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Ultra micropores in macromolecular structure of subbituminous coal vitrinite
Fuel 210 (2017) 298–306
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Full Length Article
Ultra micropores in macromolecular structure of subbituminous coal vitrinite
MARK
⁎
Yu Liu, Yanming Zhu , Wu Li, Chuanghui Zhang, Yang Wang a Key Laboratory of Coalbed Methane Resources and Reservoir Formation on Process, Ministry of Education, China University of Mining and Technology, Xuzhou 221008, China b School of Resources and Geosciences, China University of Mining and Technology, Xuzhou 221116, China
A R T I C L E I N F O
A B S T R A C T
Keywords: Ultra micropores Macromolecular structure Subbituminous coal Vitrinite Methane adsorption
Pores in coal provide surface area and volume for coalbed methane storage. In this study, a 3 dimensions (3D) macromolecular structure of subbituminous coal vitrinite was constructed, which was demonstrated to be consistent with the experimental Nuclear Magnetic Resonance (NMR) data, density data and pore volume data, to study ultra micropores formed in the macromolecule. The results showed that both accessible pores and inaccessible pores existed in the macromolecular structure and that all pores were smaller than 0.62 nm. Most of the accessible pores were formed by aliphatic chains and most of the atoms that directly touched the pore surface were hydrogen atoms. The accessible pores showed obvious fractal features, and the fractal dimension of pores detected by probes smaller than 0.5 nm is 2.73. We also found that the volume of pores seen by helium is considerably larger than that of pores seen by methane. This would result in underestimation of methane adsorption capacity in a volumetric methane adsorption experiment, where the void volume is tested by helium. For the coal sample Y-1, the methane adsorption capacity would be underestimated by 2.7 cm3/g at 10 MPa.
1. Introduction As a clean energy, coalbed methane is of great significance to energy safety and environmental protection in the United States, Australia, China and other countries. Research on the pores of coal is very important for coalbed methane exploration, as pores provide surface area for adsorbed phase methane and volume for free gas [1–6]. Pores also serve as tunnels for gas diffusion and gas flow [7,8]. Currently, many methods have been employed to study pore structures in coal, such as high pressure mercury injection, nitrogen adsorption, carbon dioxide adsorption, scanning electron microscopy, and NMR among others [1,6,9–12], and significant achievements have been made regarding such factors as pore size distributions, shapes, fractal features, and effects on adsorption [5,8,13–16] Pore systems in coal are quite complex due to their heterogeneity and wide size distribution, from micropores (< 2 nm) to macropores (greater than50 nm) [1,15,17]. In the pore systems of coal, micropores occupy a large part and have a great influence on methane adsorption in coal as these micropores provide most of the total surface area [18]. Researchers have also observed that portions of the ultra micropores (smaller than 1 nm) are related to the coal macromolecular structure [19–23]. Faulon et al. [21] used
computer-generated models studied ultra micropores, and found that many ultra micropores can be formed in the 3D coal models and these pores contributed to most of the micropores. Boursige et al., [20] and Zhou et al. [23] believed nanopores in shale were related to the molecular model and used the macro molecule to generate pores. Zhang et al. [24,25] used coal macromolecular structures to simulated methane adsorption in coal as coal macromolecular structures could provide pores for methane adsorption. Based on the statistics of Dr. Mathews, more than 134 proposed molecular level models of coal had been presented by 2010 [26], and these molecular representations of coal have greatly facilitated the study of, for instance, coalification pathways, physical evaluations, pyrolysis process representation, and methane adsorption simulation [21,22,24,25,27–29]. Following the 1990s, computer technology was applied to build 3D models of coal, which made the study of pores in macromolecule possible [26,30]. Dr. Mathews and his group have done excellent work in presenting macromolecular models of coal and the utility of coal molecular models [21,31–35]. Most of the molecular models constructed of coal recently are large scale, in which there are more than 200 atoms [26,29,36,37]. The size of these macromolecules is usually larger than 2 nm. Several large-scale molecules even have
⁎ Corresponding author at: Key Laboratory of Coalbed Methane Resources and Reservoir Formation on Process, Ministry of Education, China University of Mining and Technology, Xuzhou 221008, China. E-mail address: [email protected] (Y. Zhu).
http://dx.doi.org/10.1016/j.fuel.2017.08.069 Received 23 June 2017; Received in revised form 7 August 2017; Accepted 18 August 2017 0016-2361/ © 2017 Published by Elsevier Ltd.
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more than 10,000 atoms. Conversely, calculated from CO2 adsorption experimental data, there are many coal pores smaller than 1 nm or even smaller than 0.5 nm [1,18]. The macromolecular structure of coal is large enough to form these ultra micropores [20,21,23]. Although different methods have been used to study pores in coal, micropores in coal still warrant further study, especially ultra micropores (smaller than 1 nm). Ultra micropores are too small to be tested by scanning electron microscope (SEM) and some other visible methods. Gas injection methods are the most commonly used to study ultra micropores in coal. But it is difficult to study shapes, connectivity and other characteristics using only these methods. Moreover, different gas molecules can see different pores in coal. For example, methane can only see pores larger than 0.38 nm, helium can see pores larger than 0.26 nm, and CO2 can see pores larger than 0.33 nm [38]. This has resulted in trouble accurately describing pore characteristics. Additionally, as we know, in volumetric methane adsorption experiments in coal, helium is usually used to test void volume, and this often caused underestimation of methane adsorption capacity, especially at high pressure [39]. Coal is a mixture that contains such macerals as vitrinite, inertinite, exinite. Among them, vitrinite accounts for the largest proportion. The proportion of vitrinite in Dalianhe formation subbituminous raw coal (Yilan open-pit mine in China) is more than 85%. What is more, the macromolecular structures of different types of macerals are different. To improve the representation accuracy of macromolecular structure, we used only vitrinite separated from coal as the experimental samples. In this study, a 3D macromolecular structure of subbituminous coal vitrinite has been constructed to study pore shapes, volume distribution and fractal characteristics. Using the 3D macromolecular structure, we studied the atoms on the surface of the pores, which is very important for gas adsorption in coal, as gas adsorption is due to the interaction forces between the gas and atoms on the pore surface of coal [40]. The differences in pores seen by methane and helium were also assessed in this study, and the underestimation in methane adsorption experiment is calculated.
Fig. 1. Experimental and calculated
13
C NMR spectrum of Y-1 vitrinite sample.
calculated by the L-J 12-6 equation [42]. The density of the 3D macromolecular model is 1.30 g/cm3, which is equal to the experimental true density (1.30 g/cm3). In addition, accessible volume in the macromolecular model is 0.042 cm3/g (probe radius = 0.165 nm), which is similar to the experimental micropore volume (0.041 cm3/g) from the CO2 adsorption experiment (Dubibin-Astakhov model). Experimental data of 13C NMR in Fig. 1 shows that the two highest peaks are from 27 to 34 ppm and 125 to 135 ppm, respectively. 27–34 ppm are the chemical shifts of methyl and methylene, and 125 to 135 ppm are the chemical shifts of protonated aromatic carbon and bridgehead aromatic carbon. As the sample is subbituminous coal vitrinite sample, many aliphatic chains still exist in these vitrinites, and the macromolecule has a low aromatic carbon rate. The aromatic rings are primarily benzene and naphthalene, and all nitrogen atoms exit in the pyridine (Fig. 2). The total number of atoms in the 3D molecular structure (Fig. 4a) is 2992 and the size of the 3D lattice is 3.37 nm × 3.37 nm × 3.37 nm.
2. Materials and methods
2.3. Calculation methods for pores in the macromolecular structure
2.1. Samples
It is necessary to define pores in the macromolecular structure. As the fractal dimension of ultra pores is not an integer (3) [21], if we use different rulers to measure the same pores, the results are different. In addition, certain pores may be too small for gas molecules, such as methane and CO2 to access. These pores are insignificant when we study methane adsorption and others. Thus, it is important to study pores that can be seen by a responding molecule. In this study, we used probes to calculate pore volume and surface area based on van der Waals forces (Fig. 3). We calculated the pore space through finding out the van der Waals (vdW) surface of coal macromolecular structure (Fig. 3a, b, c). The vdW surface of the macromolecular is also the surface of ultra micropores. After we found out the surface of the pores, we can calculate volume, surface area and other information of these ultra micropores in macromolecular structure. In the calculation, we moved the probes in all the parts of the coal macromolecular structure cube evenly (interval = 0.015) to find out the vdW surface of macromolecule. When we moved the probe, there are three situations (Fig. 3a). Situation 1: the location has been occupied by the coal macromolecule (red probes). Situation 2: the location is not occupied by coal macromolecule but space around this location has been occupied (white probes). Situation 3: the location is not occupied by coal macromolecule and space around this location is also not occupied (green probes). Then, we can find that the white probes could form the vdW surface of the macromolecule. It should be noted that we did not use specific molecules to measure
The coal vitrinite sample Y-1 was collected from the Yilan open-pit mine in Heilongjiang province, China. It is from the Dalianhe Formation of the Paleogene, and the raw coal of Y-1 is famous for high vitrinite content. We chose the vitrain part from the raw coal by hand, and the results showed that in the separated vitrinite samples Y-1, the vitrinite content was 95%. The ash content of the vitrinite samples was 1.8%, and the maximum reflectivity of vitrinite (Ro,max) was 0.5%. 2.2. Macromolecular structure construction Before the 3D macromolecular structure was constructed, we represented the 2D chemical structure of the Y-1 vitrinite, primarily based on the 13C NMR spectrum and element composition. FT-IR data was also used to provide information on oxygen functional groups. 13C NMR spectrum has been demonstrated to be effective in representing 2D chemical structure [29,37]. The ACD/C NMR Predictor was used to calculate the 13C NMR chemical shift of the macromolecular structure constructed. After hundreds of adjustments, the calculated 13C NMR spectrum based on the macromolecule structure was able to match the experimental 13C NMR spectrum of the Y-1 vitrinite samples (Fig. 1). Materials Studio (Accelrys) was used for geometry optimization to construct a 3D macromolecular model. Considering that the Y-1 vitrinite sample is subbituminous vitrinite and that the structure order has not been formed [26,41], we used 16 building blocks together for geometry optimization. The universal forcefield was employed for the geometry optimization, in which the Van der Waals forces are 299
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Fig. 2. Chemical macromolecular model of Y-1 vitrinite sample (C111H136O23N2).
temperature CO2 adsorption experiment could test ultra micropores of coal samples. From the low temperature CO2 adsorption experimental data, the volume of ultra micrpores in this coal sample is 0.042 cm3/g. The calculated volume of pores seen by CO2 in established 3D coal macromolecular structure is 0.041 cm3/g. We also analyzed low temperature CO2 adsorption experimental data by employing density functional theory (DFT) and found that the volume obtained from low temperature CO2 adsorption experiment is provided by pores smaller than 0.8 nm and there were no 0.8–1.2 nm pores. In the modeling results, the pore throats of ultra micropores are smaller than 0.62 nm. On the one hand, it is normal that pores size is larger than the pore throat size. On the other hand, the method of determining pore size in 3D structure modeling results is different from that in low temperature CO2 adsorption experimental results.
pore space such as methane and carbon dioxide. We used ideal molecule whose size is the same with methane and carbon dioxide to form the surface of macromolecule. For example, if we what to know pores see by methane, we use 0.38 nm (in diameter) ideal molecule to form the vdW surface. Probes with different radii can see different pores in the macromolecule. As most of the pores were irregular in shape, for the same pore, certain parts were too small for a large probe to reach, and these parts may have been sufficiently large to fit a smaller probe. Through this method, pores were different if we used different probes. For different purposes, we can use different sized probes. There are two types of pores in the macromolecules model. One is accessible pores, which are accessible to gas fluids from the outside. The other is inaccessible pores, which are inside the macromolecules model. Inaccessible pores are separated by atoms from the outside, and gas cannot access them from outside. In other words, there are large enough tunnels connecting accessible pores and the space outside the macromolecule, and the gas molecule could enter these pores from outside. But there are no tunnels connecting inaccessible pore and the space outside the macromolecule, or the tunnels are too small for gas passing through. Inaccessible pores are also called dead pores. In experiments, pores tested by gas or mercury are all accessible pores. It is necessary to verify the calculated data by using experimental data. In this study, we used low temperature CO2 adsorption experimental data to verify the modeling results. As we know, low
2.4. Fractal characteristics of pores in the macromolecular model Fractal theory has been applied to the research of pores in coal by previous studies and the results show that fractal characteristics of pores have provided abundant useful information on pore structures, such as gas adsorption and pore evolution [9,12,14,43–45]. High pressure mercury injection and N2 adsorption experiment data are the most common data to calculate the fractal dimension of macropores (greater than50 nm) and mesopores (2–50 nm), respectively [9,12,14,43–45]. In this study, pore volume data from probes of
Fig. 3. Van der waals (vdw) surface of atoms and pores seen by different sized probe.
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Fig. 4. Ultra micropores in the 3D macromolecular structure (probe radius = 0.165 nm).
channels, which are called throat. Inner parts of these larger pores contribute a large volume and surface area. We should note that some pore throats are of a small size, and larger molecules cannot pass through these pore throats. In addition, these small throats have a great impact on gas flow and desorption [48–50]. Ultra accessible pores in the Y-1 macromolecular structure can be divided into two types based on shape: hemispherical and ink-bottle. These two kinds of pores have been proven to exist coal by gas adsorption experimental methods [51,52]. The shape of hemispherical pores is considerably simpler than that of ink-bottle pores. Hemispherical pores were largely formed on the surface of the macromolecular structure and they are usually small in size. Ink-bottle pores have a more complex shape and are of larger size. Most parts of the inkbottle pores are developed in the inner macromolecular structure. Fig. 5A and B present the pore throat size distribution of accessible pores and the pore size distribution of total pores. It should be noted that accessible pores are characterized by pore throat size distribution and total pore volume are characterized by pore size distribution. Pore throat size distribution is different from pore size distribution, especially for ink-bottle pores. For both accessible pores and inaccessible pores in the
varying size were used to determine the fractal dimension of ultra micropores in the macromolecule. As the volume of pores in macromolecules is covered by different size probes, the following equation can be defined [21,46,47]:
−dV / dv ∝ v1 − D
(1)
where V is the total accessible volume of in the macromolecular structure seen by the probe, v is the volume of the probe, and D is the fractal dimension. If we draw a log–log plot of V versus v, the fractal dimension is equal to the negative slope. More details can be seen in other places [21,46,47]. 3. Results and conclusions 3.1. Pore characteristics Fig. 4 shows the coal 3D macromolecule and accessible pores in the 3D macromolecular structure of coal vitrinite. These pores in the macromolecular structure are formed because of the absence of atoms. From Fig. 4 we can see that there are more than 15 pores in this macromolecular model, and most of the pores have irregular shapes. Certain larger pores are formed by connecting smaller pores through 301
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Fig. 5. Pore throat size distribution of accessible pores (A) and pore size distribution of total pores (B).
macromolecular structure, the pore throats are all smaller than 0.62 nm. When the probe diameter is larger than 0.62 nm, no pore can be seen in this structure, as there is no space sufficiently large to form larger pores. When we use CO2 adsorption experiment and other methods to characterize micropores in coal, pores smaller than 0.62 nm are likely the pores formed by the macromolecule. However, many larger pores have been proven to exits by high pressure mercury injection and low temperature nitrogen adsorption experiments. There is more likely no relation between pores that much larger than 0.62 nm and the macromolecular structure. There are four peaks on the accessible pore throat size distribution plot at 0.30 nm, 0.36 nm, 0.50 nm and 0.62 nm, respectively. The reason for each peak is the presence of ink-bottle pores (Fig. 5a). The ink-bottle pores have a smaller pore throat with a larger volume; thus, these pore throats correspond to a large pore volume (Fig. 5a). When we use a larger probe to test pores, these accessible pores would change to inaccessible pores. So we can find that there are no corresponding peaks in the total pore size distribution plot (Fig. 5b). For the total pores, incremental volume decreases with pore size increase (Fig. 5b). At the same time, there are many 0.62 nm pores in the macromolecular structure, which is the largest size for pores formed in the macromolecule. Fig. 6. Accessible pores and inaccessible pores in the macromolecular structure of Y-1.
3.2. Accessible pores and inaccessible pores in the macromolecular structure
Fig. 7 shows the fraction of accessible pores using different sized probes. The fraction of accessible pores decreases when the size of the probes increases on the whole, but it is in stage-changing. There are four stages from 0.26 nm to 0.62 nm, and at every stage, the fraction of accessible pores increases slightly. When the pore size is 0.26–0.31 nm (stage 1), the fraction of accessible pores is approximately 83%. The fraction at stage 2 (0.32–0.36 nm), stage 3 (0.38–0.50 nm) and stage 4 (0.52–0.62 nm) is approximately 80%, 70% and 40%, respectively. Zhang et al. [55] employed small angle neutron scattering (SANS) to test the fraction of accessible pores and found that for pores from
Both accessible pores and inaccessible pores all exit in the macromolecular structure of coal vitrinite (Fig. 6). When the probe size is 0.33 nm, the volume of accessible pores is 2.118 nm3. In contrast, the volume of inaccessible pores is approximately 0.60 nm3, contributing 20% of the total. In fact, certain pores are accessible by CO2, but these pores are inaccessible for other larger probes, as the throat is too small for larger molecules to enter. Inaccessible pores have also been demonstrated to exist in coal reservoir by small-angle neutron scattering (SANS) and ultra small-angle neutron scattering (USANS) [53–55]. 302
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Fig. 7. Proportion of accessible pores for probes of different sizes.
Fig. 9. Fractal dimension for pores in the macro molecular structure by varying the probe size.
0.5 nm to 1 nm, the fraction is approximately 37%, which is consistent with the results of this study.
aromatic rings does not tend to form pores in the 3D macromolecular. 3.4. Fractal characteristics of ultra micropores in the macro molecular structure
3.3. Atoms on the surface of ultra micro pores The atoms on the surface of ultra micro pores are very important for gas adsorption. Adsorption is formed by interaction forces between gas molecules and atoms on the coal surface [40]. The atoms on a pore surface have great impacts on the adsorption capacity of coal. Studies of atoms on the coal surface would help methane adsorption simulations, as they can provide some useful information for adsorbent modeling and this can have significant influences on final results. From the study of pores in the Y-1 macromolecular, we observed that most pores formed by aliphatic chains (Fig. 8). It should be noted that pore walls in this paper were defined as the edge of space that can be reached by the probes. It means the pore walls are not equal to the edge of the atoms in the macromolecule. Atoms near the pore wall can be divided into two categories (Fig. 8): pores touching the pore wall directly, and pores not touching the pore wall directly. Occasionally, there is a void volume between the atoms and the pore wall, and the probe cannot touch these atoms directly, and when gas adsorbed on the surface of these pores, the adsorbing gas could not be much closed with these atoms. The distance between atoms in the macromolecule and the pore wall is important for gas adsorption as the interaction force is related to this distance. Most of the atoms touching the pore wall are hydrogen atoms. In contrast, carbon atoms near the pore wall do not usually touch the pore wall directly. Oxygen atoms sometimes touch the pore wall directly, although there are not many oxygen atoms in the macromolecular structure. Aromatic rings sometimes form pores, but not often. On the one hand, this is due to the coal sample being in immature stage (subbituminous coal) and there are fewer aromatic rings in the macromolecular. On the other hand, the structure of
Fractal feature and fractal dimension can provide useful information when we study methane adsorption, pore size distribution, evolution of pores, heterogeneity of pore, and so on [9,11,12,14,43–45,56,57]. Researches on fractal dimension and fractal feature of ultra micropores in coal would help us understand ultra micropore space characteristics, methane adsorption, heterogeneity, and so on [9,11,12,14,43–45,56,57]. Previous researches have concluded that pores larger than 2.0 nm have obvious fractal features by analyzing low pressure N2 adsorption data and mercury injection data [12]. In this study, fractal characteristics of pores between 0.26 and 0.62 nm in the 3D macromolecular have been analyzed. Fig. 9 plots on the probe number versus the volume of the probes (log-log scales). From Fig. 9, it can be seen that the data points have a good correction with the fitting line (r2 = 0.9978 and 0.9998). This reflects that the ultra micropores in the macromolecular structure of vitrinite also have obvious fractal features. The fractal plots of pores between 0.26 and 0.62 nm are twostage. The first stage corresponds to the probe size at 0.26–0.50 nm and the second stage corresponds to the probe size at 0.50–0.62 nm. The fractal dimensions of the two stages are different. According to the fractal theory, the larger the fractal dimension is, the more complex the pore space will be. When the probes are smaller than 0.50 nm, the fractal dimension of pores seen by these probes is 2.73. However, when the probes are larger than 0.50 nm, the fractal dimension of pores is 2.64. There are mainly two reasons for this phenomenon. On the one hand, if the probes are relatively large, these probes cannot pass through the pore throat. Additionally, parts of ultra micropores will not Fig. 8. Atoms near the pore wall.
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Fig. 10. pores seen by probes with 0.33 nm, 0.50 nm and 0.52 nm diameter.
similar. That is because in larger pores, methane and helium both enter easily and theses pores are only different at the edge of the pores. For the ultra pores seen by helium and methane, the smaller the pore size is, the larger the difference in volume will be. In previous researches, differences in pore volume seen by helium and methane are often ignored. For example, in methane isothermal adsorption experiments, helium is used to test the void volume. These tested void volumes were considered similar to methane volumes. However, in fact, in some cases, a large error would occur. In this study, the ultra micropores seen by helium are larger than those seen by methane by 0.0334 ml/g (accessible pores). We can use this data to correct the methane isothermal adsorption curves. In volumetric methane adsorption experiment, methane adsorption amount are calculated by Eq. (2):
be seen by large probes as probes cannot enter these parts. Thus, the shapes of pores seen by larger probes are much simpler than that of pore seen by smaller pores. On the other hand, complex ink-bottle pore cannot be seen by larger probes. In Fig. 10, we compared pores seen by probes larger than 0.50 nm and smaller than 0.50 nm. Many complex ink-bottle pores exit in pores seen by probes smaller than 0.50 nm. However, when the probe size is larger than 0.50 nm, accessible pores are mainly simple hemispherical pores. 3.5. Differences of available volume by methane, helium and CO2 The diameter of helium, methane and carbon dioxide is 0.26 nm, 0.38 nm and 0.33 nm, respectively [38]. The volume seen by helium is 0.063 ml/g. In comparison, that seen by methane and CO2 is 0.029 ml/ g and 0.041 ml/g, respectively. These volume data are all accessible ultra micropore volume. The volume seen by helium is about two times that seen by methane. Fig. 11 shows the pore distribution seen by methane, carbon dioxide and helium. By comparing the three pictures, we can see that pores seen by different molecules are notably different, especially comparing pores seen by methane and helium. On the one hand, some pores can be seen by helium but these pores cannot be seen by CO2 and methane. On the other hand, pores seen by helium are much larger than those seen by CO2 and methane. These phenomena can be seen more intuitively in the slices of pores in Fig. 12. Nos. 1, 3, 4 and 8 in Fig. 12 can be seen by helium, but these pores are inaccessible to methane. All pores accessible to methane are much smaller than those of helium. No. 2 pore (in Fig. 12a) is one large pore for helium but it is two separated pores for methane. In Fig. 12b, we can see that larger inner pores in vitrinite structure seen by methane and helium are
n1 = ntotal−
PVhe ZRT1
(2)
n1 is methane adsorption amount; ntotal is the total methane amount is sample van; P is the pressure of gas in sample van; R is ideal gas constant; Z is compression factor; T1 is the temperature of sample van; Vhe is blank volume of sample van after the sample being put in, which is tested by helium. As helium can see more pores that methane, the volume tested by helium (Vhe) is larger than the methane volume (Vme):
Vh − m = Vhe−Vme
(3)
The actual methane adsorption amount (n2) is calculated by Eq. (4):
n2 = ntotal−
PVme ZRT1
Fig. 11. Ultra micropores seen by methane, carbon dioxide and helium (accessible pores).
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(4)
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Fig. 12. Slices of pores seen by helium, carbon dioxide and methane in vitrinite macromolecular structure (accessible pores).
n2 = ntotal−
P (Vhe−Vh − m) ZRT1
(5)
n2 = ntotal−
PVme PVh − m PVh − m + = n1 + ZRT1 ZRT1 ZRT1
(6)
23.05 cm3/g. However, the Langmuir volume after correction is 26.93 cm3/g. Methane adsorption capacity in coal will be underestimated if the difference in pores seen by helium and methane is not considered, especially for deep coalbed methane. From Eq. (6), we can find that the larger the pressure is, the larger the errors will be. Additionally, pressure increase with an increase of depth of coal reservoir. When a coal seam is deeper than 1000 m, the pressure is usually larger than 10 MPa. The difference in pores seen by helium and methane should not be ignored as the error would be more than 2.5 cm3/g.
Thus, we can find is the underestimated methane adsorption amount as helium can see more pores than methane. The key point is determining Vh-m. It is an easy thing to measure the volume seen by helium. However, it is difficult to measure the volume seen by methane as methane is an adsorptive gas. As we know, Vh-m is volume of pores that are accessible for helium and inaccessible for methane. The pore throat of these pores is larger than 0.26 nm and smaller than 0.38 nm. Thus, these pores are all ultra micropores. In this study, we calculated the methane ultra micropore volume and the helium ultra micropore volume in the coal macromolecular structure, and then we can get Vh-m of this coal sample. Fig. 13 shows the methane isothermal adsorption curves of Y-1 tested by an HPVA methane adsorption instrument by employing the volumetric method. In this methane adsorption experiment, helium is used to test the void volume, which is common in methane adsorption experiments. As helium and methane see different pores in the coal reservoir, we used the difference in volumes to correct the methane isothermal adsorption curves. The black point in Fig. 13 is experimental data, which is commonly used in related researches, and the red data are the correction data. From Fig. 13, we can see that the larger the pressure, the greater the error. When the pressure is 10 MPa, the error is approximately 2.7 cm3/g. The Langmuir volume before correction is PVh − m ZRT1
4. Conclusions A 3D macromolecular structure of subbituminous coal vitrinite has been constructed in this study, and the 3D macromolecule has been verified to be consistent with experimental NMR data, density data and pore volume data. Ultra micropores in the 3D macromolecular structure have been studied by using the probe method. Several conclusions have been drawn as follows: 1. Pores inner the macromolecular structures are smaller than 0.62 nm. Both accessible pores and inaccessible pores exist in the macromolecular structure. For a probe of 0.33 nm (CO2), the fraction of accessible pores is approximately 80%, and for the 0.5 nm probe, the fraction of accessible pores decreases to 40%. 2. Pores in the macromolecular structure of Y-1 are mainly formed by aliphatic chains and atoms on the surface of ultra micro pores can be divided into two types: those touching the pore surface directly (most of these are hydrogen atoms) and those that are near but do not touch the pore surface directly (most of the carbon atoms near the pore surface are this type). 3. Accessible pores in the macromolecular structure show obvious fractural features. The fractal plots are two-stage. The fractal dimension of pores seen by probes smaller than 0.5 nm is 2.73 and that of pores seen by probes larger than 0.5 nm is 2.64. 4. In this study, we provide a method to correct methane isothermal adsorption experimental data. Helium ultra micropores and methane ultra micropores could be obtained for the 3D coal structure and then these data could be used to correct the errors caused by that helium can see more pores than methane. The calculated results show that the difference in pores seen by helium and methane should not be ignored at high pressure (greater than 10 MPa). Acknowledgments The authors sincerely thank the financial support of the National Natural Science Foundation of China (No. 41472135), the Natural Science Foundation of Jiangsu Province (Grant No. BK20160243), the Scientific Research Foundation of the Key Laboratory of Coalbed Methane Resources and Reservoir Formation Process, Ministry of
Fig. 13. Experimental data and correction data of methane adsorption isothermal curves of Y-1 subbituminous coal vitrinite data. (In correction data, differences in pore volume seen by methane and helium have been considered.)
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Education (China University of Mining and Technology) (No. 2015-04) and the Research and Innovation Project for College Graduates of Jiangsu Province (No. KYLX15_1396).
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Full Length Article
Ultra micropores in macromolecular structure of subbituminous coal vitrinite
MARK
⁎
Yu Liu, Yanming Zhu , Wu Li, Chuanghui Zhang, Yang Wang a Key Laboratory of Coalbed Methane Resources and Reservoir Formation on Process, Ministry of Education, China University of Mining and Technology, Xuzhou 221008, China b School of Resources and Geosciences, China University of Mining and Technology, Xuzhou 221116, China
A R T I C L E I N F O
A B S T R A C T
Keywords: Ultra micropores Macromolecular structure Subbituminous coal Vitrinite Methane adsorption
Pores in coal provide surface area and volume for coalbed methane storage. In this study, a 3 dimensions (3D) macromolecular structure of subbituminous coal vitrinite was constructed, which was demonstrated to be consistent with the experimental Nuclear Magnetic Resonance (NMR) data, density data and pore volume data, to study ultra micropores formed in the macromolecule. The results showed that both accessible pores and inaccessible pores existed in the macromolecular structure and that all pores were smaller than 0.62 nm. Most of the accessible pores were formed by aliphatic chains and most of the atoms that directly touched the pore surface were hydrogen atoms. The accessible pores showed obvious fractal features, and the fractal dimension of pores detected by probes smaller than 0.5 nm is 2.73. We also found that the volume of pores seen by helium is considerably larger than that of pores seen by methane. This would result in underestimation of methane adsorption capacity in a volumetric methane adsorption experiment, where the void volume is tested by helium. For the coal sample Y-1, the methane adsorption capacity would be underestimated by 2.7 cm3/g at 10 MPa.
1. Introduction As a clean energy, coalbed methane is of great significance to energy safety and environmental protection in the United States, Australia, China and other countries. Research on the pores of coal is very important for coalbed methane exploration, as pores provide surface area for adsorbed phase methane and volume for free gas [1–6]. Pores also serve as tunnels for gas diffusion and gas flow [7,8]. Currently, many methods have been employed to study pore structures in coal, such as high pressure mercury injection, nitrogen adsorption, carbon dioxide adsorption, scanning electron microscopy, and NMR among others [1,6,9–12], and significant achievements have been made regarding such factors as pore size distributions, shapes, fractal features, and effects on adsorption [5,8,13–16] Pore systems in coal are quite complex due to their heterogeneity and wide size distribution, from micropores (< 2 nm) to macropores (greater than50 nm) [1,15,17]. In the pore systems of coal, micropores occupy a large part and have a great influence on methane adsorption in coal as these micropores provide most of the total surface area [18]. Researchers have also observed that portions of the ultra micropores (smaller than 1 nm) are related to the coal macromolecular structure [19–23]. Faulon et al. [21] used
computer-generated models studied ultra micropores, and found that many ultra micropores can be formed in the 3D coal models and these pores contributed to most of the micropores. Boursige et al., [20] and Zhou et al. [23] believed nanopores in shale were related to the molecular model and used the macro molecule to generate pores. Zhang et al. [24,25] used coal macromolecular structures to simulated methane adsorption in coal as coal macromolecular structures could provide pores for methane adsorption. Based on the statistics of Dr. Mathews, more than 134 proposed molecular level models of coal had been presented by 2010 [26], and these molecular representations of coal have greatly facilitated the study of, for instance, coalification pathways, physical evaluations, pyrolysis process representation, and methane adsorption simulation [21,22,24,25,27–29]. Following the 1990s, computer technology was applied to build 3D models of coal, which made the study of pores in macromolecule possible [26,30]. Dr. Mathews and his group have done excellent work in presenting macromolecular models of coal and the utility of coal molecular models [21,31–35]. Most of the molecular models constructed of coal recently are large scale, in which there are more than 200 atoms [26,29,36,37]. The size of these macromolecules is usually larger than 2 nm. Several large-scale molecules even have
⁎ Corresponding author at: Key Laboratory of Coalbed Methane Resources and Reservoir Formation on Process, Ministry of Education, China University of Mining and Technology, Xuzhou 221008, China. E-mail address: [email protected] (Y. Zhu).
http://dx.doi.org/10.1016/j.fuel.2017.08.069 Received 23 June 2017; Received in revised form 7 August 2017; Accepted 18 August 2017 0016-2361/ © 2017 Published by Elsevier Ltd.
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more than 10,000 atoms. Conversely, calculated from CO2 adsorption experimental data, there are many coal pores smaller than 1 nm or even smaller than 0.5 nm [1,18]. The macromolecular structure of coal is large enough to form these ultra micropores [20,21,23]. Although different methods have been used to study pores in coal, micropores in coal still warrant further study, especially ultra micropores (smaller than 1 nm). Ultra micropores are too small to be tested by scanning electron microscope (SEM) and some other visible methods. Gas injection methods are the most commonly used to study ultra micropores in coal. But it is difficult to study shapes, connectivity and other characteristics using only these methods. Moreover, different gas molecules can see different pores in coal. For example, methane can only see pores larger than 0.38 nm, helium can see pores larger than 0.26 nm, and CO2 can see pores larger than 0.33 nm [38]. This has resulted in trouble accurately describing pore characteristics. Additionally, as we know, in volumetric methane adsorption experiments in coal, helium is usually used to test void volume, and this often caused underestimation of methane adsorption capacity, especially at high pressure [39]. Coal is a mixture that contains such macerals as vitrinite, inertinite, exinite. Among them, vitrinite accounts for the largest proportion. The proportion of vitrinite in Dalianhe formation subbituminous raw coal (Yilan open-pit mine in China) is more than 85%. What is more, the macromolecular structures of different types of macerals are different. To improve the representation accuracy of macromolecular structure, we used only vitrinite separated from coal as the experimental samples. In this study, a 3D macromolecular structure of subbituminous coal vitrinite has been constructed to study pore shapes, volume distribution and fractal characteristics. Using the 3D macromolecular structure, we studied the atoms on the surface of the pores, which is very important for gas adsorption in coal, as gas adsorption is due to the interaction forces between the gas and atoms on the pore surface of coal [40]. The differences in pores seen by methane and helium were also assessed in this study, and the underestimation in methane adsorption experiment is calculated.
Fig. 1. Experimental and calculated
13
C NMR spectrum of Y-1 vitrinite sample.
calculated by the L-J 12-6 equation [42]. The density of the 3D macromolecular model is 1.30 g/cm3, which is equal to the experimental true density (1.30 g/cm3). In addition, accessible volume in the macromolecular model is 0.042 cm3/g (probe radius = 0.165 nm), which is similar to the experimental micropore volume (0.041 cm3/g) from the CO2 adsorption experiment (Dubibin-Astakhov model). Experimental data of 13C NMR in Fig. 1 shows that the two highest peaks are from 27 to 34 ppm and 125 to 135 ppm, respectively. 27–34 ppm are the chemical shifts of methyl and methylene, and 125 to 135 ppm are the chemical shifts of protonated aromatic carbon and bridgehead aromatic carbon. As the sample is subbituminous coal vitrinite sample, many aliphatic chains still exist in these vitrinites, and the macromolecule has a low aromatic carbon rate. The aromatic rings are primarily benzene and naphthalene, and all nitrogen atoms exit in the pyridine (Fig. 2). The total number of atoms in the 3D molecular structure (Fig. 4a) is 2992 and the size of the 3D lattice is 3.37 nm × 3.37 nm × 3.37 nm.
2. Materials and methods
2.3. Calculation methods for pores in the macromolecular structure
2.1. Samples
It is necessary to define pores in the macromolecular structure. As the fractal dimension of ultra pores is not an integer (3) [21], if we use different rulers to measure the same pores, the results are different. In addition, certain pores may be too small for gas molecules, such as methane and CO2 to access. These pores are insignificant when we study methane adsorption and others. Thus, it is important to study pores that can be seen by a responding molecule. In this study, we used probes to calculate pore volume and surface area based on van der Waals forces (Fig. 3). We calculated the pore space through finding out the van der Waals (vdW) surface of coal macromolecular structure (Fig. 3a, b, c). The vdW surface of the macromolecular is also the surface of ultra micropores. After we found out the surface of the pores, we can calculate volume, surface area and other information of these ultra micropores in macromolecular structure. In the calculation, we moved the probes in all the parts of the coal macromolecular structure cube evenly (interval = 0.015) to find out the vdW surface of macromolecule. When we moved the probe, there are three situations (Fig. 3a). Situation 1: the location has been occupied by the coal macromolecule (red probes). Situation 2: the location is not occupied by coal macromolecule but space around this location has been occupied (white probes). Situation 3: the location is not occupied by coal macromolecule and space around this location is also not occupied (green probes). Then, we can find that the white probes could form the vdW surface of the macromolecule. It should be noted that we did not use specific molecules to measure
The coal vitrinite sample Y-1 was collected from the Yilan open-pit mine in Heilongjiang province, China. It is from the Dalianhe Formation of the Paleogene, and the raw coal of Y-1 is famous for high vitrinite content. We chose the vitrain part from the raw coal by hand, and the results showed that in the separated vitrinite samples Y-1, the vitrinite content was 95%. The ash content of the vitrinite samples was 1.8%, and the maximum reflectivity of vitrinite (Ro,max) was 0.5%. 2.2. Macromolecular structure construction Before the 3D macromolecular structure was constructed, we represented the 2D chemical structure of the Y-1 vitrinite, primarily based on the 13C NMR spectrum and element composition. FT-IR data was also used to provide information on oxygen functional groups. 13C NMR spectrum has been demonstrated to be effective in representing 2D chemical structure [29,37]. The ACD/C NMR Predictor was used to calculate the 13C NMR chemical shift of the macromolecular structure constructed. After hundreds of adjustments, the calculated 13C NMR spectrum based on the macromolecule structure was able to match the experimental 13C NMR spectrum of the Y-1 vitrinite samples (Fig. 1). Materials Studio (Accelrys) was used for geometry optimization to construct a 3D macromolecular model. Considering that the Y-1 vitrinite sample is subbituminous vitrinite and that the structure order has not been formed [26,41], we used 16 building blocks together for geometry optimization. The universal forcefield was employed for the geometry optimization, in which the Van der Waals forces are 299
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Fig. 2. Chemical macromolecular model of Y-1 vitrinite sample (C111H136O23N2).
temperature CO2 adsorption experiment could test ultra micropores of coal samples. From the low temperature CO2 adsorption experimental data, the volume of ultra micrpores in this coal sample is 0.042 cm3/g. The calculated volume of pores seen by CO2 in established 3D coal macromolecular structure is 0.041 cm3/g. We also analyzed low temperature CO2 adsorption experimental data by employing density functional theory (DFT) and found that the volume obtained from low temperature CO2 adsorption experiment is provided by pores smaller than 0.8 nm and there were no 0.8–1.2 nm pores. In the modeling results, the pore throats of ultra micropores are smaller than 0.62 nm. On the one hand, it is normal that pores size is larger than the pore throat size. On the other hand, the method of determining pore size in 3D structure modeling results is different from that in low temperature CO2 adsorption experimental results.
pore space such as methane and carbon dioxide. We used ideal molecule whose size is the same with methane and carbon dioxide to form the surface of macromolecule. For example, if we what to know pores see by methane, we use 0.38 nm (in diameter) ideal molecule to form the vdW surface. Probes with different radii can see different pores in the macromolecule. As most of the pores were irregular in shape, for the same pore, certain parts were too small for a large probe to reach, and these parts may have been sufficiently large to fit a smaller probe. Through this method, pores were different if we used different probes. For different purposes, we can use different sized probes. There are two types of pores in the macromolecules model. One is accessible pores, which are accessible to gas fluids from the outside. The other is inaccessible pores, which are inside the macromolecules model. Inaccessible pores are separated by atoms from the outside, and gas cannot access them from outside. In other words, there are large enough tunnels connecting accessible pores and the space outside the macromolecule, and the gas molecule could enter these pores from outside. But there are no tunnels connecting inaccessible pore and the space outside the macromolecule, or the tunnels are too small for gas passing through. Inaccessible pores are also called dead pores. In experiments, pores tested by gas or mercury are all accessible pores. It is necessary to verify the calculated data by using experimental data. In this study, we used low temperature CO2 adsorption experimental data to verify the modeling results. As we know, low
2.4. Fractal characteristics of pores in the macromolecular model Fractal theory has been applied to the research of pores in coal by previous studies and the results show that fractal characteristics of pores have provided abundant useful information on pore structures, such as gas adsorption and pore evolution [9,12,14,43–45]. High pressure mercury injection and N2 adsorption experiment data are the most common data to calculate the fractal dimension of macropores (greater than50 nm) and mesopores (2–50 nm), respectively [9,12,14,43–45]. In this study, pore volume data from probes of
Fig. 3. Van der waals (vdw) surface of atoms and pores seen by different sized probe.
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Fig. 4. Ultra micropores in the 3D macromolecular structure (probe radius = 0.165 nm).
channels, which are called throat. Inner parts of these larger pores contribute a large volume and surface area. We should note that some pore throats are of a small size, and larger molecules cannot pass through these pore throats. In addition, these small throats have a great impact on gas flow and desorption [48–50]. Ultra accessible pores in the Y-1 macromolecular structure can be divided into two types based on shape: hemispherical and ink-bottle. These two kinds of pores have been proven to exist coal by gas adsorption experimental methods [51,52]. The shape of hemispherical pores is considerably simpler than that of ink-bottle pores. Hemispherical pores were largely formed on the surface of the macromolecular structure and they are usually small in size. Ink-bottle pores have a more complex shape and are of larger size. Most parts of the inkbottle pores are developed in the inner macromolecular structure. Fig. 5A and B present the pore throat size distribution of accessible pores and the pore size distribution of total pores. It should be noted that accessible pores are characterized by pore throat size distribution and total pore volume are characterized by pore size distribution. Pore throat size distribution is different from pore size distribution, especially for ink-bottle pores. For both accessible pores and inaccessible pores in the
varying size were used to determine the fractal dimension of ultra micropores in the macromolecule. As the volume of pores in macromolecules is covered by different size probes, the following equation can be defined [21,46,47]:
−dV / dv ∝ v1 − D
(1)
where V is the total accessible volume of in the macromolecular structure seen by the probe, v is the volume of the probe, and D is the fractal dimension. If we draw a log–log plot of V versus v, the fractal dimension is equal to the negative slope. More details can be seen in other places [21,46,47]. 3. Results and conclusions 3.1. Pore characteristics Fig. 4 shows the coal 3D macromolecule and accessible pores in the 3D macromolecular structure of coal vitrinite. These pores in the macromolecular structure are formed because of the absence of atoms. From Fig. 4 we can see that there are more than 15 pores in this macromolecular model, and most of the pores have irregular shapes. Certain larger pores are formed by connecting smaller pores through 301
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Fig. 5. Pore throat size distribution of accessible pores (A) and pore size distribution of total pores (B).
macromolecular structure, the pore throats are all smaller than 0.62 nm. When the probe diameter is larger than 0.62 nm, no pore can be seen in this structure, as there is no space sufficiently large to form larger pores. When we use CO2 adsorption experiment and other methods to characterize micropores in coal, pores smaller than 0.62 nm are likely the pores formed by the macromolecule. However, many larger pores have been proven to exits by high pressure mercury injection and low temperature nitrogen adsorption experiments. There is more likely no relation between pores that much larger than 0.62 nm and the macromolecular structure. There are four peaks on the accessible pore throat size distribution plot at 0.30 nm, 0.36 nm, 0.50 nm and 0.62 nm, respectively. The reason for each peak is the presence of ink-bottle pores (Fig. 5a). The ink-bottle pores have a smaller pore throat with a larger volume; thus, these pore throats correspond to a large pore volume (Fig. 5a). When we use a larger probe to test pores, these accessible pores would change to inaccessible pores. So we can find that there are no corresponding peaks in the total pore size distribution plot (Fig. 5b). For the total pores, incremental volume decreases with pore size increase (Fig. 5b). At the same time, there are many 0.62 nm pores in the macromolecular structure, which is the largest size for pores formed in the macromolecule. Fig. 6. Accessible pores and inaccessible pores in the macromolecular structure of Y-1.
3.2. Accessible pores and inaccessible pores in the macromolecular structure
Fig. 7 shows the fraction of accessible pores using different sized probes. The fraction of accessible pores decreases when the size of the probes increases on the whole, but it is in stage-changing. There are four stages from 0.26 nm to 0.62 nm, and at every stage, the fraction of accessible pores increases slightly. When the pore size is 0.26–0.31 nm (stage 1), the fraction of accessible pores is approximately 83%. The fraction at stage 2 (0.32–0.36 nm), stage 3 (0.38–0.50 nm) and stage 4 (0.52–0.62 nm) is approximately 80%, 70% and 40%, respectively. Zhang et al. [55] employed small angle neutron scattering (SANS) to test the fraction of accessible pores and found that for pores from
Both accessible pores and inaccessible pores all exit in the macromolecular structure of coal vitrinite (Fig. 6). When the probe size is 0.33 nm, the volume of accessible pores is 2.118 nm3. In contrast, the volume of inaccessible pores is approximately 0.60 nm3, contributing 20% of the total. In fact, certain pores are accessible by CO2, but these pores are inaccessible for other larger probes, as the throat is too small for larger molecules to enter. Inaccessible pores have also been demonstrated to exist in coal reservoir by small-angle neutron scattering (SANS) and ultra small-angle neutron scattering (USANS) [53–55]. 302
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Fig. 7. Proportion of accessible pores for probes of different sizes.
Fig. 9. Fractal dimension for pores in the macro molecular structure by varying the probe size.
0.5 nm to 1 nm, the fraction is approximately 37%, which is consistent with the results of this study.
aromatic rings does not tend to form pores in the 3D macromolecular. 3.4. Fractal characteristics of ultra micropores in the macro molecular structure
3.3. Atoms on the surface of ultra micro pores The atoms on the surface of ultra micro pores are very important for gas adsorption. Adsorption is formed by interaction forces between gas molecules and atoms on the coal surface [40]. The atoms on a pore surface have great impacts on the adsorption capacity of coal. Studies of atoms on the coal surface would help methane adsorption simulations, as they can provide some useful information for adsorbent modeling and this can have significant influences on final results. From the study of pores in the Y-1 macromolecular, we observed that most pores formed by aliphatic chains (Fig. 8). It should be noted that pore walls in this paper were defined as the edge of space that can be reached by the probes. It means the pore walls are not equal to the edge of the atoms in the macromolecule. Atoms near the pore wall can be divided into two categories (Fig. 8): pores touching the pore wall directly, and pores not touching the pore wall directly. Occasionally, there is a void volume between the atoms and the pore wall, and the probe cannot touch these atoms directly, and when gas adsorbed on the surface of these pores, the adsorbing gas could not be much closed with these atoms. The distance between atoms in the macromolecule and the pore wall is important for gas adsorption as the interaction force is related to this distance. Most of the atoms touching the pore wall are hydrogen atoms. In contrast, carbon atoms near the pore wall do not usually touch the pore wall directly. Oxygen atoms sometimes touch the pore wall directly, although there are not many oxygen atoms in the macromolecular structure. Aromatic rings sometimes form pores, but not often. On the one hand, this is due to the coal sample being in immature stage (subbituminous coal) and there are fewer aromatic rings in the macromolecular. On the other hand, the structure of
Fractal feature and fractal dimension can provide useful information when we study methane adsorption, pore size distribution, evolution of pores, heterogeneity of pore, and so on [9,11,12,14,43–45,56,57]. Researches on fractal dimension and fractal feature of ultra micropores in coal would help us understand ultra micropore space characteristics, methane adsorption, heterogeneity, and so on [9,11,12,14,43–45,56,57]. Previous researches have concluded that pores larger than 2.0 nm have obvious fractal features by analyzing low pressure N2 adsorption data and mercury injection data [12]. In this study, fractal characteristics of pores between 0.26 and 0.62 nm in the 3D macromolecular have been analyzed. Fig. 9 plots on the probe number versus the volume of the probes (log-log scales). From Fig. 9, it can be seen that the data points have a good correction with the fitting line (r2 = 0.9978 and 0.9998). This reflects that the ultra micropores in the macromolecular structure of vitrinite also have obvious fractal features. The fractal plots of pores between 0.26 and 0.62 nm are twostage. The first stage corresponds to the probe size at 0.26–0.50 nm and the second stage corresponds to the probe size at 0.50–0.62 nm. The fractal dimensions of the two stages are different. According to the fractal theory, the larger the fractal dimension is, the more complex the pore space will be. When the probes are smaller than 0.50 nm, the fractal dimension of pores seen by these probes is 2.73. However, when the probes are larger than 0.50 nm, the fractal dimension of pores is 2.64. There are mainly two reasons for this phenomenon. On the one hand, if the probes are relatively large, these probes cannot pass through the pore throat. Additionally, parts of ultra micropores will not Fig. 8. Atoms near the pore wall.
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Fig. 10. pores seen by probes with 0.33 nm, 0.50 nm and 0.52 nm diameter.
similar. That is because in larger pores, methane and helium both enter easily and theses pores are only different at the edge of the pores. For the ultra pores seen by helium and methane, the smaller the pore size is, the larger the difference in volume will be. In previous researches, differences in pore volume seen by helium and methane are often ignored. For example, in methane isothermal adsorption experiments, helium is used to test the void volume. These tested void volumes were considered similar to methane volumes. However, in fact, in some cases, a large error would occur. In this study, the ultra micropores seen by helium are larger than those seen by methane by 0.0334 ml/g (accessible pores). We can use this data to correct the methane isothermal adsorption curves. In volumetric methane adsorption experiment, methane adsorption amount are calculated by Eq. (2):
be seen by large probes as probes cannot enter these parts. Thus, the shapes of pores seen by larger probes are much simpler than that of pore seen by smaller pores. On the other hand, complex ink-bottle pore cannot be seen by larger probes. In Fig. 10, we compared pores seen by probes larger than 0.50 nm and smaller than 0.50 nm. Many complex ink-bottle pores exit in pores seen by probes smaller than 0.50 nm. However, when the probe size is larger than 0.50 nm, accessible pores are mainly simple hemispherical pores. 3.5. Differences of available volume by methane, helium and CO2 The diameter of helium, methane and carbon dioxide is 0.26 nm, 0.38 nm and 0.33 nm, respectively [38]. The volume seen by helium is 0.063 ml/g. In comparison, that seen by methane and CO2 is 0.029 ml/ g and 0.041 ml/g, respectively. These volume data are all accessible ultra micropore volume. The volume seen by helium is about two times that seen by methane. Fig. 11 shows the pore distribution seen by methane, carbon dioxide and helium. By comparing the three pictures, we can see that pores seen by different molecules are notably different, especially comparing pores seen by methane and helium. On the one hand, some pores can be seen by helium but these pores cannot be seen by CO2 and methane. On the other hand, pores seen by helium are much larger than those seen by CO2 and methane. These phenomena can be seen more intuitively in the slices of pores in Fig. 12. Nos. 1, 3, 4 and 8 in Fig. 12 can be seen by helium, but these pores are inaccessible to methane. All pores accessible to methane are much smaller than those of helium. No. 2 pore (in Fig. 12a) is one large pore for helium but it is two separated pores for methane. In Fig. 12b, we can see that larger inner pores in vitrinite structure seen by methane and helium are
n1 = ntotal−
PVhe ZRT1
(2)
n1 is methane adsorption amount; ntotal is the total methane amount is sample van; P is the pressure of gas in sample van; R is ideal gas constant; Z is compression factor; T1 is the temperature of sample van; Vhe is blank volume of sample van after the sample being put in, which is tested by helium. As helium can see more pores that methane, the volume tested by helium (Vhe) is larger than the methane volume (Vme):
Vh − m = Vhe−Vme
(3)
The actual methane adsorption amount (n2) is calculated by Eq. (4):
n2 = ntotal−
PVme ZRT1
Fig. 11. Ultra micropores seen by methane, carbon dioxide and helium (accessible pores).
304
(4)
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Fig. 12. Slices of pores seen by helium, carbon dioxide and methane in vitrinite macromolecular structure (accessible pores).
n2 = ntotal−
P (Vhe−Vh − m) ZRT1
(5)
n2 = ntotal−
PVme PVh − m PVh − m + = n1 + ZRT1 ZRT1 ZRT1
(6)
23.05 cm3/g. However, the Langmuir volume after correction is 26.93 cm3/g. Methane adsorption capacity in coal will be underestimated if the difference in pores seen by helium and methane is not considered, especially for deep coalbed methane. From Eq. (6), we can find that the larger the pressure is, the larger the errors will be. Additionally, pressure increase with an increase of depth of coal reservoir. When a coal seam is deeper than 1000 m, the pressure is usually larger than 10 MPa. The difference in pores seen by helium and methane should not be ignored as the error would be more than 2.5 cm3/g.
Thus, we can find is the underestimated methane adsorption amount as helium can see more pores than methane. The key point is determining Vh-m. It is an easy thing to measure the volume seen by helium. However, it is difficult to measure the volume seen by methane as methane is an adsorptive gas. As we know, Vh-m is volume of pores that are accessible for helium and inaccessible for methane. The pore throat of these pores is larger than 0.26 nm and smaller than 0.38 nm. Thus, these pores are all ultra micropores. In this study, we calculated the methane ultra micropore volume and the helium ultra micropore volume in the coal macromolecular structure, and then we can get Vh-m of this coal sample. Fig. 13 shows the methane isothermal adsorption curves of Y-1 tested by an HPVA methane adsorption instrument by employing the volumetric method. In this methane adsorption experiment, helium is used to test the void volume, which is common in methane adsorption experiments. As helium and methane see different pores in the coal reservoir, we used the difference in volumes to correct the methane isothermal adsorption curves. The black point in Fig. 13 is experimental data, which is commonly used in related researches, and the red data are the correction data. From Fig. 13, we can see that the larger the pressure, the greater the error. When the pressure is 10 MPa, the error is approximately 2.7 cm3/g. The Langmuir volume before correction is PVh − m ZRT1
4. Conclusions A 3D macromolecular structure of subbituminous coal vitrinite has been constructed in this study, and the 3D macromolecule has been verified to be consistent with experimental NMR data, density data and pore volume data. Ultra micropores in the 3D macromolecular structure have been studied by using the probe method. Several conclusions have been drawn as follows: 1. Pores inner the macromolecular structures are smaller than 0.62 nm. Both accessible pores and inaccessible pores exist in the macromolecular structure. For a probe of 0.33 nm (CO2), the fraction of accessible pores is approximately 80%, and for the 0.5 nm probe, the fraction of accessible pores decreases to 40%. 2. Pores in the macromolecular structure of Y-1 are mainly formed by aliphatic chains and atoms on the surface of ultra micro pores can be divided into two types: those touching the pore surface directly (most of these are hydrogen atoms) and those that are near but do not touch the pore surface directly (most of the carbon atoms near the pore surface are this type). 3. Accessible pores in the macromolecular structure show obvious fractural features. The fractal plots are two-stage. The fractal dimension of pores seen by probes smaller than 0.5 nm is 2.73 and that of pores seen by probes larger than 0.5 nm is 2.64. 4. In this study, we provide a method to correct methane isothermal adsorption experimental data. Helium ultra micropores and methane ultra micropores could be obtained for the 3D coal structure and then these data could be used to correct the errors caused by that helium can see more pores than methane. The calculated results show that the difference in pores seen by helium and methane should not be ignored at high pressure (greater than 10 MPa). Acknowledgments The authors sincerely thank the financial support of the National Natural Science Foundation of China (No. 41472135), the Natural Science Foundation of Jiangsu Province (Grant No. BK20160243), the Scientific Research Foundation of the Key Laboratory of Coalbed Methane Resources and Reservoir Formation Process, Ministry of
Fig. 13. Experimental data and correction data of methane adsorption isothermal curves of Y-1 subbituminous coal vitrinite data. (In correction data, differences in pore volume seen by methane and helium have been considered.)
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Education (China University of Mining and Technology) (No. 2015-04) and the Research and Innovation Project for College Graduates of Jiangsu Province (No. KYLX15_1396).
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