular coal samples from six collieries using the LPGA-CO2 method. The micropores in coal were assumed to be cylindrical herein, and the number of CH4 molecules captured by the microporous structures on different scales is different. The number of CH4 molecules adsorbed in the micropores based on micropores filling theory was calculated by dividing the range of the MPVD. We obtained the external SSAs by the LPGA-N2 method, and the CH4 molecules were captured by the adsorption sites on the surface of the mesopores and macropores by monolayer absorption. Based on the micropore filling and monolayer adsorption theory, quantitative relationships between the microscopic pore characteristics of coal and the CH4 adsorption capacity were constructed and verified by the measured Langmuir volume. The research results are of great significance for understanding the pore networks in coal and their influencing factors and for studying the CH4 adsorption mechanism.
1. Introduction Coalbed methane (CBM), a clean and high-efficiency energy source, is composed primarily of CH4 [1]. Compared with conventional shale reservoirs, coal reservoirs are dominated by pores of nanometer dimensions [2,3], and the CH4 is mainly stored in an adsorption state on the surface of these pores in the coal [4]. Therefore, understanding the pore networks and CH4 adsorption mechanism in micro- and mesoporous coal has practical application in the accurate prediction of CBM [5,6], CBM development and utilization [7,8], coal and gas outburst prevention and control [9,10], and geological CO2 storage [11]. Before discussing the effects of pore structures on the CH4 adsorption capacity of coal, it is beneficial to give a brief background of coal porosity and CH4 adsorption in coal. Coal is a heterogeneous material with complex pore networks, containing pores varying in size from large cracks of micron dimensions to micropores of nanometer dimensions [12,60]. The quantity of CH4 adsorbed in coal under different pressures follows the Langmuir model, whereat the Langmuir volume obtained by fitting the adsorption data using the Langmuir equation is widely used to describe the CH4 adsorption capacity of coal [13–15]. To better understand the adsorption mechanism of CBM and to accurately predict the occurrence regularity of CBM in coal seam, it is worthwhile to study the relationship between the CH4 adsorption capacity and the microscopic pore properties in coal. For many years, researchers have made considerable efforts to understand the effects of the pore structures in coal on the CH4 adsorption capacity, and the focus of these studies was mainly on the specific surface areas (SSAs) [16–18], micropore volume [19,20], and micropore size distribution (MPSD) [19,21]. The first widely accepted view is that the larger the SSAs are, the more adsorption sites are available, resulting in a higher CH4 sorption capacity of the coal [2]. Tao et al. [22,23] found a linear relationship between the Langmuir volume at 298 K and the SSAs based on the Brunauer-Emmett-Teller (BET) method (BET-SSA) using high-pressure CH4 adsorption (HPGA-CH4) and lowpressure N2 adsorption (LPGA-N2) measurements. However, Byamba et al. [24,25] found that the plot of CH4 adsorption capacity versus BET-SSA fails for adsorbents of microporosity. Comparing the results of LPGA-N2 and low-pressure CO2 adsorption (LPGA-CO2) measurements, Zhao et al. [2,26,27] noted that micropores are common in coal whose SSAs account for most of the total SSA (> 99%), and the CH4 adsorption capacity is positively related to the SSAs of the micropores. The second view is that the CH4 adsorption capacity of coal is significantly and positively related to the micropore volume [18,20,26]. On the basis of this view, Lozano-Castello et al. [17,19,21] studied the effect of the pore size distribution (PSD) on the adsorption characteristics and found that the CH4 adsorption capacity in coal not only depends on the micropore volume but also strongly depends on the MPSD. It should be noted that some fallacies are introduced when the pore characteristics obtained by LPGA-N2 and LPGA-CO2 methods are used to represent the CH4 adsorption capacity of coals. (1) Due to activation diffusion [12], BET-SSAs based on the LPGA-N2 method only measure the external surface area in the presence of microporosity [2,28]. Thus, the BET-SSAs of coal are only a very small part of the total SSA [2,27,29]; it is meaningless to characterize the CH4 adsorption capacity of microporous solids using the BET-SSAs alone. (2) The LPGA-CO2 method is widely used to obtain the properties of micropores in the size range of 0.33–1.5 nm [30]. However, for CH4 molecules with a kinetic diameter of 0.38 nm [31], the micropore structures obtained by LPGACO2 include some inaccessible areas (0.33–0.38 nm), resulting in an overestimation of the CH4 adsorption capacity of coal. In addition, the LPGA-CO2 method overestimates the surface areas because it induces swelling in coals [12]; therefore, the surface areas may be meaningless to characterize the CH4 adsorption capacity on coals. (3) The CH4 adsorption mechanisms in the micropore structures obtained by LPGACO2, and on the external surface obtained via the LPGA-N2 method are different [2,28]. The CH4 molecules are adsorbed inside the micropore
2. Materials and methods 2.1. Materials collection and preparation Fresh coal blocks were collected directly from the working faces of six collieries in China, i.e., Daning colliery in Shanxi province, Xiaoqing colliery in Liaoning province, Taoyuan and Qinan collieries in Anhui province, Pingba colliery in Henan province, and Haishiwan colliery in Gansu province (see Fig. 1). The coal samples were transported to the laboratory, crushed, and sequentially sieved into a 60–80 mesh (0.18–0.25 mm) particle size through a set of screens. 2.2. Experimental methods Proximate analysis was conducted for moisture, ash, volatile material, and fixed carbon according to the China National Standard GB/T 212-2008 via an automatic industrial analyzer (5E-MAG6600; Changsha Kaiyuan Instruments, China). Vitrinite reflectance was obtained according to the China National Standard GB/T 6948-2008 via a microscope photometer. Three replicate analyses were performed, and the proximate analysis and vitrinite reflectance results for the coal samples are listed in Table 1. HPGA-CH4 measurements were conducted by the manometric method at a constant temperature of 303 K according to the China National Standard GBT 19560-2008. The experimental instruments were similar to those used in previous studies [32] (see Fig. 2). The uncertainty in the CH4 pressure measurement was 0.001 MPa, and the uncertainty in the volume measurement was 0.05 mL. Three replicate analyses of the free volume of each reference tank and adsorption tank were performed according to the China National Standard GB/T 195602008 using the helium expansion method to minimize and assess the composition uncertainty. Coal samples weighing approximately 60 g with 60–80 mesh (0.18–0.25 mm) particle sizes were used for the HPGA-CH4 measurements, and the maximum pressure of the adsorption tests was set at 7 MPa. The adsorbed volume of CH4 was calculated by subtracting the volume of gas occupying the free volume after adsorption equilibrium was reached from the total volume of gas that was present in the reference cell [32]. The Langmuir volume was calculated by linear fitting the adsorption data using the Langmuir equation [14], and the results are shown in Table 1. 2
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Fig. 1. Schematic diagram of the sampling locations and sample preparation steps.
3. Results and discussion
Granular coal samples of the same size were used for LPGA-N2 and LPGA-CO2 measurements to avoid the effect of particle size on the microscopic pore characteristics and CH4 adsorption capacity. Before the N2 and CO2 adsorption started, the coal samples were predried (323 K for 48 h) to prevent moisture in the samples from damaging the turbomolecular pump. At the beginning of the experiment, to remove the adsorbed moisture and volatile matter, coal samples weighing approximately 0.4 g were placed in the degassing station of the automatic industrial analyzer (Autosorb-iQ2; Quantachrome Instruments, United States) and degassed at 383 K for 10 h. The uncertainty in the mass measurement was 0.0002 g, based on replicate measurements. The sample tube was then transferred to the analysis station, and the N2 and CO2 adsorption isotherms of the coal samples were measured at constant temperatures of 77 K and 273 K. The N2 adsorption/desorption isotherms were obtained at relative pressures (P/P0) ranging from 0.001 to 0.995, which consisted of 80 adsorption points and 50 desorption points. The CO2 adsorption isotherms were measured in a relative pressure range of 3 × 10-5 to 0.0289, which consisted of 50 adsorption points. For the LPGA-N2 and LPGA-CO2 measurements, the equilibrium interval was set for 4 min, the relative pressure tolerance and absolute pressure tolerance were set to 0.08% and 0.608 mmHg (0.0811 kPa), respectively.
3.1. Microscopic pore characteristics of coal determined by the LPGA-N2 and LPGA-CO2 methods 3.1.1. N2 adsorption/desorption isotherms The N2 adsorption/desorption isotherms of the six coal samples from different mines are shown in Fig. 3. The adsorption potential energy of two parallel pore walls reached approximately 3.5 times the desorption potential energy according to calculations based on the potential energy model in which the distance between the walls was almost the size of a molecule [33]. Thus, a steep uptake at a very low P/ P0 due to enhanced adsorbent-adsorptive interactions in narrow micropores indicated that there were micropores of molecular dimensions in the coal samples, resulting in micropore filling at a very low P/P0 [34]. Monolayer coverage began on the surface with comparable potential energy when the high potential energy region was filled with gas molecules. At low P/P0, Point B (the beginning of the middle almost linear section) usually corresponded to the completion of the monolayer coverage [28]. Capillary condensation was accompanied by hysteresis at moderate and high P/P0, which was dependent on the adsorption system and temperature (for the N2 adsorption isotherm, hysteresis started to occur in pores wider than 4 nm) [35,36]. When P/ P0 was close to 1, the adsorption isotherms rose sharply without limit,
Table 1 Proximate analysis and CH4 adsorption test results. Sample number
DN XQ TY QN PB HSW
Coal
Daning colliery Xiaoqing colliery Taoyuan colliery Qinan colliery Pingba colliery Haishiwan colliery
Proximate analysis (wt%)
Langmuir parameters
R0 (%)
Mad
Ad
Vdaf
FCad
VL (mL/g)
PL (MPa)
1.94 4.04 1.82 1.38 1.13 0.95
9.28 11.16 19.94 12.07 21.73 5.88
7.05 37.61 36.31 37.84 32.45 40.98
82.54 52.91 49.84 53.81 52.12 55.00
35.76 28.76 22.82 16.46 14.47 13.30
0.61 1.58 2.52 1.20 1.30 1.85
2.89 0.81 0.82 0.79 0.92 0.73
Note: Mad is the moisture content on the air-dry basis; Ad is the ash content on a dry basis; Vdaf is the volatile matter content on the dry-ash-free basis; FCad is the fixed carbon content on the air-dry basis; VL is the Langmuir volume; PL is the Langmuir pressure; R0 is the vitrinite reflectance. 3
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Fig. 2. Schematic diagram of the experimental instruments for the high-pressure CH4 adsorption test.
agglomerates of micropores and plate-like particles [38,39]. The hysteresis loop was resolved to a type H2 loop for the XQ samples. The very steep desorption branch can be attributed to pore-blocking/percolation in a narrow range of pore necks or to cavitation-induced evaporation [28], indicating that the coal samples may have contained some inkbottle pores [28,40]. In addition, for the DN and XQ coal samples, the hysteresis loops were not closed. This phenomenon is often associated with the expansion and contraction of adsorbents, especially for highrank and low-rank coals with complex pore structures [38,41,42].
indicating that a macroporous structure (pores wider than 300 nm) appeared in the coal. Based on the classification criteria for pores recommended by the International Union of Pure and Applied Chemistry (IUPAC) [28], the coal samples used in this study, as typical porous solid materials, contained micropores (< 2 nm), mesopores (2–50 nm) and macropores (> 50 nm) [37]. According to the six hysteresis loops shapes recommended by IUPAC [28], the N2 adsorption/desorption isotherms for the TY, QN, PB, and HSW coal samples exhibited type H4 hysteresis loops, indicating that the coal samples were mainly composed of non-rigid
Fig. 3. Results of the N2 adsorption/desorption isotherms: (a) DN sample; (b) XQ sample; (c) TY sample; (d) QN sample; (e) PB sample; (f) HSW sample. 4
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Fig. 4. Results of the CO2 adsorption isotherms: (a) DN sample; (b) XQ sample; (c) TY sample; (d) QN sample; (e) PB sample; (f) HSW sample.
3.1.2. CO2 adsorption isotherms For the LPGA method, LPGA-N2 measurements are not satisfactory for the quantitative assessment of the microporosity, especially in the range of ultramicropores (pore widths < 0.7 nm), due to the activation diffusion [12,43,44]. The LPGA-CO2 method focuses on studying the micropore features of adsorbents by measuring the adsorption characteristics of samples during micropore filling. The CO2 adsorption isotherms of the six coal samples from different mines are shown in Fig. 4. These CO2 adsorption isotherms had similar shapes for the DN, XQ, TY, and PB coal samples and exhibited type Ⅰ isotherms. The bump trends in the isotherms of the QN and HSW samples were not consistent with the other samples; they were closer to linear changes.
adsorption, the BET-SSAs of the six samples ranged from 0.317 to 24.539 m2/g, while the SSAs of the micropores ranged from 75.898 to 230.736 m2/g. The pore volumes obtained by LPGA-N2 were in the range of 0.001–0.021 cc/g, while the micropore volumes obtained by the LPGA-CO2 method were in the range of 0.028–0.069 cc/g. Thus, micropore structures were common for the coal samples used in this paper and accounted for most of the total SSAs (90.39–99.58%), and the micropore structures accounted for 75.61–96.55% of the total pore volumes in these coal samples. These conclusions are similar to the results obtained in the previous studies [2,47]. 3.2. Quantitative characterization of CH4 adsorption capacity based on micropore filling and surface coverage
3.1.3. Pore volumes and specific surface areas Density functional theory (DFT) and the BET methods were used to analyze the N2 adsorption isotherms of the six coal samples and to get the pore volumes and the external surface areas [18,23]. Additionally, the DFT method was adopted to analyze the CO2 adsorption isotherms and for obtaining the micropore volumes, SSAs, and MPVDs of the coal samples [45,46]. The results are displayed in Table 2. According to the comparison of the SSAs and pore volumes obtained by N2 and CO2
3.2.1. Quantitative methods Numerous studies of HPGA-CH4 on coal have shown that the Langmuir equation is the most straightforward and widely accepted model to describe the relationship between the gas pressure and the quantity of CH4 adsorbed on coal [14,48,49]. The external surface of a coal sample is assumed to be energetically homogenous on the basis of Langmuir theory, where the CH4 molecules are adsorbed only on the
Table 2 Pore volumes and SSAs of the pulverized coal samples. Methods
Fitting parameters
DN
XQ
TY
QN
PB
HSW
LPGA-N2 (BET)
Slope (1/g) Intercept (1/g) Correlation coefficient Surface area (m2/g) C constant Pore volume (cc/g) Surface area (m2/g) Fitting error (%) Pore width (nm) Pore volume (cc/g) Surface area (m2/g) Fitting error (%) Pore width (nm)
921.168 35.73 0.99995 3.639 26.78 0.006 3.264 4.276 4.52 0.067 230.605 0.731 0.349
139.843 2.072 0.99999 24.539 68.49 0.021 19.033 0.587 1.096 0.069 230.736 0.8 0.524
1284.54 54.16 0.99921 2.601 24.72 0.004 1.989 0.482 4.22 0.041 124.769 0.101 0.548
1844.64 181.8 0.99947 1.719 11.15 0.004 1.372 4.623 4.52 0.038 111.85 0.127 0.479
717.424 16.63 0.99999 4.744 44.15 0.01 3.942 0.38 4.22 0.031 96.755 0.08 0.6
10174.5 811.6 0.99897 0.317 13.54 0.001 0.252 5.049 4.22 0.028 75.898 0.257 0.627
LPGA-N2 (DFT)
LPGA-CO2 (DFT)
Note: C constant is related to the energy of adsorption in the first adsorbed layer and consequently its value is an indication of the magnitude of the adsorbent/ adsorbate interactions. 5
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Fig. 6, and the pore length of each part was calculated separately according to the pore size distribution obtained based on the LPGA-CO2 results. Micropores with cross-section diameters ranging from 0.38–0.76 nm, 0.76–0.82 nm, 0.82–0.92 nm, 0.92–1.03 nm, 1.03–1.14 nm, 1.14–1.26 nm, 1.26–1.37 nm, and 1.37–1.49 nm, can accommodate 1, 2, 3, 4, 5, 7, 8, 9, and 11 CH4 molecules, respectively. To simplify the calculation, it was assumed that CH4 molecules are arranged in a close-packed array in the micropores and the equivalent height of each layer of CH4 is 0.33 nm [27]. Finally, the quantity of CH4 adsorbed in 8 areas can be calculated according to the pore length of each part and equivalent height respectively. n
Nmic =
∑ ih i=1
Li CH4
(1)
where Nmic is the quantity of CH4 molecules adsorbed in the micropore structures; i is the theoretical number of CH4 molecules accommodating the cross-section of the cylindrical micropores; Li is the total length of the assumed cylindrical micropores; and hCH4 is the equivalent height of the CH4 molecules on the axis of assumed cylindrical micropores.
Fig. 5. Distribution of the CH4 molecules in the adsorption areas of micropores with different scales based on the MPVD of LPGA-CO2.
Li =
external surface in the form of monolayer coverage [50,51], and the quantity of CH4 adsorbed depends on the external SSA [23]. Due to the enhanced adsorbent-adsorptive interactions in micropores [13], it is assumed that the CH4 molecules are only adsorbed inside the micropore structures in the form of micropore filling [52,53], and the amount of CH4 adsorbed is limited by the micropore volumes [23,54]. Therefore, the estimated Langmuir volume was obtained by calculating the total amount of CH4 adsorbed on the external surface and inside the micropore structures. Since the kinetic diameters of CO2 (0.33 nm) and CH4 (0.38 nm) molecules are not the same [31], the probe-accessible surface measured by the LPGA-CO2 method does not coincide with the adsorption space that CH4 molecules can enter [15,24]. Therefore, the micropore volumes measured by CO2 adsorption cannot be directly converted into the amount of CH4 adsorbed inside micropore structures. Additionally, because the number of CH4 molecules that can be adsorbed inside micropores of different sizes is not the same, it was assumed that the micropores in the coal samples were cylindrical, and eight adsorption areas were identified according to the number of CH4 molecules occupying the micropores with different scales, as shown in Fig. 5 and
4Vi πdi2
(2)
where Vi is the total micropore volumes in a certain adsorption area and di is the average micropore diameter of this adsorption area.
Nmes & mac =
SSA(N2 − BET ) SACH4
(3)
where Nmes & mac is the quantity of CH4 molecules adsorbed on the external surface in the form of monolayer adsorption; SSA(N2 − BET ) is the external SSA calculated by the BET method for LPGA-N2; and SACH4 is the equivalent surface area occupied by a CH4 molecule arranged in a close-packed array [28] and has a value of 1.251 × 10−19 m2. 3.2.2. CH4 molecule distribution characteristics in pore structures with different scales The numbers of CH4 molecules in micropore structures with different sizes were calculated by Eq. (1) and Eq. (2). Based on the BETSSAs obtained by the LPGA-N2 method, the total numbers of CH4 molecules adsorbed on the external surface were calculated by Eq. (3). The distribution characteristics of the CH4 molecules adsorbed in the adsorption areas with different scales are shown in Fig. 7. For the six coal samples, the number of CH4 molecules adsorbed by micropores in the size range of 0.38–0.76 nm accounted for 38–55% of the total amount adsorbed and made up the largest proportion in the nine adsorption areas. The quantity of CH4 adsorbed in the form of micropore filling accounted for 74–99% of the total amount adsorbed, and the XQ coal sample had the largest external SSA, so that the amount of CH4 adsorbed on the external surface in the form of monolayer coverage accounted for 26% of the total amount adsorbed. Similar calculated results were obtained in other studies [52], but the CH4 molecules in the micropore structures were not adsorbed on the surface of the micropores in the form of surface coverage. 3.3. Discussion of the microscopic pore properties and CH4 adsorption capacity 3.3.1. Correlations between the microscopic pore characteristics and the Langmuir volume The relationships between the microscopic pore characteristics and the measured Langmuir volumes obtained from the HPGA-CH4, LPGAN2, and LPGA-CO2 measurements (Tables 1 and 2) are shown in Fig. 8. There was not a good correlation between the CH4 adsorption capacity of the coals and the pore volumes or external SSAs obtained by the LPGA-N2 measurements, as shown in Fig. 8 (a) and (d). However, a very good correlation between the CH4 adsorption capacity of the coals and
Fig. 6. Numbers of CH4 molecules in micropores with different scales. 6
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Fig. 7. Distribution of the adsorbed CH4 molecules in pore structures with different scales.
3.3.2. Correlations between the measured and estimated Langmuir volume To facilitate a comparison with the HPGA-CH4 results, the quantity of CH4 molecules adsorbed in the coal was converted into the adsorbed volume of CH4 under the standard conditions using Eq. (4).
the micropore volumes or SSAs obtained by the LPGA-CO2 measurements existed for the six coal samples used in this study. Similar calculated results were obtained in previous studies [46,55,56]. Finally, the total pore volumes and total SSAs were calculated by adding the pore volumes and SSAs obtained by the LPGA-N2 and LPGA-CO2 methods. Compared with the micropore volumes and SSAs obtained by LPGA-CO2, the total pore volumes and total SSAs did not better express the CH4 adsorption capacity, as shown in Fig. 8 (c) and (f). The reason may be that different adsorption forms in the micropore structures and on the external surface of the coal led to different effects on the CH4 adsorption capacity [23,28,54]. In addition, according to the micropore volumes of the DN and XQ samples (Table 2), the samples have larger micropore volumes but smaller adsorption capacities (Fig. 7), which can be attributed to the different MPVDs and micropore volumes of the areas inaccessible to the CH4 molecules (see Fig. 5) [57]. Therefore, although the best relationship exists between the micropore properties and the measured Langmuir volume, we still do not recommend the direct comparison of the CH4 adsorption capacity with the pore properties obtained by LPGA-CO2.
Vmic − PV & BET − SSA = =22.4 ×
Nmic + Nmes & mac Na
(4)
where Vmic-PV&BET-SSA is the estimated Langmuir volume based on micropore filling and monolayer adsorption theory and Na is Avogadro's number, with a value of 6.02 × 1023. In this paper, the adsorption was assumed to be two-dimensional and to take place on an imaginary surface (Gibbs dividing surface) [28]. The adsorbed volumes of CH4 were calculated based on the SSAs obtained by the LPGA-N2 and LPGACO2 methods using Eqs. (5) and (6).
Vmic − SSA = =22.4 ×
SSA(CO2− DFT ) Na SACH4
(5)
VBET − SSA = =22.4 ×
Nmes & mac Na
(6)
Fig. 8. Correlations between the microscopic pore characteristics and the measured Langmuir volume. 7
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intrusion tests have been extensively studied [15,56,58,59]. However, similar to the BET-SSAs, the fractal dimension based on N2 adsorption can only characterize the surface properties of pores in a limited range. Therefore, confirmation of the ability of these properties to represent the overall pore structures in coal is need.
Table 3 Measured and estimated Langmuir volumes calculated using the microscopic pore properties. Sample
DN XQ TY QN PB HSW
Measured Langmuir volume
Estimated Langmuir volume
VL (mL/g)
VBET-SSA (mL/g)
Vmic-SSA (mL/g)
Vmic-PV&BET-SSA (mL/g)
4. Conclusions
35.76 28.76 22.82 16.46 14.47 13.30
1.08 7.30 0.77 0.51 1.41 0.09
68.62 68.65 37.12 33.28 28.79 22.58
33.33 28.19 20.78 18.93 16.13 14.68
In this study, a new quantitative method for estimating the CH4 adsorption capacity of coal was proposed. Based on micropore filling and monolayer coverage theory, nine adsorption areas with different scales were constructed for the coal, and the distribution of the CH4 molecules in pore structures with different scales was obtained. By a comparison with the Langmuir volumes obtained from HPGA-CH4 measurements, this quantitative method was verified. The conclusions can be summarized as follows: (1) The probe-accessible area of the LPGA method is determined by the type of probe, temperature, and the pressure range. The surface characteristics of coal obtained by N2 and CO2 adsorption are not compatible. In this study, the external SSAs and pore volumes obtained by LPGA-N2 ranged from 0.317 to 24.539 m2/g and from 0.001 to 0.021 cc/g, respectively, while the SSAs and micropore volumes obtained by the LPGA-CO2 method ranged from 75.898 to 230.736 m2/g and from 0.028 to 0.069 cc/g, respectively. (2) The quantity of CH4 adsorbed in the form of micropore filling accounted for 74–99% of the total amount adsorbed, and the amount of CH4 adsorbed by the micropores in the size range of 0.38–0.76 nm accounted for 38–55% of the total amount adsorbed and made up the largest proportion in the nine adsorption areas. (3) CH4 molecules were adsorbed on the external surface in the form of monolayer coverage, and they were adsorbed on the micropore structures in the form of micropore filling. Thus, the SSAs and micropore volumes obtained by CO2 adsorption correlated better with the CH4 adsorption capacity of coal than the total SSAs and pore volumes, and the ratio of the SSAs of the micropores to the total SSA was higher than the ratio between the quantity of CH4 adsorbed in the micropores and the total amount adsorbed in the coal. (4) The estimated Langmuir volumes based on micropore filling and monolayer coverage theory were very similar to the measured Langmuir volumes. Therefore, the CH4 adsorption capacity of coal is determined by both the accessible MPVD and external surface areas in coal.
Fig. 9. Comparison of the measured and estimated adsorbed volume of CH4.
where VBET-SSA is the estimated Langmuir volume based on the BETSSAs obtained by the LPGA-N2 method and Vmic-SSA is the estimated Langmuir volume based on the DFT-SSAs obtained by the LPGA-CO2 method. The estimated Langmuir volumes based on different methods were obtained and are shown in Table 3. The relationships between the estimated Langmuir volumes and the measured Langmuir volumes are shown in Fig. 9. The estimated Langmuir volumes obtained based on the SSAs obtained by the LPGA-N2 measurements were much smaller than the measured values, indicating that only a very small portion of CH4 adsorbed in coal is present on the external surface. Regarding the estimated Langmuir volume obtained based on the SSAs obtained by the LPGA-CO2 measurements, the estimated Langmuir volumes were much larger than the measured values, indicating that the amount of CH4 adsorbed in the micropores is limited by the pore volume rather than the surface area, and it is not suitable to use the surface area to characterize the adsorption amount. Therefore, regardless of the adsorption forms of CH4 in different pore structures, it is unreliable to simply compare the SSAs with the CH4 adsorption capacity of coal. Similar views have been published stating that surface areas of coals obtained by CO2 adsorption are meaningless and should not be reported [12]. When the CH4 adsorption capacities of coal samples are compared, the BET-SSAs obtained by N2 adsorption should not be reported, due to the presence of micropores [15]. A very good relationship existed between the measured Langmuir volumes and the estimated Langmuir volumes based on micropore filling and surface coverage theory (see Fig. 9), which demonstrated that the adsorption capacity of coal was determined by both the accessible MPVD and the external surface areas of the CH4 molecules. Note that the relationships between the Langmuir parameters and the fractal characteristics obtained by the LPGA-N2 and mercury
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