A Comparative Investigation of the Adsorption Characteristics of CO₂, O₂ and N₂ in Different Ranks of Coal

Abstract

The adsorption mechanism of carbon dioxide, oxygen and nitrogen in coal is important for preventing and controlling coal spontaneous combustion and for understanding the technology of CO₂ storage in goaf. Adsorption amount and adsorption heat are key adsorption parameters that are required to understand the material and energy conversions during adsorption in coal. In this study, we studied the factors that influence the adsorption amounts and adsorption heat values of carbon dioxide, oxygen and nitrogen in coal by testing four different coal samples using conventional coal quality analysis, low-pressure nitrogen and carbon dioxide adsorption, Fourier transform infrared spectroscopy and three gas adsorption experiments at different temperatures. Then, we analyzed the relationships between the structural parameters of the coal samples and the adsorption amounts and the adsorption heat values of carbon dioxide, oxygen and nitrogen. The results show that the adsorption isotherms of carbon dioxide conform to the Langmuir equation, and the adsorption isotherms of oxygen and nitrogen conform to Henry’s law between 0 and 110 kPa. The adsorption amounts of carbon dioxide, oxygen and nitrogen decreased with an increase in temperature, and the change in the rate of the adsorption amount with temperature was determined by the adsorption heat. The results of the pore structure show that the pores of the coal samples are composed of mesopores and micropores; the micropores contribute to the main specific surface area. The micropore and mesopore structures are the main determinants of the adsorption amounts of carbon dioxide, oxygen and nitrogen in coal. The gas adsorption heat is affected by the pore structure and the chemical composition of coal. The adsorption heat of nitrogen correlates positively with the pore structure of the coal. The adsorption heat of oxygen correlates positively with the ash, elemental nitrogen, elemental sulfur and mineral contents of the coal. The adsorption heat of carbon dioxide correlates positively with the elemental sulfur content of the coal.

1. Introduction

Coal spontaneous combustion (CSC) fires are major thermodynamic disasters in coal mines [1,2] which directly affect efficient coal mining, threaten the occupational health and life of workers, and destroy the ecosystem around a mining area [3,4]. Underground mining is the main coal mining method, and this method leaves goaf behind the working face after the coal is mined out. The goaf is the main location of spontaneous combustion fires due to the presence of residual coal and serious air leakage in the goaf [5,6,7]. Inert gases such as N₂ and CO₂ can be injected into goaf to effectively prevent and extinguish fires in the goaf [8,9,10,11]; recent studies have recommended injecting flue gas from power plants (mainly composed of N₂ and CO₂) into the goaf to prevent coal spontaneous combustion [12,13]. This has the additional benefit of reducing CO₂ emissions. Coal is a natural porous adsorbent for many gases [14,15,16]. Since CSC begins with the physisorption of O₂ in coal [17,18], injecting inert or flue gas into a goaf, reduces the adsorption of O₂ due to the competitive adsorption of CO₂, O₂ and N₂ in coal, thus preventing CSC [19]. Hence, studying the physisorption characteristics of CO₂, O₂ and N₂ in coal is imperative to prevent and control CSC and store CO₂ in goaf.

The physisorption of gas in coal is a typical heat and mass transfer process. The adsorption amount and adsorption heat, which reflect the material and energy transfer characteristics of the process [20], are the most widely studied adsorption parameters. Currently, there are many studies on the adsorption behaviors of CO₂, CH₄ and N₂ in coal for coalbed methane exploitation and CO₂ geological storage [21,22,23]. Some researchers have also studied the process of CH₄ replacement in coal by injecting CO₂ or N₂ [24,25,26,27]. In addition to external factors (temperature and pressure), the gas adsorption amount is determined by coal properties (such as coal rank, maceral, moisture, minerals, pore characteristics, molecular organization and particle size of coal) [28,29,30,31,32,33,34,35,36,37]; the gas adsorption heat is affected by the macerals, pore characteristics and molecular organization of the coal [38,39,40]. In addition, the adsorption amount and adsorption heat are related to the critical properties of the gas [41,42,43]. The adsorption amount and adsorption heat are key adsorption parameters that are required to understand the material and energy conversions during adsorption in coal. At present, the relationship between adsorption amount and adsorption heat is not clear. Few studies have compared the difference in the influencing factors of adsorption amount and adsorption heat.

The physisorption behaviors of O₂ in coal and the influencing factors have been widely studied. Lu et al. tested the physisorption amounts of O₂ by using four different coal samples at low temperatures [17,18]. The results showed that the adsorption amount of O₂ was related to temperature and coal particle size. Tan et al. measured the pore characteristics of five different coals and the physisorption amount of O₂ at room temperature using mercury intrusion porosimetry (MIP) and oxygen adsorption with chromatography (OAC) and concluded that the adsorption amount of O₂ was proportional to the pore volume of nanopores in coal [14]. Tan et al. also studied the physisorption behaviors of O₂ in low-rank coal microscopically using the grand canonical Monte Carlo (GCMC) method [44]. The results showed that the adsorption amount of O₂ was positively correlated with the micropore structure of coal. Deng et al. studied the physisorption mechanism of oxygen molecules on the coal surface side chain containing sulfur and phosphorus groups using quantum chemistry calculation, and the results showed that the oxygen molecule had a strong interaction with the coal surface side chain containing sulfur and phosphorus groups [45,46]. Furthermore, Wu et al. studied the difference in adsorption behaviors of CO₂, O₂ and N₂ in coal by constructing a molecular model of bituminous coal and using the GCMC method [19]. In conclusion, the three gases can be ordered in terms of adsorption amount and adsorption heat as CO₂ > O₂ > N₂. Although comparative studies have been conducted on the adsorption behaviors of CO₂, O₂ and N₂ in coal, the differences in the main influencing factors of the adsorption characteristics of the three gases in coal are still unclear. The main objectives of this research are to explore the influence of coal properties on the adsorption characteristics of CO₂, O₂, and N₂ in coal, and to compare the factors affecting the adsorption amounts and adsorption heat values of the three gases. We tested the coal properties of different ranks of coal, the adsorption amounts and adsorption heat values of CO₂, O₂ and N₂ in different coal samples, and then analyzed the relationships between the coal properties and the adsorption parameters to discover the differences in the adsorption behaviors of CO₂, O₂ and N₂ in coal.

2. Experimental Procedures

2.1. Coal Sample Preparation

Chengzhuang, Jinjia, Daliuta and Donghuai coal mines in China were visited for the coal sample collection. According to the national standard method GB/T 5751-2009 [47], the coals of the Chengzhuang coal mine in Qinshui coalfield are classified as anthracite; the coals of the Jinjia coal mine in Liupanshui coalfield belong to lean coal; the coals of the Daliuta coal mine in Dongsheng coalfield belong to fat coal; the coals of the Donghuai coal mine in Baise coalfield are classified as lignite. The coals of the four coalfields cover the low-rank coal and high-rank coal, and can be sampled to conduct the study.

Table 1. Geological information of the coal samples.

Sample	Coal Mine	Coal Seam	Coal Field	Geological Formation
CZ	Chengzhuang	3	Qinshui	Shanxi formation of the lower Permian system
JJ	Jinjia	18	Liupanshui	Longtan formation of the upper Permian system
DL	Daliuta	5	Dongsheng	Yan’an formation of the middle Jurassic system
DH	Donghuai	1	Baise	Nadu formation of the lower Tertiary system

shows the geological information of the coal samples. Representative fresh coal blocks were collected from the working face of the underground mines following the national standard method GB/T 482-2008 (sampling of coal seams) [48]. The collected coal blocks were covered with several layers of plastic membrane and sealed with adhesive tape to avoid oxidation. Then, the collected coal blocks were delivered to the laboratory for coal sample preparation. Considering the heterogeneity of coal, several small coal blocks were chosen randomly from the original coal samples. Then, they were crushed and sieved into relatively homogeneous sizes (60–80 mesh for measurement of pore structure and gas adsorption experiments, commonly used in the literatures; 200 mesh for measurement of chemical structure). The coal quality parameters of the samples, including the maximum vitrinite reflectance (R_o,m), proximate analysis, ultimate analysis and maceral composition, are listed in

Table 2. Coal quality parameters of the coal samples.

Properties	CZ	JJ	DL	DH
Coal Type	Anthracite	Lean coal	Fat coal	Lignite
Ro,m (%)	2.37	2.04	0.76	0.58
Proximate Analysis (%, air-drying base)
M	0.72	0.54	3.62	3.17
A	13.88	15.20	5.38	42.02
V	7.54	8.88	31.84	27.96
FC	77.59	75.38	59.16	26.85
Ultimate Analysis (%, air-drying base)
C	77.59	76.63	73.30	39.33
H	2.89	3.30	4.48	3.48
O	3.48	2.89	11.72	9.06
N	1.21	1.20	1.03	1.57
S	0.24	0.26	0.47	1.37
Maceral Composition (%)
VI	67.26	68.12	49.45	72.02
IN	28.56	30.00	47.80	1.19
EX	–	–	1.10	2.98
MI	4.18	1.88	1.65	23.81

Notes: R_o,m, maximum vitrinite reflectance; M, moisture; A, ash; V, volatile; FC, fixed carbon; C, carbon element; H, hydrogen element; O, oxygen element; N, nitrogen element; S, sulfur element; VI, vitrinite; IN, inertinite; EX, exinite, MI, mineral.

. The maximum vitrinite reflectance (R_o,m) and maceral composition of the coal samples were performed with a microscope photometer (MPV-III, Leitz Company, Stuttgart, Germany) following the national standard GB/T 6948–2008 [49]. Coal macerals were determined by the point counting technique following the scheme of the International Committee for Coal and Organic Petrology (ICCP) [50]. The proximate analysis of the coal samples was carried out with an SDLA618 industrial analyzer following the national standard GB/T 212–2008 [51], and the ultimate analysis was carried out with a Vario EL element analyzer following the national standard GB/T 214–2007 [52].

2.2. Pore Structure Characterization

The gas adsorption methods, i.e., low-pressure nitrogen adsorption (LP-N₂GA) at 77 K and low-pressure carbon dioxide adsorption (LP-CO₂GA) at 273.15 K, using an ASAP 2020 automatic surface area and pore size analyzer (Micromeritics Instrument, Atlanta, GA, USA), were used to analyze the pore structure of the coal samples. The surface area, pore volume and pore size distribution (PSD) of the coal samples were obtained using the density functional theory (DFT). In this study, the IUPAC method (micropores, <2 nm; mesopores, 2–50 nm; macropores, >50 nm) was adopted for pore classification [53].

2.3. Chemical Structure Characterization

The chemical structures of the coal samples were analyzed using Fourier transform infrared spectroscopy (FTIR). The FTIR tests were performed using a TIR Vertex 80v spectrometer (Bruker Corporation, Karlsruhe, Germany). The chemical structures of the coal samples were obtained by using a peak fitting analysis of the FTIR spectrum. The apparent aromaticity, f_a, was calculated as follows [29]:

$$\frac{H_{al}}{H}=\frac{H_{al}}{H_{al}+H_{ar}}=\frac{A_{2800–3000}}{A_{2800–3000}+A_{700–900}}$$

(1)

$$\frac{C_{al}}{C}=\left(\frac{H_{al}}{H}\times \frac{H}{C}\right)/\frac{H_{al}}{C_{al}}$$

(2)

$$f_a^{}=1-\frac{C_{al}}{C}$$

(3)

where H_al/H is the ratio of aliphatic (H_al) to total hydrogen atoms (H).

The 2800–3000 cm⁻¹ region of the spectrum is for the aliphatic (H_al) stretching vibration and the 700–900 cm⁻¹ region is for the aromatic hydrogen (H_ar) out-of-plane deformation [29]. Therefore, the integral area of the two regions can be used to calculate the H_al/H. H/C is the ratio of hydrogen atoms to carbon atoms, calculated from the ultimate analysis; H_al/C_al is valued at approximately 1.8 for coals; C_al/C represents the aliphatic carbon fraction.

The 2940–3000 cm⁻¹ region is for the absorption of aliphatic CH₃ asymmetric stretching vibration and the 2900–2940 cm⁻¹ region is for the aliphatic CH₂ asymmetric stretching vibration. A(CH₂)/A(CH₃) (the length of aliphatic chains) is determined as follows [29]:

$$\frac{A\left(\mathrm{C}{\mathrm{H}}_2\right)}{A\left(\mathrm{C}{\mathrm{H}}_3\right)}=\frac{A_{2900-2940}}{A_{2940-3000}}$$

(4)

The absorption bands around 1600 cm⁻¹ are due to the aromatic nucleus (C=C) stretching vibration.

The 1650–1800 cm⁻¹ region is assigned to the C=O group vibration. The ”C” factor (the ratio of C=O to C=C groups) is calculated using Equation (5) [32].

$${}^{’}{C}^{’}=\frac{\mathrm{C}=\mathrm{O}}{\mathrm{C}=\mathrm{O}+\mathrm{C}=\mathrm{C}}=\frac{A_{1650-1800}}{A_{1650-1800}+A_{1600}}$$

(5)

2.4. Measurement of Adsorption Isotherms

The adsorption isotherms of CO₂, O₂ and N₂ were measured using an ASAP 2020 experimental system (Micromeritics Instrument, Atlanta, GA, USA) with a volumetric method. Considering that the actual conditions inside a goaf are close to room temperature and atmospheric pressure [54], the equilibrium pressure and the equilibrium temperature of the adsorption experiments were set between 0 and 110 kPa and between 303.15 and 323.15 K, respectively.

3. Adsorption Models and Thermodynamics

3.1. Adsorption Model

A reasonable adsorption model quantitatively describes the adsorption isotherms. In addition, the adsorption thermodynamic parameters can be obtained using the adsorption model to indirectly understand the adsorption mechanism [55]. At low pressures (in the low-pressure region of Henry’s law), gas adsorption isotherms follow Henry’s law [56]

$$n=K_{H}p$$

(6)

where n is the adsorption amount (mmol·g⁻¹), K_H is the Henry’s law constant (mmol·g⁻¹·kPa⁻¹), and p is the equilibrium pressure (kPa).

The gas adsorption isotherms at low pressure are also modeled by the virial equation as follows [57]:

$$\ln \frac{n}{p}=A_0+A_{1}n+A_2{n}^2+\cdot \cdot \cdot$$

(7)

where A₀, A₁ and A₂ are the virial constants.

When the adsorption amount is small, the high-order term of the virial equation can be neglected, and Equation (7) can be written as follows:

$$\ln \frac{n}{p}=A_0+A_{1}n$$

(8)

Equation (8) shows that when the adsorption amount tends to zero, the virial equation transforms into Henry’s law:

$$\underset{n\to 0}{\lim }\frac{n}{p}=\exp \left(A_0\right)=K_H$$

(9)

According to Equation (9), Henry’s law constant can be obtained by the virial constant A₀.

Since the model parameters are few and have clear physical significance, the Langmuir equation is widely used in research and engineering applications. The Langmuir equation is generally written as [58]:

$$n=\frac{abp}{1+bp}$$

(10)

where a is the saturation adsorption amount (mmol/g) and b is the Langmuir constant (kPa⁻¹).

3.2. Adsorption Thermodynamics

Gas adsorption is usually exothermic; the heat released during the adsorption process is referred as the adsorption heat. The adsorption heat includes the integral heat and differential heat of adsorption [59]. The integral heat is the heat released by the adsorption of n mol of gas, and the differential heat of adsorption is the heat released by the adsorption of a mol of gas. The differential heat, which is also called the isosteric heat of adsorption, directly determines the adsorption intensity and so it is widely studied [60]. In this paper, the adsorption heat refers to the isosteric heat of adsorption. The isosteric heat of adsorption can be obtained using the Clausius–Clapeyron equation as follows [61]:

$${\left(\frac{d\ln p}{dT}\right)}_n=-\frac{\mathrm{\Delta }H}{R{T}^2}$$

(11)

where p is the pressure (kPa), T is the temperature (K), $\mathrm{\Delta }H$ is the isosteric heat of adsorption (kJ/mol), R is the universal gas constant (8.314 J·mol⁻¹·K⁻¹), and subscript n refers to a fixed adsorption amount.

According to Equation (6), for a fixed adsorption amount, n

$$d\ln n=d\ln K_H+d\ln p=0$$

(12)

substituting the relation $d\ln p=-d\ln K_H$ into Equation (11) yields Van’t Hoff’s equation [56]

$$\frac{d\ln K_H}{dT}=\frac{\mathrm{\Delta }{H}_0}{R{T}^2}$$

(13)

where $\mathrm{\Delta }{H}_0$ is the isosteric heat of adsorption in Henry’s law region (kJ/mol) [57].

Integrating Equation (13) yields

$$\ln K_H=-\frac{\mathrm{\Delta }{H}_0}{R}\frac{1}{T}+C_0$$

(14)

where C₀ is the integration constant. The adsorption heat in the Henry’s law region can be obtained from the linear correlation between lnK_H and 1/T. If the adsorption isotherms satisfy the virial equation, the adsorption heat in the Henry’s law region can be obtained from the linear correlation between A₀ and 1/T.

4. Results and Discussion

4.1. Adsorption Characteristics of CO₂, O₂ and N₂ in Coal

4.1.1. Adsorption Amounts of CO₂, O₂ and N₂ in Coal

The adsorption isotherms of CO₂, O₂ and N₂ of the coal samples at three different temperatures are shown in Figure 1. Figure 1 shows that at the experimental pressure ranges, the CO₂ adsorption amounts of the coal samples increase with an increase in pressure, but the increasing rate gradually decreases. All the CO₂ adsorption isotherms in Figure 1 exhibit type-I isotherms according to IUPAC classification. In addition, the O₂ and N₂ adsorption amounts of the coal samples increase linearly with an increase in pressure. The CO₂ adsorption isotherms of the coal samples were fitted by using the Langmuir equation, and the O₂ and N₂ adsorption isotherms of the coal samples were fitted using Henry’s law. The fitting results are summarized in

Table 3. Fitting results of the adsorption isotherms of the three gases.

Sample	Temperature (K)	CO2-Langmuir Model			CO2-Virial Model			O2-Henry Model		N2-Henry Model
		a (mmol·g−1)	b (kPa−1)	R2	A0	A1	R2	KH (×10−4 mmol ·g−1·kPa−1)	R2	KH (×10−4 mmol ·g−1·kPa−1)	R2
CZ	303.15	1.1287	0.0153	0.9991	−3.8830	−1.5816	0.9995	7.0127	0.9990	4.2964	0.9978
	313.15	1.0616	0.0122	0.9997	−4.2133	−1.5789	0.9985	5.6471	0.9969	3.5041	0.9993
	323.15	0.9769	0.0097	0.9997	−4.5665	−1.5652	0.9996	4.6192	0.9989	2.9663	0.9997
JJ	303.15	0.7525	0.0114	0.9991	−4.5798	−2.3537	0.9934	3.4816	0.9995	1.8373	0.9988
	313.15	0.7037	0.0090	0.9993	−4.9591	−2.2248	0.9962	2.9138	0.9996	1.6147	0.9996
	323.15	0.6249	0.0067	0.9994	−5.3317	−2.6907	0.9812	2.3799	0.9996	1.3883	0.9985
DL	303.15	0.6794	0.0138	0.9980	−4.4371	−2.8189	0.9930	2.7785	0.9997	1.9320	0.9768
	313.15	0.6767	0.0094	0.9992	−4.8843	−2.5881	0.9920	2.3230	0.9994	1.7510	0.9852
	323.15	0.5838	0.0084	0.9991	−5.1692	−2.8890	0.9919	2.0020	0.9980	1.5646	0.9935
DH	303.15	0.5102	0.0152	0.9966	−4.6033	−3.8698	0.9876	2.4098	0.9897	1.7860	0.9961
	313.15	0.4964	0.0106	0.9983	−5.0551	−3.6292	0.9875	1.7204	0.9844	1.6283	0.9987
	323.15	0.4437	0.0086	0.9990	−5.4084	−3.8621	0.9867	1.2260	0.9762	1.4962	0.9999

. From Table 3, it can be seen that the Langmuir model fits the CO₂ adsorption isotherms well with R² > 0.99, and the Henry model fits the O₂ and N₂ adsorption isotherms well with R² > 0.97.

Figure 1 shows that temperature significantly affects the adsorption amounts of the gases; as temperature increases, the adsorption amounts of CO₂, O₂ and N₂ all decrease. Figure 2 shows the adsorption amounts of CO₂, O₂ and N₂ of the coal samples at different temperatures under atmospheric pressure (1.013 × 10⁵ Pa) according to the Langmuir and Henry models in Table 3; as temperature increases under atmospheric pressure, the adsorption amounts of the gases by the coal samples decrease linearly. For all the coal samples, the CO₂ adsorption amounts at the experimental temperatures are significantly greater than the O₂ and N₂ adsorption amounts. For the CZ, JJ and DL samples, the O₂ adsorption amounts are greater than the N₂ adsorption amounts at the given temperatures. For the DH sample, the O₂ adsorption amounts are greater than the N₂ adsorption amounts at 303.15 and 313.15 K, but the O₂ adsorption amount is less than the N₂ adsorption amount at 323.15 K. Figure 2 shows that the decreased rate of O₂ adsorption amount with an increase in temperature is greater than that of N₂, and this is the reason why the O₂ adsorption amount in the DH sample at high temperature is less than the N₂ adsorption amount.

In addition, the gas adsorption amounts of the coal samples at room temperatures and under atmospheric pressure decreased in the following order: CO₂ > O₂ > N₂. The properties of the three gases [41,62] are shown in

Table 4. Properties of the gases used in this study.

Properties/Gases	CO2	O2	N2
Molecular Mass, m (g/mol)	44	32	28
Critical Temperature, Tc (K)	304.2	154.6	126.2
Critical Pressure, Pc (MPa)	7.4	5.0	3.4
Van der Waals Attractive Constant, a (kJ2/mol2Pa)	0.365	0.139	0.137
Kinetic Diameter, σk (nm)	0.330	0.346	0.364

. According to Table 4, the adsorption amounts of three gases increased with an increase in the critical temperature and pressure. Consistent with previous studies [41,42], the critical parameters of the gases are important factors that affect the adsorption amount. This indicates that the adsorption of the gases is similar to the liquefaction of the gases. The higher the critical pressure and temperature, the easier the gas is adsorbed onto the coal’s surface. In addition, the adsorption amounts of the three gases increased with a decrease in the molecular kinetic diameter, because the smaller the molecular diameter, the more micropores can be entered and the greater the adsorption amount.

4.1.2. Adsorption Heats of CO₂, O₂ and N₂ in Coal

The Henry’s law constants of the O₂ and N₂ adsorption isotherms in Table 3 were used to calculate the O₂ and N₂ adsorption heats of the coal samples. First, the virial equation was used to fit the CO₂ adsorption isotherms (Table 3); Table 3 shows that the virial model can also describe the CO₂ adsorption isotherms well with R² > 0.98. Then, Henry’s law constants of the CO₂ adsorption isotherms were calculated from the virial constant, A₀, in Table 3 according to Equation (9). Figure 3 shows the relationships between lnK_H and 1/T for CO₂, O₂ and N₂. Linear fitting was performed on all the data in Figure 3 and the fitting results are shown in

Table 5. Fitting results of isometric adsorption curves.

Sample	Gas	Fitting Formula	R2	−ΔH0 (kJ·mol−1)
CZ	CO2	lnKH = 3345.6/T − 14.912	0.9986	27.82
	O2	lnKH = 2045.1/T − 14.009	0.9999	17.00
	N2	lnKH = 1815.9/T − 13.747	0.9984	15.10
JJ	CO2	lnKH = 3682.0/T − 16.723	0.9998	30.61
	O2	lnKH = 1861.5/T − 14.098	0.9969	15.48
	N2	lnKH = 1370.9/T − 13.119	0.9960	11.40
DL	CO2	lnKH = 3593.2/T − 16.312	0.9882	29.87
	O2	lnKH = 1606.5/T − 13.491	0.9988	13.36
	N2	lnKH = 1032.1/T − 11.953	0.9967	8.58
DH	CO2	lnKH = 3947.3/T − 17.636	0.9973	32.82
	O2	lnKH = 3308.9/T − 19.242	0.9996	27.51
	N2	lnKH = 867.33/T − 11.492	0.9999	7.21

(the linear function fits all curves well with R² > 0.98). Then, the adsorption heats of CO₂, O₂ and N₂ of the coal samples were calculated using the slope of the linear fitting formulas, as shown in Table 5. Table 5 shows that the adsorption heats of CO₂, O₂ and N₂ range from 7.21 to 32.82 kJ/mol. It also shows that the adsorption is physical. For all the coal samples, the gas adsorption heat decreased in the following order: CO₂ > O₂ > N₂. According to Table 4, the adsorption heats of the gases are closely related to the Van der Waals attractive constant; an increase in the Van der Waals attractive constant of the gas increases the gas adsorption heat. This reveals that the nature of the gas adsorption by coal is Van der Waals force; the greater the Van der Waals force between the gas and coal molecules, the greater the gas adsorption heat for a given coal sample.

In addition, Figure 3 and Table 5 show that the larger the adsorption heat, the greater the slope of the linear relationship between lnK_H and 1/T. This indicates that adsorption heat affects the change rate of Henry’s law constant with temperature; the greater the adsorption heat, the greater the change rate of Henry’s law constant with temperature and the greater the change rate of adsorption amount with temperature at the same pressure. Hence, adsorption heat affects adsorption amount. As shown in Figure 2; the O₂ adsorption heat is greater than the N₂ adsorption heat, and the decrease in the rate of the O₂ adsorption amount with temperature is greater than that of N₂ for all the coal samples. This also explains why Henry’s law constant and the O₂ adsorption amount are greater than those of N₂ at 303.15 and 313.15 K for the DH sample, while Henry’s law constant and adsorption amount of O₂ are lower than those of N₂ at 323.15 K, as shown in Figure 2d.

4.2. Pore and Chemical Structure Characteristics of Coal

4.2.1. Pore Structure Characteristics of Coal

The PSD of the coal samples obtained by the LP-N₂GA and LP-CO₂GA experiments are shown in Figure 4 and Figure 5. Figure 4 shows that the pore diameter range of the coal samples measured by the LP-N₂GA experiment as 1.2–16 nm, and the PSD curves show main peaks at 2–4 nm. Figure 4 also shows the pore type of the coal samples is mainly mesopores (2–50 nm) with a few micropores (<2 nm). Figure 5 shows that the pore diameter range of the coal samples measured by the LP-CO₂GA experiment is 0.4–1.1 nm, and the PSD curves show main peaks at 0.4–0.6 nm. Figure 4 and Figure 5 show that the LP-N₂GA experiment measures mesopores and micropores, while the LP-CO₂GA experiment measures micropores. The micropore parameters of the coal samples were obtained by adding the analysis results of the LP-N₂GA and LP-CO₂GA experiments, and the mesopores parameters of the coal samples were obtained from the analysis results of the LP-N₂GA experiments. The comprehensive pore parameters of the coal samples are shown in

Table 6. Pore structure parameters of the coal samples.

Sample	St (m2/g)	Smic (m2/g)	Smes (m2/g)	Vt (cm3/g)	Vmic (cm3/g)	Vmes (cm3/g)
CZ	179.42	144.14	35.28	0.1227	0.0447	0.0780
JJ	104.37	87.65	16.72	0.0663	0.0290	0.0373
DL	80.15	73.54	6.61	0.0390	0.0233	0.0157
DH	62.94	56.60	6.34	0.0405	0.0195	0.0210

Notes: S_t, total surface area; V_t, total pore volume; S_mic, micropore surface area; V_mic, micropore pore volume; S_mes, mesopore surface area; V_mes, mesopore pore volume.

. Table 6 shows that the total surface area and pore volume of the coal samples range from 62.94 to 179.42 m²/g and from 0.0390 to 0.1227 cm³/g, respectively. It can be seen from Table 6 that the surface area of total pore, micropore and mesopore of the coal samples increased with an increase in coal rank. In addition, the surface area of the micropores was significantly larger than that of the mesopores for all the coal samples, indicating that the micropores mainly contribute to the surface area of coal. Table 6 also shows that the total pore volume of the DL sample was the smallest; its micropore volume was slightly larger than its mesopore volume. The micropore volumes of the other three coal samples were smaller than their respective mesopore volumes.

4.2.2. Chemical Structure Characteristics of Coal

The FTIR spectra of the coal samples are shown in Figure 6. Figure 6 shows that the FTIR spectra of the coal samples have similar shapes and absorbance peaks, but the relative intensities of the absorbance peaks are different. It shows that the four coal samples have the same main functional groups, but the ratio of the groups varies in each coal sample. In this study, 700–900, 1585–1615, 1650–1800 and 2800–3000 cm⁻¹ regions of the FTIR spectra were selected to obtain the chemical structure parameters of coal [29]. The 700–900 cm⁻¹ region of the FTIR spectra is attributed to the aromatic structures with different aromatic hydrogens. Figure 6 shows that there are several absorbance peaks in the 700–900 cm⁻¹ region of the FTIR spectra of the coal samples. The 730–770, 800–860 and 860–900 cm⁻¹ regions are assigned to the aromatic nucleus with from three to four, two and one adjacent hydrogens, respectively. The 1585–1615 cm⁻¹ region of the FTIR spectra is caused by the stretching vibration of the aromatic nucleus with different aromatic hydrogens of coal. Figure 6 shows that all the coal samples have one absorbance peak at around 1600 cm⁻¹. The 1650–1800 cm⁻¹ region of the FTIR spectra is caused by the stretching vibration of C=O groups, and all the coal samples have weak absorbance peaks in this region. The 2800–3000 cm⁻¹ region of the FTIR spectra is attributed to the aliphatic structures, and Figure 6 shows that all the samples have two absorbance peaks in this region. The detailed chemical structure parameters of the coal samples were obtained by peak fitting the above four regions of the FTIR spectra using the OMNIC software, as shown in

Table 7. Chemical structure parameters of the coal samples.

Sample	fa	Hal/H	A(CH2)/A(CH3)	’C’
CZ	0.9786	0.0862	0.7471	0.3013
JJ	0.9703	0.1036	0.2468	0.2458
DL	0.6904	0.7599	3.6485	0.4616
DH	0.7114	0.4892	2.3060	0.4972

. Table 7 shows that the aromaticity of two low-rank coal samples (DL and DH) is less than that of two high-rank coal samples (CZ and JJ). In addition, the H_al/H, the A(CH₂)/A(CH₃) and the ”C” factor of the two low-rank coal samples (DL and DH) are greater than those of the two high-rank coal samples (CZ and JJ). The results show that with an increase in coalification degree, the content of aliphatic structures and oxygen-containing functional groups of coal gradually decreases, and the aromaticity gradually increases (consistent with previous research results).

4.3. Influencing Factors Analysis of Gas Adsorption Characteristics

In this paper, two analytical techniques, including Pearson’s correlation analysis and linear regression analysis, were used to analyze the relationships between coal properties and adsorption amounts (at 303.15 K under atmospheric pressure) and adsorption heats of CO₂, O₂ and N₂. First, a Pearson correlation analysis was used to preliminarily judge the correlations. According to Pearson’s correlation coefficients, the significant influencing factors of gas adsorption characteristics were determined. Then, a linear regression analysis was performed on the relationships between the influencing factors and adsorption parameters to verify the correlations. Pearson’s correlation coefficient, r, is widely used to reflect the degree of the linear correlation between two variables (the r value ranges from −1 to 1) [63]. The greater the absolute value of r, the higher the correlation between the two variables. A positive r value indicates that two variables are positively correlated, and a negative r value indicates that the two variables are negatively correlated. The resulting r values are summarized in

Table 8. Pearson’s correlation coefficients between adsorption parameters and coal properties.

X/Y	Adsorption Amount			Adsorption Heat
	CO2	O2	N2	CO2	O2	N2
Smic	0.9901	0.9899	0.9478	−0.9022	−0.4048	0.9781
Vmic	0.9809	0.9890	0.9390	−0.8796	−0.3808	0.9859
Smes	0.9558	0.9847	0.9309	−0.8071	−0.2718	0.9790
Vmes	0.9423	0.9815	0.9379	−0.7596	−0.1811	0.9563
fa	0.6784	0.7359	0.5838	−0.5750	−0.3322	0.8859
Hal/H	−0.5778	−0.6737	−0.5371	0.3740	0.0478	−0.7888
A(CH2)/A(CH3)	−0.4565	−0.5570	−0.4019	0.2720	0.0441	−0.7070
‘C’	−0.5544	−0.5899	−0.4090	0.5481	0.5031	−0.8035
M	−0.6142	−0.6815	−0.5224	0.4994	0.2815	−0.8420
A	−0.4528	−0.3324	−0.2636	0.7670	0.9896	−0.4613
V	−0.6737	−0.7406	−0.5942	0.5413	0.2620	−0.8777
FC	0.7070	0.6660	0.5294	−0.8417	−0.8307	0.8391
C	0.6209	0.5438	0.4272	−0.8427	−0.9434	0.7109
H	−0.5558	−0.6762	−0.6052	0.2349	−0.2882	−0.6816
O	−0.5594	−0.6455	−0.4923	0.3976	0.1458	−0.7921
N	−0.3603	−0.2322	−0.1701	0.7001	0.9851	−0.3620
S	−0.6498	−0.5861	−0.4592	0.8422	0.9094	−0.7601
VI	0.0474	0.2009	0.1542	0.3160	0.6837	0.1920
IN	0.2893	0.1539	0.1050	−0.6459	−0.9661	0.2728
MI	−0.4757	−0.3811	−0.2679	0.7581	0.9877	−0.5628

Notes: Red numbers represent a high positive correlation (0.9 ≤ r < 1); orange numbers represent a moderate positive correlation (0.7 ≤ r < 0.9); blue numbers represent a high negative correlation (−1 < r ≤ −0.9); green numbers represent a moderate negative correlation (−0.9 < r ≤ −0.7); black numbers represent a low correlation (|r| < 0.7).

.

Table 8 shows that the adsorption amounts of CO₂, O₂ and N₂ are all highly positively correlated with the pore structure parameters of the coal samples, including the surface area and pore volume of the micropores and mesopores. The relationships between the adsorption amounts of CO₂, O₂ and N₂ and the pore structure parameters of the coal samples are shown in Figure 7 (linear regression analysis was performed on the data in Figure 7). Figure 7 shows that the correlation coefficients, R², are greater than 0.8, which proves that the adsorption amounts of the gases are highly positively correlated with the micropore and mesopore structural parameters of coal. This indicates that the micropores and mesopores are the main adsorption and storage sites for gases. The higher the pore content of coal, the more the adsorption sites, and the greater the adsorption amount. In addition, the correlation coefficients between the micropore structural parameters and the adsorption amounts of the gases are greater than those between the mesopore structural parameters and the adsorption amount of the gases. Table 6 shows that the surface area of micropores is significantly larger than that of mesopores, which indicates that gas adsorption mainly occurs in the micropores of coal.

Table 8 also shows that the CO₂ and O₂ adsorption heats are negatively correlated with the pore structure parameters of the coal samples, while the N₂ adsorption heat is positively correlated with the pore structure parameters of the coal samples. The relationships between the adsorption heats of CO₂, O₂ and N₂ and the pore structure parameters of the coal samples are shown in Figure 8 (linear regression analysis was performed on the data in Figure 8). Figure 8 shows that the correlation coefficients, R², between the N₂ adsorption heat and the pore structure parameters are greater than 0.9, which proves that there is a high positive correlation between the N₂ adsorption heat and pore structure parameters of the coal samples. Some studies [64,65] have calculated the methane adsorption heat in slit pores with different sizes, and the results have shown that methane adsorption heat decreases with an increase in pore size. Due to the superposition of the adsorption force of adjacent pore walls in micropores, the adsorption potential energy of micropores is higher than that of flat surface. Hence, the more micropores, the greater the gas adsorption heat. The high positive correlation between the N₂ adsorption heat and pore structure parameters of the coal samples shows that the pore structure of coal is the main factor determining the N₂ adsorption heat. However, there are no positive correlations between the adsorption heats of CO₂ and O₂ and pore structure parameters of the coal samples. The adsorption heat reflects the strength of the interaction between the gas and coal molecules at each adsorption site. In addition to pore structure of coal, gas adsorption heat may also be affected by the chemical composition of coal. The relationships between gas adsorption heat and chemical composition of coal should also be analyzed.

Table 8 shows that the adsorption heats of CO₂ and O₂ are positively correlated with the ash, elemental nitrogen, elemental sulfur and mineral contents of the coal samples. The relationships between adsorption heats of CO₂, O₂ and N₂ and coal quality parameters are shown in Figure 9. Figure 9 shows that the correlation coefficient, R², between the O₂ adsorption heat and the ash, elemental nitrogen, and mineral contents of the coal samples are greater than 0.9 (high correlation). There is a moderate positive correlation between O₂ adsorption heat and elemental sulfur content, and the correlation coefficient is greater than 0.8. The correlation coefficient between the O₂ adsorption heat and the ash content of the coal samples is the highest, followed by the mineral content. Ash mainly comes from non-combustible minerals in coal. Pyrite (FeS₂) is a typical mineral in coal [66], and it reacts with water and oxygen at room temperature with a large heat release. Some studies [67,68] have shown that pyrite can promote the process of low-temperature oxidation of coal. The existence of minerals can enhance the interaction between coal and O₂, and consequently, the mineral content of coal is the main influencing factor of the O₂ adsorption heat in this study. The elemental sulfur in coal contains organic and inorganic sulfur [46]. Inorganic sulfur in coal is mainly in the form of sulfur compounds in minerals. The organic sulfur in coal refers to the sulfur combined with the organic molecular of coal. Deng et al. found a strong interaction between sulfur-containing functional groups and O₂ in coal [46], and consequently, O₂ adsorption heat can also be affected by the elemental sulfur content of coal. The elemental nitrogen in coal is mainly in the form of organic matter [69]. The high correlation between O₂ adsorption heat and elemental nitrogen content indicates that the nitrogen-functional groups in the coal molecular structure may have a strong interaction with O₂.

Figure 9 also shows that there is a moderate positive correlation between the CO₂ adsorption heat and the elemental sulfur content of the coal samples, and the correlation coefficient is greater than 0.7. The correlation coefficients between the CO₂ adsorption heat and the ash, elemental nitrogen, and mineral contents of the coal samples are all less than 0.6, showing that CO₂ adsorption heat has low correlations with the three factors. Fan et al. found that the presence of sulfur-functional groups in coal improve the adsorption affinity of coal molecules for CO₂ [70], and consequently, the elemental sulfur content of coal is the main influencing factor of the CO₂ adsorption heat in this study. In addition, Table 8 shows that there is a moderate positive correlation between N₂ adsorption heat and the aromaticity, fixed carbon, carbon content of the coal samples, indicating that N₂ adsorption heat is also affected by the chemical structure of coal.

The above results show that the adsorption amounts and adsorption heat values of the three gases have different influencing factors. The pore structure of coal, especially the micropores, is the main factor determining the adsorption amounts of the three gases. The adsorption heat of the three gases is affected by the pore structure and chemical composition of coal. For N₂, the pore structure is the main factor determining the adsorption heat. For CO₂ and O₂, the chemical composition of coal is the main factor determining the adsorption heat.

5. Conclusions

In this paper, the properties of four coal samples were tested using a coal quality analysis, LP-N₂GA, LP-CO₂GA, and FTIR. Then, the adsorption isotherms of CO₂, O₂ and N₂ of the coal samples were measured at three different temperatures, and the adsorption amounts and adsorption heat values of CO₂, O₂ and N₂ were obtained. The effects of the properties of the coal samples on adsorption amount and adsorption heat were analyzed. The following conclusions can be drawn from this research:

(1)

In this study, the relationship between gas adsorption amount and adsorption heat in coal and the influencing factors were further clarified. The greater the gas adsorption heat, the greater the change rate of the gas adsorption amount with temperature in coal. The pore structure of the coal, especially the micropore structure, are the main factors that determine the gas adsorption amounts in coal. Gas adsorption heat is affected by the pore structure and chemical composition of the coal.

(2)

The differences in the main influencing factors of the adsorption characteristics of CO₂, O₂, and N₂ in coal were explored. For the three gases, the pore structure of coal is the main factor that determines the adsorption amount. The main influencing factors of the adsorption heat of the three gases are different. The N₂ adsorption heat is mainly affected by the pore structure of coal, and the CO₂ and O₂ adsorption heats are mainly affected by the chemical composition of coal. Specifically, the elemental sulfur content of coal is the main influencing factor of CO₂ adsorption heat, and the mineral content of coal is the main influencing factor of O₂ adsorption heat.

(3)

The results of this study are helpful to understand the adsorption mechanism of CO₂, O₂, and N₂ in coal, and the results provide basic gas adsorption data for the fire prevention and control technology of injecting inert gas and the technology of CO₂ storage in goaf. The coal properties can be used to predict the gas adsorption parameters and to evaluate the gas adsorption ability of different coals. The gas adsorption parameters can be used to numerically simulate the process of injecting inert gas into a goaf for optimizing the gas injection parameters.

(4)

This study has several limitations. In this study, only four types of coal with single particle size were selected, and only the adsorption behaviors of single gases in coals were studied. There are crushed coals with different particle sizes and bulk coals in the field, and competitive adsorption of multi-component gases exists in the goaf. In the future, more types of coals should be collected to study the adsorption behaviors of single and multi-component gases in crushed coals with different particle sizes and bulk coal. A new experimental device should also be constructed to study the mechanism of O₂ replacement in coal by injecting CO₂ or N₂. In addition, the types of functional groups and mineral in coals and their effects on gas adsorption characteristics should be investigated in further research.