Study on Adsorption Model of Deep Coking Coal Based on Adsorption Potential Theory

Abstract

With the exhaustion of coal resources in shallow coal seams, many mining areas have moved to deep mining, and the coal storage environment is obviously affected by the mining depth, mainly manifested as the increase of gas pressure and temperature, which makes the adsorption characteristics of deep coal seam gas much more complicated than shallow coal seam. Based on this, this paper chooses Pingdingshan coking coal as the research object, using Hsorb-2600 high-temperature and high-pressure gas adsorption instrument to carry on isothermal adsorption experiment. According to the adsorption theory and the uniqueness of the adsorption characteristics cure, the adsorption model was analyzed and studied. The results show that the predicted curve of coal seam gas adsorption isotherm is in good agreement with the measured curve, the relative error is less than 10%, and the adsorption characteristic curve is logarithmic. At the same time, the model is used to study the variation of adsorbed gas amount with mining depth. The results show that the adsorbed gas amount increases first and then decreases with coal burial depth.

1. Introduction

The development and utilization of coking coal play a vital role in the development of Chinese coal industry and is an indispensable resource for our economic construction [1–3]. For a long time, the mining depth of coking coal is generally lower than that of anthracite [4], and the focus of gas control is mainly on highly metamorphic coal represented by anthracite, and the research on coking coal mining area is less, but with the depletion of shallow coal resources, many mining areas have been transferred to deep mining [5–7]. Deep mining means that while little research has been done on the influence of coking coal on gas adsorption under high temperature and high pressure, adsorption characteristics of deep coal seam gas are the basis of coalbed methane development, and the date of methane adsorption is also the necessary basic parameter for predicting and analyzing coalbed methane reasoures [8–10]. Therefore, it is necessary to study the gas adsorption characteristics in deep coking coal mining area for the safe mining of deep coal seams and the effective control of gas disaster [11].

A lot of studies have been done on the influence of temperature and pressure on the adsorption performance of coal. Levy et al., Bustin and Clarkson, and Sakurovs et al. [12–14] found that the gas adsorption amount on the coal body surface is directly proportional to the pressure and inversely proportional to the temperature. By studying the adsorption/desorption of anthracite coal at -30°C to 30°C, Wang et al. [15] found that the temperature has great influence on the gas adsorption isotherm of coal, and the lower the temperature is, the greater the gas adsorption amount of coal; Zhao et al. [16] mainly focused on the single factor of temperature and studied the gas adsorption characteristics under high-temperature conditions and found that the gas adsorption amount increases with the temperature. It can be seen from the above that most of the early scholars’ studies on the occurrence law of coal seam methane were carried out under low temperature and low pressure and mainly focused on the influence of a single factor. In the process of coalbed methane reserve prediction, in order to explore the relationship between methane gas volume adsorbed by coal and pressure at different temperatures, it is necessary to consider the influence of temperature and pressure on coal adsorption. Therefore, it is of great significance to study the influence of temperature and pressure on methane gas volume adsorbed by coking coal.

At present, the research on predicting the variation of coalbed methane with burial depth has been paid much attention in the evaluation of coalbed methane reserves. The results of Zhao et al.’s [17] study on the effect of deep coalbed methane reservoir show that the relationship between temperature and coal bed adsorption capacity is negative, which is far greater than the positive correlation of formation pressure, resulting in the existence of a critical depth of gas content in deep coalbed, indicating that temperature and pressure jointly affect the adsorption characteristics of coal bed, so the shallow adsorption model is not applicable to deep coal bed. Nie et al. [18] predicted the gas content of deep coal seam. The results show that the existing adsorption model can be used to predict the gas content of shallow coal seam within 800 m, while the combined effect of temperature and pressure should be considered to predict the gas content of deep coal seam above 800 m. To sum up, with the increase of mining depth, the adsorption capacity of coal has a significant change; whether the original adsorption model is applicable has yet to be verified [19–21]. The adsorption of methane on coking coal belongs to the range of physical adsorption [22–24]. The physical adsorption force is mainly the dispersion force, and the dispersion force is independent of temperature. At the same time, the adsorption potential theory holds that the adsorption potential is unique to the volume of the adsorption space and does not change with temperature [25–28].

Based on the adsorption potential theory, the adsorption characteristics of coking coal are studied, the adsorption characteristics curves of coking coal are calculated, and the relationship between the adsorption characteristics and the temperature, pressure, and methane adsorption capacity is established. On this basis, the calculation model of methane adsorption capacity of coking coal under the combined action of temperature and pressure is deduced, and the characterization constants are solved. At the same time, the calculation equation of methane adsorption by coking coal under geological conditions is established by using this model and the prediction of gas content variation with burial depth is studied based on this equation, in order to improve the safety of deep coking coal mining and provide an important basis for the prevention and control of gas outburst.

2. Isothermal Adsorption Experiment of Coking Coal

2.1. Coal Sampling

The main coking coal production and reserve bases in China are mainly concentrated in North China, East China, and South China, and Pingdingshan mining area is the main area in South China. Based on high-temperature and high-pressure methane adsorption experiments, this paper investigates the gas adsorption response characteristics of coking coal in deep coal seam and selects coking coal (soft and hard) samples from Pingdingshan, Henan Province, for the determination of basic parameters. The determination results of the basic parameters of the coal sample are shown in Table 1.

Table 1

The basic parameters of coal samples.

Numbering	True density (g/cm³)	Apparent density (g/cm³)	Porosity (%)	Coefficient of firmness	Industrial analysis of coal
Numbering	True density (g/cm³)	Apparent density (g/cm³)	Porosity (%)	Coefficient of firmness	Moisture content (%)	Ash content (%)	Volatile matter (%)
PY	1.38	1.35	2.17	0.84	0.49	18.25	24.91
PR	1.41	1.33	5.67	0.38	0.76	10.36	21.36

2.2. Determination of Experimental Temperature and Pressure Parameters

2.2.1. Description of Sampling Sites

Pingdingshan Coal Mine is located in the middle and west of Pingdingshan Coal Field, Henan Province. The administrative region is under the jurisdiction of Xinhua District, Pingdingshan City. Geographical coordinates are as follows: 113° 11 $'$ 45 $^{″}$ to 113° 22 $'$ 30 $^{″}$ east, 33° 40 $'$ 15 $^{″}$ to 33° 48 $'$ 45″ north. Pingdingshan coalfield is located in the eastward extension of Qinling latitudinal structure, and under the double control and influence of latitudinal structure and Huaiyang mountain type, a series of axial NW folds are formed, and NW-oriented tension-torsional and compression-torsional faults are developed, accompanied by a small number of NE-trending tension-torsional faults. The coal sampling location of this paper is Pingdingshan Mine 12 Ji 15-31050 face, buried depth of 994 m (Figure 1), coal for coking coal.

Figure 1

Face sampling map.

2.2.2. Determination of Experimental Temperature and Pressure Parameters

According to the survey data, the maximum value of average geothermal gradient is 4.6°C/100 m, while the minimum value is 3.2°C/100 m, and the average value is 3.9°C/100 m; the maximum value of average reservoir pressure gradient is 1.293 MPa/100 m, while the minimum value is 0.42 MPa/100 m, and the average value is 0.86 MPa/100 m.

Since the maximum gas pressure of 6.3 MPa in Pingdingshan Mine is about 1000-1100 m, and combined with the research purposes and the actual situation of the experimental device, the maximum equilibrium pressure of this experiment is determined to be 11 MPa, and the temperature parameters are 30°C, 50°C, 70°C, and 90°C.

2.3. Experimental Device and Process

With the help of Hsorb-2600 high-temperature and high-pressure gas adsorption instrument, the isothermal adsorption experiment was carried out. The experimental equipment is shown in Figure 2. The highest temperature of the instrument can reach 600°C, and the lowest is -196°C, while the maximum pressure is 20 MPa, and the minimum is 0.04 MPa. It can be used to measure the adsorption/desorption of methane by coal at any temperature and pressure with this range. In terms of temperature pressure and accuracy, the instrument has a wider temperature range and a wider range of analyzable items than other common gas sorption apparatus.

Figure 2

Hsorb-2600 high-temperature and high-pressure gas adsorbent instrument.

The experimental adsorbent is 99.999% high-purity methane, and the experimental procedure is as follows: (1)

The prepared coal sample for high-temperature and high-pressure adsorption experiment shall be put into the sample tube, then click on the pretreatment, and be dried for 4 hours at 105°C

(2)

After the pretreatment, the sample tube shall be removed after cooling then installed for testing

(3)

Computer set test parameters: the maximum adsorption equilibrium pressure is set to 11 MPa, 11 equilibrium pressure points, and the experiment temperature is set to 30°C. The instrument can automatically record the adsorption amount after the instrument reaches adsorption equilibrium, and the adsorption data of different adsorption equilibrium pressure points are obtained

(4)

Change the experimental temperature. High-temperature and high-pressure methane adsorption experiments at different temperatures (50°C, 70°C, and 90°C) were carried out on soft and hard coal of Liulin and Pingdingshan Mine

The isothermal adsorption characteristics of Pingdingshan coking coal (soft and hard) samples at constant pressure 11 MPa and different temperatures (30°C, 50°C, 70°C, and 90°C) were studied in this paper, and 8 experiments were carried out in total.

3. Analysis of Experimental Results

3.1. Isothermal Adsorption Line

Because the maximum temperature of methane is -82.6°C and the maximum pressure is 4.59 MPa, which exceeds the critical temperature and pressure of methane, methane adsorption becomes supercritical adsorption at this experimental temperature and pressure [29]. The adsorption capacity of Gibbs is obtained by isothermal adsorption experiment (Figure 3). The adsorption capacity of Gibbs is the difference between actual adsorption density and gas phase density, and the absolute adsorption quantity indicates the actual adsorption quantity of the solid adsorption system. It can be seen that the excess adsorption quantity is less than the absolute adsorption quantity. Because the absolute adsorption quantity cannot be measured directly, the excess adsorption quantity has a certain influence on the study of adsorption model. Therefore, in the study of isothermal adsorption characteristics and model, the excess adsorption should be converted to the absolute adsorption, and then, the absolute adsorption was used for model study.

Figure 3

Isothermal adsorption line of methane adsorbed by coking coal.

(b)

Isothermal adsorption line of methane by PY

3.2. Correction for Excess Adsorption

According to the definition of absolute adsorption capacity, the relationship between excess adsorption capacity and absolute adsorption capacity is as follows [30]: $\begin{matrix} (1) & V_{ad} = \frac{V_{ex}}{1 - (ρ_{g} / ρ_{a})}, \end{matrix}$ where $V_{ad}$ is excess adsorption, cm³/g; $V_{ex}$ is absolute adsorption, cm³/g; $ρ_{g}$ is gas phase density, g/cm³; and $ρ_{a}$ is adsorption phase density, g/cm³.

From formula (1), the density of free phase ( $ρ_{g}$ ) and the density of adsorbed phase ( $ρ_{a}$ ) must be determined in order to realize the conversion from excess adsorption to absolute adsorption. The free phase density can be calculated experimentally, and the expression is as follows: $\begin{matrix} (2) & ρ_{g} = \frac{M p}{R T} . \end{matrix}$

The density of adsorbed phase in supercritical condition cannot be obtained directly by experiments. Previous scholars mostly used liquid phase method and Langmuir model to calculate the density of adsorbed phase to correct the absolute adsorption capacity. Because there are many parameters in Langmuir fitting method, it will be affected by many factors, while the liquid phase method considers not only the temperature but also the pressure, so the liquid phase method is used to calculate the density of adsorption phase to correct the absolute adsorption. The expression is as follows [31]: $\begin{matrix} (3) & ρ_{a} = \frac{ρ_{b}}{\exp [0.0025 (T - T_{b})]}, \end{matrix}$ where $ρ_{a}$ is the adsorption phase density, $ρ_{b}$ is the free phase density, and $T_{b}$ is the critical temperature of methane.

The correction result of absolute adsorption capacity is shown in Figure 4.

Figure 4

Corrected curve of absolute adsorption capacity.

(b)

PY corrected absolute adsorption curve

The error bar results of the two are shown in Figure 5.

Figure 5

Absolute adsorption capacity error bar.

(b)

PY absolute adsorption error bar

As shown in Figures 3 and 5, the absolute adsorption amount is greater than the excess adsorption amount, and both temperature and pressure affect the difference between the two. In the low-pressure stage (0-4 MPa), the difference between the two is small, and with the increase of pressure, the difference gradually increases; with the increase of temperature, the difference between the two also gradually increases.

4. Adsorption Characteristic Curve

The relationship between adsorption potential and adsorption space is unique. In order to study the adsorption mechanism of deep coking coal on methane, the adsorption potential theory was introduced, the adsorption potential and adsorption space were calculated, and the adsorption characteristic curve is obtained. According to the adsorption potential theory proposed by Polanyi, the relationship between adsorption potential and pressure is as follows [32]: $\begin{matrix} (4) & ε = \int_{P_{i}}^{P_{0}} \frac{R T}{P} d P = R T Ln \frac{p_{0}}{p_{i}}, \end{matrix}$ where $ε$ is the adsorption potential, J/mol; $P_{0}$ is the virtual saturated vapor pressure of methane, MPa; $P_{i}$ is the equilibrium pressure of ideal gas at constant temperature, MPa; and $R$ is the universal gas constant, with a value of 8.314 J/(mol·K).

Under supercritical conditions, the empirical formula established by Dubinin is used to calculate the virtual saturated vapor pressure of methane [33, 34]. $\begin{matrix} (5) & P_{0} = P_{c} {[\frac{T}{T_{c}}]}^{k}, \end{matrix}$ where $P_{c}$ is the critical pressure of methane, with a value of 4.62 MPa; $T_{c}$ is the critical temperature of methane, 190.6 K; and $K$ is the coefficient, with the general value of 2.

The formula for calculating $ω$ of the adsorption space is as follows [35]: $\begin{matrix} (6) & ω = \frac{V_{ad} M}{22400 ρ_{a}}, \end{matrix}$ where $ω$ is the adsorption space, cm³/g; $M$ is the molecular weight of methane, g/mol; $V_{ad}$ is the absolute adsorption capacity of coal for methane, g/mol; and $ρ_{a}$ is the adsorption phase density, g/cm³. The expression is expressed as follows [36, 37]: $\begin{matrix} (7) & ρ_{a} = \frac{ρ_{b}}{\exp [0.0025 (T - T_{b})]}, \end{matrix}$ where $ρ_{a}$ is the adsorption phase density, $ρ_{b}$ is the boiling point density, and $T_{b}$ is the critical temperature of methane.

The absolute adsorption amount of $V_{ad}$ is known from (1): $\begin{matrix} (8) & V_{ad} = \frac{V_{ex}}{1 - (ρ_{g} / ρ_{a})} . \end{matrix}$

From equations (4) to (8), it can be seen that through the isothermal adsorption curve, the relationship curve between adsorption potential and adsorption space can be obtained, namely, the adsorption characteristic curve of $ε - ω$ . The isothermal adsorption data of two groups of coking coal samples are processed by the method described in this paper to obtain the $ε - ω$ curve, as shown in Figure 6.

Figure 6

Characteristic curve of coke coal adsorbing methane.

(b)

It can be seen from Figure 6 that the adsorption curves of two groups of coking coal samples at 4 temperatures are almost on the same curve, which shows that the adsorption curve is independent of temperature, and the adsorption curve of coal decreases with the increase of adsorption space. Therefore, the parameters of the adsorption model can be obtained by fitting the adsorption date at a certain temperature which can be used to predict the adsorption amount at different temperatures and pressures.

The expression of the adsorption characteristic curve accords with the logarithmic expression $ε = a \ln (ω) + b$ . According to the equation, when the adsorption potential $ε$ is 0, the space between the isopotential surface and the adsorbent surface is called the adsorption limit space; at this time, the adsorption volume $ω$ is called the limit adsorption phase volume, equivalent to the adsorption saturated mass volume. The correlation coefficient is shown in Tables 2 and 3.

Table 2

Pingdingshan soft medium fitting formula.

Temperature (°C)	Coal sample	Polynomial relation	$R^{2}$	Standard error
30	Pingdingshan coking coal Soft coal	$ε = - 8.27 \ln (ω) - 24.34$	0.9998	$a$	$b$
50				0.0256	0.0829
70
90

Table 3

Pingdingshan hard medium fitting formula.

Temperature (°C)	Coal sample	Polynomial relation	$R^{2}$	Standard error
30	Pingdingshan coking coal Hard coal	$ε = - 8.07 \ln (ω) - 23.24$	0.9987	$a$	$b$
50				0.0191	0.0644
70
90

5. Derivation of Methane Adsorption Model of Deep Coking Coal

Based on the isothermal adsorption experimental data of coking coal, the adsorption model considering the combined effect of temperature and pressure can be derived by fitting the expression of $ε - ω$ adsorption characteristic $ε = a \ln (ω) + b$ . Assuming that the methane density is a certain value within a certain range above the critical temperature, the adsorption amount substitutes the adsorption volume, and the comprehensive finishing formulas (4)–(8) and the relationship between the adsorption amount, temperature, and pressure can be expressed as follows: $\begin{matrix} (9) & V = e^{A \times T (2 \times \ln T - \ln p - 8.970) + B} \times \{1 - \frac{16.032 \times \exp [0.0025 \times (T - T_{b})] \times P}{3516.822 \times T}\} . \end{matrix}$

Take logarithms on both sides of the equation to get $\begin{matrix} (10) & \ln V = A \times T \times (2 \times \ln T - \ln p - 8.970) + B + \ln \{1 - \frac{16.032 \times \exp [0.0025 \times (T - T_{b})] \times P}{3516.822 \times T}\}, \end{matrix}$ where $A$ and $B$ are the coefficients, and the logarithm of the adsorption amount is calculated by using the isothermal adsorption data of the coking coal sample at a certain temperature, namely, $\ln V$ ; if the relationship between $\ln V$ and $P$ is fitted by origin, then the coefficients $A$ and $B$ are known, and then, plug them into formula (9) to obtain the methane adsorption model at that temperature.

As the depth increases, the gas pressure and the formation temperature are changing. The maximum value of average reservoir pressure gradient is 1.293 MPa/100 m, the minimum value is 0.42 MPa/100 m, and the average value is 0.86 MPa/100 m from 2-2 known mining area. $\begin{matrix} (11) & p = (\frac{h}{100}) \times 0.86, \end{matrix}$ where $h$ is the depth of burial, m.

Due to the direct relationship between formation temperature and depth, the maximum value of average geothermal gradient in the mining area is 4.6°C/100 m, while the minimum value is 3.2°C/100 m, and the average value is 3.9°C/100 m. $\begin{matrix} (12) & T = (\frac{h}{100}) \times 3.9, \end{matrix}$ where $h$ is the depth of burial, m.

Based on the adsorption model of coking coal with the change of temperature and pressure, $V = e^{A \times T (2 \times \ln T - \ln p - 8.970) + B} \times \{1 - ((16.032 \times \exp [0.0025 \times (T - T_{b})] \times P) / (3516.822 \times T))\}$ , the calculation model of the change of coking coal adsorption with depth can be obtained by substituting formulas (11) and (12) into the model. The model expression is as follows: $\begin{matrix} (13) & V = e^{A \times (0.039 \times h + 294.15) \times [2 \times \ln (0.039 \times h + 294.15) - \ln (h) - 2.194] + B} \times [1 - 0.00004 \times \frac{\exp [0.0025 \times (0.039 \times h + 84)] \times h}{0.039 \times h + 294.15}] . \end{matrix}$

6. Validation of Adsorption Model

It is very important to study the variation law of gas content in coal seam with burial depth, because the common adsorption model has better fitting effect on shallow coal seam and poorer fitting effect on deep coal seam. The adsorption model deduced in this paper can be used to know the adsorption characteristics of coking coal at different temperatures and pressures, and the application range is wide. In order to further verify the reliability of the model, 8 groups of coking coal isotherm adsorption data were used to verify the model derived in this paper, and the error analysis method was used to analyze the difference between the adsorption amount calculated by the model in this paper and the measured adsorption amount.

Eight groups of isothermal adsorption data of coking coal are selected to calculate the adsorption amount of coal bed gas: (1) using the data of two groups of coking coal samples at 30°C, calculate the logarithmic value of the adsorption amount, namely, $\ln V$ , and use the origin to draw a graph to fit the relationship between $\ln V$ and $P$ ; then, the values of $A$ and $B$ (Table 4) are known; (2) taking the coefficient $A$ and $B$ values into formula (9) to calculate the adsorption amount of coking coal samples at 50°C, 70°C, and 90°C, respectively. The predicted and measured values are shown in Figure 7. (3) Based on the prediction value of 8 coking coal samples and the measured value in laboratory, the error is calculated and is used to verify the model. The error result is shown in Figure 8. The error bar is shown in Figure 9.

Table 4

Fitting results of isothermal adsorption test data of hard coal.

Temperature/°C	Coal sample	$A$	$B$	$R^{2}$
30	Soft coal	$- 0.00129 \pm 0.000027$	$3.22681 \pm 0.0114$	0.9953
30	Hard coal	$- 0.00128 \pm 0.000025$	$3.27841 \pm 0.0103$	0.9944

Figure 7

Comparison between predicted isothermal adsorption line of coking coal sample model and measured isothermal adsorption line.

Figure 8

Comparison of predicted value error of coking coal sample model.

(b)

Error comparison of PY coal sample model

Figure 9

Coking coal sample prediction error bar.

(b)

The isothermal adsorption lines predicted by the model and measured isothermal adsorption lines of different coal samples (Pingdingshan hard coal and Pingdingshan soft coal) at different temperatures (30°C, 50°C, 70°C, and 90°C) are shown in Figure 7. It can be seen from Figure 7 that the predicted and measured isotherms of each coal sample under different temperatures are similar, and the predicted and measured isotherms of Pingdingshan soft coal are better fitted than those of Pingdingshan hard coal. The authors think that the reason for this phenomenon is that compared with the total specific surface area of coking coal soft coal and hard coal, the former is always significantly greater than the latter, and the gas adsorption capacity is significantly higher than that of hard coal with the same metamorphic degree. Therefore, the fitting degree of hard coal is relatively low. The fitting between the adsorption model prediction and the measured isotherm of each coal sample is better under high pressure. It can be seen from Figures 8 and 9 that the predicted value of coking coal sample is close to the measured value, and the relative error is less than 10%, among which the predict and the measured value of coking coal under low pressure is larger than that under high pressure, and the error between the predicted and measured is smaller. It is shown that the model derived from the adsorption potential theory can predict the methane adsorption by coking coal with high accuracy, which indicates that the model derived from the adsorption potential theory is feasible. The model expression is as follows:

Soft coal $\begin{matrix} (14) & V = e^{- 0.00129 \times T (2 \times \ln T - \ln p - 8.970) + 3.22681} \times \{1 - \frac{16.032 \times \exp [0.0025 \times (T - T_{b})] \times P}{3516.822 \times T}\} . \end{matrix}$

Hard coal $\begin{matrix} (15) & V = e^{- 0.00128 \times T (2 \times \ln T - \ln p - 8.970) + 3.27841} \times \{1 - \frac{16.032 \times \exp [0.0025 \times (T - T_{b})] \times P}{3516.822 \times T}\} . \end{matrix}$

In order to take into account the amount of gas adsorption at different temperatures and pressures, formulas (11) and (12) show the variation of coal seam pressure and temperature with the change of depth. $A$ and $B$ values of the coking coal samples in Table 4 are taken into formula (13), and the model of the change of gas adsorption amount with mining depth of Pingdingshan coking coal is obtained. The model expression is as follows:

Soft coal $\begin{matrix} (16) & V = e^{- 0.00129 \times (0.039 \times h + 294.15) \times [2 \ln (0.039 \times h + 294.15) - \ln (h) - 2.194] + 3.22681} \times [1 - 0.00004 \frac{e^{0.0025 \times (0.039 \times h + 84)} \times h}{0.039 \times h + 294.15}] . \end{matrix}$

Hard coal $\begin{matrix} (17) & V = e^{- 0.00128 \times (0.039 \times h + 294.15) \times [2 \ln (0.039 \times h + 294.15) - \ln (h) - 2.194] + 3.27841} \times 0.000043346 \frac{e^{0.0025 \times (0.039 \times h + 8)} \times h}{0.039 \times h + 294.15}] . \end{matrix}$

The results are shown in Figure 10.

Figure 10

Variation law of coal seam gas content with buried depth.

From Figure 10, it can be seen that the adsorption amount of coking coal in the two groups is consistent with the depth, first increasing with the depth, then decreasing with the depth. Combined with Figure 3, the reason is that the adsorption gas of coking coal increases with the increase of pressure and decreases with the increase of temperature, which shows that the adsorption of temperature and pressure on coking coal is competitive. When the burial depth of coking coal is less than the burial depth corresponding to the maximum adsorption capacity of coking coal, the pressure plays a major role, while when the burial depth equals the burial depth corresponding to the maximum adsorption capacity of coking coal, the major role is temperature.

7. Conclusion

(1)

The absolute adsorption capacity is greater than the excess adsorption capacity, and the temperature and pressure have a certain impact on the difference between the two values. When the temperature increases, the difference between the two values decreases, while when the pressure increases, the difference between the two values increases

(2)

Based on the adsorption potential theory. The adsorption curves of $ε - ω$ calculated from isothermal adsorption data of coking coal are independent of temperature, and characteristic curves are logarithmic

(3)

The coking coal adsorption model derived based on the adsorption potential theory has high prediction accuracy and can predict the adsorption amount of coking coal at different temperatures and pressures and obtain isotherm adsorption lines

(4)

By using the derived adsorption model of coking coal, it is found that the adsorption capacity of coking coal increases first and then decreases with the increase of the coal seam depth

Footnotes

Data Availability

Some or all data, models, or code generated or used during the study are available from the corresponding author. These materials can be requested directly from the corresponding author if needed.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

This study was financially supported by the National Natural Science Foundation of China (52074107).

References

Yang

J.-H.

Yang

Z.-Q.

Physical simulation and theoretical evolution for ground fissures triggered by underground coal mining

PLoS One 2018 13

9596874

3, article e0192886

10.1371/journal.pone.0192886

2-s2.0-85049249939

Cao

Dai

L. C.

Sun

H. T.

Wang

Zhao

Yang

Zhao

Guo

Experimental study of the impact of gas adsorption on coal and gas outburst dynamic effects

Process Safety and Environmental Protection 2019 128

9596874

158 166

10.1016/j.psep.2019.05.020

2-s2.0-85067430084

Shi

Zhang

Jiang

A case study of fracture law and stress distribution characteristics of surrounding rock of working face in deep mines

Geotechnical and Geological Engineering 2019 37

9596874

4 2935 2948

10.1007/s10706-019-00810-7

2-s2.0-85060330130

Ning

Ren

Methane adsorption on shales and application of temperature-related composite models based on dual adsorption modes

Journal of Petroleum Science and Engineering 2022 208, article 109379

9596874

10.1016/j.petrol.2021.109379

Feng

P. R.

On the problems and countermeasures in deep mining of coal mine

Energy and Energy Conservation 2018 2 40 41

Wang

Z. F.

Tang

Yue

G. W.

Kang

Xie

Physical simulation of temperature influence on methane sorption and kinetics in coal: benefits of temperature under 273.15K

Fuel 2015 158

9596874

207 216

10.1016/j.fuel.2015.05.011

2-s2.0-84930640583

Jasieńko

The nature of coking coals

Fuel 2020 53

9596874

3 131 146

Wang

Z. F.

Study on methane adsorption characteristics of anthracite in deep coal seams

Coal Mine Safety 2021 52

9596874

6 28 33

Dubinin

M. M.

Stoeckli

H. F.

Homogeneous and heterogeneous micropore structures in carbonaceous adsorbents

Journal of Colloid and Interface Science 1980 75

9596874

1 34 42

10.1016/0021-9797(80)90346-X

2-s2.0-0001769664

10.

Stoeckli

H. F.

Microporous carbons and their characterization: the present state of the art

Carbon 1990 28

9596874

1 1 6

10.1016/0008-6223(90)90086-E

2-s2.0-0025635487

11.

Liu

G. F.

Zhang

Z. X.

Zhang

X. D.

Pore distribution recularity and adsorption desorption characteristics of gas coal and coking coal

Journal of Rock Mechanics and Engineering 2009 28

9596874

8 1587 1592

12.

Levy

J. H.

Day

S. J.

Killingley

J. S.

Methane capacities of Bowen Basin coals related to coal properties

Fuel 1997 76

9596874

9 813 819

10.1016/S0016-2361(97)00078-1

2-s2.0-0002850976

13.

Bustin

R. M.

Clarkson

C. R.

Geological controls on coalbed methane reservoir capacity and gas content

International Journal of Coal Geology 1998 38

9596874

1-2 3 26

10.1016/S0166-5162(98)00030-5

2-s2.0-0032467642

14.

Sakurovs

Day

Weir

Temperature dependence of sorption of gases by coals and charcoals

International Journal of Coal Geology 2007 73

9596874

3 250 258

15.

Wang

Z. F.

Kang

Yue

G. W.

Study on gas adsorption characteristics of anthracite in low temperature environment

Zhongzhou Coal 2014 6

9596874

1 4

16.

Zhao

L. J.

Qin

C. F.

Adsorption behavior of deep coalbed methane under high temperature and pressure

Journal of Geology of Colleges and Universities 2013 19

9596874

4 648 654

17.

Zhao

L. J.

Qin

Shen

Adsorption behavior and abudance prediction model of deep coal methan

Geology of Colleges and Universities 2012 18

9596874

3 553 557

18.

Nie

H. Y.

J. S.

Zhang

Prediction of gas content in deep coal seams in Jiaozuo coalfield

Coal Mine Safety 2009 40

9596874

6 79 82

19.

X. P.

Wang

Z. F.

Ren

H. Y.

Prediction for CH₄ isothermal adsorption curve of coal at low temperature based on adsorption potential theory

Coal Mine Safety 2017 48

9596874

5 22 25

20.

Chai

S. Y.

Niu

Study on coal adsorption supercritical methane based on adsorption potential theory

Coal Mine Safety 2017 48

9596874

1 21 23

21.

Jia

Zhang

X. B.

Wei

H. W.

Research on parameters of adsorption potential via methane adsorption of different types of coal

Journal of Coal 2015 40

9596874

8 1859 1864

22.

Yang

Ren

An adsorption-permeability model of coal with slippage effect under stress and temperature coupling condition

Journal of Natural Gas Science and Engineering 2019 71, article 102983

9596874

10.1016/j.jngse.2019.102983

2-s2.0-85072048652

23.

Xiong

Liang

L. X.

Liu

X. G.

Adsorption characteristics of shale to CH₄ based on adsorption potential theory

Science and Technology Herald 2014 32

9596874

17 19 22

24.

Guan

X. S.

Study on methane adsorption above critical temperature by adsorption potential theory

Natural Gas Chemical Industry 2003 5 28 31

25.

Tang

M. G.

Zhang

H. L.

Duan

S. Z.

Study on the effect of temperature on methane adsorption and desorption in coal based on Langmuir model

Coal Science and Technology 2021 49

9596874

5 182 189

26.

X. B.

Chen

Lin

X. Y.

Application of adsorption potential theory in the fractionation of coalbed gas during the process of adsorption/desorption

Journal of Geology 2008 10

9596874

1382 1389

27.

Xiong

Liu

X. J.

Liang

L. X.

Adsorption model of shale to CH₄ based on adsorption potential theory and its application

Journal of Chengdu University of Technology (Natural Science Edition) 2014 41

9596874

5 604 611

28.

Yang

Liu

Clarkson

Quantification of temperature-dependent sorption isotherms in shale gas reservoirs: experiment and theory

SPE Journal 2022 1 19

10.2118/205897-PA

29.

Yang

J. Z.

Chen

Wei

Modeling of methane/shale excess adsorption under reservoir conditions

SPE Reservoir Evaluation & Engineering 2018 21

9596874

4, article 180076 1027 1034

10.2118/180076-PA

2-s2.0-85058522753

30.

Zhang

M. J.

Yang

M. G.

Yan

J. W.

Study on supercritical adsorption characteristics of coal with medium and high rank

Journal of Safety Science of China 2021 31

9596874

8 53 61

31.

Jiang

Lin

Molecular dynamics investigation of conversion methods for excess adsorption amount of shale gas

Journal of Natural Gas Science and Engineering 2018 49

9596874

241 249

10.1016/j.jngse.2017.11.006

2-s2.0-85034654869

32.

Xie

Liang

Y. P.

Zou

Q. L.

Wang

Prediction model for isothermal adsorption curves based on adsorption potential theory and adsorption behaviors of methane on granular coal

Energy & Fuels 2019 33

9596874

3 1910 1921

10.1021/acs.energyfuels.8b03946

2-s2.0-85062825125

33.

Huang

Jiang

Chen

Investigation of variation in shale gas adsorption capacity with burial depth: insights from the adsorption potential theory

Journal of Natural Gas Science and Engineering 2020 73, article 103043

9596874

10.1016/j.jngse.2019.103043

34.

Xiong

Liu

X. J.

Liang

L. X.

Study on the pseudo-saturation vapor pressure of the methane on shales

Journal of Southwest Petroleum University (Natural Science Edition) 2015 37

9596874

4 90 100

35.

Xiong

Liu

Liang

Application of adsorption potential theory to methane adsorption on organic-rich shales at above critical temperature

Environmental Earth Sciences 2018 77

9596874

3 89 92

10.1007/s12665-018-7247-3

2-s2.0-85041387285

36.

Song

Wang

L.’a.

Zeng

Zhan

Gong

Application of adsorption potential theory in prediction of CO₂ and CH₄ adsorption on carbon molecular sieves

Adsorption Science & Technology 2018 36

9596874

9-10 1669 1686

10.1177/0263617418802570

2-s2.0-85056874390

37.

Chen

Liu

Jiang

Huang

Tan

Zuo

Effect of adsorbed phase density on the correction of methane excess adsorption to absolute adsorption in shale

Chemical Engineering Journal 2021 420, article 127678

9596874

10.1016/j.cej.2020.127678