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. 2020 Dec 29;6(1):702–714. doi: 10.1021/acsomega.0c05236

Study for the Effect of Temperature on Methane Desorption Based on Thermodynamics and Kinetics

Zheng Gao †, Dongmin Ma †,‡,§,*, Yue Chen †, Chao Zheng †, Jinxiang Teng †
PMCID: PMC7807784  PMID: 33458523

Abstract

graphic file with name ao0c05236_0016.jpg

Desorption hysteresis is important for primary gas production. Temperature may cause serious changes in the methane adsorption/desorption behaviors. In order to study the mechanism of methane desorption and desorption hysteresis, three sets of samples of long-flame coal, coking coal, and anthracite were collected, and experiments such as microscopic composition determination, liquid nitrogen adsorption, and isothermal adsorption/desorption were performed. From the perspectives of desorption kinetics, desorption thermodynamics, and methane occurrence state, the differences in methane and methane desorption characteristics and the desorption hysteresis mechanism are discussed. The results show that at the same temperature, anthracite (SH3#) has the largest saturated adsorption capacity and residual adsorption capacity, followed by coking coal (SGZ11#), and long-flame coal (DFS4#) has the smallest. As the temperature increases, the theoretical desorption rate and residual adsorption capacity of anthracite (SH3#) and coking coal (SGZ11#) will increase first and then decrease. Temperature and methane desorption do have positive effects, but temperature may have a threshold for promoting methane desorption. It is necessary to comprehensively consider the influence of temperature on the activation of gas molecules and the pore structure of coal. Under the premise of a certain temperature, as the pressure increases, the desorption hysteresis rate changes in a logarithmic downward trend, the methane desorption hysteresis rate in the low-pressure stage (P < 4 MPa) is large, and the methane desorption hysteresis rate in the high-pressure stage (P > 4 MPa) is lower; during the isobaric adsorption process, the adsorption capacity of anthracite (SH3#) increases the fastest, followed by SGZ11#, and that of DFS4# is the smallest. In the low-pressure stage (P < 4 MPa), the adsorption capacity increases significantly with the increase in pressure, but in the high-pressure stage (P > 4 MPa), the adsorption capacity does not change significantly with pressure, instead gradually stabilizes. Under the same pressure, the molecular free path of methane increases with temperature. Under the premise of constant temperature, in the low-pressure stage (0 < P < 4 MPa), when the pressure continues to decrease, the free path of methane molecules increases significantly, resulting in a decrease in diffusion capacity. In the high-pressure stage (4 < P < 8 MPa), when the pressure continues to decrease, the free path of methane molecules does not change significantly; the sample desorption process of three sets of samples DFS4#, SGZ11#, and SH3# occurs, and the intermediate adsorption heat is greater than the isometric adsorption heat during the adsorption process, indicating that the desorption process needs to continuously absorb heat from outside the system. The energy difference produced in the process of adsorption and desorption causes the desorption hysteresis effect. The greater the difference in the isometric heat value of adsorption, the more significant the hysteresis is.

1. Introduction

China’s CBM resources account for roughly one-third of the low-, medium-, and high-rank coals.1 The study of coalbed methane adsorption/desorption is of great significance to the development of coalbed methane. Experimental studies have shown that coalbed methane adsorption has many influencing factors including coal rank, temperature, pressure, particle size, moisture content, pore structure, and so forth.2−4 The desorption hysteresis phenomenon is the gap between the desorption curve and the adsorption curve during the adsorption/desorption process.5−8 In the past few decades, a large number of literature has been reported on CH4 sorption on coal, among which a considerable amount of literature indicate that there is a desorption hysteresis in the process of methane desorption.9−11 In engineering practice, the mining of coalbed methane is mainly a desorption process, so it is necessary to focus on the problem of coalbed methane desorption and the essence of desorption hysteresis. Among them, temperature is an important factor in the adsorption, desorption, and seepage of methane in coal reservoirs.

The ability of coal to adsorb methane is greatly affected by temperature. In recent years, many researchers have conducted studies on temperature-dependent adsorption, but we still have not reached a comprehensive conclusion.12 It is basically agreed that the methane adsorption capacity in coal decreases with increasing temperature,13−16 but based on the temperature effect, there are few reports on analyzing the hysteresis of methane desorption from the perspective of thermodynamics and kinetics. Some researchers believe that the hysteresis of desorption is due to the fact that methane molecules enter the micropores with poor connectivity under high pressure and cause pore deformation. The methane molecules retained in the micropores cannot be desorbed from the pores because of the narrowing of the pore throat channels.7,17,18 There are also studies that suggest that pore deformation is not the main factor causing desorption hysteresis, and the solution phase of gas may be the primary factor.19 In addition, the hysteresis of gas adsorption may also be due to gas molecules forming gas clusters in the mesopores.20 In addition, some researchers believe that the water in the pores of coal also plays an important role in preventing methane desorption.21−23 Predecessors have carried out a lot of work on the influencing factors of methane adsorption/desorption. To date, the methane-coal sorption hysteresis has become a common observation, yet it remains difficult to explain. However, based on the principle of thermodynamics, there are few reports on the study of temperature on the desorption mechanism and desorption hysteresis of methane.

In this paper, coal samples with different levels of metamorphism are the research objects, including long-flame coal (Dafosi 4# coal), coking coal (Shanggaozhai 11# coal), and anthracite (Sihe 3# coal). By studying the material composition, pore structure, and adsorption/desorption characteristics of coal samples, a comprehensive analysis of the difference in adsorption/desorption characteristics and the desorption hysteresis effect from various aspects such as isotherm adsorption, isobaric adsorption, desorption kinetics, desorption thermodynamics, methane occurrence state, and so forth is carried out. We tried to reveal the nature of desorption hysteresis from the energy point of view, hoping to provide a theoretical reference for coalbed methane development.

2. Results and Discussion

2.1. Pore Characteristics

The results of the liquid nitrogen adsorption experiment are shown in Table 1 and Figure 1. The specific surface area of DFS4# is the largest, SH3# is the second, and SGZ11# is the smallest, indicating that the coal rank increases and the specific surface area first decreases and then increases.

Table 1. Liquid Nitrogen Adsorption Results.

    specific surface area ratio of each aperture section/%
   pore volume ratio of each diameter section/%
sample specific surface area (m2/g) <10 nm 10–100 nm >100 nm pore volume (mL/g) <10 nm 10–100 nm >100 nm
DFS4# 11.46 90.51 9.25 0.24 0.019 47.47 43.37 9.16
SGZ11# 0.34 81.51 17.58 0.91 0.001 30.00 54.00 16.00
SH3# 2.04 95.30 4.66 0.04 0.002 67.61 26.72 5.67
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Figure 1.

Figure 1

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Isothermal adsorption curve of liquid nitrogen (a) DFS4#, (b) SGZ11#, and (c) SH3#.

Analyzing the characteristics of the liquid nitrogen adsorption/desorption curves of the three samples shows that the desorption curve of DFS4# coal is obviously higher than the adsorption curve, and the hysteresis loop is obvious. When the relative pressure is low (0 < P/P0 < 0.5), the adsorption curves and the desorption basically coincide, and the inflection point appears when the relative pressure P/P0 is 0.5, indicating that there is a cylindrical hole with one end open and a certain amount of ink bottle holes. The adsorption and desorption curves of SGZ11# are close to parallel, the hysteresis loop is small, and there is no obvious inflection point when the relative pressure is 0.5, indicating that the pores are dominated by slit flat pores, which is beneficial to the desorption and diffusion of coalbed methane. The adsorption and desorption curves of SH3# coal are similar. After the relative pressure is less than 0.9 to 0.1, there is no closed point, and the inflection point is not obvious. The pore type is mainly slit-shaped pores, and there are also a small number of open pores.

The FHH equation is used to indirectly calculate the fractal dimension of pores,24,25 and the formula is as follows

2.1. 1

where V is the volume of gas adsorbed at equilibrium pressure p, cm3/g; V0 is the volume of gas adsorbed by the monolayer, cm3/g; p0 is the saturated vapor pressure of gas adsorption, MPa; p is the equilibrium pressure of gas adsorption, MPa; A is the slope under the relationship curve of ln(V/V0) and ln(ln(p0/p)), which depends on the fractal dimension of the sample; and B is a constant, fractal dimension

2.1. 2

The calculation uses liquid nitrogen desorption data. Because the molar free energy change caused by desorption is smaller than the adsorption process, the adsorption state corresponding to the desorption process is more stable. In addition, the adsorption mechanism of methane in the micropores is different in different pressure sections. In the low-pressure section (0 < P/P0 < 0.5), nitrogen is adsorbed on the micropores. The force between gas molecules and coal molecules is mainly van der Waals force, while in the high-pressure section (0.5 < P/P0 < 1), nitrogen is mainly adsorbed on mesopores and macropores, mainly by capillary aggregation.

Therefore, in order to characterize different pore structures, it is necessary to calculate the fractal dimensions in sections, namely, the low-pressure section (0 < P/P0 < 0.5) fractal dimension D1 and the high-pressure section fractal dimension D2 (Figure 2 and Table 2). The pore fractal dimension D1 values of low, medium, and high coal rank samples are 2.29, 2.35, and 2.27, respectively, which change in an inverted “V” shape with the increase in coal rank. The D2 values are 2.75, 2.65, and 2.89, respectively, which vary with coal rank. In contrast to D1, during the process of surface coalification, the changes in coal pore surface properties and pore structure are not linear, but fluctuating.

Figure 2.

Figure 2

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FHH fractal model curves of different coal samples (a) DFS4#, (b) SGZ11#, and (c) SH3#.

Table 2. FHH Fractal Dimension of Different Coal Samples.

sample A1 D1 = A1 + 3 A2 D2 = A2 + 3
DFS4# –0.71 2.29 –0.25 2.75
SGZ11# –0.65 2.35 –0.35 2.65
SH3# –0.73 2.27 –0.11 2.89
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2.2. Adsorption/Desorption Experiment Results

The adsorption/desorption data at five temperature points of the three coal samples DFS4#, SGZ11#, and SH3# are shown in Figure 3, and the fitting results are shown in Table 3. As the temperature increases, the saturated adsorption capacity of the three coal samples DFS4#, SGZ11#, and SH3# decreases significantly (Figure 4a), and the adsorption constants also show similar characteristics (Figure 4b) and have a good linear relationship. The degrees of fit are all greater than 0.9. Because the adsorption of methane gas molecules on the coal surface belongs to physical adsorption, heating up increases the activity of methane molecules, which promotes the transformation of methane molecules from an adsorbed state to a free state. In comparison, at the same temperature, the SH3# coal sample has the largest saturated adsorption capacity, followed by the SGZ11# coal sample, and the smallest is the DFS4# coal sample.

Figure 3.

Figure 3

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Isothermal adsorption/desorption curves at different temperatures of (a) DFS4#, (b) SGZ11#, and (c) SH3#.

Table 3. Fitting Results of Isothermal Adsorption/Desorption Experimental Data at Different Temperatures.

      Langmuir fitted
 Langmuir + C fitted
sample moisture-equilibrated/% temperature/°C a b R2 a b c R2
DFS4# 10.14 25 11.563 0.448 0.992 8.623 0.701 0.949 0.996
    30 11.566 0.396 0.990 8.341 0.619 0.994 0.997
    35 11.079 0.382 0.993 8.040 0.597 0.973 0.998
    40 10.725 0.374 0.993 7.698 0.543 1.039 0.999
    45 10.238 0.382 0.993 7.380 0.568 1.009 0.998
SGZ11# 3.01 25 16.370 0.513 0.998 14.130 0.807 0.930 0.995
    30 15.730 0.506 0.998 13.380 0.801 1.020 0.997
    35 15.210 0.493 0.997 12.330 0.795 1.490 0.995
    40 14.730 0.487 0.997 11.720 0.811 1.570 0.993
    45 13.890 0.486 0.999 11.390 0.791 1.210 0.991
SH3# 4.19 25 37.030 0.430 0.998 29.850 0.721 3.250 0.995
    30 35.240 0.410 0.998 27.860 0.715 3.290 0.992
    35 33.970 0.370 0.997 25.920 0.706 3.340 0.993
    40 32.450 0.340 0.997 23.760 0.695 3.560 0.994
    45 30.910 0.310 0.999 22.320 0.687 3.120 0.996
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Figure 4.

Figure 4

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Relationship between temperature, maximum adsorption capacity (a), and adsorption constant (b).

The theoretical desorption rate refers to the ratio of the amount of coalbed methane desorbed to the saturated adsorption amount when the pressure drops to the scarce pressure during the decompression desorption process. The formula is shown in eq 3.

2.2. 3

in the formula, ζ is the theoretical desorption rate of coalbed methane, %; aa is the saturated adsorption capacity of the coalbed methane adsorption process, cm3/g; and c is the residual adsorption capacity under scarce pressure, cm3/g.

It can be seen from Figure 5 that the desorption rate of different types of coal samples at the same temperature can be sorted as follows: SGZ11# > DFS4# > SH3#. As the temperature increases, the theoretical desorption rate of coalbed methane decreases first and then tends to increase, indicating that temperature is not completely positive for desorption and temperature may have a critical value for promoting methane desorption. However, because the experimental temperature setting is limited to five temperature points, the specific temperature inflection point needs to be discussed.

Figure 5.

Figure 5

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Theoretical desorption rate of coalbed methane.

The desorption hysteresis rate means that when the porous solid is used as the adsorbent, the adsorption curve of the adsorbate does not overlap with the desorption curve and the desorption line is always on the left side of the adsorption line. This phenomenon is called desorption hysteresis.26 According to the aforementioned Langmuir equation and desorption equation, the desorption hysteresis rate (δ) can be obtained, which is eq 4.

2.2. 4

in the formula, Va is the adsorption capacity under the coal reservoir pressure p, cm3/g, and Vd is the adsorption capacity of coalbed methane desorption to pressure p, cm3/g.

The change trend of the desorption hysteresis rate of coal samples of different metamorphism levels at the same temperature and different equilibrium pressures is shown in Figure 6 above. The analysis shows that regardless of the coal sample type, as the pressure increases, the desorption hysteresis rate changes logarithmically, the low-pressure hysteresis rate is large, and the high-pressure hysteresis rate is small. This is because the adsorbed methane is affected by the unit pressure drop, and its desorption is highly sensitive in the high-pressure stage, but weak in the low-pressure stage. In the high-pressure stage (which can be considered to be greater than the critical pressure of methane of 4.62 MPa), for every 1 MPa decrease in pressure, the adsorption value of the desorption process is close to that of the adsorption process, and the hysteresis is not obvious; in the low-pressure stage, the unit pressure drop is weakly sensitive to methane desorption, the pressure decreases, and the adsorbed methane cannot be immediately desorbed from the surface of the coal matrix. In addition, the desorption hysteresis rate under the same temperature and pressure can be sorted as follows: SH3#, SGZ11#, and DFS4#. Careful analysis reveals that the desorption hysteresis rates of coal samples with different metamorphic degrees are relatively small and similar in size at the high-pressure stage. In the low-pressure stage, the difference is relatively large, which also reflects the difference in the desorption sensitivity of the unit pressure drop in different pressure stages.

Figure 6.

Figure 6

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Change in desorption hysteresis ratio under the same temperature and different pressures.

Under the same pressure, the methane adsorption capacity of the same coal sample shows a linear decrease with the increase in temperature (Figure 7). Because the higher the temperature, the more violent the movement of methane molecules and the greater the molecular kinetic energy can be, which is not conducive to adsorption, but is conducive to the adsorption of methane. It is desorbed from the pore surface into a free state. At the same temperature, the adsorption capacity and adsorption rate of samples of different coal ranks are significantly different. Taking 40 °C as an example, the adsorption capacity of SH3# increases fastest during the adsorption process, followed by SGZ11#, and that of DFS4# is the smallest. In the low-pressure stage (P < 4 MPa), as the pressure increases, the adsorption capacity increases significantly and the adsorption rate is faster, but in the high-pressure stage (P > 4 MPa), the adsorption capacity increases slowly (Figure 8). In other words, the temperature is constant and the pressure increases. When it reaches a certain value, the adsorption capacity tends to be stable and no longer increases.

Figure 7.

Figure 7

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Relationship between temperature and adsorption capacity under isobaric conditions of (a) DFS4#, (b) SGZ11#, and (c) SH3#.

Figure 8.

Figure 8

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Relationship between pressure and adsorption capacity of different coal samples.

In general, SH3# has the largest residual adsorption capacity, SGZ11# is the second, and DFS4# is the smallest, indicating that the higher the coal rank, the more difficult it is to desorb methane and the greater the residual methane adsorption (Figure 9). As the temperature increases, there are certain differences in the changes in the residual adsorption capacity of the three coal samples DFS4#, SGZ11#, and SH3# (Figure 9). The residual adsorption capacity of SH3# and SGZ11# increases first and then decreases, and the inflection point is 40 °C, while the residual adsorption capacity of DFS4# is less affected by the temperature. Comparing the relationship between temperature and saturated adsorption capacity and residual adsorption capacity, it is found that as temperature increases, the saturated adsorption capacity of different coal ranks shows a decreasing trend, but its influence on the residual adsorption capacity is more complicated. The temperature can not only affect the activity of gas molecules but also change the pore structure and surface properties of coal.27−29 The change in residual adsorption capacity with temperature is actually the superposition of the abovementioned two effects, and the effect of temperature on the pore structure and surface properties of middle- and high-rank coals is more complicated than that of lower rank coals.

Figure 9.

Figure 9

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Relationship between residual adsorption capacity and temperature.

At lower temperatures, the effect of temperature on methane desorption is not obvious. When the temperature increases to 40 °C, the pore and fissure structure in the coal will change and the organic small molecules in the coal will fall off and have a certain blocking effect on the pore throat. However, when the temperature continues to increase, potential pores in the coal will continue to develop and gradually evolve into channels for methane desorption, thereby facilitating methane desorption (Figure 10). The strong-to-weak transition temperature is about 40 °C. However, the effect of temperature on pore structure changes in low-rank coal is limited.

Figure 10.

Figure 10

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Schematic diagram of the effect of temperature on the pore structure.

2.3. Thermodynamic Characteristics

Using the experimental data of isothermal adsorption and desorption, the isosteric heat of adsorption/desorption of coalbed methane can be calculated indirectly through the Clausius–Clapeyron equation.30,31 The formula is as follows

2.3. 5
2.3. 6

According to the abovementioned relationship

2.3. 7

in the formula, qst is the isosteric heat of adsorption, kJ/mol; f is the fugacity, Pa; T is the temperature, K; R is the gas constant, take 8.314 J/(mol·K); B is the slope of linear fitting relationship; P is the balance pressure of gas adsorption, MPa; and Z is the compression factor.

Different adsorption capacities are set, and the corresponding isometric heat of adsorption during the pressure increase adsorption and decompression desorption process of DFS4#, SGZ11#, and SH3# (Figure 11) is calculated. The results show that when the amount of adsorption is constant, the heat of adsorption released by the boost adsorption is less than the heat of adsorption–desorption, indicating that there is an energy difference between the adsorption and desorption processes. From the energy point of view, adsorption and desorption are not completely reversible. To desorb the same adsorbed amount of methane, energy must be absorbed from the external environment, which is the essential reason for the hysteresis of desorption.

Figure 11.

Figure 11

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Relationship between adsorption capacity and adsorption heat.

As the amount of adsorption increases, the heat of isobaric adsorption increases linearly, indicating that adsorption is a continuous exothermic process. In the process of boosting pressure, the SH3# isometric adsorption heating value is the largest, that is, the released heating value is the largest, and it is easier to adsorb methane, followed by DFS4#, and that of SGZ11# is the smallest. In the process of depressurization, the SH3# isometric adsorption heat value is the largest, that is, the absorption heat value is the largest and desorption is the most difficult, followed by DFS4#, and that of SGZ11# is the smallest.

2.4. Pore Structure Analysis

Studies have shown that the ink bottle-shaped holes have the strongest adsorption capacity for methane, followed by slit flat holes, cylindrical holes, and wedge-shaped holes.32 It is difficult for supercritical gas to physically adsorb on the surface of mesoporous or macroporous adsorbents. In microporous adsorbents, because of the superposition of the adsorption potential energy of adjacent pore walls, the interaction between gas and solid molecules in the micropores is enhanced, and a large amount of gas accumulates in the micropores. The interaction between molecules and gas molecules has also been enhanced.33 The pore characteristics of coal directly affect the adsorption/desorption capacity of coal. The main reason is the pore throat structure. Because of the small pore throat and strong adsorption capacity of the ink bottle, the difficulty of desorption increases. Compared with SGZ11# and DFS4#, SH3# has the largest adsorption capacity and a larger desorption hysteresis. Moreover, the D2 of SH3# is the largest, indicating that its pore structure is more complicated and it also increases the difficulty of desorption. Relatively speaking, DFS4# develops open pores, so the adsorption capacity is poor, but desorption is easier and the hysteresis is small. In addition, the DFS4# fractal dimension D2 value is small, indicating that the pore structure is relatively simple, which is beneficial to desorption.

2.5. Desorption Kinetic Analysis

The kinetic process of methane desorption is a process of desorption–diffusion–percolation. The diffusion of methane in the coal matrix complies with Fick’s law. The essence of diffusion is the result of the irregular movement of gas molecules, and the speed of gas molecule diffusion can be expressed by the mean free path. The formula for the molecular mean free path is as follows

2.5. 8

among them, K is Boltzmann’s constant, 1.38 × 10–23, J/K; T is the absolute temperature, K; π is 3.14; d is the methane molecular diameter, 0.414 nm; and P is the gas pressure, MPa.

Under the same pressure, the molecular free path of methane increases with temperature. Under the premise of constant temperature, in the low-pressure stage (0 < P < 4 MPa), when the pressure continues to decrease, the free path of methane molecules increases significantly, which leads to a decrease in diffusion capacity; in the high-pressure stage (4 < P < 8 MPa), when the pressure continues to decrease, the free path of methane molecules does not change significantly (Figure 12).

Figure 12.

Figure 12

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Relationship between the free path of methane molecules and pressure.

The large and medium pores of methane are mainly laminar or turbulent flow, transition pores or small pores are mainly diffusion or adsorption, and micropores are mainly adsorption. The desorption of methane is the reverse process of adsorption. The desorption of methane starts from macropores, mesopores, small pores, and micropores. The coal matrix is a porous body, and the methane molecules in the micropores are finally desorbed. At this time, the pressure is low, which makes the methane diffuse in the micropores for a long time, which makes the methane in the high-rank coal matrix with highly developed micropores be very high. It is difficult to desorb, and both the desorption hysteresis ratio and residual adsorption capacity can be reflected. Therefore, it comprehensively shows that the desorption hysteresis of high-rank coal is relatively large.

2.6. Desorption Thermodynamic Analysis

Because of metamorphism, medium- and low-rank coals are mainly small-micropores (10–100 nm), and high-rank coals are mainly micropores (less than 10 nm), so the ability to adsorb methane is different.34,35 With the generation of adsorption during the adsorption process, the coal–CH4 adsorption equilibrium system becomes more stable. The methane molecules adsorbed on the inner surface of the coal need to absorb more energy to get rid of the van der Waals force with the coal surface during desorption. The experimental results show that the increase in temperature inhibits adsorption. As the temperature increases, the activation energy of CH4 increases, so the saturated adsorption capacity of the coal becomes smaller, the adsorption capacity decreases, and the desorption capacity increases. The methane process is an exothermic process, and the desorption process is an endothermic process. The isometric heat of adsorption in the desorption process is greater than that in the adsorption process, indicating that the energy released by adsorption is less than the energy required for desorption. From the perspective of thermodynamics, the adsorption and desorption of methane in coal are not completely reversible, and the result will inevitably cause desorption hysteresis. Some researchers studied the temperature change during the adsorption/desorption process of methane in granular coal, and the results showed that the temperature of the test chamber increased when the pressure was increased, and the temperature of the test chamber decreased when the pressure was decompressed. However, the temperature dropped during desorption is lower than the temperature increased during adsorption, indicating that the same amount of methane needs to be desorbed to absorb more heat from the external environment.36,37 Therefore, it comprehensively shows that methane desorption has a desorption hysteresis, and the energy difference between before and after adsorption and desorption will cause desorption hysteresis.

2.7. Analysis of the Methane Occurrence State

The occurrence state of methane in coal reservoirs is mainly the adsorption state and free state. For the methane in the adsorption state, it is reflected from the perspective of thermodynamics that the isometric heat of adsorption during desorption is greater than the equivalent heat of adsorption during adsorption. Because the sample used in the isotherm adsorption experiment is 60–80 mesh coal, the original pore-fracture structure of the coal reservoir was destroyed by the external force during the process of making the experimental sample. During this process, part of the pores were blocked, and it was similar to the original coal reservoir. In comparison, the granular coal in the sample produced more tiny holes and cracks. For methane in the free state, the isothermal adsorption experiment is pressure-boosted adsorption, so the free methane molecules can enter the micropores under high pressure. Some closed pores will cause the pore structure to deform (the pore throat becomes narrower) after inhaling methane. The adsorbed methane is restricted by narrow pore channels and cannot be desorbed from the pores.38 In actual production, because of drainage, pressure reduction, and fracturing, the original pore and fracture structure of coal reservoirs are also destroyed, and some methane desorption channels are blocked, resulting in desorption hysteresis.

The author attributed the desorption hysteresis effect to two points. First, the isometric heat of adsorption (absorption energy) required for desorption of methane in the adsorbed state is greater than the isometric heat of adsorption (release energy) during adsorption. When the methane in the adsorbed state changes to a free state, it needs to absorb energy from the external environment. Second, the methane in the free state enters the tiny pores under high pressure, which causes deformation of the coal matrix and changes in the pore structure, which results in limited methane desorption and desorption hysteresis. At this time, a large pressure difference (energy) is required to desorb the blocked methane.

3. Conclusions

Major conclusions in this work can be summarized as follows:

As the degree of coal metamorphism increases, the ability of coal to adsorb methane is significantly enhanced. At the same temperature, the saturated adsorption capacity, desorption hysteresis rate, and residual adsorption capacity of SH3# are the largest, followed by SGZ11#, and the smallest is the DFS4#. As the temperature increases, the theoretical desorption rate and residual adsorption capacity of SH3# and SGZ11# show a trend of first increasing and then decreasing. Temperature and methane desorption are not completely positive effects. Temperature may have a critical value for promoting methane desorption. The effect of temperature on the activation of gas molecules and the pore structure of coal should be considered comprehensively. As the pressure increases, the desorption hysteresis rate changes in a logarithmic downward trend. The methane desorption hysteresis rate in the low-pressure stage (P < 4 MPa) is large, and the methane desorption hysteresis rate in the high-pressure stage (P > 4 MPa) is lower.

In the isobaric adsorption process, the adsorption capacity of SH3# increases the fastest, followed by SGZ11#, and that of DFS4# is the smallest. In the low-pressure stage (P < 4 MPa), with the increase in pressure, the adsorption capacity increases significantly. However, in the high-pressure stage (P > 4 MPa), the adsorption capacity does not change significantly with pressure and gradually stabilizes. Under the same pressure, the molecular free path of methane increases with temperature. Under the premise of constant temperature, in the low-pressure stage (0 < P < 4 MPa), when the pressure continues to decrease, the free path of methane molecules increases significantly, which leads to a decrease in diffusion capacity; in the high-pressure stage (4 < P < 8 MPa), when the pressure continues to decrease, the free path of methane molecules does not change significantly; in the three coal samples DFS4#, SGZ11#, and SH3#, the intermediate adsorption heat in the desorption process is greater than the isometric adsorption heat in the adsorption process, indicating that the desorption process needs to continuously absorb heat from outside the system. The energy difference produced in the process of adsorption and desorption causes the desorption hysteresis effect. The greater the difference in the isometric heat value of adsorption, the more significant the hysteresis.

4. Samples and Methods

4.1. Sample Material Composition

The samples were collected from the Dafosi coal mine in the southern Ordos Basin of China, the coal cores in the Shanggaozhai borehole in the eastern Ordos Basin of China, and the Sihe coal mine in the southern Qinshui Basin of China. Specifically, the no. 4 coal seam sample (DFS4#) is directly collected from the 40105-working face of Dafosi coal mine, the no. 11 coal sample (SGZ11#) is taken from the coal core of the Shanggaozhai coal mine, and the no. 3 coal seam sample (SH3#) is collected directly from the W2302-working face of the Sihe coal mine (Figure 13). The coal quality analysis was conducted in accordance with the coal industry standards of the People’s Republic of China (GB/T 212-2008, GB/T 212-2008, and GB/T 476-2001), and the results are listed in Tables 4 and 5.

Figure 13.

Figure 13

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Simplified location map of the study area.

Table 4. Microscopic Component Determination Results of Samples.

      maceral composition/%
sample coal rank Ro,max/% vitrinite inertinite liptinite mineral
DFS4# long-flame coal 0.43 22.8 68.1 2.2 6.9
SGZ11# coking coal 1.26 69.8 14.2 0 16
SH3# anthracite 3.27 61.8 29.6 0 8.6
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Table 5. Industrial Analysis Results.

  proximate analysis/%
sample moisture ash volatile matter fixed carbon
DFS4# 4.65 15.74 32.95 46.66
SGZ11# 0.96 6.94 16.62 75.48
SH3# 3.55 13.64 6.38 76.43
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The sample is mainly used for methane adsorption/desorption measurement and the cryogenic liquid nitrogen adsorption test. The original sample is placed in a pulverizer and crushed into powder with a particle size of 0.18–0.23 mm. Then, part of the powder samples were placed in a vacuum dryer at 50 °C to completely dry and to remove free moisture in the coal. Other samples were strictly made of samples with moisture balance according to the American Society for Testing and Materials (ASTM) standards.39

4.2. Low-Pressure Nitrogen Adsorption Experiment

Low-pressure nitrogen adsorption experiment uses an ASAP specific surface and pore size analyzer. The ASAP2020 specific surface and pore size analyzer produced by Beckman Coulter, USA, has a specific surface area measurement range of >0.000 5 m2/g and a pore size range of 0.35–500 nm. The temperature of liquid nitrogen is 77 K, and the purity is greater than 99.99%. Before the experiment, the coal sample was dried in advance, and then, the coal sample was made into a powder sample with a particle size of 0.18–0.23 mm. The Brunauer–Emmett–Teller theory model was used to calculate their specific surface areas, and the Barrett–Joyner–Halenda model was used to calculate pore structures. According to the decimal classification system of Hodot (1966), micropores (<10 nm), transition pores (10–100 nm), mesopores (100–1000 nm), and macropores (>1000 nm) are analyzed in detail.40−43

4.3. Isothermal Adsorption/Desorption Measurements

The methane adsorption/desorption experiment was conducted using a volumetric method.44 The adsorption/desorption experiment instrument adopts the AST-2000 large-sample coalbed methane isotherm adsorption/desorption simulation experiment instrument independently developed by Xi’an University of Science and Technology (Figure 14).

Figure 14.

Figure 14

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Experimental device of AST-2000 for methane adsorption/desorption.

The experiment temperature is set at five temperature points, 25, 30, 35, 40, and 45 °C. The maximum pressure of the experiment is 8 MPa, and the adsorption/desorption equilibrium time is 12 h.

In the process of methane adsorption, the experimental data are described by the Langmuir (eq 9) equation.45 Because of the hysteresis of desorption, the desorption process data are described by the desorption equation (Langmuir + C) (eq 10) proposed by Ma et al.46

4.3. 9
4.3. 10

in the formula, Va is the adsorption capacity under the coal reservoir pressure p, cm3/g; Vd is the adsorption capacity of coalbed methane desorption to pressure p, cm3/g; a is the limit adsorption capacity of the coal sample, cm3/g; b is the comprehensive parameters of adsorption and desorption rate and adsorption heat; and c is the constant or residual adsorption capacity, cm3/g.

Acknowledgments

This work is supported by the National Natural Science Foundation of China (41902175), the Shanxi Province Science and Technology Major Special Funding Project (20201101002), the Shaanxi Province Natural Science Basic Research Program Funding Project (2019JQ-245), and The Open Project Funding Project of the Key Laboratory of Coal Resources Exploration and Comprehensive Utilization of the Ministry of Natural Resources (KF2019-2). The authors also thank the editor and anonymous reviewers very much for valuable comments and suggestions that have greatly improved the manuscript.

The authors declare no competing financial interest.

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