Combined effects of pore structure and surface chemistry on water vapor adsorption characteristics of coal: Equilibrium, thermodynamic and kinetic studies

2.2.1 Proximate and ultimate analysis

Prior to isotherm measurements, proximate and ultimate analysis were conducted to acquire information regarding the textural properties of the coals. The proximate analysis, including fixed carbon, volatile matters, ash and moisture, was conducted following the National Standard of China (GB/T 212–2022). The ultimate analysis was carried out using a Flash EA2000 elemental analyzer (Thermo Fisher Scientific, USA). The general information of the coal samples determined by proximate and ultimate analysis was reported in Table 1 (Liu et al., 2019).

2.2.2 Meso- and Micro-Porosity

The meso- and micro-porosity of the coals were examined by means of both N₂ and CO₂ adsorption experiments using an ASAP 2020 M instrument (Micrometrics Instruments Corporation, USA). Prior to each measurement, the as-received coal samples with a particle size range of + 10–8 mesh were automatically degassed by heating at 383 K under a high vacuum level (10^-5 ∼ 10^-6 Torr) for about 10 h to remove moisture and some other volatile matters. The adsorption–desorption isotherms of N₂ were collected at 77 K under relative pressures up to 0.99, while the adsorption isotherms of CO₂ were collected at 273 K under relative pressures up to 0.033.

At each pressure point, the equilibrium of adsorption–desorption was achieved as pressure remains constant for 30 s. The tolerance of pressure was set at 6.67 mbar (5 mmHg). The isotherm was generated automatically by the instrument’s software. In addition, the volume of pore space, specific surface area (SSA) and pore size distribution (PSD) were evaluated according to multiple theoretical models, namely, BET, Dubinin–Radushkevich (D–R), Dubinin–Astakhov (D–A), Barrett–Joyner–Halenda (BJH), and Density Functional Theory (DFT) (Mastalerz et al., 2010; Fatma and Turkan, 2019).

2.2.3 Fourier transfor infrated spectrometry (FTIR)

Surface chemistry of the coal samples was characterized by FTIR spectrometry using a Nicelet 6700 instrument (Thermo Fisher Scientific, USA). Samples for the measurement were prepared using the potassium bromide (KBr) pellet technique, where the powdered sample was mixed with KBr at 1:150. The spectral was recorded in the wavenumber region of 400 ∼ 4000 cm⁻¹ with a resolution of 4 cm⁻¹. The infrared spectral was disposed by Fourier calculation to distinguish the different types of surface functional group.

4.1.1 Mesopore analysis

Low-pressure adsorption–desorption N₂ isotherms at 77 K are presented in Fig. 1(a). As plotted in the figure, all the isotherms are type Ⅳ according to the IUPAC classification (Ladavos, 2012). Curve of this type is characteristic of porous solids with distribution of narrow and wide mesopores. In comparison, DL coal exhibits the highest affinity to N₂, followed by ZL, GY, and DT coals in sequence. Thus, the adsorption capacity of N₂ is considerably reduced with increasing coal rank. In addition, the isotherms are characterized by a conspicuous adsorption–desorption hysteresis loop within relative pressures above 0.45. The appearance of hysteresis loop implies that evaporation is not coinciding with condensation process, which is usually explained by the theory of capillary condensation (Ustinov, 2009). The shape of hysteresis loop for DL coal and GY coal agree with de Boer type B and may indicate the distribution of slit shaped pores, whereas ZL coal and DT coal exhibit type C hysteresis loop and may reflect the distribution of wedge-shaped pores (Boer and Lippens, 1964).

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Fig. 1

(a) N₂ adsorption–desorption isotherms at 77 K, and (b) mesopore size distribution of the samples.

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The mesopore size distribution calculated by BJH model is displayed in Fig. 1(b). It is apparent that all the curves exhibit multimodal distribution, indicating that the samples have continuous PSD at the mesopore scale. DL coal has the richest distribution of mesopore, with a prominent band at around 12 nm. The distribution of mesopore for ZL coal has a prominent band at around 41 nm, while GY coal and DT coal are subjected to prominent bands at around 44 nm.

The pore parameters determined by N₂ adsorption–desorption are summarized in Table 2. The BET surface area and the DFT total pore area of the coal samples are within the ranges of 0.586 ∼ 1.498 m²·g⁻¹ and 0.108 ∼ 0.764 m²·g⁻¹, respectively. Moreover, the DFT total pore volume and BJH adsorption pore volume are within the ranges of 1.607 ∼ 6.831 × 10^-3 cm³·g⁻¹ and 0.660 ∼ 2.267 × 10^-3 cm³·g⁻¹, respectively, while BJH average pore width is within the range of 10.92 ∼ 23.12 nm. In comparison, either BET surface area or pore volume is significantly reduced with an increase of coal rank. These observations confirm the finding of Okolo et al. (2015) that polycondensation reactions during the coalification process may lead to the translations of mesopores into micropores. This effect may significantly change the microstructure of coalbeds, leading to a decrease in mesopore volume for higher-ranked coals. Actually, N₂ molecule is not able to penetrate the microporosity of coal matrix due to the activated diffusion effect and pore shrinkage of coal at 77 K (Mastalerz et al., 2012; Erdogan and Kopac, 2019). As a result, the BET surface area and pore volume may be much lower than reality.

4.1.2 Micropore analysis

Low-pressure adsorption isotherms of CO₂ at 273 K are illustrated in Fig. 2(a). According to IUPAC classification, all the curves belong to type Ⅰ, where the characteristic of adsorption is restricted to monolayer (Mastalerz et al., 2008). Overall, the uptake capacity of CO₂ on each of the sample is much higher than N₂, which is correlated with the higher binding affinity of coal with CO₂ molecules than N₂ molecules (Zhao et al., 2016). Considering the coal rank, there is a poor association between CO₂ adsorption and coal maturity, where GY coal (low-volatile bituminous) is proved to be subjected to the highest CO₂ adsorption capacity.

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Fig. 2

(a) CO₂ adsorption isotherms on the coal samples at 273 K, and (b) micropore size distributions of the coal samples.

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The micropore size distribution estimated by DFT method is plotted in Fig. 2(b). Interestingly, DL, ZL and DT coals exhibit unimodal distribution with prominent bands at approximately 0.89 nm, 0.85 nm and 0.90 nm, respectively. To the contrary, GY coal exhibits multimodal distribution with prominent bands at approximately 0.60 nm, 0.75 nm, and 0.86 nm. These results confirm that a higher connectivity of micropore is expected for high-ranked coals compared to low-ranked coals, as a consequence of the conversion of closed-pore into open-pore porosity during the coalification process (Zhao et al., 2016).

The micropore parameters determined by CO₂ are shown in Table 3. As depicted in the table, the D–R SSA, D–A SSA and DFT total pore area are varied for different rank coals, ranging from 54.54 ∼ 222.42 m²·g⁻¹, 45.77 ∼ 160.87 m²·g⁻¹ and 33.48 ∼ 83.24 m²·g⁻¹, respectively. Interestingly, these values are much higher than that determined by N₂. This is because the measurement of CO₂ adsorption was conducted at a higher temperature (273 K), thus overcoming the restriction of activated diffusion for N₂ molecules (77 K), allowing CO₂ molecules to access the finest porosity (Guo et al., 2019). The micropore volume of GY coal (low-volatile bituminous) is larger than any other coal sample, suggesting that the pore system for this coal rank is less constricted among the coal samples.

4.1.3 Surface chemistry analysis

The surface chemistry of the coal samples determined by FTIR analysis is presented in Fig. 3, where each peak in the FTIR spectra represents a distinct type of surface functional group (Mastalerz et al., 2010). As depicted in Fig. 3, the coal samples are characterized by heterogeneous chemical properties containing multiple types of surface functional groups. Each of the curve exhibits a broad hydroxyl distribution with a prominent band at approximately 3450 cm⁻¹. This group is derived from the surface hydroxyls under the influence of adsorbed water molecules (Liu et al., 2018). The peaks at wave numbers of approximately 1600 cm⁻¹ is an indication of amide carbonyl group (–C = O), while the prominent bands at approximately 1000 cm⁻¹ are contributed to clays and mineral matter (Li et al., 2015). In comparison, DL coal (lignite) is characterized by stronger FTIR adsorption peaks than the other coal samples, suggesting that low-ranked coals possess higher density of surface functional groups than high-ranked coals.

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Fig. 3

FTIR spectra of the coal samples.

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4.2.1 Adsorption isotherms

The experiments of water vapor adsorption were performed at temperatures of 288, 298 and 308 K. The obtained adsorption isotherms are shown in Fig. 4. It is apparent that the profile of all the isotherms is very similar, corresponding to type Ⅱ of the IUPAC classification (Ladavos et al., 2012). Curves of this form are characteristics of carbonaceous materials with medium density of surface functional groups (Nishino, 2001). The isotherms reveal three separate regions, each of which is the indication of a specific adsorption mechanism. At relative pressures below 0.2, a rapid increase of uptake capacity is observed, due to the strong binding forces between water molecule and the surface functional groups. With the increase of relative pressure, the surface functional groups are gradually occupied and water molecule starts to interact with pre-adsorbed water molecules in the form of clusters. This is shown as linear increases in the middle part of the isotherms. At the final stage of the isotherm (p/p₀ greater than 0.6), there is a sudden increment in uptake capacity, which is related to the formation of larger clusters and capillary condensation (Li et al., 2019).

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Fig. 4

Water vapor adsorption isotherms and fitting of the modified BET model to the experimental data.

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Further, Fig. 4 shows that there is a negative correlation between water vapor uptake capacity and temperature, particularly at higher relative pressures. According to Horikawa et al. (2013), water molecule is subjected to higher kinetic energy at a higher temperature and is prone to be released from the adsorbed phase. The validity of this assumption is verified by the results of this study. Regarding coal rank, it is clear that the equilibrium uptake capacity of DL coal is the highest, followed by ZL, GY, and DT coals in sequence, thus pointing out that the affinity of coal matrix with water vapor is inversely proportional to the degree of coalification. According to Mccutcheon et al. (2001), this is because the number of surface functional groups decreases with the increasing coal maturity, leading to lower average bond energy between water molecules and coal matrix. Combining these results with porosity and surface chemistry analysis, it is inferred that surface chemistry is a dominant factor governing water vapor adsorption. Instead, only a portion of the pore volume is filled with water molecules even at the saturation pressure, which is shown as a sudden increment in water vapor uptake capacity as relative pressures larger than 0.6.

4.2.2 Modeling of the adsorption isotherms

A comparison between the experimental data and the fitting values with modified BET model is shown in Fig. 4, and the parameters under different experimental conditions are summarized in Table 4. Obviously, the modified BET model provides good fits to the experiment data with high correlation coefficients (R² greater than 0.99) in all the cases. Thereby, the modified BET model is applicable to the representation of water vapor adsorption data. As depicted in Table 4, the monolayer capacity (n₀) reduces with the increase of temperature, suggesting that the significance of primary sites decreases with temperature. This is in agreement with the existing studies (Do et al., 2009; Busch and Gensterblum, 2011; Švábová et al., 2011). Meanwhile, the calculated values of n₀ are decreased with coal rank, which is agree with the assumption that higher density of surface functional groups may promote the affinity of water molecule with coal (Arif et al., 2017). In comparison, energies of the primary sites (K₁) are around one magnitude larger than the secondary sites (K₂), indicating that the binding of coal-water needs more energy than the binding between water molecules.

4.3.1 Surface potential (Ω)

Fig. 5 illustrates the surface potential (Ω) of water vapor on the coal samples at elevated temperatures. Obviously, Ω is negative under all experimental conditions, and the calculated values of Ω are decreased with the increase of relative pressure. Ω represents a criterion of work needed to attain adsorption equilibrium, where the higher values of Ω may lead to the greater adsorptive capacities of water vapor (Song et al., 2017). Accordingly, the reduction of Ω with relative pressure can be explained by the fact that more isothermal work is required to load water molecules onto secondary sites than primary sites. In addition, the values of Ω are close to zero at the initial stages of water vapor adsorption. This is because the chemical potential of water molecules contacted with coal is equal to that uncontacted with coal at low surface coverage (Ridha and Webley, 2010).

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Fig. 5

Surface potentials of water vapor at elevated temperatures.

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According to Fig. 5, Ω exhibits a notable increase upon a temperature increase from 288 K to 308 K. This trend is consistent with decrease of water vapor uptake capacity with an increase in temperature. Therefore, higher temperature not only contributes to the loss of water vapor uptake capacity, but also lowers the work needed to attain equilibrium. Interestingly, there is a positive correlation between the surface potential of water vapor and coal rank. This observation may probably be ascribed to variations of surface chemistry and pore structure among different rank coals as addressed in Section 4.1. In coalification, the homogeneity of coal structure is gradually promoted, and therefore less work is required for the fluctuation of water molecules (Wang et al., 2014).

4.3.2 Gibbs free energy change (ΔG)

Gibbs free energy change (ΔG) represents the isothermal work required to load the molecules to a definite level under isobaric conditions, which can be used as a criterion for evaluating the spontaneity and equilibrium of adsorption (Zhou et al., 2011). The estimated ΔG of water vapor as a function of relative pressure is shown in Fig. 6. It is noticed that ΔG is negative in all cases, suggesting that water vapor adsorption is spontaneous under all the experimental conditions. ΔG first decreases with relative pressure, exhibiting minimum under medium relative pressures (p/p₀ = 0.3 ∼ 0.5), and then increases significantly at higher relative pressures. This parabolic behavior indicates that the interaction of water vapor with primary sites has a higher degree of spontaneity than that of secondary sites. According to Mofarahi and Bakhtyari (2015), the higher degree of spontaneity corresponds to screened active sites. Considering the coal rank, the estimated values of ΔG for higher-ranked coals are much larger than lower-ranked coals, indicating that water molecules need lower isothermal work to be loaded on higher-ranked coal than lower-ranked coal.

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Fig. 6

Gibbs free energy change of water vapor at different temperatures.

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4.3.3 Isosteric heat of adsorption (Q_st) and enthalpy change (ΔH)

Isosteric heat of adsorption Q_st (−ΔH, enthalpy change) is a significant parameter to reveal the interplay among gases or vapors and a porous system (Duan et al., 2016). The estimated isosteric heat of adsorption and entropy change is shown in Fig. 7. Interestingly, either Q_st or ΔH differs as a function of surface coverage in isothermal conditions. Indeed, the isosteric heat of adsorption uniformly decreased with an increase of surface coverage, indicating a high level of coal surface heterogeneity. This observation is in coincidence with the classification of primary and secondary sites adsorption as discussed in Section 4.2. Accordingly, the higher Q_st in lower surface coverage is attributed to the interaction of water molecules with primary sites, while the decreased Q_st in higher uptake stage may result from bonding of water molecules on secondary sites (i.e., on top of the previously adsorbed water molecules or within the hydrophobic pore). This result is agreed with the assumption that water molecules can form stronger bonds with primary sites than secondary sites.

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Fig. 7

Isosteric heat of adsorption and enthalpy change of water vapor.

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Fig. 7 shows that Q_st are within the range of 43 ∼ 75 kJ·mol⁻¹ for temperatures of 288 ∼ 308 K, which is larger than the heat of condensation (43.99 kJ·mol⁻¹ at 298 K), except for DL coal at high loadings (above 3.25 mmol·g⁻¹). In addition, isosteric heat of water vapor is larger than methane on a similar ranked coal, which is usually below 20 kJ·mol⁻¹ (Du et al., 2021). The observed discrepancy is considered to result from the formation of hydrogen bonds, which is much larger than van der Waals forces between non-polar molecules and inner pore space. Therefore, water molecules are subjected to higher affinity with surface functional groups, forcing methane molecules to adsorb on lower energy sites with the presence of water. Interestingly, the isosteric heat seems to be a function of the degree of coalification. This effect is observed particularly at the initial stage, where adsorption on primary sites is predominantly. As stated by Dang et al. (2017), surface functional groups are close to each other for lower-ranked coal, facilitating the formation of hydrogen bonds and water clusters.

4.3.4 Entropy change (ΔS)

Entropy is a criterion for evaluating the degree of irregularity or the rearrangement patterns of a thermodynamic system (Mofarahi and Bakhtyari, 2015). The entropy change (ΔS) represents the interactions of adsorbate − adsorbent and the restricted translation of the adsorbate molecules (Duan et al., 2016). The estimated ΔS as a function of water vapor uptake are shown in Fig. 8. It is noted that ΔS is negative under all the experimental conditions, suggesting that the distribution of water molecule is transmitted from a random state to a relatively ordered state in the process of adsorption. Thus, the adsorption water vapor creates a considerable reduction in the degree of freedom of the water-coal system, which is considered to be associated with the generation of more stable rearrangements on coal surface (Du et al., 2022). Nevertheless, there does not appear to be any significant increment in ΔS with the increase of temperature, indicating that a considerable amount of water molecules are trapped in the pore space as a free form instead of binding on coal surface.

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Fig. 8

Entropy change of water vapor at different temperature.

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The calculated ΔS vary from − 243.95 to − 137.16 J·(mol·K)^-1 for a temperature range of 288 ∼ 308 K. The values of ΔS increase significantly as water vapor uptake increases, indicating a higher level of heterogeneity of coal surface. This decline follows from the assumption that water molecules are only partly trapped in the pores, some three-dimensional translational entropy is still existed. Du et al. (2021) have reported that the entropy changes of methane adsorption on different rank coals are within the ranges of − 82 to − 87 J·(mol·K)^-1 and − 6.10 to − 62.5 J·(mol·K)^-1, respectively. In comparison, ΔS of water vapor is much smaller than methane, suggesting that the degree of irregularity of methane in coalbeds is much higher than water vapor. It is thus concluded that the binding force of water vapor with coal matrix is much stronger than methane, which may probably be derived from the stronger interaction of water molecules with surface functional groups.

4.4.1 Adsorption kinetic isotherms

For numerical modeling of adsorption kinetics, only the initial adsorption period was taken into account, where water vapor adsorbs at a higher rate (Liu et al., 2023). From unipore model (Eq. (10)), the estimated adsorption kinetic data at 288, 298, 308 K are plotted as function of time square for the initial stage of adsorption (V_t/V_∞<0.5), and the fitting results are depicted in Fig. 9. It is found that unipore model can provide good fits to water vapor adsorption kinetics with correlation coefficients (R²) exceed 0.99 in all the cases. The determined effective diffusivity (D/r_p²) and diffusion coefficient (D) are shown in Table 5. It is found that the estimated D/r_p² and D is around 10^-5 ∼ 10^-6 s⁻¹ and 10^-11 ∼ 10^-12 m²·s⁻¹, respectively, which is on the same order of magnitude with a previous study by Charrière and Behra (2010). The effective diffusivity of methane on different rank coals has been estimated at around 10^-4 s⁻¹ (Naveen et al., 2017). These are much higher than the values determined in the present study, which is partly attributed to the discrepancies of the equilibrium pressures of water vapor (0.34 ∼ 1.12 kPa) and methane (3.0 ∼ 8.0 MPa). In addition, the higher affinity between water molecules and coal matrix may be another influencing factor. In in-situ coal seam, a considerable amount of the pore space is filled with water molecules and the surface of coal becomes more hydrophilic (Charrière and Behra, 2010). Thereby, the presence of water may hinder methane molecules to the inner pore space of coalbeds, thus negatively affect the adsorption kinetics of methane.

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Fig. 9

Fitting results of adsorption kinetic data at different temperatures: (a) DL, (b) ZL, (c) GY, (d) DT.

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As depicted in Table 5, the values of both D/r_p² and D are increased with temperature. This can be explained in terms of molecular kinetics change of water molecules with temperature. As temperature increases, the kinetic energy of water molecule raises, and the frequency and amplitude of molecular vibration enhances. In this process, the strength of irregular thermal motion of water molecule is expanded, leading to higher adsorption kinetics (Du et al., 2022). With respect to coal rank, diffusion coefficient for DL coal is the largest, followed by ZL and DT and GY coals in sequence. Accordingly, diffusion coefficient is reduced with coal rank. This trend is in good agreement with the change of surface functional group density with coal rank, but it is difficult to find any correlation between diffusion coefficients and pore structure. Therefore, surface chemistry may probably be the leading factor for water vapor adsorption kinetics under the operating pressure (p/p₀ = 0.2).

4.4.2 Diffusion activation energy (E_a)

From Arrhenius law (Eq. (12)), diffusion coefficients of water vapor ln (D) were plotted as function of 1/T. The fitting process is described in Fig. 10, and the estimated diffusion activation energy E_a are plotted in Table 6. Obviously, Arrhenius law fits the adsorption kinetic data well with the R² values all larger than 0.90. Diffusion activation energy E_a for ZL coal is larger than the other coals, indicating that the movement of water molecules within the pore space of ZL coal needs to overcome a higher potential barrier. Charrière et al. (2010) have reported that E_a is governed by kinetic diameter of gas molecule, pore morphology, and surface coverage. Therefore, it is reasonable to assume that the morphology of the pore system in ZL coal (high-volatile bituminous) is more complex and less inter-connected than the other rank of coals.

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Fig. 10

Estimation of the diffusion activation energy E_a using Arrhenius law.

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