Water saturation characteristics of coal of different ranks and its effect on capillary pressure

Saturation characteristics of water and capillary pressure are important for hydrofracturing or water flooding, which is widely adopted in dust suppression, methane displacement, and gas and coal outburst elimination. In this paper, we have studied the water saturation characteristics of coal samples with different coal ranks and their effect on capillary pressure. It was found that the isothermal adsorption of water vapor from coal samples can be divided into three processes: monolayer adsorption, multilayer adsorption, and capillary condensation. The dent isothermal adsorption model can well describe water vapor adsorption of coal samples, indicating water molecules were first adsorbed on the first‐order adsorption site of pore surfaces at low relative humidity and then on the second‐order adsorption site with increasing relative humidity. An obvious hysteresis occurred in the process of water imbibition and drainage. A capillary pressure of ~325 MPa or even larger was required to displace the water from the coal. Besides, micro‐ and mesopores play a more important role in capillary pressure. The capillary pressure of coal samples was positively correlated with wettability at lower water saturation, but it is not significant at higher capillary pressures. Therefore, the article's results provide a new direction for solving the water‐locking effect in coal seams.


| INTRODUCTION
Coalbed methane is a type of natural clean energy with high combustion energy and low air pollution.With the increase of coal mining depth, the efficient recovery of coalbed methane is the focus of current research. 1Accurate prediction of gas content is a necessary technology to improve methane extraction and provides a reasonable technical of gas disaster prevention. 2 However, enhanced coalbed methane recovery (ECBM) technology is the main way to improve recovery rate, such as hydrofracturing, water flooding, hydroslotting, deep-hole blasting, and CO 2 -ECBM.Recently, a promising waterless technique (liquid nitrogen fracturing) was proposed by Longinos et al. [3][4][5][6] Among these, hydrofracturing or water flooding involving water injection into coal seams is still widely adopted. 7,8The injected water diffuses in coal cracks or fractures.Then, it is adsorbed on pore surface and drastically affected by the wettability and capillary pressure.The injected water is the wetting phase, whereas in situ coalbed methane is the nonwetting phase.Capillary pressure not only exists in the water injection process but also in the subsequent gas drainage process. 9Methane cannot sweep away water in the pores and fractures until the capillary pressure exceeds a threshold value and then migrates to coal seam boreholes.
Water in coal primarily exists in the form of free water, adsorbed water, and crystalline water.Free water exists in coal fractures, [10][11][12][13][14] while adsorbed water exists in pore and fracture surfaces and crystalline water exists in coal body. 15,16When water enters into coal fractures or pores, a three-phase interface (coal-water-methane) is formed.The complex interactions among the three phases will disturb the equilibrium state of gas adsorption, affecting methane desorption and diffusion in coal.The methane adsorption and desorption capacity are closely related to porosity and critical pore scale. 17The larger the porosity, the larger the desorption rate.Feng et al. found that methane adsorption capacity of coal is controlled by micropores and transition pores and also affected by fractal dimension (D n ). 18Additionally, the effect of moisture on methane desorption of different rank coal is also determined by pore structure. 19Negative pressure is an important factor in gas extraction and is key in controlling methane recovery rate. 20revious studies have reported that functional groups of coal can significantly affect water adsorption.Nishino found that the equilibrium water content of different coals was proportional to the carboxyl group content of coal; the larger the carboxyl group content, the greater the equilibrium water content of coal. 21Prinz et al. reported that the water absorption capacity of low-rank coal under a low relative pressure was primarily affected by oxygencontaining functional groups, and the water vapor adsorption capacity was also affected by coal rank. 22Besides, the equilibrium water content of coal first decreases and then increases with the increase of coal rank.Švábová et al. found that the water adsorption volume of coal is linearly correlated with the total amount of hydroxyl and carboxyl groups (with a correlation coefficient of 0.998). 235][26] Arendt et al. found that fluid diffusion in porous media is influenced by the interfacial tension, capillary pressure, and wettability. 27Meanwhile, the capillary pressure is affected by permeability, pore structure, wettability, and other factors of coal or rock. 28,291][32] Yassin et al. found that capillary pressure is significantly affected by reservoir wettability and microscopic pore structure. 33Besides, various scholars have found a close relationship between coal ranks and the wettability of coal seams and capillary pressure. 34,35herefore, the study of capillary pressure is highly significant for improving the gas or oil recovery rate. 36revious studies also extensively discussed the relationship between P c and S W (P c , capillary pressure, S W , saturation of water). 37,38Tokunaga et al. experimentally obtained the equilibrium relationship between the full range of water saturation and capillary pressure of shale by using the water vapor adsorption and pressure plate methods and found that the water receding curve of shale had considerable hysteresis; and the capillary pressure of shale can often reach several hundred MPa. 39Ma et al. found that the capillary pressure of shale with low permeability can reach hundreds of MPa, and the high capillary pressure is why the shale water cannot easily drain out of the shale.Meanwhile, interbedded water affects gas extraction. 40enerally, the in situ water content of coal is low, so the effect of water on methane recovery (or gas drainage) is not significant and ignored, and water saturation characteristics and capillary pressure of coal have rarely been studied in the past.However, with the wide application of hydraulic fracturing and water flooding in coal mines in recent years, water saturation characteristics and capillary pressure of coal have a significant impact on water injection.The water saturation capacity of coal determines how much water the coal can absorb, and the capillary force determines the migration capacity of water and methane in coal, which eventually affects the effectiveness of water injection and gas extraction.In this study, we discussed the water saturation characteristics of coal with different ranks and its effect on capillary pressure.

| Coal sample location distribution
Coal samples used in our experiments were collected from three different coal mines, that is, Jinmei Group Changping Company (CP), Pingmei No.4 mine (PM), and Xiadian Coal Mine (XD), locations of which are shown in Figure 1.The CP company is roughly located in the middle of Jincheng City and Changzhi City in Shanxi Province.The PM is located in Pingdingshan City, Henan Province, and XD is also located in Ruzou county belonging to Pingdingshan City, Henan Province.Proximate and ultimate results of these coal samples are given in Table 1.

| Pore structure measurement
Pore distribution of coal sample was characterized by lowtemperature nitrogen adsorption method and highpressure mercury intrusion method which are widely used in determining pore distribution of coal.Test equipment for low-temperature nitrogen adsorption method was an automatic specific surface analyzer (Sorb 4800S).An automatic mercury intrusion meter (IV 9500; McMuritik Co., Ltd.) was used for high-pressure mercury intrusion method.Coal samples were oven-dried at 105°C for 24 h to remove intrinsic and extrinsic moisture.Drying procedure may affect pore structure of materials.The selected drying temperature (105°C) and time in the present work were considered to be most suitable for coal. 41,42

| Fourier-transform infrared spectroscopy
An infrared spectrometer (Bruker VERTEX 80v) was used to measure surface functional groups of coal samples.The instrument provides a resolution better than 0.2 cm −1 of calibration point spectra.

| Wettability
Wettability is an important factor affecting water saturation and capillary pressure.Sharifigaliuk et al. compared conventional methods (contact angle, spontaneous imbibition, and floatation) for the evaluation of wettability in shales and found that the order of reliability of the conventional techniques is spontaneous imbibition > contact angle > floatation. 43Usually, contact angle is mostly used to evaluate wettability of coal by sessile, pendant, or captive drop method. 44In the present work, the contact angle of coal sample was measured by sessile drop method using a standard contact angle measuring instrument (KRUSS).The contact angles were calculated using an open-source program Image J. 45 There are two ways to prepare samples for measuring contact angles, that is, discs compressed from coal powder and slices cut from large coal blocks. 44Compressed discs may change compositions and structures of coal surface, affecting measurement results.Therefore, coal slices were used in our experiments.The slices were carefully polished and cleaned before experiment.

| Experiment procedure
To maintain integrity of microporous structures of coal samples and make them reach isothermal adsorption equilibrium faster, three coal samples with different ranks were crushed to 60-80 mesh in our experiments.The schematic and photograph of the experimental setup are shown in Figure 2.
Experiment procedures were as follows: 1. Coal samples (~10 g) were put into flasks and dried in a constant temperature oven at 110°C for 24 h. 2.Then, flasks were sealed and placed in a desiccator with desiccant.Coal samples were cooled to experimental temperature and weighed on an electric balance with an accuracy of 0.1 mg.

Put flasks into another desiccator with saturated
inorganic salt solution at the bottom.The desiccator was placed in an incubator setting at the experimental temperature.4. Weigh coal samples every 8 h, and flasks were kept sealed during the process.Then, put coal samples immediately back into the incubator.

Water vapor adsorption of coal sample reaches
equilibrium when variation of coal sample weight is less than 10 mg.Change saturated inorganic salt solution in the desiccator and repeat steps (3) to (4).
Seven different saturated inorganic salt solutions were used in our experiments, including LiCl, MgCl 2 ,  | 2075 NaBr, NaCl, KBr, KCl, and K 2 SO 4 , with relative humidity ranging from 0.11 to 0.97.The relative humidity and its corresponding capillary pressure were calculated 39 and given in Table 2.

| Isothermal adsorption model
Isotherm model indicates equilibrium relationship between adsorbed amount and pressure of adsorbate at a constant temperature and provides information on pore structure and adsorption capacity of porous materials. 46,47uitable isothermal adsorption model helps to understand the adsorption mechanism of water vapor in coal samples.
There are various models used to fit isothermal water adsorption of rock, such as Langmuir, Brunauer-Emmett-Teller (BET), Dubinin-Serpinsky (DS), D'Arcy-Watt (DW), Guggenheim-Anderson-de Boer (GAB), double log polynomial, Frenkel−Halsey−Hill, and Dent. 48,49Previous studies indicate that GAB and Dent model perform well for water vapor adsorption in shales. 50onsidering inorganic and organic composition and pore structure of coal is different from those of shale, we selected Langmuir, Freundlich, improved GAB, DW, and Dent model to describe water adsorption behavior of coal and tried to find a most suitable model for coal.

Langmuir model
Langmuir model is the most widely used model to describe adsorption equilibrium based on monolayer filling of noninteracting molecules. 51It assumes that each adsorption site has only one adsorbent molecule and pore surface is uniformly adsorbed.Adsorption equation is as follows: where q is adsorption capacity of coal sample (cm 3 /g); a 1 and b 1 are the adsorption constants, and p is relative pressure.

Freundlich isotherm
This model is an isothermal adsorption equation proposed by Freundlich, which considers that adsorbent surface is not uniform and adsorption force on the adsorbent molecules are not the same. 52The adsorption equation was as follows: It can be transformed to where a 2 and b 2 are adsorption constants.

Improved GAB isotherm
Based on Langmuir single-molecule adsorption and BET multimolecule adsorption, Anderson and Hall proposed the GAB isothermal adsorption model and introduced new parameters based on the GAB model, 53 which can describe multilayer adsorption phenomenon.The adsorption equation is as follows: where a 4 and b 4 are adsorption constants and c and d are the introduced parameters.

DW isotherm
This model is used to describe the monolayer and multilayer adsorption phenomena of adsorbates on the oxidized surface of the adsorbent. 54The adsorption equation was as follows: where a 4 , b 4 , c 2 , and d 2 are adsorption constants.

Dent isotherm
The model distinguishes two adsorption types: one that occurs at the first-order adsorption site and the other is that water molecules can combine with water molecules on the first-order adsorption site to form the second-order adsorption site, and can also combine with water molecules on the formed second-order adsorption site.The model assumes that the properties of water molecules in each second-order adsorption layer (i.e., the second, third, and fourth layers) are identical. 55The adsorption equation was as follows: where a 5 is the adsorption constant, b 5 is the adsorption constant with respect to the adsorption capacity at the first-order adsorption sites, and c 3 is the adsorption constant which correlates with the adsorption capacity of the second-order adsorption sites.

| Pressure plate imbibition-drainage curve test
The pressure plate method was used to measure water imbibition-drainage of coal sample according to the standard of the American Society for Testing and Materials. 56igure 3 shows schematic of the experimental setup.The experimental setup consisted of an ISCO pump, a porous ceramic plate, a constant temperature incubator, and gas pipelines.Besides, crushed samples were used in our experiments.
Capillary pressure refers to the pressure difference between the two sides of the curved interface of a twophase immiscible solution (such as oil and water) in a capillary tube, and the direction is toward the concave surface of the interface.The calculation formula is as follows: where θ is contact angle (°), σ is surface tension of bulk liquid adsorbate (N/m), and r is the capillary radius (nm).The capillary pressure measurement method is based on the Kelvin equation, 57 which can also be used to explain capillary condensation and is expressed as follows: where p/p 0 is relative pressure, T is isothermal temperature, V r is molar volume of bulk liquid adsorbate (mL), and R is the ideal gas constant.
Combining with the Laplace equation, capillary pressure can be expressed as where P c is the capillary pressure in the porous medium, MPa.| 2077 curves showed slightly upward trends at low relative pressure (0-0.5)."Hysteresis loop" arose at a higher relative pressure (0.5-0.99).Adsorption-desorption curves indicate that the PM coal sample contained many impermeable pores with one end closed and few inkbottle pores.XD and CP coal samples contained various open holes and ink-bottle pores.BJH (Barrett, Joyner, and Halenda) method was used to calculate pore volumes and specific surface areas of the coal samples, as shown in Figure 5.According to IUPAC recommendation, the classification of pores is as follows 58,59 : (i) pores with widths exceeding about 50 nm are called macropores; (ii) pores of widths between 2 and 50 nm are called mesopores; (iii) pores with widths not exceeding about 2 nm are called micropores.
In the present work, the pore volumes and specific surface areas of the three coal samples were primarily distributed in the mesopore range; the pores of the PM coal sample were distributed in the mesopore or even macropore range, and the micropore development was more obvious than that of the XD and CP coal samples.
Figure 6 gives mercury injection curves of three coal samples.Mercury intrusion and withdrawal curves have obvious hysteresis loops.Pressure-dependent cumulative volume of CP and XD coal sample increased slowly in the range of macropores and sharply in the range of mesopore, pinhole, and micropore, indicating that CP and XD coal sample contain more mesopores, pinholes and micropores.Meanwhile, CP and XD coal samples have larger "hysteresis loops," indicating that the connectivity between macropores and mesopores is better than that between pinholes and micropores, and XD coal sample has larger "hysteresis loop," which indicates that it has more open pores.The inflection point of injection mercury curve of the PM coal sample is relatively earlier in the range of the macropore curve, indicating that PM coal sample contains more macropores, and the area of the "hysteresis loop" is smaller, which shows that it contains more semiclosed pores and closed pores.Therefore, it can be derived that CP and XD coal samples contain more mesopores, pinholes, and micropores, and fewer macropores, and the connectivity between macropores and mesopores is better than that between pinholes and micropores; PM coal sample contain more macropores and semi-closed and closed pores.

| Water vapor adsorption and desorption isotherms
Figure 7 shows relationship between equilibrium water content and relative humidity of coal samples with different ranks.Isothermal adsorption of water vapor of coal samples can be divided into three processes: monolayer adsorption, monolayer adsorption to multilayer adsorption, and capillary condensation (schematic of the three stages is given in Figure 7B).water molecules in the internal pores of coal samples formed aquariums with each other, which resulted in an increase in water adsorption volume.
Figure 8 shows water vapor adsorption and desorption isotherms of different coal samples.There are differences in the water content of coal samples of different coal ranks at different relative humidity.The water content of PM coal sample is the highest, which is primarily related to its largest pore volume and specific surface area as mentioned above.Meanwhile, water contact angle of PM coal sample was smallest, indicating the strongest wettability among three coal samples | 2079 (Figure 8B).CP coal sample with the lowest wettability had the smallest pore volume and surface area.
Figure 8C shows the Fourier-transform infrared (FTIR) spectra of different coal samples.Ratios of the fitted areas of the fractional peaks of various functional groups in the hydroxyl band of three coal samples are listed in Table 3.Previous studies have found that the adsorption of water molecules in coal pores is mainly subject to functional groups (especially hydroxyl and carboxyl groups). 60The phenolic hydroxyl group has a greater effect on water adsorption capacity, whereas the alcohol hydroxyl group, intermolecular hydrogen bond, and free hydroxyl group have a smaller effect on the adsorption of water molecules.As shown in Figure 8C, CP and XD coal samples contained more oxygen-containing functional groups.PM coal sample had more phenolic hydroxyl groups, and CP coal sample had more alcohol hydroxyl groups.In addition, PM coal sample contained a certain amount of carboxyl groups and a large number of C=O and C-O functional groups, whereas XD and CP coal samples had no carboxyl groups.PM coal sample indicates strongest water absorption capacity, followed by XD and CP coal samples.

| Adsorption models
To further understand the mechanism of water vapor adsorption on the pore surface, adsorption isothermal data of coal samples were fitted using the isothermal adsorption model described above, as shown in Figure 9. Fitted parameters are listed in Table 4. Fitting curves by the Langmuir model are not given, owing to poor fitting accuracy.Figure 9 indicates that the fitting results of PM coal sample using the improved GAB model is poor at low relative pressures (0-0.11),whereas the fitting results of XD and CP coal samples using the Freundlich model are poor compared with those of other models.DW and Dent models demonstrated the optimum fitting accuracy for all coal samples.In addition, the Dent model can be used to reveal the first and second adsorption site energies on the pore surface, 50,61,62 which can better understand the water vapor adsorption pattern of the coal samples.As mentioned above, for Dent model, b 5 and c 3 indicate adsorption capacities at the first-and the secondorder adsorption sites, respectively.It can be concluded from Table 4 that adsorption capacities at the first-order adsorption sites are larger than those at the second-order adsorption sites, indicating that the adsorption energy at the first-order adsorption site was larger.Wan et al. calculated thermodynamic parameters of water vapor adsorption on coal and found that coal sample had a larger adsorption energy for first-order adsorption, 60 indicating that the potential energy of water molecules at the first-order adsorption site was much greater than that at the second-order adsorption site.
Based on fitting results of the adsorption site constants b 5 and c 3 , the adsorption volume at the first and second adsorption sites can be calculated using Equations ( 10) and ( 11 (10) where q 1 and q 2 are the moisture adsorption capacities at the first-and second-order adsorption sites of the coal sample, respectively (mg/g).
Figure 10 shows adsorption capacity at the first-and second-order adsorption sites under different relative humidity.Water molecules were first adsorbed at the first-order adsorption site of the pore surface at low relative humidity and then at the second-order adsorption site with the increase in relative humidity.For CP and XD coal samples, the water vapor adsorption capacity at the first-order adsorption site turned to be constant when the relative humidity was larger than 0.6.At the same time, it kept increasing for the PM coal sample owing to its larger specific surface area and pore volume.When the relative humidity is greater than 0.6, the adsorption capacity at the second-order adsorption site increased sharply for all coal samples.Additionally, the water vapor adsorption capacity of the PM coal sample was largest and that of CP coal sample was smallest, which is owing to the differences in the specific surface area of coal samples.

| Capillary pressure
Different water vapor adsorption capacities (or water contents) under different relative humidity led to differences in water saturation in pore systems, which affects the capillary pressure. 64igure 11 shows a relationship between water content (water/coal) and capillary pressure.Water content of the PM coal sample was largest under the same capillary pressure owing to highest specific surface area of microand mesopores (Figure 11B).Water content of the XD coal sample was slightly higher than that of the CP coal sample, but the difference in water content of these two coal samples was not significant due to similar specific surface area (Figure 11B).It is interesting that the CP coal sample had largest specific surface area of macropores (Figure 11C) but lowest water content, indicating that micro-and mesopores play a more important role in capillary pressure.Besides, imbibition and drainage curves of coal samples show obvious hysteresis.
Figure 12 shows the relationship between water saturation and capillary pressure.When the capillary pressure was less than 5 MPa, the water saturation of coal samples changed slightly.When the capillary pressure was above 5 MPa, the water saturation decreased significantly, indicating that a larger capillary pressure was required to displace water from coal pores.A driving force of ~325 MPa or even larger was required to completely displace adsorbed water.Tokunaga et al. found that a high capillary pressure of more than several hundred MPa is required to displace the water from the shale. 39Due to the low permeability of coal seams, the displacement water in coal is limited, resulting in "water lock effect." Additionally, under capillary pressure, the water saturation of PM coal sample was highest, while the water saturation of CP sample was the lowest.As mentioned above, pore distribution of PM sample was primarily concentrated in the range of micropores, and the average pore diameter of coal was small in this pore range, that the micropore diameter of the coal is critical the magnitude of capillary pressure in the low water range.6][67] In the range of low water saturation, capillary pressures of the coal samples were in positive correlation with the wettability.However, there is no positive correlation between capillary pressure and wettability of coal samples when water saturation is larger.

| CONCLUSIONS
Water vapor saturation characteristics and capillary pressure are important parameters for hydrofracturing or water flooding.In the present work, we experimentally investigated water imbibition-drainage characteristics under different relative humidity using water vapor adsorption and pressure plate method.At a low relative humidity (0-0.11), the water content of the coal samples increased linearly with the relative humidity.When the relative humidity is larger than 0.56, the water molecules formed water clusters and the water adsorbed volume increased rapidly.
Dent isothermal adsorption model can well describe water vapor adsorption of coal, indicating water molecules were first adsorbed on the first-order adsorption site of pore surfaces at low relative humidity and then on the second-order adsorption site with increasing relative humidity.An obvious hysteresis occurred in the process of water imbibition and drainage.A ~325 MPa or even higher driving force is required to displace the water from the coal.Micro-and mesopores play a more important role in capillary pressure.Capillary pressures of coal samples were positively correlated with wettability at lower water saturation, but were not significant at higher capillary pressure.
Coal is a type of porous media with many micro-and mesopores and has large capillary pressure.Capillary pressure can affect water injection and methane recovery.The effect of capillary pressure of coal on water injection and drainage needs to be further studied, which is more practical to improve methane recovery performance.

NOMENCLATURE
A d ash content of coal on a dry basis a i , b i , c i , d i adsorption constants C daf weight percent carbon on a dry, ash-free basis F cd fixed carbon content of coal H daf weight percent hydrogen on a dry, ash-free basis M ad moisture content of coal on air dry basis N daf weight percent nitrogen on a dry, ash-free basis O daf weight percent oxygen on a dry, ash-free basis p relative pressure p/p 0 relative pressure P c capillary pressure in porous medium q adsorption capacity of coal sample (cm 3 /g) q 1 , q 2 moisture adsorption capacities at the first-and second-order adsorption sites of the coal sample r capillary radius R ideal gas constant R 0 mean vitrinite reflectance S daf weight percent sulfur on a dry, ash-free basis T isothermal temperature V daf volatile matter content of coal on a dry, ash-free basis V r molar volume of bulk liquid adsorbate θ contact angle σ surface tension of bulk liquid adsorbate

F I G U R E 2
Schematic and photograph of the experiment setup.(A) Schematic.(B) Photogragh.LIANG ET AL.

3 | RESULTS AND DISCUSSION 3 . 1 |
Coal characterization 3.1.1| Pore distribution The results of the low-temperature liquid nitrogen experiments are given in Figure 4. Adsorption and desorption F I G U R E 3 Schematic of the experiment setup.LIANG ET AL.

F I G U R E 6
Mercury injection curves of coal samples.CP, Jinmei Group Changping Company; PM, Pingmei No.4 mine; XD, Xiadian Coal Mine.(A) (B) F I G U R E 7 Relationship between equilibrium water content and relative humidity of coal sample.(A) Water content under different relative humidity, I: monolayer adsorption, II: monolayer to multilayer adsorption, III: capillary coalescence.(B) Schematic of water adsorption at different stages (e.g., I, Ⅱ, Ⅲ from top to bottom).

F
I G U R E 11 Relationship between water content and capillary pressure.(A) Water content versus capillary pressure, (B) specific surface area measured by low-temperature nitrogen adsorption method, and (C) specific surface area measured by high-pressure mercury intrusion method.CP, Jinmei Group Changping Company; GAB, Guggenheim-Anderson-de Boer; PM, Pingmei No.4 mine; XD, Xiadian Coal Mine.F I G U R E 12 Relationship between water saturation and capillary pressure.CP, Jinmei Group Changping Company; PM, Pingmei No.4 mine; XD, Xiadian Coal Mine.
Proximate results and composite of coal samples.
Equilibrium relative humidity of coal samples (30°C), and the corresponding capillary pressure.
T A B L E 2 Ratios of fitting areas of various functional groups in hydroxyl band.Fitting parameters of different adsorption models.